
831 F.Supp. 202 (1993)
LOTUS DEVELOPMENT CORPORATION, Plaintiff,
v.
BORLAND INTERNATIONAL, INC., Defendant.
Civ. A. No. 90-11662-K.
United States District Court, D. Massachusetts.
June 30, 1993.
As Amended August 19, 1993.
*203 *204 *205 *206 James C. Burling, Jeffrey B. Rudman, Hale & Dorr, Boston, MA, Henry B. Gutman, Kerry L. Konrad, O'Sullivan, Graev & Karabell, New York City, for plaintiff.
Peter E. Gelhaar, Donnelly, Conroy & Gelhaar, Boston, MA, Gary L. Reback, Peter N. Detkin, Andrew G. Konstantaras, Isabella E. Fu, Wilson, Sonsini, Goodrich & Rosati, Palo Alto, CA, for defendant.

OPINION
KEETON, District Judge.
On July 31, 1992, the court allowed, in part, a motion for summary judgment filed by plaintiff Lotus Development Corporation ("Lotus") and denied the cross motion for summary judgment by defendant Borland International, Incorporated ("Borland"). After extended procedural maneuvering, the parties agreed to try remaining liability issues without a jury. An explanation of the proceedings leading up to the trial is essential to precise identification of the issues raised by the parties in the nonjury trial of February 1-3 and March 31  April 2, 1993.

I. Earlier Proceedings.

A. Partial Summary Judgment.
This Opinion assumes the reader's familiarity with the Memorandum and Order allowing, in part, Lotus's motion for summary judgment. That document was published as Lotus Dev. Corp. v. Borland Int'l, Inc., 799 F.Supp. 203 (D.Mass.1992) (July 31 Memorandum and Order). In addition, the terminology used in this Opinion follows the terminology set forth in detail in the earlier Memorandum and Order. Id. at 206-208. Background information appears in two earlier documents issued by this court. The first is a Memorandum and Order in this case, Lotus Dev. Corp. v. Borland Int'l, Inc., 788 F.Supp. 78 (D.Mass.1992). The second is an opinion in a related case involving claims of infringement of copyrights for the Lotus 1-2-3 program. Lotus Dev. Corp. v. Paperback Software Int'l, 740 F.Supp. 37 (D.Mass.1990).
*207 The July 31 Memorandum and Order explained the standard to be applied in this case for determining copyrightability issues:
FIRST, in making the determination of "copyrightability," the decisionmaker must focus upon alternatives that counsel may suggest, or the court may conceive, along the scale from the most generalized conception to the most particularized, and choose some formulation, some conception of the "idea," "system," "process," "procedure," or "method"  for the purpose of distinguishing between the idea, system, process, procedure, or method and its expression.
.   .   .   .   .
SECOND, the decisionmaker must focus upon whether an alleged expression of the idea, system, process, procedure, or method is limited to elements essential to expression of that idea, system, process, procedure, or method (or is one of only a few ways of expressing the idea, system, process, procedure, or method) or instead includes identifiable elements of expression not essential to every expression of that idea, system, process, procedure, or method.
THIRD, having identified elements of expression not essential to every expression of the idea, system, process, procedure, or method, the decisionmaker must focus on whether those expressive elements, taken together, are a substantial part of the allegedly copyrightable "work."
Borland, 799 F.Supp. at 211 (quoting Borland, 788 F.Supp. at 90 (quoting Lotus Dev. Corp. v. Paperback Software Int'l, 740 F.Supp. 37, 60-61 (D.Mass.1990)) (all emphases omitted)).
Applying this test, I determined that the "idea," "system," "process," "procedure," or "method" of the Lotus 1-2-3 program is a menu-driven electronic spreadsheet whose
user interface involves a system of menus, each menu consisting of less than a dozen commands, arranged hierarchically, forming a tree in which the main menu is the root/trunk of the tree and submenus branch off from higher menus, each submenu being linked to a higher menu by operation of a command, so that all the specific spreadsheet operations available in Lotus 1-2-3 are accessible through the paths of the menu command hierarchy.
Id. at 216-17. (The meanings of menu command, menu structure and menu tree are explained at greater length below.) I concluded also that
as a matter of law, Borland's Quattro products infringe the Lotus 1-2-3 copyright because of (1) the extent of copying of the "menu commands" and "menu structure" that is not genuinely disputed in this case, (2) the extent to which the copied elements of the "menu commands" and "menu structure" contain expressive aspects separable from the functions of the "menu commands" and "menu structure," and (3) the scope of those copied expressive aspects as an integral part of Lotus 1-2-3.
Id. at 223 (original emphasis).
Nevertheless, I concluded that determining the scope of relief in this case depends on resolution of disputed factual contentions because Lotus contended and Borland disputed "that the copying of separable expressive elements of the Lotus 1-2-3 user interface into the Quattro programs was greater than the minimum essential to constituting a substantial part of the Lotus 1-2-3 work," which I had determined on motion for summary judgment not to be genuinely in dispute. Id. In other words, there is no genuine dispute of fact that the Quattro and Quattro Pro programs infringe, but fact issues remain as to the scope of impermissible copying. Specific fact issues apparent on the record at that time concerned (1) whether Borland copied the long prompts of Lotus 1-2-3, (2) whether the long prompts contain expressive elements, and (3) the extent (if any) that functional constraints limit the number of possible ways that the Lotus menu command hierarchy could have been arranged at the time of its creation. See Order Regulating Jury Trial, September 30, 1992 (Docket No. 232) at 20.
In addition, I concluded that Lotus was entitled to summary judgment against Borland on the affirmative defense of waiver, but not on the affirmative defenses of laches and *208 estoppel. See Borland, 799 F.Supp. at 222-23.

B. Further Proceedings Before Trial.
Up to the time of the court's ruling of July 31, 1992, the parties' contentions concerned issues raised in the allegations of the "original complaint" filed July 2, 1990, concerning infringement of Lotus 1-2-3 by Quattro and Quattro Pro's "emulation interface." Trial for the remaining liability issues in the original complaint was scheduled before a jury. In January 1993, this court permitted Lotus to file a supplemental complaint alleging copyright infringement by Borland in programs containing a "Key Reader" feature (which is described in some detail in the August 12, 1993 Opinion that addresses the issues of the "Key Reader" phase of the trial)  specifically in Quattro Pro versions 2.0, 3.0, 4.0, SE, 4.01 and Quattro Pro for Windows. See Docket 250, Exh. A.
After these developments and as the parties were preparing for trial of issues raised in the original complaint, the parties entered into a series of stipulations that altered the nature of the proceedings. See Stipulation and Order Regulating Trial (Docket No. 330); Stipulation and Order Regulating Key Reader Trial (Docket No. 349).
The first set of stipulations concerned trial of issues raised in the original complaint. These stipulations
govern the trial of all issues not previously finally decided by way of summary judgment concerning Borland's alleged liability herein, and all its defenses thereto, excluding the issues raised by Lotus' Supplemental Complaint concerning the "Key Reader" feature (the "Phase I Trial").
Docket No. 330, ¶ 1. With respect to issues raised in the original complaint, the parties waived jury trial for the liability issues that had previously been scheduled for the Phase I trial.
With respect to the long prompts, the parties stipulated that:
1. The order of display of the long prompts within the "1-2-3-compatible" modes of Quattro and Quattro Pro follows the order of display of the menu commands within those modes, and each such long prompt provides a short textual description of the command to which it relates.
2. Lotus shall not contend, in this action or any appeal therefrom, that Borland has copied the long prompts of Lotus 1-2-3 in Quattro or Quattro Pro.
3. Borland shall not contend, in this action or any appeal therefrom, that Borland has not copied the long prompts of Lotus 1-2-3 in Quattro or Quattro Pro.
4. Neither party shall contend, in this action or any appeal therefrom, that the issue of whether or not Borland copied the long prompts of Lotus 1-2-3 in either Quattro or Quattro Pro is material to any other issue that has been or will be resolved in this case.
Docket No. 330, Exh. A, ¶¶ 1-4.
The second set of stipulations "govern[s] the trial of all liability issues (including any defenses thereto) raised by Lotus' Supplemental Complaint concerning the `Key Reader' feature (the `Phase II Trial')." Docket No. 349, ¶ 1. For trial of the liability issues raised by the supplemental complaint, the parties waived their rights to trial by jury. Id.

C. Summary of Issues Before the Court.
Phase I of the trial was held on February 1-3, 1993. At that time, the issues before the court were the scope of infringement by Borland and Borland's affirmative defenses of laches and estoppel (the affirmative defense of waiver having been resolved at summary judgment). After the close of Borland's evidence, however, Borland was allowed leave to amend its answer to assert an affirmative defense of fair use. See Memorandum and Order, March 30, 1993 (Docket No. 353). In response, Lotus moved for judgment on partial findings. See Fed. R.Civ.P. 52(c). After hearing in open court and for the reasons stated on the record, I allowed Lotus's motion for judgment on the issue of Borland's fair use defense to the original complaint (Phase I).
Phase II of the liability trial was held on March 31-April 2, 1993. The issues presented to the court included the full range of liability determinations for the "Key Reader" *209 supplemental complaint. In addition, the parties tried Borland's defenses (to the "Key Reader" complaint) of waiver, laches, estoppel, and fair use.
This opinion addresses the issues raised in Phase I of the trial. On August 12, 1993, the court released an Opinion resolving the issues raised in Phase II.

II. Scope of Infringement in Phase I Trial.
As I understand the parties' stipulations and arguments, Lotus does not now contend that Borland copied the entire 1-2-3 interface. Rather, Lotus claims that Borland has illegally copied the Lotus 1-2-3 "menu commands" and "menu structure." Accordingly, the only issues before the court concern copying of the menu commands and structure.
Borland contends that copying of menu commands and structure is permissible because of functional constraints on formulation of the menu commands and structure. To the extent that Borland contends that the menu commands and structure as a whole are not copyrightable, Borland's contention was rejected as a matter of law at summary judgment. Nothing Borland presented at the Phase I trial alters my view that there is no genuine dispute that "a large part of the structure and arrangement of the menu commands is not driven entirely by functional considerations." 799 F.Supp. at 218.
Although I determined that no genuine dispute of fact had to be resolved in order to determine that the menu commands and structure contain protectable expression, I also determined that disputed factual contentions might have to be resolved to determine the scope of infringement. Among factors bearing on the scope of infringement are (1) the scope of copying, and (2) the nature of the copied work. Given the implications of the idea and the functional considerations, what is the extent of the expression? If there is "essentially only one way to express an idea," complete copying is permissible. Concrete Mach. Co. v. Classic Lawn Ornaments, Inc., 843 F.2d 600, 606 (1st Cir.1988). If there are "only a limited number of ways of expressing the idea," then proof of "near identity" of copied expression is required to show infringement. Id. For a work "embodying only one of an infinite variety of ways of expressing an idea," duplication or near identity is not required. Id. at 607. Consequently, there is a "sliding scale" that determines the scope of copyright protection. Accordingly, I first examine more closely the scope of copying and then examine how much of this copying was impermissible.

A. Menu Commands and Structure  Scope of Copying.

1. Defining and describing "menu commands and menu structure."
Omitting details not relevant for resolution of any dispute in this case, one may describe the idea of menu commands and menu structure in the following way.
Each spreadsheet program described in the evidence before the court has a set of basic executable operations that a user may invoke. Each executable operation does something with data in a spreadsheet (e.g., erases data in a spreadsheet cell), fixes parameters of a spreadsheet (e.g., width of a column in a given spreadsheet), fixes parameters of the program (e.g., hardware configuration or default settings), or performs some other function such as printing or saving a spreadsheet.
For each spreadsheet program before the court, the number of executable operations is large. Also, the possible methods of presenting available operations to the user is large. One simple approach would be to give each operation a unique name. If this were done, however, the large number of unique names would make it difficult for a user to remember and invoke them expeditiously.
A common way of overcoming this problem is to develop a menu hierarchy. The first level of the hierarchy presents the user with a "menu" consisting of a limited number of "menu commands." Some of these menu commands may be executable operations (e.g., "Quit") causing the program to do something (i.e., terminate). When the user invokes an executable command, the program performs the corresponding operation and does not present any further menu options. *210 To proceed farther in the hierarchy, the user must start again and select a different option.
Other menu commands are not in the set of executable operations; instead they are "internal" menu commands, each of which substitutes a new menu in place of the menu in which the internal command appears. Like the menu it replaces, the substituted menu (or "submenu") may consist of a combination of executable commands and internal commands.
The menu commands and menu structure are commonly described as a "tree." The imagery is imperfect, however, unless one thinks of a rather unusual tree that has a leaf or two as well as branches at most junctures. In this imagery, some of the choices at each juncture may be branches and others may be leaves. Each branch or leaf has a name. The "name" of the branch or leaf is a "menu command" within the program's "menu tree". The user starts at the trunk, and by choosing a branch, starts a climb upward. (One may, of course, also envision an upside-down tree, with the user working downward.)
If instead of choosing a branch at the first juncture the user chooses an executable operation, no climb occurs. A name (menu command) corresponding to an executable operation is a leaf of the tree. Having reached that leaf, the user cannot climb farther; no new branches are presented. Instead, the operation is executed. To climb farther (or elsewhere in the tree), the user must go back at least a bit (or all the way to the beginning) and choose branches up to a higher level. As long as the user invokes an internal menu command (a branch) at each juncture, the program presents to the user a new set of branches and leaves, and by choosing a branch the user climbs higher.
The height of the climb (the number of branches that the user must select before reaching a "leaf" or executable operation) varies depending on which choices the user makes at each juncture. Thus, if "Quit" is selected at the first level, the user makes no climb; the user has selected a leaf, not a branch.
To format a cell as currency data in Lotus 1-2-3, the user climbs three levels up  choosing the range branch, followed by the format branch, followed by the currency leaf.
Switching the imagery to an upside-down tree (a more common convention in computer software discussion), envision a downward progression. For example, the following is a graphic display of the part of the tree a user would climb (or descend) to select the currency operation.
                               [root/trunk of the tree]
      [Branch]       [Branch]                               [...]
      Worksheet       Range              Copy               [...]           System              Quit
        [...]                      [a leaf/executable       [...]    [a leaf/executable   [a leaf/executable
                                       operation]                        operation]           operation]
                                               [...]
      Format    Label        Erase             [...]                   Transpose
                [...]        [leaf]            [...]                     [leaf]
                                               [...]
    Fixed    Scientific      Currency          [...]
    [leaf]     [leaf]         [leaf]
*211 The term "menu tree" refers to the structure of all of the branches and leaves in the menu hierarchy as well as the names of those branches and leaves (i.e., the names of the menu commands).
In the July 31 Memorandum and Order, I concluded that the definition of the "idea," "system," "process," "procedure," or "method" of Lotus 1-2-3 includes the set of executable operations (leaves) of the tree (although not necessarily the menu command name assigned to each operation). As part of the "idea", the determination of the function of each executable operation is not protected by copyright law.
The menu tree expresses to the program user, in hierarchical fashion, the array of available operations. Even though the executable operations are not copyrightable, the menu tree is copyrightable because the (hierarchical) arrangement of the definition and identification of executable operations contains expression. Accordingly, in resolving the parties' motions for summary judgment, I concluded that many of the details of the menu tree in Lotus 1-2-3 were not a part of the "idea," "system," "process," "procedure," or "method" of the Lotus 1-2-3 program, but rather a part of the expression of that idea.

2. The Lotus and Borland menu trees.
The original complaint alleges infringement of Lotus's copyright in Lotus 1-2-3 version 2.0 (and earlier versions). In deciding the issues before the court, I have examined both Lotus 1-2-3 version 2.0 and version 2.01. Version 2.01 is a copyrighted derivative work based on version 2.0. Borland points to no differences between these programs that would have a bearing on any issue in this case. A comparison of the menu tree for Lotus version 2.0 (Exhibit 524) and the menu tree accessible through the version 2.01 program also demonstrates no differences material to this litigation. Indeed, the parties earlier stipulated (1) that the menu commands are the same and are displayed in an identical fashion to the user, and (2) that no difference exists between the user interfaces that would have any effect on the issues in this case. See O'Connor Dec'n, Docket No. 108, Exh. H. Accordingly, I will refer to the menu tree generically as the Lotus 1-2-3 menu tree although I have examined both versions 2.0 and 2.01.
The Lotus 1-2-3 menu tree contains approximately 469 menu commands. See Kieras Dec'n, V:8 at ¶ 66.
(The record in this case consists of nine volumes of material. Citations to this record are formatted as Volume:Tab; thus "V:8" means Volume V, Tab 8.)
Portions of the menu tree are illustrated at various places in the Exhibits. The entire tree is set out in Exhibit 524, A-C, E (the "Flesher Exhibits" which were originally submitted with the summary judgment materials). As the number of commands suggests, the menu tree is quite large.
The Quattro and Quattro Pro programs have both a native menu tree and a "1-2-3 emulation" menu tree. I do not understand Lotus to contend that the native menu tree infringes any Lotus copyright. Accordingly, when I refer to the Quattro or Quattro Pro menu trees, I refer only to the menu tree used in the program's 1-2-3 emulation interface.
The Quattro menu tree contains approximately 3370 menu commands. (Kieras Dec'n, V:8 at ¶ 77.) This menu tree is illustrated in Flesher Exhibit B. The Quattro Pro version 1.0 menu tree contains approximately 5215 commands (Id. at ¶ 66.) This menu tree is illustrated in Flesher Exhibit A.
The Quattro Pro program has been released in several versions, specifically versions 1.0, 2.0, 3.0, 4.0, 4.01, SE, and Quattro Pro for Windows. Only versions 1.0, 2.0, 3.0, and 4.0 contain the emulation interface. In deciding issues for Phase I of the trial, therefore, when I refer, without further specification, to the Quattro Pro menu tree, I refer only to the emulation menu tree in Quattro Pro versions 1.0, 2.0, 3.0, and 4.0.
The entire Lotus menu tree is contained within both the Quattro and Quattro Pro version 1.0 menu trees. For example, the first menu in Quattro Pro version 1.0 contains *212 an identical copy of the 1-2-3 menu commands, in the same order, but with one new command inserted ("View"). Invoking a Borland command that is identical to a Lotus command produces a menu that is an identical copy of the Lotus submenu, but (in some cases) with one or two new commands inserted. Thus, each menu or submenu in Lotus 1-2-3 is reproduced identically, but with the insertion in the Quattro and Quattro Pro menu trees of some new menu commands and any submenus associated with the new menu commands.
Put another way, both the Quattro and Quattro Pro version 1.0 menu trees consist of a virtually identical copy of the entire 1-2-3 menu tree, with new branches or leaves inserted at various places.
Although the above comparison focuses only on version 1.0 of the Quattro Pro menu tree, the scope of copying remains the same for versions 2.0, 3.0, and 4.0. The only difference among the emulation menu trees in Quattro Pro versions 1.0, 2.0, 3.0, and 4.0, is that each successive version added new commands. See Warfield Dep'n, III:40 at 72-73. Thus, later versions also contain a virtually identical copy of the Lotus menu tree, with still more new branches or leaves added.
The presentation of the commands in the Quattro and Quattro Pro programs indicates which commands are found in the 1-2-3 menu tree and which are Borland's insertions. In Quattro, the new (and only the new) menu commands are followed by a dot at the place where the new command is inserted into the tree. Thus, in Quattro, the "Install" command was inserted into the first level menu followed by a dot. The submenu of "Install" does not have these same dot designations. Such a designation is unnecessary for this submenu, however, because everything within the newly inserted "Install" branch of the tree is new.
Quattro Pro uses the same approach for differentiating 1-2-3 menu commands and added menu commands, with the exception of "View" in Quattro Pro's first menu, which has no designation as an inserted command but whose submenu consists of commands each followed by a dot. In addition, in the Quattro Pro menus, a line generally appears separating added menu commands from original 1-2-3 menu commands.
The disparity in total number of menu commands between the 1-2-3 menu tree and the Quattro and Quattro Pro menu trees is large, but does not alter the scope of copying. Most of the new commands are clustered together far up in the tree (or down in the upside down tree). For those menus that exist in the Lotus 1-2-3 menu tree, the number of added menu commands is rarely more than one or two. The effect is similar to an identical copy of a book with some paragraphs and lengthy footnotes inserted, and some voluminous appendices attached at the end.
In short, I adhere to my earlier conclusion that no reasonable factfinder could find that Borland did not take from Lotus 1-2-3 the menu commands and menu command structure substantially as they were. Further, I find that Borland produced a virtually identical copy of 1-2-3 menu tree, albeit with additions, in its Quattro and Quattro Pro emulation interfaces.

B. Nature of the Work  Scope of Illicit Copying.

1. Scope of limitations imposed by functional considerations.

a. The functional considerations.
Borland advanced the following "constraints" on design of a menu tree.
(1) Each menu command was chosen to tell the user the purpose of the menu command and its function.
(2) Each menu command was selected so that it had a different first letter from the other menu commands within the same menu.
(3) Each menu was set up to have only about seven choices (witnesses referred to this as the "seven plus or minus two rule," i.e., no menu should have fewer than five or more than nine commands).
(4) The menus were structured so that words within the menu that dealt with similar functions were grouped together.

*213 (5) Executable operations that were likely to be frequently used were located near the top of the (upside down) tree.
(6) Menu commands within a menu were arranged from left to right in order of decreasing frequency of use.
(7) Commands in submenus were grouped under the menu command to which they relate.
See VII:A:6. Borland also proffered an eighth functional "constraint" of having each menu fit on one line of a computer screen. If this constraint were followed, each menu could have no more than 80 characters (the number of characters across a standard computer terminal screen).
Borland refers to the above items as "constraints" on design of a menu tree. Lotus contends that they are "guidelines" or "rules of thumb." The difference in terminology is largely if not entirely semantic. Nevertheless, the different terms raise different images. "Constraint" implies a rule that must not be violated. If "constraint" is defined this way, the eight listed items are not "constraints." Each of them is violated somewhere in the Lotus 1-2-3 menu tree (except possibly the second, which has been violated in other menu trees, e.g., Excel 3.0 with "Save" and "Save As" in the same menu, and the last, which was violated in SuperCalc). Moreover, the alleged "constraints" are full of terms that offer little guidance on how to conform. For example, when is one menu command "similar" to another? The answer may be easy in some cases and entirely within the discretion of the programmer in others.
"Guideline," or "rule of thumb," is a more accurate description. Each of these terms implies a directive that is not always to be followed. Even these terms, however, ordinarily imply a precise rule. The first item listed above is hardly precise, even though it does limit the possible forms of a menu tree. Accordingly, I will refer to these as functional "considerations."

b. Impact of functional considerations on form of the menu tree.
The parties dispute the impact of the eight functional considerations (listed above) on the freedom of expression in forming a menu tree. For the following reasons I conclude that the Lotus 1-2-3 menu tree is just one of a great variety of possible expressions that are consistent with the functional considerations listed above and the specific set of executable operations used in Lotus 1-2-3.
First, none of the proffered functional considerations is overriding or dictates any specific result. Each may be violated. Most are violated at one or more points within the Lotus 1-2-3 menu tree. Indeed, the considerations are often competing and must be traded off against each other. See, e.g., Gottheil Dep'n, IX:11 at 143-64; Olson Dep'n, III:32 at 117-18. No functional considerations are offered for guiding the determination of how to trade off competing concerns. Borland provided no credible evidence explaining how functional considerations could completely control formation of the menu tree.
Second, the "quality" of the menu tree depends on the peculiarities (i.e., the particular tastes) of the individual using the program. See, e.g., Bosworth Dep'n, I:1 at 389-90. For this to be true, there must be a variety of possible menu trees for the user to choose from. In this regard, Borland programs offer a "menu builder" that enables users to alter, customize, and create menu trees. If functional considerations restricted the possible expression of the menu tree to a limited number of possibilities, there would be little or no need for a user to modify it.
Third, even Borland's experts acknowledge that, given all of the various functional considerations, at least a limited range of choices remains for individual menu commands. See Liddle Dep'n, II:27 at 121; Olson Dec'n, V:13 at ¶ 35. Thus, "Copy" could be called "Replicate," "Duplicate," "Reproduce," "Repeat," "Ditto," etc. "Range" could be "Block," "Scope," "Extent," "Cells," etc. Although some experts contend that certain words and menu structure are preferable to others, these same experts contend that the words Lotus selected did not matter for 1-2-3's success. See Liddle Dec'n, V:11, ¶ 55; Olson Dec'n, V:13, ¶¶ 36, 38. In any event, even if there were as few as two acceptable words for each menu command (given the other *214 functional considerations), there would be 2 raised to the 469th power possible menu trees (an astronomical number) having precisely the same menu structure as the 1-2-3 menu tree, but with variations in menu command names. See Emery Dec'n, V:3, ¶ 85. Even if only half of the menu commands had more than one possible name (given the other functional considerations), there are over 2234 possible menu trees having the same menu structure.
In listing these examples, I do not mean to suggest that the alternatives for menu command names are so few, nor to imply that every synonym for a command word is suitable in view of the other functional considerations. Rather, I merely note the breadth of possible menu trees that may be achieved in this manner as a factor bearing upon whether implementation of the idea, system, process, procedure, or method underlying the Lotus 1-2-3 menu tree is capable of a wide variety of expression.
Also, in presenting this analysis, I do not imply that counting possible variations in individual words is decisive of the breadth of possible expressions for literary works in general. It would not necessarily be significant, for example, to determine how many ways instructions for a simple game can be expressed solely by examining possible alternatives for individual words. Nevertheless, variations of the words in the menu tree represent a material consideration in the context of this case because of (1) the nature of the menu tree, which unlike an English sentence, permits substitution of individual words without changing the meaning of the menu tree, (2) the size of the menu tree, and (3) the structure of the menu tree.
If the designer of a menu tree chooses not to copy the structure of Lotus 1-2-3, the designer's freedom of expression and range of possible expressions for the menu tree expand dramatically. See Emery Dec'n, V:3, ¶ 84. Nothing in the materials before me supports an inference that functional considerations alone control the structure of the menu tree. Indeed, Borland's experts implicitly acknowledge alternatives for the structure of the 1-2-3 menu tree. See Liddle Dec'n, V:11, ¶ 56; Olson Dec'n, V:13, ¶ 38.
Finally, a number of other spreadsheet programs use vastly different menu trees. The existence of vastly different menu trees in other commercial programs supports the conclusion that the Lotus 1-2-3 menu tree is but one of many possible forms for a menu tree.
Borland contends, however, that the differences in menu trees between programs such as Lotus 1-2-3 and Excel are due to differences in the programs' functionality. That is, Borland argues that because the executable operations (leaves of the tree) are different and the visual displays are different (e.g., pop-up menus vs. text on a single line), the menu trees are different. Borland contends that, as a result, the existence of other commercial programs with menu trees vastly different from the 1-2-3 menu tree (and each other) is not probative of the degree of freedom of expression that exists in formulating the 1-2-3 menu tree.
I reject Borland's contentions for the following reasons. Although differences in program functionality may explain some differences between menu trees, the differences in functionality cannot explain the breadth of differences among menu trees used in the various programs. For example, functional considerations do not explain why the "File" menu command is left-most in the Excel menu tree and fifth from the left in the 1-2-3 menu tree. Borland does not suggest or offer any evidence explaining how the (unspecified) differences in functionality among 1-2-3, Excel, and Quattro's native mode affect placement of the "File" command within the first menu. Similarly, 1-2-3 places the copy and move command in the first level of the menu tree. In Excel they are in the second level.
The differences among menu trees in the various programs submitted are so large that they are, in a practical sense if not literally, incapable of enumeration. The broad scope of these differences cannot be explained in terms of differences in functionality. Indeed, Borland offers no evidence or argument providing a reasoned explanation (as opposed to an unsupported assertion) of how the magnitude of differences could be explained by any *215 differences in functionality. I conclude that many of the differences are due to different choices about how to express to the user the available user choices about all the particular operations that the program can perform.
In argument, Borland placed primary emphasis on an expert's assertion that the set of possible menu command names is "not large." See Olson Dep'n, III:32 at 54-59. As a preliminary matter, I find that this testimony is entitled to little, if any, weight. Nothing purports to explain how the expert reached this conclusion. In fact, this expert admits that she has never attempted to determine how large the set is. An expert's unexplained and unsupported assertion, even if received into evidence, is scant basis for reaching a reasoned finding.
In addition, the testimony is unclear whether the expert meant that there was a small set of choices for individual command names, or the set of all menu command names. In an earlier declaration this expert conceded that there is a "very narrow range" of suitable words for individual commands. See Olson Dec'n, V:13 at ¶¶ 35-36. As observed above, even if (given all the functional considerations) only half the commands have only one alternative label, the possible number of menu trees that differ in detail remains very high. Consequently, what this expert meant by "not a large set" may be entirely consistent with a determination that the number of possible ways of expressing the menu tree is without limitations that are material to the separation between idea or function and expression.
Finally, even assuming that the alternatives for menu command names were few, when I take into account as well the options available for structure, I find that the number of possible choices again expands dramatically. Thus, what Borland copied from 1-2-3 was not limited to aspects dictated by functional considerations. Rather, Borland copied the entire menu tree, much of which was the free expression of the creators of Lotus 1-2-3.

c. Conclusion.
As Borland practically conceded in closing argument, application of functional considerations does not restrict the expression of the menu tree to essentially only one form. (See Docket 333 at 3-52.) Further, I find that although functional considerations may have some effect on the design of a menu tree, they do not impose any practical limitation on the possible forms of expression to a number far enough short of infinity that any way of expressing the number in English words has come into common usage. The set of executable operations in Lotus 1-2-3 is large and the possible structural variations are enormous. The menu tree is capable of a very wide variety of expressions.
Borland has not argued or provided any evidence that any specific aspect of menu structure or command names, short of the entire menu tree, is dictated solely or influenced mainly by functional considerations. Moreover, Borland has used a virtually identical copy of the 1-2-3 menu tree. Accordingly, this case on its facts does not present any issue that might arise on a finding of copying of something short of virtually the entire menu tree.

2. Originality.
In its closing argument, Borland asserted that, because of functional considerations, creation of the menu tree did not require sufficient originality to justify protection under copyright law.

a. Originality doctrine.
The Supreme Court recently addressed the requirement of originality in Feist Publications, Inc. v. Rural Tel. Serv. Co., 499 U.S. 340, 111 S.Ct. 1282, 113 L.Ed.2d 358 (1991). The Opinion for the Court in Feist observed that the requirement that a work be "original" derives from the Constitution. The Court described the originality requirement as follows.
The sine qua non of copyright is originality. To qualify for copyright protection, a work must be original to the author. Original, as the term is used in copyright, means only that the work was independently created by the author (as opposed to copied from other works), and that it possesses at least some minimal degree of creativity. To be sure, the requisite level *216 of creativity is extremely low; even a slight amount will suffice. The vast majority of works make the grade quite easily, as they possess some creative spark, no matter how crude, humble or obvious it might be.
Id., 499 U.S. at ___, 111 S.Ct. at 1287 (internal quotation marks and citations omitted).
The Court held that copying from the white pages of a telephone book was permissible. To reach this conclusion, the Court first confirmed the firmly established principle that facts (e.g., the names, towns and telephone numbers in the white pages) are not copyrightable. The Court also confirmed that "even a directory that contains absolutely no protectable written expression, only facts, meets the constitutional minimum for copyright protection if it features an original selection or arrangement." Id., 499 U.S. at ___, 111 S.Ct. at 1289. In this circumstance, "the copyright is limited to the particular selection or arrangement." Id., 499 U.S. at ___, 111 S.Ct. at 1290.
Applying these two basic principles, the Court determined that the selection and arrangement of facts in the plaintiff's telephone book, i.e., selection of all people who applied for phone service and arrangement in alphabetical order, was "devoid of even the slightest trace of creativity." Id., 499 U.S. at ___, 111 S.Ct. at 1296.
[O]riginality is not a stringent standard; it does not require that facts be presented in an innovative and surprising way. It is equally true, however, that the selection or arrangement of facts cannot be so mechanical or routine as to require no creativity whatsoever.
Id. Indeed, the selection of all people and placement in alphabetical order was not at all original to the plaintiff  phone books had been arranged in that fashion for years. Plaintiff's white pages were nothing but a "garden-variety" phone book. Id.

b. Originality in this case.
Relying on Feist, Borland contends that the eight "rules" regarding functionality listed above demonstrate that the form of the menu tree (including menu command names and structure) is not original. For the following reasons, I find that the menu tree is "original."
As explained above, the menu tree of Lotus 1-2-3 may be viewed as an arrangement of the executable operations as "leaves" of the "menu tree," with internal commands ("branches") leading through the structure to the "leaves." Altogether, the tree contains 469 labels to explain the arrangement. This text and arrangement presents the set of executable operations to the program user. Thus, the specific operations could be viewed as (uncopyrightable) facts and the menu tree as an arrangement (with textual labels) of the facts. Even viewed in this light, most favorably to Borland, the menu tree easily satisfies the originality requirement discussed in Feist.
The functional considerations Borland propounds are not at all comparable to application of a rule of alphabetical ordering of executable operations.
Borland's "rules" are violated with regularity in the 1-2-3 menu tree. In contrast, the rule of alphabetical ordering was not violated in the Feist white pages.
Also, the functional considerations listed above were not "an age old practice, firmly rooted in tradition and common place." Feist, 499 U.S. at ___, 111 S.Ct. at 1297.
Moreover (except in a few places where rules of alphabetical ordering differ) one who is given the names, addresses and numbers in a phone book, can generate the alphabetical ordering by routine and mechanical application of rules, with only one possible outcome. In contrast, the text for the menu commands and the menu structure itself are not dictated by mechanical application of the functional considerations. As noted above, a wide variety of menu trees is possible.
In sum, the 1-2-3 menu tree "make[s] the grade quite easily, as it possess[es] some creative spark...." Feist, 499 U.S. at ___, 111 S.Ct. at 1287.
Borland nevertheless contends that, because functional considerations played a role in formulating the 1-2-3 menu tree, the menu tree is not copyrightable. Borland's *217 argument is susceptible of two interpretations, both lacking merit.
First, one may interpret this argument as a contention that the functional considerations so permeate formulation of the menu tree that the menu tree is not separable from the "idea" of the program. This form of argument has nothing to do with the amount of creativity or originality involved. Derivation of a scientific formula may require a great deal of creativity and produce an original result. If the formula fails the copyrightability test, it is because the formula is not expressive  independently of creativity or originality. Casting the argument in terms of originality doctrine rather than separability does nothing to assist resolution of the issues in this case, and may lead to confusion. In any event, to the extent Borland raises the same separability argument that it has raised before, but dressed now in terms of originality, that argument was previously rejected by the court for good reason, and is now rejected again.
Alternatively, Borland may be understood as contending that any work whose form is restricted to any material extent by functional considerations is not original. Without more, this contention is invalid on its face. Any original literary work is formulated according to functional considerations imposed by language, a desire for clarity, and a desire to express the ideas conveyed. As one of Borland's experts concedes, the first functional consideration (conveying the nature of executable operations) is not materially different from a functional consideration for selection of words in any English writing. See Olson Dep'n, III:32 at 54. Accordingly, this type of "functional consideration" can remove a writing from copyright protection only if it restricts the forms of expression (that are separable from the idea or function of the work) to a limited number. Thus, cases referring to functional considerations and decided under originality doctrine, including those cited by Borland, uniformly refer to limits on the number of forms of expression given functional considerations.

See Victor Lalli Enter., Inc. v. Big Red Apple, Inc., 936 F.2d 671, 673 (2d Cir.1991) ("purely functional grids that offer no opportunity for variation"); Sinai v. California Bureau of Automotive Repair, 25 U.S.P.Q.2d 1809 [1992 WL 470699] (N.D.Cal.1992) ("limited number of ways" to arrange information in chart); New Haven Copper Co. v. Eveready Mach. Co., 229 U.S.P.Q. 838 [1986 WL 269] (D.Conn.1986) (column headings "dictated by functional considerations"); Merritt Forbes & Co. v. Newman Inv. Sec., Inc., 604 F.Supp. 943, 951-52 (S.D.N.Y.1985) (no originality if "form of expression is dictated solely by functional considerations"; determining that fact issue exists over whether concept is "capable of varied expressions"); Decorative Aides Corp. v. Staple Sewing Aides Corp., 497 F.Supp. 154, 157 (S.D.N.Y.1980) (what was similar was "dictated by functional considerations"), aff'd without op., 657 F.2d 262 (2d Cir.1981). Cf. Feist, [499 U.S. at ___], 111 S.Ct. at 1296 (routine and mechanical application of single rule).
Thus, Borland's argument fails because, as above, a wide variety of expression is possible for the Lotus 1-2-3 menu tree.

C. Value of Expert Testimony.
In reaching the conclusions above, I have read and weighed the expert testimony offered by the parties. For the following reasons, however, much of this testimony has little weight in relation to the issues of law and fact that are decisive of the outcome in this case.
First, most of the testimony expresses conclusions, without any reasoned explanation of the basis for the conclusions. Second, much of the testimony uses terms such as "system" or "a large number" that the experts do not define. As factfinder, I choose not to abandon my factfinding responsibility by accepting an expert's proposed unexplained choice. This is my usual practice, and for even stronger reasons I proceed in this way when the expert's testimony uses terms specially defined by the expert to have meanings that incorporate into the terminology substantive choices that have important policy implications, without examining and explaining reasons for the policy choices and whether they *218 are consistent with applicable statutes and precedents.
Finally, much of the testimony is based on explicit or implicit assumptions about copyright law that are incorrect. For example, one expert testified that she was unsure of whether design of a menu tree is creative. In defining creativity, however, the expert explained that creativity required some "inventive leap." Olson Dec'n, III:32 at 124-35. Of course, this type of creativity  the inventive leap or new idea  is not required for copyrightable expression. See Feist, 499 U.S. at ___, 111 S.Ct. at 1296 (novelty or innovation not required). Expression is copyrightable, even when it is a new expression (e.g., a new novel about young love) of an old idea (i.e., boy meets girl).

D. Conclusion.
In sum, I conclude that each of the Borland emulation interfaces contains a virtually identical copy of the 1-2-3 menu tree and that the 1-2-3 menu tree is capable of a wide variety of expression.

III. Affirmative Defenses for Phase I.

A. Laches.
Borland has the burden of proving laches. Costello v. United States, 365 U.S. 265, 282, 81 S.Ct. 534, 543, 5 L.Ed.2d 551 (1961). A defense of laches has been established if the defendant proves that (1) the plaintiff inexcusably or unreasonably delayed in bringing an infringement action, and (2) defendant was prejudiced by this delay. See id. See also 3 Nimmer on Copyright § 12.06.
The chronology of the principal events bearing upon Borland's defense of laches commences in January 1987, when Lotus filed suit in the Paperback case. Borland was developing Quattro at the time. Before including the 1-2-3 emulation interface in Quattro, Borland secured a legal opinion that the program did not infringe Lotus's copyright. In late September 1987, Borland announced Quattro, Borland's first spreadsheet product. In November, Borland shipped the Quattro product. Quattro was advertised widely, one advertisement appearing in a November 1987 issue of "Lotus Magazine."
In early 1988, the Quattro product was discussed at a high-level Lotus meeting. The evidence concerning this meeting supports an inference that certain Lotus executives discussed the possibility that Borland would change Quattro if Lotus threatened suit. The evidence does not prove, however, that Lotus delayed filing suit or kept silent on the issue of infringement for this reason. I find that Lotus may have discussed the possibility that Borland would change its product, but that this was not a factor in Lotus's decision not to file suit in 1988.
Some time after the meeting, Lotus decided not to file suit against Borland then. In addition, Lotus adopted a policy of not commenting on possible infringement by, or legal action against, Borland.
In September 1988, less than one year after Borland shipped Quattro, Borland acquired the "Surpass" spreadsheet technology (from "Surpass Software Systems") for approximately $2.4 million. This included a software program that had been called "Surpass." The Surpass program's only menu tree was a copy of the 1-2-3 menu tree. After acquiring Surpass, Borland removed the Surpass product from the market. Borland then re-engineered Surpass to become the Quattro Pro product, having a 1-2-3 compatible menu tree as just one of the possible menu trees available. Quattro Pro version 1.0 was released in November 1989.
Near the end of June 1990, this court handed down its decision in the Paperback case. The day after the decision was released, Borland filed an action in California seeking a declaration of noninfringement. On July 2, 1990, Lotus filed the original complaint in the present action.

1. Delay.
The period between Borland's release of Quattro and Lotus's filing of the instant action was approximately 2½ years. This amount of time, standing alone, does not dictate a finding that the delay was unreasonable.

*219 Cf. Roulo v. Russ Berrie & Co., 886 F.2d 931, 942 (7th Cir.1989) ("A two year delay in filing an action following knowledge of the infringement has rarely been held sufficient to constitute laches."), cert. denied, 493 U.S. 1075 [110 S.Ct. 1124, 107 L.Ed.2d 1030] (1990); Hoste v. Radio Corp. of America, 654 F.2d 11 (6th Cir.1981) (per curiam) (error to grant summary judgment based on laches for suit filed after 13 year delay); Boothroyd Dewhurst, Inc. v. Poli, 783 F.Supp. 670, 680 (D.Mass 1991) (four year delay may not constitute laches).
Whether this amount of delay was unreasonable or inexcusable depends on the motives for delay. Thus, Judge Learned Hand observed that
it is inequitable for the owner of a copyright, with full notice of an intended infringement, to stand inactive while the proposed infringer spends large sums of money in its exploitation, and to intervene only when his speculation has proved a success. Delay under such circumstances allows the owner to speculate without risk with the other's money; he cannot possibly lose, and he may win.
Haas v. Feist, 234 F. 105, 108 (S.D.N.Y. 1916). On the other hand, delay used to evaluate and prepare a complicated claim may be reasonable. See, e.g., Paperback, 740 F.Supp. at 82. Similarly, delay to determine whether the scope of proposed infringement will justify the cost of litigation may be permissible. See, e.g., Boothroyd Dewhurst, 783 F.Supp. at 680-81. In the circumstances of the present case, I find that Lotus's delay in filing suit was reasonable and excusable.
First, I reject Borland's contention that Lotus's delay in bringing suit is of the kind addressed in Haas, i.e., in order to speculate with Borland's money. Borland relies primarily on the failure of Lotus to file an action in the early part of 1988. Borland contends that Lotus then knew enough about Borland's plans that Lotus should have notified Borland immediately if Lotus intended to claim infringement and that Lotus did not do so because Lotus was afraid that Borland would change Borland's product. Borland contends, in other words, that Lotus waited to file suit in an effort to trap Borland into expending large sums of money on Borland's spreadsheet products and, later, to reap the benefits of Borland's investment.
I find, however, that the evidence Borland presented does not support Borland's contentions. At the time of the 1988 meeting, Borland had already developed, advertised, and shipped Quattro. The possibility that Borland would adjust Quattro to remove the copy of the Lotus 1-2-3 menu tree was marginal in significance at the time of this meeting. For this reason, reinforced by the findings stated above, I do not find the evidence sufficient to persuade me, as factfinder, to draw the inference that Lotus waited to sue hoping that its competitor's product would succeed and enable Lotus to reap enhanced damages.

See Russell v. Price, 612 F.2d 1123, 1126 (9th Cir.1979) (conclusion that plaintiff was not speculating on defendant's success supported by fact that plaintiff was also seeking to exploit the copyrighted material), cert. denied sub nom., Drebin v. Russell, 446 U.S. 952 [100 S.Ct. 2919, 64 L.Ed.2d 809] (1980).
I find that Lotus delayed bringing suit for the purpose of awaiting resolution of the Paperback and Mosaic cases. Throughout 1988, Lotus was involved in extensive litigation in Paperback and Mosaic. This litigation was hotly contested. If Lotus had lost the Paperback case, Lotus's claims against Borland would have been difficult to maintain. Thus, by waiting to file suit, Lotus avoided expensive duplicative litigation all of which might have been unsuccessful if Lotus lost in Paperback. This avoided a risk of needlessly wasting court and party resources. Once the Paperback case was resolved by the trial court, Lotus filed suit against Borland almost immediately. I cannot say that this was unreasonable.
Borland contends, nevertheless, that Lotus's delay was unreasonable in part because Lotus kept silent about its belief that Borland's product infringed. Lotus responds that it was satisfied that Borland knew of the infringement claims because of (1) Phillipe Kahn's (Borland's chairman's) strong public reaction condemning Lotus for filing the Paperback *220 case, and (2) a public statement Lotus issued before Quattro was shipped, that appeared in the May 26, 1987 issue of PC Magazine (Exh. 28 at 162-63). In the public statement, Lotus represented that it did not claim copyright over the ideas of a two-line moving cursor interface or context sensitive help. Lotus then characterized its suit against Paperback and Mosaic as protecting against companies that copied "all of the ways in which 1-2-3 communicates to the user, including its menu structure and sequence, word selection, and macro language design...."
I find that Lotus reasonably believed that Borland was aware of Lotus's potential claims against Quattro and Quattro Pro. Borland "was far too sophisticated to need being led by the hand." Famous Music Corp. v. Bay State Harness Horse Racing & Breeding Assoc., Inc., 554 F.2d 1213, 1215 (1st Cir.1977) (rejecting estoppel defense). In light of this, I cannot say that Lotus's decision not to comment on the infringing nature of Quattro or Quattro Pro makes Lotus's delay in this case unreasonable or inexcusable.
In weighing equities, some courts decline to permit a laches defense by a "deliberate pirate," Haas, 234 F. at 108, or less harshly stated, a "deliberate infringer."

See 3 Nimmer on Copyrights, § 12.06 at 12-107 (delay "may not be a bar against one who knew of plaintiff's asserted rights, or as against a deliberate infringer") (footnotes omitted).
I find that Borland (1) knew of Lotus's copyright, (2) knew that Lotus was acting to protect that copyright, and (3) deliberately introduced a virtually identical copy of the Lotus 1-2-3 menu tree into its 1-2-3 emulation interfaces.
The fact that Borland did secure a noninfringement opinion from a prestigious law firm is relevant, of course. Nevertheless, Lotus is not in any way accountable for that opinion. Indeed, Borland offers no evidence that Borland gave any notice to Lotus of Borland's seeking legal advice or of the substance of that advice. It is a rather curious twist of argument to suggest that a copyright owner has a duty of notice to the infringer when the infringer has enough concern about its own actions that it seeks a legal opinion privately but refrains from giving any kind of notice to the copyright owner.
Borland contends that the Paperback suit could not constitute notice that Lotus was enforcing its copyright because the issues in Paperback and this case are not identical. The fact that the issues are not identical, however, is far from decisive. More to the point is the fact that Borland was aware of Lotus's assertion of copyright protection for the 1-2-3 program and in particular for the form of its menu tree.
Borland next argues that Lotus had not sufficiently formulated its precise contentions of what aspects of Borland's products infringe Lotus's copyright until May of 1992  almost two years into this case. Again, this has little to do with the fact that Borland was aware of Lotus's assertion of copyright protection for Lotus 1-2-3 and in particular for the form of its menu tree.

2. Prejudice.
The defense of laches requires that defendant suffer prejudice. Typical forms of prejudice include: death or unavailability of an important witness, dulling of memories, loss of relevant records, and continuing investments and outlays by the alleged infringer in connection with the operation of its business. See Eisenman Chemical Co. v. NL Indus., Inc., 595 F.Supp. 141, 147 (D.Nev.1984). Borland argues only the last form of prejudice. To demonstrate prejudice, Borland points to marketing costs and acquisition of the Surpass technology.
To constitute prejudice, however, these expenses must have been incurred as a result of Lotus's delay in bringing suit. Where an infringer was aware of a plaintiff's copyright, as Borland indisputably was, courts have phrased this point as a requirement that the actions be taken in reliance on the plaintiff's delay in bringing suit.

See Russell, 612 F.2d at 1126; In Design v. Lauren Knitwear Corp., 782 F.Supp. 824, 831 (S.D.N.Y.1991); Steinberg v. Columbia *221 Pictures Indus., Inc., 663 F.Supp. 706, 716 (S.D.N.Y.1987).
For the following reasons, I conclude that Borland has not proved that it took any action in reliance on Lotus's delay in bringing suit.
First, I find that Borland would have invested in and entered the spreadsheet market whether or not Lotus delayed in bringing suit. Phillipe Kahn testified that the decision to include the 1-2-3 emulation interface in Quattro was made not long before the product shipped. (I:14 at 362). Of course, this initial decision to include the 1-2-3 emulation interface was made before Lotus could have objected.
The Surpass technology, acquired in 1988, was used to form the basis for Quattro Pro. This was less than one year after Borland shipped Quattro. Borland presented no evidence that it would not have acquired Surpass had Lotus taken action earlier. Moreover, Quattro already had a 1-2-3 emulation interface. It would not be reasonable to infer that other aspects of Surpass than its copy of the Lotus 1-2-3 menu tree had no influence on Borland's decision. I find that Borland has not proved that it acquired the Surpass technology in reliance on Lotus's delay in bringing suit.
I observe also that Borland filed a declaratory judgment action immediately after the decision in the Paperback case. Borland seeks to explain the timing of the filing of the declaratory judgment action by presenting evidence that Borland was responding to recent conflicting reports that Lotus would file suit against Borland. Even if I credited this self-serving assertion, unsupported by any objective evidence, however, I would not infer that Borland had ever relied on Lotus's failure to assert infringement to conclude that Lotus would never file suit. Moreover, a senior Borland official averred that the Borland Board of Directors had been informed before the decision in the Paperback case that Lotus intended to sue Borland if Lotus prevailed in Paperback. (Leyton Dec'n, VI:10, ¶ 5.) Nevertheless Borland, like Lotus, awaited the outcome of the Paperback case. Significantly, when Borland filed, it sought a declaration of noninfringement, but omitted any specific request for a declaration of unenforceability due to laches or estoppel.
Based on the evidence before me, I find that Borland developed and marketed Quattro and Quattro Pro in reliance on (1) the noninfringement opinion, and (2) the hope that Lotus would lose the Paperback litigation. Further, I find that Borland has not proved that it took any actions in reliance on Lotus's delay in bringing suit. Finally, I find that reliance, even if it had occurred, would have been unreasonable in the circumstances shown by the evidence in this case.

B. Estoppel.
The parties apparently agree that, to establish a defense of estoppel, Borland must prove that Lotus engaged in (1) conduct that induced Borland to change its position in good faith, or (2) conduct on which a reasonable person would rely. See Precious Metals Associates, Inc. v. Commodity Futures Trading Comm'n, 620 F.2d 900, 908 (1st Cir.1980). In view of this agreement, I need not and do not consider whether this interpretation of Precious Metals and other precedents is more generous to Borland's estoppel claim than a more precise understanding of the precedents would be.
To establish estoppel, Borland relies primarily on Lotus's delay in bringing suit and Lotus's failure to inform Borland of Lotus's belief that the Borland products infringe. For the reasons explained in Section A above, I find that (1) Lotus did not intend that Borland infer from Lotus's silence that copying of the menu tree was permissible, (2) Borland was aware of Lotus's copyright, (3) Borland did not rely on the silence of Lotus to Borland's detriment, and (4) any reliance by Borland in the circumstances of this case would have been unreasonable and unjustifiable.
Borland also offers a collection of actions or statements by Lotus that Borland contends entitled Borland to infer that Lotus would not sue Borland for copyright infringement. Borland cites a January 1987 Info-World article, released before Lotus had any reason to know of Borland's Quattro product. *222 The article purports to quote a Lotus spokesman, Greg Jarboe:
"Some folks have misinterpreted that what we have done is to copyright the spreadsheet or the two-line [command] interface, neither of which we are trying to do," Jarboe said. The suit was targeted at two vendors who had "copied 99 percent" of a Lotus product, he said, adding that the company is considering issuing a position statement to clarify the limits of its copyright.
InfoWorld, January 26, 1987. Even assuming this is an accurate quote, something Mr. Jarboe denies, I find that it would not be reasonable to launch a spreadsheet product in reliance on this statement. First, as Borland's general counsel concedes, II:20 at 272, the statement does not purport to disavow filing suit against future products that infringe Lotus's copyright in a manner different from the Paperback suit. A characterization of the Paperback case as involving "clones" is not reasonably interpreted as expressing an intention not to sue other infringers as well as makers of "clones." Second, the article refers to an upcoming position statement (the PC Magazine statement quoted in Section III.A, above). Although Borland contends that none of Borland's responsible representatives saw this position statement (a contention that I find questionable in light of their other activities), their failure to see and take account of that position statement, along with acting on the assumption that no such statement had been made, was unreasonable. Thus, to the extent Borland claims that it relied on the InfoWorld statement, it was unreasonable for Borland to rely on that statement while failing to take further steps to determine what Lotus's position statement contained.
Borland next cites the fact that Lotus Magazine published advertisements for Borland's products. I find that it would not be reasonable for Borland to assume that the acceptance of the advertisement in Lotus Magazine showed that Lotus had determined that it would make no infringement claim against Borland. Following Borland's line of reasoning, one would conclude that by allowing competitors to run advertisements in Lotus Magazine, Lotus Development Corporation agreed that the competitor's advertising claims were correct (e.g., that Borland's products are superior, as the advertisements implied) and that Lotus wanted individuals to purchase from Lotus's competitors. Merely stating this chain of inference is enough to expose its unreasonableness. I find, instead, that the fact that Lotus Magazine accepted the Borland advertisement indicated a policy of accepting advertisements  even from competitors. Moreover, on the evidence before me I cannot find, as factfinder, that the plaintiff in this case, Lotus Development Corporation, controlled the decision-making process about what appears in Lotus Magazine. Accordingly, it was not reasonable for Borland to infer that Lotus Development Corporation was making any statement concerning possible copyright infringement when Lotus Magazine accepted the advertisement.
Borland next cites examples of occasions where Lotus personnel interacted with Borland personnel at trade shows and with respect to new products and services, without mentioning any belief that the Borland products infringe. Nothing in these materials suggests that the Lotus personnel involved had the actual or apparent authority, or even sufficient knowledge, to comment on whether or not Lotus believed that Borland infringed a copyright or whether Lotus intended to file an action in the future. Moreover, nothing in the record shows that the individuals involved actually said anything that would support an inference by Borland that copying of the menu tree was permissible. Accordingly, I find that Borland could not reasonably interpret these communications to mean that Lotus would not file suit.
In sum, I find that both separately and taken as a whole, the events, conduct, and communications that Borland points to in an effort to bolster claims for estoppel fall far short of supporting estoppel.

C. Conclusion.
For the reasons explained above, I find that Lotus's claims in Phase I of the trial are not barred by laches or estoppel. In presenting its case on the affirmative defenses, Borland offers a number of proposed inferences *223 that this court might draw, based loosely on evidence before the court. Although I have not explicitly referred to each of Borland's individual contentions in this Opinion, I have examined all of the contentions and have found them without merit.
