## 2 Background
### Tool-Object-Product Model (TOP Model)  
The Tool-Object-Product (TOP) [33, 34] model is a graphic model of the problem shown as a combination of the action tool, action object, and action product in the form of a transformed action object. The useful action of tool T on object O realised via field (F)  
Figure 2: FA and CLD models of a dry-erase marker (patent US006048121A [43]): (**a**) FA model with identified conflicts: conflict 1—the case should be larger to increase the durability of the useful function but should be smaller to assure the object portability; conflict 2—the plug must cover the top of the absorbent medium to avoid damage or an undesirable contact between the ink and another surface, and should not cover the top to facilitate the useful function; conflict 3—the plug must firmly cover the top of the absorbent medium to avoid accidental leakage of ink but must also be soft enough to be practical for anyone; (**b**) CLD model. (Source of figures: [32]).  
results in the transformation of object O into a useful product (U.P.). The action is denoted by an arrow, while the transformation is denoted by a double arrow (Figure 3a).  
If a necessary useful action (F\({}_{\text{us}}\)) that transforms object O into a useful product (U.P.) is accompanied by an undesirable impact (F\({}_{\text{hm}}\)) on object O, thus producing a harmful product (H.P.) (Figure 3b) or a worsened level of another system function, one is faced with a conflict problem or problems to be solved.  
An isomorphic graphic representation of the TOP model in a more traditional form for functional models is shown below (Figure 3c).  
Comparison of Figures 1 and 3c indicates that the TOP model is just an extension of the combined SF model including the results of useful and harmful interactions (Figure 4).  
Figure 4: Outlining the SF component in the TOP model: (**a**) classic representation; (**b**) functional representation (Figure 5) (developed by authors).  
Figure 3: (**a**) TOP representation of useful functional interaction ((developed by authors based on [34]); (**b**) TOP representation of co-occurring useful and harmful interactions (TOP model) (developed by authors based on [34]); (**c**) Graphic representation of the TOP model as a conflict structure model (developed by authors).  
Figure 4 shows that the TOP model is a combined SF model, subdivided into two different SFs--a useful effective and a harmful one, with two additional elements--the results of useful and harmful interactions. Thus, the object of an action (product) is represented twice in the model--before it has been acted upon by the tool and after the action. The advantage of this representation is the extension of the solution search beyond the transformation of the tool-product interaction (for example, the search for ways to destroy the already formed harmful product); in turn, the disadvantage is the limitation caused by conflicts, in which both conflictive functions are realised by the same substance participants. Cases with, for example, different objects of useful and harmful functions, etc., are not considered. The construction of a coherent tree of TOP models of a TS part allows for the creation of an O2-A-R diagram (Object-Action-Object-Result-Diagram) [44] of the TS and for the identification of alternative problems, which, when solved, would provides the same useful result.