The TRS could not be proven terminating. The proof attempt took 60016 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (302ms), SubtermCriterion (1ms), DependencyGraph (268ms), PolynomialLinearRange4iUR (5995ms), DependencyGraph (214ms), PolynomialLinearRange8NegiUR (20881ms), DependencyGraph (249ms), ReductionPairSAT (timeout)].
| app#(app(app(app(filter2, false), f), x), xs) | → | app#(filter, f) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(cons, app(f, x)), app(app(map, f), xs)) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(f, x) | app#(app(app(app(filter2, true), f), x), xs) | → | app#(app(cons, x), app(app(filter, f), xs)) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(f, x) | app#(app(app(app(filter2, true), f), x), xs) | → | app#(filter, f) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(map, f), xs) | app#(app(app(app(filter2, true), f), x), xs) | → | app#(app(filter, f), xs) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(app(app(filter2, app(f, x)), f), x), xs) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(app(filter2, app(f, x)), f), x) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(filter2, app(f, x)) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(filter2, app(f, x)), f) | |
| app#(app(app(app(filter2, true), f), x), xs) | → | app#(cons, x) | app#(app(app(app(filter2, false), f), x), xs) | → | app#(app(filter, f), xs) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(cons, app(f, x)) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(map, f) |
| app(app(\, x), x) | → | e | app(app(\, e), x) | → | x | |
| app(app(\, x), app(app(., x), y)) | → | y | app(app(\, app(app(/, x), y)), x) | → | y | |
| app(app(/, x), x) | → | e | app(app(/, x), e) | → | x | |
| app(app(/, app(app(., y), x)), x) | → | y | app(app(/, x), app(app(\, y), x)) | → | y | |
| app(app(., e), x) | → | x | app(app(., x), e) | → | x | |
| app(app(., x), app(app(\, x), y)) | → | y | app(app(., app(app(/, y), x)), x) | → | y | |
| app(app(map, f), nil) | → | nil | app(app(map, f), app(app(cons, x), xs)) | → | app(app(cons, app(f, x)), app(app(map, f), xs)) | |
| app(app(filter, f), nil) | → | nil | app(app(filter, f), app(app(cons, x), xs)) | → | app(app(app(app(filter2, app(f, x)), f), x), xs) | |
| app(app(app(app(filter2, true), f), x), xs) | → | app(app(cons, x), app(app(filter, f), xs)) | app(app(app(app(filter2, false), f), x), xs) | → | app(app(filter, f), xs) |
Termination of terms over the following signature is verified: app, e, map, false, true, \, filter2, ., /, filter, cons, nil