The TRS could not be proven terminating. The proof attempt took 60001 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (750ms), SubtermCriterion (1ms), DependencyGraph (700ms), PolynomialLinearRange4iUR (9871ms), DependencyGraph (611ms), PolynomialLinearRange8NegiUR (27364ms), DependencyGraph (644ms), ReductionPairSAT (timeout)].
| app#(i, app(app(., x), y)) | → | app#(app(., app(i, y)), app(i, x)) | app#(app(app(app(filter2, false), f), x), xs) | → | app#(filter, f) | |
| app#(app(., app(app(., x), y)), z) | → | app#(., x) | 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(., app(app(., x), y)), z) | → | app#(., y) | 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#(i, app(app(., x), y)) | → | app#(i, x) | app#(app(., app(app(., x), y)), z) | → | app#(app(., x), app(app(., y), z)) | |
| app#(i, app(app(., x), y)) | → | app#(., app(i, y)) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(app(filter2, app(f, x)), f), x) | |
| app#(i, app(app(., x), y)) | → | app#(i, y) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(filter2, app(f, x)) | |
| app#(app(., app(app(., x), y)), z) | → | app#(app(., y), z) | app#(app(app(app(filter2, true), f), x), xs) | → | app#(cons, x) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(filter2, app(f, x)), f) | 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(., 1), x) | → | x | app(app(., x), 1) | → | x | |
| app(app(., app(i, x)), x) | → | 1 | app(app(., x), app(i, x)) | → | 1 | |
| app(app(., app(i, y)), app(app(., y), z)) | → | z | app(app(., y), app(app(., app(i, y)), z)) | → | z | |
| app(app(., app(app(., x), y)), z) | → | app(app(., x), app(app(., y), z)) | app(i, 1) | → | 1 | |
| app(i, app(i, x)) | → | x | app(i, app(app(., x), y)) | → | app(app(., app(i, y)), app(i, x)) | |
| 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, 1, map, false, true, filter2, ., filter, cons, nil, i