The TRS could not be proven terminating. The proof attempt took 60006 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (452ms), SubtermCriterion (1ms), DependencyGraph (398ms), PolynomialLinearRange4iUR (5931ms), DependencyGraph (386ms), PolynomialLinearRange8NegiUR (17994ms), DependencyGraph (365ms), ReductionPairSAT (timeout)].
| app#(app(*, x), app(app(+, y), z)) | → | app#(+, app(app(*, x), y)) | 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(*, x), app(app(+, y), z)) | → | app#(app(+, app(app(*, x), y)), app(app(*, x), z)) | 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(*, x), app(app(+, y), z)) | → | app#(*, x) | |
| 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(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(*, x), app(app(+, y), z)) | → | app#(app(*, x), z) | app#(app(app(app(filter2, false), f), x), xs) | → | app#(app(filter, f), xs) | |
| app#(app(*, x), app(app(+, y), z)) | → | app#(app(*, x), y) | 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), app(app(+, y), z)) | → | app(app(+, app(app(*, x), y)), app(app(*, x), z)) | 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, map, *, false, true, +, filter2, filter, cons, nil