The TRS could not be proven terminating. The proof attempt took 60045 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (560ms), SubtermCriterion (1ms), DependencyGraph (508ms), PolynomialLinearRange4iUR (6211ms), DependencyGraph (449ms), PolynomialLinearRange8NegiUR (11173ms), DependencyGraph (493ms), ReductionPairSAT (timeout)].
| app#(h, app(h, x)) | → | app#(h, x) | app#(app(map, fun), app(app(cons, x), xs)) | → | app#(fun, x) | |
| app#(app(app(app(filter2, false), fun), x), xs) | → | app#(filter, fun) | app#(app(map, fun), app(app(cons, x), xs)) | → | app#(app(cons, app(fun, x)), app(app(map, fun), xs)) | |
| app#(app(app(app(filter2, true), fun), x), xs) | → | app#(app(cons, x), app(app(filter, fun), xs)) | app#(h, app(h, x)) | → | app#(app(f, app(h, x)), x) | |
| app#(app(app(app(filter2, true), fun), x), xs) | → | app#(app(filter, fun), xs) | app#(app(app(app(filter2, true), fun), x), xs) | → | app#(cons, x) | |
| app#(app(app(app(filter2, false), fun), x), xs) | → | app#(app(filter, fun), xs) | app#(app(filter, fun), app(app(cons, x), xs)) | → | app#(app(app(app(filter2, app(fun, x)), fun), x), xs) | |
| app#(h, app(h, x)) | → | app#(h, app(app(f, app(h, x)), x)) | app#(g, app(g, x)) | → | app#(h, app(g, x)) | |
| app#(g, app(h, app(g, x))) | → | app#(g, x) | app#(h, app(h, x)) | → | app#(f, app(h, x)) | |
| app#(app(map, fun), app(app(cons, x), xs)) | → | app#(map, fun) | app#(app(filter, fun), app(app(cons, x), xs)) | → | app#(app(app(filter2, app(fun, x)), fun), x) | |
| app#(g, app(g, x)) | → | app#(g, app(h, app(g, x))) | app#(app(filter, fun), app(app(cons, x), xs)) | → | app#(app(filter2, app(fun, x)), fun) | |
| app#(app(app(app(filter2, true), fun), x), xs) | → | app#(filter, fun) | app#(g, app(g, x)) | → | app#(g, x) | |
| app#(app(filter, fun), app(app(cons, x), xs)) | → | app#(fun, x) | app#(app(filter, fun), app(app(cons, x), xs)) | → | app#(filter2, app(fun, x)) | |
| app#(app(map, fun), app(app(cons, x), xs)) | → | app#(cons, app(fun, x)) | app#(app(map, fun), app(app(cons, x), xs)) | → | app#(app(map, fun), xs) |
| app(g, app(h, app(g, x))) | → | app(g, x) | app(g, app(g, x)) | → | app(g, app(h, app(g, x))) | |
| app(h, app(h, x)) | → | app(h, app(app(f, app(h, x)), x)) | app(app(map, fun), nil) | → | nil | |
| app(app(map, fun), app(app(cons, x), xs)) | → | app(app(cons, app(fun, x)), app(app(map, fun), xs)) | app(app(filter, fun), nil) | → | nil | |
| app(app(filter, fun), app(app(cons, x), xs)) | → | app(app(app(app(filter2, app(fun, x)), fun), x), xs) | app(app(app(app(filter2, true), fun), x), xs) | → | app(app(cons, x), app(app(filter, fun), xs)) | |
| app(app(app(app(filter2, false), fun), x), xs) | → | app(app(filter, fun), xs) |
Termination of terms over the following signature is verified: f, g, app, map, false, true, filter2, filter, h, cons, nil