The TRS could not be proven terminating. The proof attempt took 60044 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (445ms), SubtermCriterion (1ms), DependencyGraph (407ms), PolynomialLinearRange4iUR (5383ms), DependencyGraph (349ms), PolynomialLinearRange8NegiUR (15458ms), DependencyGraph (351ms), ReductionPairSAT (timeout)].
| 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#(f, app(g, x)) | → | app#(g, app(f, x)) | |
| app#(app(app(app(filter2, true), fun), x), xs) | → | app#(app(cons, x), app(app(filter, fun), xs)) | app#(app(app(app(filter2, true), fun), x), xs) | → | app#(app(filter, fun), xs) | |
| app#(f, app(g, x)) | → | app#(g, app(g, x)) | 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#(f, app(g, x)) | → | app#(g, app(g, app(g, x))) | app#(f, app(g, x)) | → | app#(f, x) | |
| app#(f, app(g, x)) | → | app#(g, x) | app#(f, app(g, x)) | → | app#(g, app(g, app(f, 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#(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#(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(f, app(g, x)) | → | app(g, app(g, app(f, x))) | app(f, app(g, x)) | → | app(g, app(g, app(g, 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, cons, nil