The TRS could not be proven terminating. The proof attempt took 60046 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (524ms), SubtermCriterion (1ms), DependencyGraph (495ms), PolynomialLinearRange4iUR (5403ms), DependencyGraph (430ms), PolynomialLinearRange8NegiUR (12257ms), DependencyGraph (467ms), ReductionPairSAT (timeout)].
| app#(app(minus, app(s, x)), app(s, y)) | → | app#(minus, app(p, app(s, 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(div, app(s, x)), app(s, y)) | → | app#(s, y) | |
| app#(app(div, app(s, x)), app(s, y)) | → | app#(id, y) | app#(app(minus, app(s, x)), app(s, y)) | → | app#(s, x) | |
| app#(id, app(p, x)) | → | app#(s, app(id, x)) | app#(app(minus, app(s, x)), app(s, y)) | → | app#(s, y) | |
| app#(app(div, app(s, x)), app(s, y)) | → | app#(app(div, app(app(minus, x), app(id, y))), app(s, y)) | app#(id, x) | → | app#(s, app(s, x)) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(map, f), xs) | app#(app(minus, app(s, x)), app(s, y)) | → | app#(p, app(s, y)) | |
| app#(id, app(p, x)) | → | app#(id, app(s, app(id, x))) | app#(app(div, app(s, x)), app(s, y)) | → | app#(app(minus, x), app(id, y)) | |
| app#(id, x) | → | app#(s, app(s, app(s, x))) | app#(app(div, app(s, x)), app(s, y)) | → | app#(minus, x) | |
| app#(app(div, app(s, x)), app(s, y)) | → | app#(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y))) | app#(id, app(p, x)) | → | app#(id, x) | |
| app#(id, x) | → | app#(s, x) | app#(app(minus, app(s, x)), app(s, y)) | → | app#(p, app(s, x)) | |
| app#(app(div, app(s, x)), app(s, y)) | → | app#(div, app(app(minus, x), app(id, 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(minus, app(s, x)), app(s, y)) | → | app#(app(minus, app(p, app(s, x))), app(p, app(s, 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(minus, x), 0) | → | x | app(app(minus, app(s, x)), app(s, y)) | → | app(app(minus, app(p, app(s, x))), app(p, app(s, y))) | |
| app(p, app(s, x)) | → | x | app(app(div, 0), app(s, y)) | → | 0 | |
| app(app(div, app(s, x)), app(s, y)) | → | app(s, app(app(div, app(app(minus, x), app(id, y))), app(s, y))) | app(id, x) | → | x | |
| app(id, x) | → | app(s, app(s, app(s, x))) | app(id, app(p, x)) | → | app(id, app(s, app(id, x))) |
Termination of terms over the following signature is verified: id, app, 0, minus, s, p, div, map, cons, nil