The TRS could not be proven terminating. The proof attempt took 60029 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (140ms), SubtermCriterion (1ms), DependencyGraph (102ms), PolynomialLinearRange4iUR (2703ms), DependencyGraph (93ms), PolynomialLinearRange8NegiUR (8190ms), DependencyGraph (77ms), ReductionPairSAT (timeout)].
| 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#(size, app(app(node, x), xs)) | → | app#(app(map, size), xs) | app#(app(plus, app(s, x)), y) | → | app#(plus, x) | |
| app#(sum, app(app(cons, x), xs)) | → | app#(plus, x) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(map, f), xs) | |
| app#(size, app(app(node, x), xs)) | → | app#(sum, app(app(map, size), xs)) | app#(app(plus, app(s, x)), y) | → | app#(s, app(app(plus, x), y)) | |
| app#(size, app(app(node, x), xs)) | → | app#(map, size) | app#(size, app(app(node, x), xs)) | → | app#(s, app(sum, app(app(map, size), xs))) | |
| app#(app(plus, app(s, x)), y) | → | app#(app(plus, 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#(sum, app(app(cons, x), xs)) | → | app#(sum, xs) | |
| app#(sum, app(app(cons, x), xs)) | → | app#(app(plus, x), app(sum, xs)) |
| 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(sum, app(app(cons, x), xs)) | → | app(app(plus, x), app(sum, xs)) | app(size, app(app(node, x), xs)) | → | app(s, app(sum, app(app(map, size), xs))) | |
| app(app(plus, 0), x) | → | 0 | app(app(plus, app(s, x)), y) | → | app(s, app(app(plus, x), y)) |
Termination of terms over the following signature is verified: plus, app, node, 0, s, map, sum, size, cons, nil