The TRS could not be proven terminating. The proof attempt took 60001 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (242ms), SubtermCriterion (1ms), DependencyGraph (223ms), PolynomialLinearRange4iUR (4651ms), DependencyGraph (176ms), PolynomialLinearRange8NegiUR (10878ms), DependencyGraph (175ms), 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#(app(maxlist, x), app(app(cons, y), ys)) | → | app#(maxlist, y) | app#(height, app(app(node, x), xs)) | → | app#(app(maxlist, 0), app(app(map, height), xs)) | |
| app#(app(maxlist, x), app(app(cons, y), ys)) | → | app#(le, x) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(map, f), xs) | |
| app#(height, app(app(node, x), xs)) | → | app#(map, height) | app#(height, app(app(node, x), xs)) | → | app#(app(map, height), xs) | |
| app#(height, app(app(node, x), xs)) | → | app#(maxlist, 0) | app#(app(maxlist, x), app(app(cons, y), ys)) | → | app#(if, app(app(le, x), y)) | |
| app#(app(maxlist, x), app(app(cons, y), ys)) | → | app#(app(if, app(app(le, x), y)), app(app(maxlist, y), ys)) | app#(app(le, app(s, x)), app(s, y)) | → | app#(app(le, x), y) | |
| app#(app(maxlist, x), app(app(cons, y), ys)) | → | app#(app(maxlist, y), ys) | app#(app(maxlist, x), app(app(cons, y), ys)) | → | app#(app(le, x), y) | |
| app#(height, app(app(node, x), xs)) | → | app#(s, app(app(maxlist, 0), app(app(map, height), xs))) | 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(le, app(s, x)), app(s, y)) | → | app#(le, x) |
| 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(le, 0), y) | → | true | app(app(le, app(s, x)), 0) | → | false | |
| app(app(le, app(s, x)), app(s, y)) | → | app(app(le, x), y) | app(app(maxlist, x), app(app(cons, y), ys)) | → | app(app(if, app(app(le, x), y)), app(app(maxlist, y), ys)) | |
| app(app(maxlist, x), nil) | → | x | app(height, app(app(node, x), xs)) | → | app(s, app(app(maxlist, 0), app(app(map, height), xs))) |
Termination of terms over the following signature is verified: app, true, node, 0, height, le, s, if, map, false, maxlist, nil, cons