The TRS could not be proven terminating. The proof attempt took 60004 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (329ms), SubtermCriterion (1ms), DependencyGraph (245ms), PolynomialLinearRange4iUR (3820ms), DependencyGraph (216ms), PolynomialLinearRange8NegiUR (8556ms), DependencyGraph (238ms), ReductionPairSAT (timeout)].
| app#(app(times, app(s, x)), y) | → | app#(app(plus, app(app(times, x), y)), y) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(f, x) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(cons, app(f, x)), app(app(map, f), xs)) | app#(double, xs) | → | app#(s, 0) | |
| app#(double, xs) | → | app#(map, app(times, app(s, app(s, 0)))) | app#(app(plus, app(s, x)), y) | → | app#(plus, x) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(map, f), xs) | app#(double, xs) | → | app#(app(map, app(times, app(s, app(s, 0)))), xs) | |
| app#(inc, xs) | → | app#(app(map, app(plus, app(s, 0))), xs) | app#(inc, xs) | → | app#(plus, app(s, 0)) | |
| app#(app(times, app(s, x)), y) | → | app#(plus, app(app(times, x), y)) | app#(inc, xs) | → | app#(map, app(plus, app(s, 0))) | |
| app#(app(times, app(s, x)), y) | → | app#(times, x) | app#(app(plus, app(s, x)), y) | → | app#(s, app(app(plus, x), y)) | |
| app#(double, xs) | → | app#(s, app(s, 0)) | app#(app(times, app(s, x)), y) | → | app#(app(times, x), y) | |
| app#(inc, xs) | → | app#(s, 0) | app#(double, xs) | → | app#(times, app(s, app(s, 0))) | |
| app#(app(plus, app(s, x)), y) | → | app#(app(plus, x), y) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(map, f) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(cons, app(f, x)) |
| app(app(plus, 0), y) | → | y | app(app(plus, app(s, x)), y) | → | app(s, app(app(plus, x), y)) | |
| app(app(times, 0), y) | → | 0 | app(app(times, app(s, x)), y) | → | app(app(plus, app(app(times, x), y)), y) | |
| app(inc, xs) | → | app(app(map, app(plus, app(s, 0))), xs) | app(double, xs) | → | app(app(map, app(times, app(s, app(s, 0)))), 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)) |
Termination of terms over the following signature is verified: plus, app, 0, inc, s, times, map, double, cons, nil