The TRS could not be proven terminating. The proof attempt took 60003 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (281ms), SubtermCriterion (1ms), DependencyGraph (242ms), PolynomialLinearRange4iUR (5098ms), DependencyGraph (215ms), PolynomialLinearRange8NegiUR (12676ms), DependencyGraph (202ms), ReductionPairSAT (timeout)].
| ap#(dropLast, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap#(cons, x) | ap#(dropLast, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap#(ap(cons, x), ap(dropLast, ap(ap(cons, y), ys))) | |
| ap#(last, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap#(cons, y) | ap#(ap(map, f), xs) | → | ap#(ap(ap(if, ap(isEmpty, xs)), f), xs) | |
| ap#(ap(map, f), xs) | → | ap#(ap(if, ap(isEmpty, xs)), f) | ap#(ap(ap(if, false), f), xs) | → | ap#(map, f) | |
| ap#(ap(ap(if, false), f), xs) | → | ap#(ap(map, f), ap(dropLast, xs)) | ap#(last, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap#(ap(cons, y), ys) | |
| ap#(dropLast, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap#(dropLast, ap(ap(cons, y), ys)) | ap#(ap(ap(if, false), f), xs) | → | ap#(dropLast, xs) | |
| ap#(ap(map, f), xs) | → | ap#(if, ap(isEmpty, xs)) | ap#(ap(ap(if, false), f), xs) | → | ap#(cons, ap(f, ap(last, xs))) | |
| ap#(dropLast, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap#(ap(cons, y), ys) | ap#(ap(ap(if, false), f), xs) | → | ap#(last, xs) | |
| ap#(last, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap#(last, ap(ap(cons, y), ys)) | ap#(ap(ap(if, false), f), xs) | → | ap#(ap(cons, ap(f, ap(last, xs))), ap(ap(map, f), ap(dropLast, xs))) | |
| ap#(ap(ap(if, false), f), xs) | → | ap#(f, ap(last, xs)) | ap#(ap(map, f), xs) | → | ap#(isEmpty, xs) | |
| ap#(dropLast, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap#(cons, y) |
| ap(ap(map, f), xs) | → | ap(ap(ap(if, ap(isEmpty, xs)), f), xs) | ap(ap(ap(if, true), f), xs) | → | nil | |
| ap(ap(ap(if, false), f), xs) | → | ap(ap(cons, ap(f, ap(last, xs))), ap(ap(map, f), ap(dropLast, xs))) | ap(isEmpty, nil) | → | true | |
| ap(isEmpty, ap(ap(cons, x), xs)) | → | false | ap(last, ap(ap(cons, x), nil)) | → | x | |
| ap(last, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap(last, ap(ap(cons, y), ys)) | ap(dropLast, nil) | → | nil | |
| ap(dropLast, ap(ap(cons, x), nil)) | → | nil | ap(dropLast, ap(ap(cons, x), ap(ap(cons, y), ys))) | → | ap(ap(cons, x), ap(dropLast, ap(ap(cons, y), ys))) |
Termination of terms over the following signature is verified: isEmpty, dropLast, last, ap, if, map, false, true, cons, nil