The TRS could not be proven terminating. The proof attempt took 60005 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (850ms), SubtermCriterion (1ms), DependencyGraph (760ms), PolynomialLinearRange4iUR (5846ms), DependencyGraph (696ms), PolynomialLinearRange8NegiUR (20392ms), DependencyGraph (727ms), ReductionPairSAT (timeout)].
| 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#(app(ack, app(succ, x)), y) | → | app#(app(ack, x), app(succ, 0)) | app#(app(app(app(filter2, true), f), x), xs) | → | app#(app(cons, x), app(app(filter, f), xs)) | |
| app#(app(ack, app(succ, x)), app(succ, y)) | → | app#(ack, x) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(f, x) | |
| app#(app(app(app(filter2, true), f), x), xs) | → | app#(filter, f) | app#(app(app(app(filter2, true), f), x), xs) | → | app#(app(filter, f), xs) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(app(app(filter2, app(f, x)), f), x), xs) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(filter2, app(f, x)) | |
| app#(app(ack, app(succ, x)), y) | → | app#(succ, 0) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(map, f) | |
| app#(app(ack, app(succ, x)), app(succ, y)) | → | app#(app(ack, app(succ, x)), y) | app#(app(app(app(filter2, false), f), x), xs) | → | app#(filter, f) | |
| app#(app(ack, app(succ, x)), app(succ, y)) | → | app#(ack, app(succ, x)) | app#(app(ack, app(succ, x)), app(succ, y)) | → | app#(app(ack, x), app(app(ack, app(succ, x)), y)) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(map, f), xs) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(app(filter2, app(f, x)), f), x) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(filter2, app(f, x)), f) | app#(app(app(app(filter2, true), f), x), xs) | → | app#(cons, x) | |
| app#(app(ack, app(succ, x)), app(succ, y)) | → | app#(succ, x) | app#(app(app(app(filter2, false), f), x), xs) | → | app#(app(filter, f), xs) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(cons, app(f, x)) | app#(app(ack, 0), y) | → | app#(succ, y) | |
| app#(app(ack, app(succ, x)), y) | → | app#(ack, x) |
| app(app(ack, 0), y) | → | app(succ, y) | app(app(ack, app(succ, x)), y) | → | app(app(ack, x), app(succ, 0)) | |
| app(app(ack, app(succ, x)), app(succ, y)) | → | app(app(ack, x), app(app(ack, app(succ, x)), 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(filter, f), nil) | → | nil | |
| app(app(filter, f), app(app(cons, x), xs)) | → | app(app(app(app(filter2, app(f, x)), f), x), xs) | app(app(app(app(filter2, true), f), x), xs) | → | app(app(cons, x), app(app(filter, f), xs)) | |
| app(app(app(app(filter2, false), f), x), xs) | → | app(app(filter, f), xs) |
Termination of terms over the following signature is verified: app, succ, 0, ack, map, false, true, filter2, filter, cons, nil