The TRS could not be proven terminating. The proof attempt took 60000 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (1922ms), SubtermCriterion (1ms), DependencyGraph (1851ms), PolynomialLinearRange4iUR (timeout), PolynomialLinearRange4iUR (-3ms), PolynomialLinearRange8NegiUR (30001ms), ReductionPairSAT (timeout)].
| app#(not, app(app(and, x), y)) | → | app#(or, app(not, x)) | 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(app(app(filter2, true), f), x), xs) | → | app#(app(cons, x), app(app(filter, f), xs)) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(f, x) | app#(not, app(app(or, x), y)) | → | app#(not, y) | |
| app#(app(and, app(app(or, y), z)), x) | → | app#(app(and, x), y) | app#(not, app(app(and, x), y)) | → | app#(app(or, app(not, x)), app(not, y)) | |
| 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(and, x), app(app(or, y), z)) | → | app#(app(and, x), y) | |
| app#(app(and, app(app(or, y), z)), x) | → | app#(app(or, app(app(and, x), y)), app(app(and, x), z)) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(filter2, app(f, x)) | |
| app#(app(and, x), app(app(or, y), z)) | → | app#(app(or, app(app(and, x), y)), app(app(and, x), z)) | app#(app(and, app(app(or, y), z)), x) | → | app#(app(and, x), z) | |
| app#(app(map, f), app(app(cons, x), xs)) | → | app#(map, f) | app#(app(app(app(filter2, false), f), x), xs) | → | app#(filter, f) | |
| app#(not, app(app(or, x), y)) | → | app#(not, x) | app#(app(and, app(app(or, y), z)), x) | → | app#(or, app(app(and, x), y)) | |
| app#(app(and, app(app(or, y), z)), x) | → | app#(and, x) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(map, f), xs) | |
| app#(app(and, x), app(app(or, y), z)) | → | app#(or, app(app(and, x), y)) | app#(app(and, x), app(app(or, y), z)) | → | app#(app(and, x), z) | |
| app#(not, app(app(or, x), y)) | → | app#(app(and, app(not, x)), app(not, y)) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(app(filter2, app(f, x)), f), x) | |
| app#(not, app(app(and, x), y)) | → | app#(not, y) | app#(not, app(app(and, x), y)) | → | app#(not, x) | |
| app#(app(app(app(filter2, true), f), x), xs) | → | app#(cons, x) | app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(filter2, app(f, x)), f) | |
| app#(app(and, x), app(app(or, y), z)) | → | app#(and, x) | app#(app(app(app(filter2, false), f), x), xs) | → | app#(app(filter, f), xs) | |
| app#(not, app(app(or, x), y)) | → | app#(and, app(not, x)) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(cons, app(f, x)) |
| app(not, app(not, x)) | → | x | app(not, app(app(or, x), y)) | → | app(app(and, app(not, x)), app(not, y)) | |
| app(not, app(app(and, x), y)) | → | app(app(or, app(not, x)), app(not, y)) | app(app(and, x), app(app(or, y), z)) | → | app(app(or, app(app(and, x), y)), app(app(and, x), z)) | |
| app(app(and, app(app(or, y), z)), x) | → | app(app(or, app(app(and, x), y)), app(app(and, x), z)) | 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: not, app, or, map, false, true, filter2, filter, cons, nil, and