The TRS could not be proven terminating. The proof attempt took 60001 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (1901ms), SubtermCriterion (1ms), DependencyGraph (1855ms), PolynomialLinearRange4iUR (8073ms), DependencyGraph (1709ms), PolynomialLinearRange8NegiUR (24423ms), DependencyGraph (1712ms), 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(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#(app(:, app(app(+, x), y)), z) | → | app#(+, app(app(:, x), z)) | app#(app(app(app(filter2, true), f), x), xs) | → | app#(filter, f) | |
| app#(app(:, z), app(app(+, x), app(f, y))) | → | app#(g, z) | app#(app(app(app(filter2, true), f), x), xs) | → | app#(app(filter, f), xs) | |
| app#(app(:, z), app(app(+, x), app(f, y))) | → | app#(app(:, app(app(g, z), y)), app(app(+, x), a)) | app#(app(:, app(app(+, x), y)), z) | → | app#(app(:, y), z) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(app(app(filter2, app(f, x)), f), x), xs) | app#(app(:, app(app(:, x), y)), z) | → | app#(app(:, x), app(app(:, y), z)) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(filter2, app(f, x)) | app#(app(:, app(app(:, x), y)), z) | → | app#(:, y) | |
| app#(app(:, z), app(app(+, x), app(f, y))) | → | app#(:, app(app(g, z), y)) | 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#(app(:, app(app(+, x), y)), z) | → | app#(:, x) | |
| app#(app(:, app(app(+, x), y)), z) | → | app#(app(+, app(app(:, x), z)), app(app(:, y), z)) | app#(app(:, app(app(+, x), y)), z) | → | app#(app(:, x), z) | |
| app#(app(:, z), app(app(+, x), app(f, y))) | → | app#(app(+, x), a) | app#(app(map, f), app(app(cons, x), xs)) | → | app#(app(map, f), xs) | |
| app#(app(:, app(app(:, x), y)), z) | → | app#(app(:, y), z) | app#(app(:, z), app(app(+, x), app(f, y))) | → | app#(app(g, z), y) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(app(filter2, app(f, x)), f), x) | app#(app(:, app(app(+, x), y)), z) | → | app#(:, y) | |
| app#(app(app(app(filter2, true), f), x), xs) | → | app#(cons, x) | app#(app(:, z), app(app(+, x), app(f, y))) | → | app#(+, x) | |
| app#(app(filter, f), app(app(cons, x), xs)) | → | app#(app(filter2, app(f, x)), f) | 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(:, app(app(:, x), y)), z) | → | app#(:, x) |
| app(app(:, app(app(:, x), y)), z) | → | app(app(:, x), app(app(:, y), z)) | app(app(:, app(app(+, x), y)), z) | → | app(app(+, app(app(:, x), z)), app(app(:, y), z)) | |
| app(app(:, z), app(app(+, x), app(f, y))) | → | app(app(:, app(app(g, z), y)), app(app(+, x), a)) | 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: g, app, a, map, false, true, +, :, filter2, filter, cons, nil