MAYBE

The TRS could not be proven terminating. The proof attempt took 43505 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (56ms), SubtermCriterion (1ms), DependencyGraph (31ms), PolynomialLinearRange4iUR (1264ms), DependencyGraph (27ms), PolynomialLinearRange8NegiUR (6380ms), DependencyGraph (19ms), ReductionPairSAT (35494ms), DependencyGraph (18ms), SizeChangePrinciple (32ms)].

The following open problems remain:

Open Dependency Pair Problem 1

Dependency Pairs

app#(app(filter, f), app(app(cons, x), xs)) → app#(filter, f)app#(app(filter, f), app(app(cons, x), xs)) → app#(app(app(consif, app(f, x)), x), app(app(filter, f), xs))
app#(app(filter, f), app(app(cons, x), xs)) → app#(app(filter, f), xs)app#(app(app(consif, true), x), ys) → app#(cons, x)
app#(app(filter, f), app(app(cons, x), xs)) → app#(app(consif, app(f, x)), x)app#(app(filter, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(filter, f), app(app(cons, x), xs)) → app#(consif, app(f, x))app#(app(app(consif, true), x), ys) → app#(app(cons, x), ys)

Rewrite Rules

app(app(app(consif, true), x), ys) → app(app(cons, x), ys)app(app(app(consif, false), x), ys) → ys
app(app(filter, f), nil) → nilapp(app(filter, f), app(app(cons, x), xs)) → app(app(app(consif, app(f, x)), x), app(app(filter, f), xs))

Original Signature

Termination of terms over the following signature is verified: app, false, true, consif, filter, nil, cons