The following DP Processors were used

Problem 1 remains open; application of the following processors failed [DependencyGraph (27ms), SubtermCriterion (1ms), DependencyGraph (9ms), PolynomialLinearRange4iUR (597ms), DependencyGraph (7ms), PolynomialLinearRange8NegiUR (4364ms), DependencyGraph (9ms), ReductionPairSAT (2299ms), DependencyGraph (6ms), SizeChangePrinciple (14ms)].

The following open problems remain:

Open Dependency Pair Problem 1

Dependency Pairs

ap^#(ap(ff, x), x)	→	ap^#(ff, x)	ap^#(ap(ff, x), x)	→	ap^#(ap(x, ap(ff, x)), ap(ap(cons, x), nil))
ap^#(ap(ff, x), x)	→	ap^#(cons, x)	ap^#(ap(ff, x), x)	→	ap^#(x, ap(ff, x))
ap^#(ap(ff, x), x)	→	ap^#(ap(cons, x), nil)

Rewrite Rules

ap(ap(ff, x), x)

→

ap(ap(x, ap(ff, x)), ap(ap(cons, x), nil))

Original Signature

Termination of terms over the following signature is verified: ff, ap, cons, nil