MAYBE

The TRS could not be proven terminating. The proof attempt took 14940 ms.

The following DP Processors were used

Problem 1 remains open; application of the following processors failed [DependencyGraph (31ms), SubtermCriterion (1ms), DependencyGraph (11ms), PolynomialLinearRange4iUR (766ms), DependencyGraph (8ms), PolynomialLinearRange8NegiUR (3041ms), DependencyGraph (7ms), ReductionPairSAT (10805ms), DependencyGraph (7ms), SizeChangePrinciple (16ms)].

The following open problems remain:

Open Dependency Pair Problem 1

Dependency Pairs

ap^#(ap(ap(g, x), y), ap(s, z))	→	ap^#(ap(x, y), 0)		ap^#(ap(ap(g, x), y), ap(s, z))	→	ap^#(ap(ap(g, x), y), ap(ap(x, y), 0))
ap^#(ap(ap(g, x), y), ap(s, z))	→	ap^#(ap(g, x), y)		ap^#(ap(ap(g, x), y), ap(s, z))	→	ap^#(x, y)
ap^#(ap(ap(g, x), y), ap(s, z))	→	ap^#(g, x)

Rewrite Rules

ap(f, x)

→

x

ap(ap(ap(g, x), y), ap(s, z))

→

ap(ap(ap(g, x), y), ap(ap(x, y), 0))

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, ap