MAYBE

The TRS could not be proven terminating. The proof attempt took 20553 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (30ms), SubtermCriterion (1ms), DependencyGraph (17ms), PolynomialLinearRange4iUR (621ms), DependencyGraph (12ms), PolynomialLinearRange8NegiUR (3725ms), DependencyGraph (7ms), ReductionPairSAT (15986ms), DependencyGraph (6ms), SizeChangePrinciple (13ms)].

The following open problems remain:

Open Dependency Pair Problem 1

Dependency Pairs

f#(f(y, z), f(x, f(a, x))) → f#(x, a)f#(f(y, z), f(x, f(a, x))) → f#(a, y)
f#(f(y, z), f(x, f(a, x))) → f#(a, z)f#(f(y, z), f(x, f(a, x))) → f#(f(a, z), f(x, a))
f#(f(y, z), f(x, f(a, x))) → f#(f(f(a, z), f(x, a)), f(a, y))

Rewrite Rules

f(f(y, z), f(x, f(a, x))) → f(f(f(a, z), f(x, a)), f(a, y))

Original Signature

Termination of terms over the following signature is verified: f, a