TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60042 ms.

The following DP Processors were used

Problem 1 was processed with processor DependencyGraph (30ms).
 | – Problem 2 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (3ms), PolynomialLinearRange4iUR (586ms), DependencyGraph (3ms), PolynomialLinearRange8NegiUR (6491ms), DependencyGraph (3ms), ReductionPairSAT (timeout)].

The following open problems remain:

Open Dependency Pair Problem 2

Dependency Pairs

a^#(f, a(f, a(g, a(g, x))))	→	a^#(f, a(f, x))		a^#(f, a(f, a(g, a(g, x))))	→	a^#(f, x)
a^#(f, a(f, a(g, a(g, x))))	→	a^#(f, a(f, a(f, x)))

Rewrite Rules

a(f, a(f, a(g, a(g, x))))

→

a(g, a(g, a(g, a(f, a(f, a(f, x))))))

Original Signature

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

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

a^#(f, a(f, a(g, a(g, x))))	→	a^#(g, a(g, a(g, a(f, a(f, a(f, x))))))		a^#(f, a(f, a(g, a(g, x))))	→	a^#(f, a(f, x))
a^#(f, a(f, a(g, a(g, x))))	→	a^#(g, a(f, a(f, a(f, x))))		a^#(f, a(f, a(g, a(g, x))))	→	a^#(f, x)
a^#(f, a(f, a(g, a(g, x))))	→	a^#(f, a(f, a(f, x)))		a^#(f, a(f, a(g, a(g, x))))	→	a^#(g, a(g, a(f, a(f, a(f, x)))))

Rewrite Rules

a(f, a(f, a(g, a(g, x))))

→

a(g, a(g, a(g, a(f, a(f, a(f, x))))))

Original Signature

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

Strategy

The following SCCs where found

a^#(f, a(f, a(g, a(g, x)))) → a^#(f, a(f, x))	a^#(f, a(f, a(g, a(g, x)))) → a^#(f, x)
a^#(f, a(f, a(g, a(g, x)))) → a^#(f, a(f, a(f, x)))