Termination w.r.t. Q of the following Term Rewriting System could not be shown:
Q restricted rewrite system:
The TRS R consists of the following rules:
p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))
Q is empty.
Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
P(p(b(a(x0)), x1), p(x2, x3)) → P(p(x3, a(x2)), p(b(a(x1)), b(x0)))
P(p(b(a(x0)), x1), p(x2, x3)) → P(x3, a(x2))
P(p(b(a(x0)), x1), p(x2, x3)) → P(b(a(x1)), b(x0))
The TRS R consists of the following rules:
p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
Q DP problem:
The TRS P consists of the following rules:
P(p(b(a(x0)), x1), p(x2, x3)) → P(p(x3, a(x2)), p(b(a(x1)), b(x0)))
P(p(b(a(x0)), x1), p(x2, x3)) → P(x3, a(x2))
P(p(b(a(x0)), x1), p(x2, x3)) → P(b(a(x1)), b(x0))
The TRS R consists of the following rules:
p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We deleted some edges using various graph approximations
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
P(p(b(a(x0)), x1), p(x2, x3)) → P(p(x3, a(x2)), p(b(a(x1)), b(x0)))
P(p(b(a(x0)), x1), p(x2, x3)) → P(x3, a(x2))
P(p(b(a(x0)), x1), p(x2, x3)) → P(b(a(x1)), b(x0))
The TRS R consists of the following rules:
p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [13,14,18] contains 1 SCC with 2 less nodes.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
P(p(b(a(x0)), x1), p(x2, x3)) → P(p(x3, a(x2)), p(b(a(x1)), b(x0)))
The TRS R consists of the following rules:
p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.