(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
p(p(b(a(x0)), x1), p(x2, x3)) → p(p(b(x2), a(a(b(x1)))), p(x3, x0))
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
P(p(b(a(x0)), x1), p(x2, x3)) → P(p(b(x2), a(a(b(x1)))), p(x3, x0))
P(p(b(a(x0)), x1), p(x2, x3)) → P(b(x2), a(a(b(x1))))
P(p(b(a(x0)), x1), p(x2, x3)) → P(x3, x0)
The TRS R consists of the following rules:
p(p(b(a(x0)), x1), p(x2, x3)) → p(p(b(x2), a(a(b(x1)))), p(x3, x0))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(3) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
P(p(b(a(x0)), x1), p(x2, x3)) → P(x3, x0)
P(p(b(a(x0)), x1), p(x2, x3)) → P(p(b(x2), a(a(b(x1)))), p(x3, x0))
The TRS R consists of the following rules:
p(p(b(a(x0)), x1), p(x2, x3)) → p(p(b(x2), a(a(b(x1)))), p(x3, x0))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.