(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(g(x), g(y)) → f(p(f(g(x), s(y))), g(s(p(x))))
p(0) → g(0)
g(s(p(x))) → p(x)
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:
F(g(x), g(y)) → F(p(f(g(x), s(y))), g(s(p(x))))
F(g(x), g(y)) → P(f(g(x), s(y)))
F(g(x), g(y)) → F(g(x), s(y))
F(g(x), g(y)) → G(s(p(x)))
F(g(x), g(y)) → P(x)
P(0) → G(0)
The TRS R consists of the following rules:
f(g(x), g(y)) → f(p(f(g(x), s(y))), g(s(p(x))))
p(0) → g(0)
g(s(p(x))) → p(x)
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 0 SCCs with 6 less nodes.
(4) TRUE