(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
c(z, x, a) → f(b(b(f(z), z), x))
b(y, b(z, a)) → f(b(c(f(a), y, z), z))
f(c(c(z, a, a), x, a)) → z
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:
C(z, x, a) → F(b(b(f(z), z), x))
C(z, x, a) → B(b(f(z), z), x)
C(z, x, a) → B(f(z), z)
C(z, x, a) → F(z)
B(y, b(z, a)) → F(b(c(f(a), y, z), z))
B(y, b(z, a)) → B(c(f(a), y, z), z)
B(y, b(z, a)) → C(f(a), y, z)
B(y, b(z, a)) → F(a)
The TRS R consists of the following rules:
c(z, x, a) → f(b(b(f(z), z), x))
b(y, b(z, a)) → f(b(c(f(a), y, z), z))
f(c(c(z, a, a), x, a)) → z
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 4 less nodes.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
C(z, x, a) → B(b(f(z), z), x)
B(y, b(z, a)) → B(c(f(a), y, z), z)
B(y, b(z, a)) → C(f(a), y, z)
C(z, x, a) → B(f(z), z)
The TRS R consists of the following rules:
c(z, x, a) → f(b(b(f(z), z), x))
b(y, b(z, a)) → f(b(c(f(a), y, z), z))
f(c(c(z, a, a), x, a)) → z
Q is empty.
We have to consider all minimal (P,Q,R)-chains.