(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
c(c(b(c(x)))) → b(a(0, c(x)))
c(c(x)) → b(c(b(c(x))))
a(0, x) → c(c(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:
C(c(b(c(x)))) → A(0, c(x))
C(c(x)) → C(b(c(x)))
A(0, x) → C(c(x))
A(0, x) → C(x)
The TRS R consists of the following rules:
c(c(b(c(x)))) → b(a(0, c(x)))
c(c(x)) → b(c(b(c(x))))
a(0, x) → c(c(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 1 SCC with 1 less node.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
A(0, x) → C(c(x))
C(c(b(c(x)))) → A(0, c(x))
A(0, x) → C(x)
The TRS R consists of the following rules:
c(c(b(c(x)))) → b(a(0, c(x)))
c(c(x)) → b(c(b(c(x))))
a(0, x) → c(c(x))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.