(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
h(X) → g(X)
g(a) → f(b)
f(X) → h(a)
a → b
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:
H(X) → G(X)
G(a) → F(b)
F(X) → H(a)
F(X) → A
The TRS R consists of the following rules:
h(X) → g(X)
g(a) → f(b)
f(X) → h(a)
a → b
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:
G(a) → F(b)
F(X) → H(a)
H(X) → G(X)
The TRS R consists of the following rules:
h(X) → g(X)
g(a) → f(b)
f(X) → h(a)
a → b
Q is empty.
We have to consider all minimal (P,Q,R)-chains.