(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)
ab

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)
ab

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)
ab

Q is empty.
We have to consider all minimal (P,Q,R)-chains.