(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(X) → g(h(f(X)))

Q is empty.

(1) Overlay + Local Confluence (EQUIVALENT transformation)

The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.

(2) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(X) → g(h(f(X)))

The set Q consists of the following terms:

f(x0)

(3) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

(4) Obligation:

Q DP problem:
The TRS P consists of the following rules:

F(X) → F(X)

The TRS R consists of the following rules:

f(X) → g(h(f(X)))

The set Q consists of the following terms:

f(x0)

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