(0) Obligation:

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

f(f(a)) → c

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(f(a)) → c

The set Q consists of the following terms:

f(f(a))

(3) DependencyPairsProof (EQUIVALENT transformation)

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

(4) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following rules:

f(f(a)) → c

The set Q consists of the following terms:

f(f(a))

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

(5) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(6) TRUE