(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x) → s(x)
f(s(s(x))) → s(f(f(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:
F(s(s(x))) → F(f(x))
F(s(s(x))) → F(x)
The TRS R consists of the following rules:
f(x) → s(x)
f(s(s(x))) → s(f(f(x)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.