(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → cons(0, f(s(0)))
f(s(0)) → f(p(s(0)))
p(s(0)) → 0
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(0) → cons(0, f(s(0)))
f(s(0)) → f(p(s(0)))
p(s(0)) → 0
The set Q consists of the following terms:
f(0)
f(s(0))
p(s(0))
(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(0) → F(s(0))
F(s(0)) → F(p(s(0)))
F(s(0)) → P(s(0))
The TRS R consists of the following rules:
f(0) → cons(0, f(s(0)))
f(s(0)) → f(p(s(0)))
p(s(0)) → 0
The set Q consists of the following terms:
f(0)
f(s(0))
p(s(0))
We have to consider all minimal (P,Q,R)-chains.
(5) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
(6) Obligation:
Q DP problem:
The TRS P consists of the following rules:
F(s(0)) → F(p(s(0)))
F(0) → F(s(0))
The TRS R consists of the following rules:
f(0) → cons(0, f(s(0)))
f(s(0)) → f(p(s(0)))
p(s(0)) → 0
The set Q consists of the following terms:
f(0)
f(s(0))
p(s(0))
We have to consider all minimal (P,Q,R)-chains.