(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → cons(0)
f(s(0)) → f(p(s(0)))
p(s(X)) → X
Q is empty.
(1) AAECC Innermost (EQUIVALENT transformation)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is
p(s(X)) → X
The TRS R 2 is
f(0) → cons(0)
f(s(0)) → f(p(s(0)))
The signature Sigma is {
f,
cons}
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → cons(0)
f(s(0)) → f(p(s(0)))
p(s(X)) → X
The set Q consists of the following terms:
f(0)
f(s(0))
p(s(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(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(p(s(0)))
p(s(X)) → X
The set Q consists of the following terms:
f(0)
f(s(0))
p(s(x0))
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)))
The TRS R consists of the following rules:
f(0) → cons(0)
f(s(0)) → f(p(s(0)))
p(s(X)) → X
The set Q consists of the following terms:
f(0)
f(s(0))
p(s(x0))
We have to consider all minimal (P,Q,R)-chains.