(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → s(0)
f(s(0)) → s(0)
f(s(s(x))) → f(f(s(x)))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic Path Order [LPO].
Precedence:
[f1, s1] > 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(s(0)) → s(0)
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → s(0)
f(s(s(x))) → f(f(s(x)))
Q is empty.