(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(s(X), X) → f(X, a(X))
f(X, c(X)) → f(s(X), X)
f(X, X) → c(X)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Precedence:
f2 > c1 > s1 > a1
Status:
f2: multiset
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(s(X), X) → f(X, a(X))
f(X, c(X)) → f(s(X), X)
f(X, X) → c(X)
(2) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(3) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) TRUE