(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(c(X, s(Y))) → f(c(s(X), Y))
g(c(s(X), Y)) → f(c(X, s(Y)))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
g1 > f1
g1 > c2 > s1
Status:
c2: [2,1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(c(X, s(Y))) → f(c(s(X), Y))
g(c(s(X), Y)) → f(c(X, s(Y)))
(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