(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:
Polynomial interpretation [POLO]:
POL(c(x1, x2)) = 2·x1 + 2·x2
POL(f(x1)) = x1
POL(g(x1)) = 2 + 2·x1
POL(s(x1)) = 1 + x1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
g(c(s(X), Y)) → f(c(X, s(Y)))
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(c(X, s(Y))) → f(c(s(X), Y))
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(c(x1, x2)) = x1 + 2·x2
POL(f(x1)) = 2·x1
POL(s(x1)) = 1 + x1
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))
(4) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(5) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(6) YES