(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(a, x) → g(a, x)
g(a, x) → f(b, x)
f(a, x) → f(b, x)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(a) = 2
POL(b) = 0
POL(f(x1, x2)) = 1 + x1 + x2
POL(g(x1, x2)) = x1 + x2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(a, x) → g(a, x)
g(a, x) → f(b, x)
f(a, x) → f(b, 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