(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:
Knuth-Bendix order [KBO] with precedence:
g2 > f2 > b > a
and weight map:
a=2
b=1
f_2=1
g_2=0
The variable weight is 1With 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) YES