(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
minus(minus(x)) → x
minus(h(x)) → h(minus(x))
minus(f(x, y)) → f(minus(y), minus(x))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(f(x1, x2)) = 2 + 2·x1 + 2·x2
POL(h(x1)) = 1 + 2·x1
POL(minus(x1)) = 2·x1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
minus(h(x)) → h(minus(x))
minus(f(x, y)) → f(minus(y), minus(x))
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
minus(minus(x)) → x
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Knuth-Bendix order [KBO] with precedence:
trivial
and weight map:
minus_1=1
The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
minus(minus(x)) → x
(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