(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
or(x, x) → x
and(x, x) → x
not(not(x)) → x
not(and(x, y)) → or(not(x), not(y))
not(or(x, y)) → and(not(x), not(y))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(and(x1, x2)) = 2 + 2·x1 + x2
POL(not(x1)) = 2·x1
POL(or(x1, x2)) = 2 + 2·x1 + x2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
or(x, x) → x
and(x, x) → x
not(and(x, y)) → or(not(x), not(y))
not(or(x, y)) → and(not(x), not(y))
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
not(not(x)) → x
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Knuth-Bendix order [KBO] with precedence:
trivial
and weight map:
not_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:
not(not(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