YES Termination w.r.t. Q proof of SK90_2.36.ari

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

implies(not(x), y) → or(x, y)
implies(not(x), or(y, z)) → implies(y, or(x, z))
implies(x, or(y, z)) → or(y, implies(x, z))

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Knuth-Bendix order [KBO] with precedence:
implies2 > or2 > not1

and weight map:

not_1=1
implies_2=0
or_2=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:

implies(not(x), y) → or(x, y)
implies(not(x), or(y, z)) → implies(y, or(x, z))
implies(x, or(y, z)) → or(y, implies(x, z))


(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