Certification Problem

Input (TPDB TRS_Standard/SK90/2.36)

The rewrite relation of the following TRS is considered.

implies(not(x),y) or(x,y) (1)
implies(not(x),or(y,z)) implies(y,or(x,z)) (2)
implies(x,or(y,z)) or(y,implies(x,z)) (3)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Rule Removal

Using the Knuth Bendix order with w0 = 1 and the following precedence and weight functions
prec(or) = 0 weight(or) = 1
prec(implies) = 1 weight(implies) = 0
prec(not) = 3 weight(not) = 1
all of the following rules can be deleted.
implies(not(x),y) or(x,y) (1)
implies(not(x),or(y,z)) implies(y,or(x,z)) (2)
implies(x,or(y,z)) or(y,implies(x,z)) (3)

1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.