Certification Problem

Input (TPDB TRS_Standard/Mixed_TRS/jones4)

The rewrite relation of the following TRS is considered.

p(m,n,s(r)) p(m,r,n) (1)
p(m,s(n),0) p(0,n,m) (2)
p(m,0,0) m (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(0) = 2 weight(0) = 1
prec(p) = 0 weight(p) = 0
prec(s) = 3 weight(s) = 2
all of the following rules can be deleted.
p(m,n,s(r)) p(m,r,n) (1)
p(m,s(n),0) p(0,n,m) (2)
p(m,0,0) m (3)

1.1 R is empty

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