Certification Problem

Input (TPDB TRS_Equational/AProVE_AC_04/AC01)

The rewrite relation of the following equational TRS is considered.

plus(x,0) → x (1)
plus(x,s(y)) → s(plus(x,y)) (2)

Associative symbols: plus

Commutative symbols: plus

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 AC Rule Removal

Using the non-linear polynomial interpretation over the naturals
[plus(x1, x2)] = 1 + 2 · x2 + 2 · x1 + 2 · x1 · x2
[0] = 0
[s(x1)] = 3 + 1 · x1
the rules
plus(x,0) → x (1)
plus(x,s(y)) → s(plus(x,y)) (2)
can be deleted.

1.1 R is empty

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