Certification Problem

Input (COPS 267)

The rewrite relation of the following conditional TRS is considered.

size(empty) → 0
size(push(x,y)) → s(size(x))
m → s(s(s(s(0))))
pop(empty) → empty
pop(push(x,y)) → x | le(size(x),m) ≈ true
top(empty) → eentry
top(push(x,y)) → y | le(size(x),m) ≈ true
le(x,0) → false
le(0,s(x)) → true
le(s(x),s(y)) → le(x,y)

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ConCon @ CoCo 2020)

1 Almost-orthogonal

The given (extended) properly oriented, right-stable, oriented 3-CTRS is almost-orthogonal, since there are no conditional critical pairs.