Certification Problem

Input (COPS 523)

The rewrite relation of the following conditional TRS is considered.

add(0,y) y
add(s(x),y) s(add(x,y))
mul(0,y) 0
mul(x,0) 0
mul(s(x),s(y)) s(add(mul(x,s(y)),y))
leq(0,0) T
leq(s(x),0) F
leq(0,s(y)) T
leq(s(x),s(y)) leq(x,y)
n(xd,xm,xy) add(xd,add(mul(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))))))))))))))),xm),mul(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))),xy))) | leq(0,xd) ≈ T, leq(xd,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))))))))))))))) ≈ T, leq(0,xm) ≈ T, leq(xm,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) ≈ T

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.