Problem: -(+(x,y)) -> +(-(x),-(y)) +(-(x),-(y)) -> -(+(x,y)) Proof: AT confluence processor Complete TRS T' of input TRS: -(+(x,y)) -> +(-(x),-(y)) +(-(x),-(y)) -> -(+(x,y)) T' = (P union S) with TRS P:-(+(x,y)) -> +(-(x),-(y)) +(-(x),-(y)) -> -(+(x,y)) TRS S: S is left-linear and P is reversible. CP(S,S) = CP(S,P union P^-1) = PCP_in(P union P^-1,S) = We have to check termination of S: Qed