Problem: f(f(x,y),z) -> f(x,f(y,z)) f(x,y) -> f(y,x) Proof: AT confluence processor Complete TRS T' of input TRS: f(f(x,y),z) -> f(x,f(y,z)) f(x,y) -> f(y,x) T' = (P union S) with TRS P:f(f(x,y),z) -> f(x,f(y,z)) f(x,y) -> f(y,x) 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