Problem: +(0(),x) -> x +(1(),-(1())) -> 0() +(+(x,y),z) -> +(x,+(y,z)) +(x,y) -> +(y,x) Proof: Church Rosser Transformation Processor (ac): f5_AC(0(),x) -> x f5_AC(1(),-(1())) -> 0() AC critical peaks: joinable AC-KBO Processor: precedence: 1 > - > f5_AC > 0 weight function: w0 = 2 w(0) = 7 w(f5_AC) = w(1) = 2 w(-) = 1 problem: Qed