YES Problem: +(0(),x) -> x +(x,0()) -> x +(1(),-(1())) -> 0() +(-(1()),1()) -> 0() -(0()) -> 0() -(-(x)) -> x -(+(x,y)) -> +(-(x),-(y)) +(+(x,y),z) -> +(x,+(y,z)) +(x,y) -> +(y,x) Proof: Church Rosser Transformation Processor (ac): f4_AC(0(),x) -> x f4_AC(x,0()) -> x f4_AC(1(),-(1())) -> 0() f4_AC(-(1()),1()) -> 0() -(0()) -> 0() -(-(x)) -> x -(f4_AC(x,y)) -> f4_AC(-(x),-(y)) AC critical peaks: joinable AC-RPO Processor: precedence: 1 > 0 > - > f4_AC status: problem: Qed