Problem: +(0(),x) -> x +(-(x),x) -> 0() +(+(x,y),z) -> +(x,+(y,z)) +(x,y) -> +(y,x) -(0()) -> 0() -(-(x)) -> x -(+(x,y)) -> +(-(x),-(y)) Proof: Church Rosser Transformation Processor (ac): f4_AC(0(),x) -> x f4_AC(-(x),x) -> 0() -(0()) -> 0() -(-(x)) -> x -(f4_AC(x,y)) -> f4_AC(-(x),-(y)) AC critical peaks: joinable AC-KBO Processor: precedence: - > 0 > f4_AC weight function: w0 = 4 w(f4_AC) = 5 w(0) = 4 w(-) = 0 problem: Qed