YES Time: 0.070 Problem: Equations: plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4)) plusAC(x2,x3) -> plusAC(x3,x2) plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4) plusAC(x3,x2) -> plusAC(x2,x3) TRS: zero(sharp()) -> sharp() plusAC(x,sharp()) -> x plusAC(zero(x),zero(y)) -> zero(plusAC(x,y)) plusAC(zero(x),one(y)) -> one(plusAC(x,y)) plusAC(one(x),one(y)) -> zero(plusAC(x,plusAC(y,one(sharp())))) Proof: AC-KBO Processor: precedence: plusAC > one ~ zero ~ sharp weight function: [one](x0) = x0 + 7, [zero](x0) = x0 + 4, [sharp] = 2, [plusAC](x0, x1) = x0 + x1 problem: Equations: plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4)) plusAC(x2,x3) -> plusAC(x3,x2) plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4) plusAC(x3,x2) -> plusAC(x2,x3) TRS: Qed