YES Time: 0.044 Problem: Equations: orAC(orAC(x2,x3),x4) -> orAC(x2,orAC(x3,x4)) orAC(x2,x3) -> orAC(x3,x2) andAC(andAC(x2,x3),x4) -> andAC(x2,andAC(x3,x4)) andAC(x2,x3) -> andAC(x3,x2) orAC(x2,orAC(x3,x4)) -> orAC(orAC(x2,x3),x4) orAC(x3,x2) -> orAC(x2,x3) andAC(x2,andAC(x3,x4)) -> andAC(andAC(x2,x3),x4) andAC(x3,x2) -> andAC(x2,x3) TRS: not(not(x)) -> x orAC(not(x),not(y)) -> not(andAC(x,y)) Proof: Matrix Interpretation Processor: dimension: 1 interpretation: [not](x0) = x0 + 8, [andAC](x0, x1) = x0 + x1 + 12, [orAC](x0, x1) = x0 + x1 + 7 orientation: not(not(x)) = x + 16 >= x = x orAC(not(x),not(y)) = x + y + 23 >= x + y + 20 = not(andAC(x,y)) problem: Equations: orAC(orAC(x2,x3),x4) -> orAC(x2,orAC(x3,x4)) orAC(x2,x3) -> orAC(x3,x2) andAC(andAC(x2,x3),x4) -> andAC(x2,andAC(x3,x4)) andAC(x2,x3) -> andAC(x3,x2) orAC(x2,orAC(x3,x4)) -> orAC(orAC(x2,x3),x4) orAC(x3,x2) -> orAC(x2,x3) andAC(x2,andAC(x3,x4)) -> andAC(andAC(x2,x3),x4) andAC(x3,x2) -> andAC(x2,x3) TRS: Qed