YES Time: 0.144 Problem: Equations: NAC(NAC(x3,x4),x5) -> NAC(x3,NAC(x4,x5)) NAC(x3,x4) -> NAC(x4,x3) maxAC(maxAC(x3,x4),x5) -> maxAC(x3,maxAC(x4,x5)) maxAC(x3,x4) -> maxAC(x4,x3) maxxAC(maxxAC(x3,x4),x5) -> maxxAC(x3,maxxAC(x4,x5)) maxxAC(x3,x4) -> maxxAC(x4,x3) NAC(x3,NAC(x4,x5)) -> NAC(NAC(x3,x4),x5) NAC(x4,x3) -> NAC(x3,x4) maxAC(x3,maxAC(x4,x5)) -> maxAC(maxAC(x3,x4),x5) maxAC(x4,x3) -> maxAC(x3,x4) maxxAC(x3,maxxAC(x4,x5)) -> maxxAC(maxxAC(x3,x4),x5) maxxAC(x4,x3) -> maxxAC(x3,x4) TRS: h(L(x)) -> 0() h(NAC(x,y)) -> maxAC(h(x),h(y)) maxAC(0(),x) -> x maxAC(x,0()) -> x maxAC(s(x),s(y)) -> s(maxxAC(x,y)) maxxAC(0(),x) -> x maxxAC(x,0()) -> x maxxAC(s(x),s(y)) -> s(maxAC(x,y)) Proof: Matrix Interpretation Processor: dimension: 1 interpretation: [s](x0) = x0 + 12, [0] = 14, [h](x0) = x0 + 1, [L](x0) = 8x0 + 14, [maxxAC](x0, x1) = x0 + x1 + 4, [maxAC](x0, x1) = x0 + x1 + 1, [NAC](x0, x1) = x0 + x1 + 4 orientation: h(L(x)) = 8x + 15 >= 14 = 0() h(NAC(x,y)) = x + y + 5 >= x + y + 3 = maxAC(h(x),h(y)) maxAC(0(),x) = x + 15 >= x = x maxAC(x,0()) = x + 15 >= x = x maxAC(s(x),s(y)) = x + y + 25 >= x + y + 16 = s(maxxAC(x,y)) maxxAC(0(),x) = x + 18 >= x = x maxxAC(x,0()) = x + 18 >= x = x maxxAC(s(x),s(y)) = x + y + 28 >= x + y + 13 = s(maxAC(x,y)) problem: Equations: NAC(NAC(x3,x4),x5) -> NAC(x3,NAC(x4,x5)) NAC(x3,x4) -> NAC(x4,x3) maxAC(maxAC(x3,x4),x5) -> maxAC(x3,maxAC(x4,x5)) maxAC(x3,x4) -> maxAC(x4,x3) maxxAC(maxxAC(x3,x4),x5) -> maxxAC(x3,maxxAC(x4,x5)) maxxAC(x3,x4) -> maxxAC(x4,x3) NAC(x3,NAC(x4,x5)) -> NAC(NAC(x3,x4),x5) NAC(x4,x3) -> NAC(x3,x4) maxAC(x3,maxAC(x4,x5)) -> maxAC(maxAC(x3,x4),x5) maxAC(x4,x3) -> maxAC(x3,x4) maxxAC(x3,maxxAC(x4,x5)) -> maxxAC(maxxAC(x3,x4),x5) maxxAC(x4,x3) -> maxxAC(x3,x4) TRS: Qed