YES Problem: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x Proof: DP Processor: DPs: +#(-(x,y),z) -> +#(x,z) +#(-(x,y),z) -> -#(+(x,z),y) TRS: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x Matrix Interpretation Processor: dim=1 interpretation: [-#](x0, x1) = x0 + 3, [+#](x0, x1) = x0 + 4, [+](x0, x1) = x0 + 1, [-](x0, x1) = x0 + 1 orientation: +#(-(x,y),z) = x + 5 >= x + 4 = +#(x,z) +#(-(x,y),z) = x + 5 >= x + 4 = -#(+(x,z),y) +(-(x,y),z) = x + 2 >= x + 2 = -(+(x,z),y) -(+(x,y),y) = x + 2 >= x = x problem: DPs: TRS: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x Qed