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 CDG Processor: DPs: +#(-(x,y),z) -> +#(x,z) +#(-(x,y),z) -> -#(+(x,z),y) TRS: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x graph: +#(-(x,y),z) -> +#(x,z) -> +#(-(x,y),z) -> +#(x,z) +#(-(x,y),z) -> +#(x,z) -> +#(-(x,y),z) -> -#(+(x,z),y) Restore Modifier: DPs: +#(-(x,y),z) -> +#(x,z) +#(-(x,y),z) -> -#(+(x,z),y) TRS: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x SCC Processor: #sccs: 1 #rules: 1 #arcs: 2/4 DPs: +#(-(x,y),z) -> +#(x,z) TRS: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x Matrix Interpretation Processor: dimension: 1 interpretation: [+#](x0, x1) = x0 + 1, [+](x0, x1) = x0, [-](x0, x1) = x0 + 1 orientation: +#(-(x,y),z) = x + 2 >= x + 1 = +#(x,z) +(-(x,y),z) = x + 1 >= x + 1 = -(+(x,z),y) -(+(x,y),y) = x + 1 >= x = x problem: DPs: TRS: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x Qed