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