YES Problem: plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z)) plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4))) Proof: DP Processor: DPs: plus#(s(X),plus(Y,Z)) -> plus#(s(s(Y)),Z) plus#(s(X),plus(Y,Z)) -> plus#(X,plus(s(s(Y)),Z)) plus#(s(X1),plus(X2,plus(X3,X4))) -> plus#(X2,X4) plus#(s(X1),plus(X2,plus(X3,X4))) -> plus#(X3,plus(X2,X4)) plus#(s(X1),plus(X2,plus(X3,X4))) -> plus#(X1,plus(X3,plus(X2,X4))) TRS: plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z)) plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4))) Arctic Interpretation Processor: dimension: 1 interpretation: [plus#](x0, x1) = x1 + 0, [plus](x0, x1) = 1x1 + 0, [s](x0) = x0 + 3 orientation: plus#(s(X),plus(Y,Z)) = 1Z + 0 >= Z + 0 = plus#(s(s(Y)),Z) plus#(s(X),plus(Y,Z)) = 1Z + 0 >= 1Z + 0 = plus#(X,plus(s(s(Y)),Z)) plus#(s(X1),plus(X2,plus(X3,X4))) = 2X4 + 1 >= X4 + 0 = plus#(X2,X4) plus#(s(X1),plus(X2,plus(X3,X4))) = 2X4 + 1 >= 1X4 + 0 = plus#(X3,plus(X2,X4)) plus#(s(X1),plus(X2,plus(X3,X4))) = 2X4 + 1 >= 2X4 + 1 = plus#(X1,plus(X3,plus(X2,X4))) plus(s(X),plus(Y,Z)) = 2Z + 1 >= 2Z + 1 = plus(X,plus(s(s(Y)),Z)) plus(s(X1),plus(X2,plus(X3,X4))) = 3X4 + 2 >= 3X4 + 2 = plus(X1,plus(X3,plus(X2,X4))) problem: DPs: plus#(s(X),plus(Y,Z)) -> plus#(s(s(Y)),Z) plus#(s(X),plus(Y,Z)) -> plus#(X,plus(s(s(Y)),Z)) plus#(s(X1),plus(X2,plus(X3,X4))) -> plus#(X3,plus(X2,X4)) plus#(s(X1),plus(X2,plus(X3,X4))) -> plus#(X1,plus(X3,plus(X2,X4))) TRS: plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z)) plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4))) KBO Processor: argument filtering: pi(s) = [0] pi(plus) = [0,1] pi(plus#) = [0,1] weight function: w0 = 1 w(plus#) = w(plus) = 1 w(s) = 0 precedence: plus# ~ plus ~ s problem: DPs: TRS: plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z)) plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4))) Qed