YES Problem: 2nd(cons(X,n__cons(Y,Z))) -> activate(Y) from(X) -> cons(X,n__from(s(X))) cons(X1,X2) -> n__cons(X1,X2) from(X) -> n__from(X) activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__from(X)) -> from(X) activate(X) -> X Proof: DP Processor: DPs: 2nd#(cons(X,n__cons(Y,Z))) -> activate#(Y) from#(X) -> cons#(X,n__from(s(X))) activate#(n__cons(X1,X2)) -> cons#(X1,X2) activate#(n__from(X)) -> from#(X) TRS: 2nd(cons(X,n__cons(Y,Z))) -> activate(Y) from(X) -> cons(X,n__from(s(X))) cons(X1,X2) -> n__cons(X1,X2) from(X) -> n__from(X) activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__from(X)) -> from(X) activate(X) -> X Usable Rule Processor: DPs: 2nd#(cons(X,n__cons(Y,Z))) -> activate#(Y) from#(X) -> cons#(X,n__from(s(X))) activate#(n__cons(X1,X2)) -> cons#(X1,X2) activate#(n__from(X)) -> from#(X) TRS: Arctic Interpretation Processor: dimension: 1 usable rules: interpretation: [cons#](x0, x1) = x0, [from#](x0) = 4x0 + 0, [activate#](x0) = x0, [2nd#](x0) = x0 + -16, [n__from](x0) = 5x0 + 1, [s](x0) = 2x0 + -7, [cons](x0, x1) = x0 + x1 + -16, [n__cons](x0, x1) = 1x0 + x1 + -2 orientation: 2nd#(cons(X,n__cons(Y,Z))) = X + 1Y + Z + -2 >= Y = activate#(Y) from#(X) = 4X + 0 >= X = cons#(X,n__from(s(X))) activate#(n__cons(X1,X2)) = 1X1 + X2 + -2 >= X1 = cons#(X1,X2) activate#(n__from(X)) = 5X + 1 >= 4X + 0 = from#(X) problem: DPs: TRS: Qed