/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Proof: DP Processor: DPs: first#(s(X),cons(Y,Z)) -> activate#(Z) activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) activate#(n__from(X)) -> activate#(X) activate#(n__from(X)) -> from#(activate(X)) activate#(n__s(X)) -> activate#(X) activate#(n__s(X)) -> s#(activate(X)) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X TDG Processor: DPs: first#(s(X),cons(Y,Z)) -> activate#(Z) activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) activate#(n__from(X)) -> activate#(X) activate#(n__from(X)) -> from#(activate(X)) activate#(n__s(X)) -> activate#(X) activate#(n__s(X)) -> s#(activate(X)) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X graph: activate#(n__from(X)) -> activate#(X) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__from(X)) -> activate#(X) -> activate#(n__s(X)) -> activate#(X) activate#(n__from(X)) -> activate#(X) -> activate#(n__from(X)) -> from#(activate(X)) activate#(n__from(X)) -> activate#(X) -> activate#(n__from(X)) -> activate#(X) activate#(n__from(X)) -> activate#(X) -> activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) activate#(n__from(X)) -> activate#(X) -> activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__from(X)) -> activate#(X) -> activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__s(X)) -> activate#(X) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__s(X)) -> activate#(X) -> activate#(n__s(X)) -> activate#(X) activate#(n__s(X)) -> activate#(X) -> activate#(n__from(X)) -> from#(activate(X)) activate#(n__s(X)) -> activate#(X) -> activate#(n__from(X)) -> activate#(X) activate#(n__s(X)) -> activate#(X) -> activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) activate#(n__s(X)) -> activate#(X) -> activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__s(X)) -> activate#(X) -> activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> activate#(X2) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__first(X1,X2)) -> activate#(X2) -> activate#(n__s(X)) -> activate#(X) activate#(n__first(X1,X2)) -> activate#(X2) -> activate#(n__from(X)) -> from#(activate(X)) activate#(n__first(X1,X2)) -> activate#(X2) -> activate#(n__from(X)) -> activate#(X) activate#(n__first(X1,X2)) -> activate#(X2) -> activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) activate#(n__first(X1,X2)) -> activate#(X2) -> activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> activate#(X2) -> activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> activate#(X1) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__first(X1,X2)) -> activate#(X1) -> activate#(n__s(X)) -> activate#(X) activate#(n__first(X1,X2)) -> activate#(X1) -> activate#(n__from(X)) -> from#(activate(X)) activate#(n__first(X1,X2)) -> activate#(X1) -> activate#(n__from(X)) -> activate#(X) activate#(n__first(X1,X2)) -> activate#(X1) -> activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) activate#(n__first(X1,X2)) -> activate#(X1) -> activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> activate#(X1) -> activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) -> first#(s(X),cons(Y,Z)) -> activate#(Z) first#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__s(X)) -> s#(activate(X)) first#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__s(X)) -> activate#(X) first#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__from(X)) -> from#(activate(X)) first#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__from(X)) -> activate#(X) first#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__first(X1,X2)) -> activate#(X1) first#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__first(X1,X2)) -> activate#(X2) SCC Processor: #sccs: 1 #rules: 6 #arcs: 36/64 DPs: activate#(n__from(X)) -> activate#(X) activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) activate#(n__s(X)) -> activate#(X) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Arctic Interpretation Processor: dimension: 1 usable rules: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X interpretation: [activate#](x0) = 3x0 + 0, [first#](x0, x1) = 1x0 + 3x1 + 0, [n__from](x0) = 1x0 + 0, [n__s](x0) = x0 + -1, [from](x0) = 1x0 + 0, [n__first](x0, x1) = x0 + x1 + -3, [activate](x0) = x0, [cons](x0, x1) = x0 + x1 + 0, [s](x0) = x0 + -1, [nil] = 0, [first](x0, x1) = x0 + x1 + -3, [0] = 0 orientation: activate#(n__from(X)) = 4X + 3 >= 3X + 0 = activate#(X) activate#(n__first(X1,X2)) = 3X1 + 3X2 + 0 >= 3X2 + 0 = activate#(X2) activate#(n__first(X1,X2)) = 3X1 + 3X2 + 0 >= 3X1 + 0 = activate#(X1) activate#(n__first(X1,X2)) = 3X1 + 3X2 + 0 >= 1X1 + 3X2 + 0 = first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) = 1X + 3Y + 3Z + 3 >= 3Z + 0 = activate#(Z) activate#(n__s(X)) = 3X + 2 >= 3X + 0 = activate#(X) first(0(),X) = X + 0 >= 0 = nil() first(s(X),cons(Y,Z)) = X + Y + Z + 0 >= X + Y + Z + 0 = cons(Y,n__first(X,activate(Z))) from(X) = 1X + 0 >= 1X + 0 = cons(X,n__from(n__s(X))) first(X1,X2) = X1 + X2 + -3 >= X1 + X2 + -3 = n__first(X1,X2) from(X) = 1X + 0 >= 1X + 0 = n__from(X) s(X) = X + -1 >= X + -1 = n__s(X) activate(n__first(X1,X2)) = X1 + X2 + -3 >= X1 + X2 + -3 = first(activate(X1),activate(X2)) activate(n__from(X)) = 1X + 0 >= 1X + 0 = from(activate(X)) activate(n__s(X)) = X + -1 >= X + -1 = s(activate(X)) activate(X) = X >= X = X problem: DPs: activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) activate#(n__s(X)) -> activate#(X) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Restore Modifier: DPs: activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) activate#(n__s(X)) -> activate#(X) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Arctic Interpretation Processor: dimension: 1 usable rules: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X interpretation: [activate#](x0) = x0 + 0, [first#](x0, x1) = x0 + 4x1 + -8, [n__from](x0) = 0, [n__s](x0) = x0, [from](x0) = 0, [n__first](x0, x1) = x0 + 4x1 + 4, [activate](x0) = x0 + 0, [cons](x0, x1) = x1 + -4, [s](x0) = x0, [nil] = 1, [first](x0, x1) = x0 + 4x1 + 4, [0] = 2 orientation: activate#(n__first(X1,X2)) = X1 + 4X2 + 4 >= X2 + 0 = activate#(X2) activate#(n__first(X1,X2)) = X1 + 4X2 + 4 >= X1 + 0 = activate#(X1) activate#(n__first(X1,X2)) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) = X + 4Z + 0 >= Z + 0 = activate#(Z) activate#(n__s(X)) = X + 0 >= X + 0 = activate#(X) first(0(),X) = 4X + 4 >= 1 = nil() first(s(X),cons(Y,Z)) = X + 4Z + 4 >= X + 4Z + 4 = cons(Y,n__first(X,activate(Z))) from(X) = 0 >= 0 = cons(X,n__from(n__s(X))) first(X1,X2) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = n__first(X1,X2) from(X) = 0 >= 0 = n__from(X) s(X) = X >= X = n__s(X) activate(n__first(X1,X2)) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = first(activate(X1),activate(X2)) activate(n__from(X)) = 0 >= 0 = from(activate(X)) activate(n__s(X)) = X + 0 >= X + 0 = s(activate(X)) activate(X) = X + 0 >= X = X problem: DPs: activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) activate#(n__s(X)) -> activate#(X) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Restore Modifier: DPs: activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) activate#(n__s(X)) -> activate#(X) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Arctic Interpretation Processor: dimension: 1 usable rules: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X interpretation: [activate#](x0) = x0, [first#](x0, x1) = x0 + x1 + 0, [n__from](x0) = 4, [n__s](x0) = x0 + 0, [from](x0) = 4, [n__first](x0, x1) = 2x0 + x1 + 0, [activate](x0) = x0, [cons](x0, x1) = x1 + 0, [s](x0) = x0 + 0, [nil] = 2, [first](x0, x1) = 2x0 + x1 + 0, [0] = 1 orientation: activate#(n__first(X1,X2)) = 2X1 + X2 + 0 >= X1 = activate#(X1) activate#(n__first(X1,X2)) = 2X1 + X2 + 0 >= X1 + X2 + 0 = first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) = X + Z + 0 >= Z = activate#(Z) activate#(n__s(X)) = X + 0 >= X = activate#(X) first(0(),X) = X + 3 >= 2 = nil() first(s(X),cons(Y,Z)) = 2X + Z + 2 >= 2X + Z + 0 = cons(Y,n__first(X,activate(Z))) from(X) = 4 >= 4 = cons(X,n__from(n__s(X))) first(X1,X2) = 2X1 + X2 + 0 >= 2X1 + X2 + 0 = n__first(X1,X2) from(X) = 4 >= 4 = n__from(X) s(X) = X + 0 >= X + 0 = n__s(X) activate(n__first(X1,X2)) = 2X1 + X2 + 0 >= 2X1 + X2 + 0 = first(activate(X1),activate(X2)) activate(n__from(X)) = 4 >= 4 = from(activate(X)) activate(n__s(X)) = X + 0 >= X + 0 = s(activate(X)) activate(X) = X >= X = X problem: DPs: activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) activate#(n__s(X)) -> activate#(X) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Restore Modifier: DPs: activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) activate#(n__s(X)) -> activate#(X) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Arctic Interpretation Processor: dimension: 1 usable rules: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X interpretation: [activate#](x0) = 2x0 + 4, [first#](x0, x1) = 2x0 + 2x1 + 4, [n__from](x0) = 6, [n__s](x0) = 1x0 + 5, [from](x0) = 6, [n__first](x0, x1) = x0 + x1, [activate](x0) = x0 + 1, [cons](x0, x1) = x1 + 5, [s](x0) = 1x0 + 5, [nil] = 0, [first](x0, x1) = x0 + x1 + 0, [0] = 5 orientation: activate#(n__first(X1,X2)) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) = 3X + 2Z + 7 >= 2Z + 4 = activate#(Z) activate#(n__s(X)) = 3X + 7 >= 2X + 4 = activate#(X) first(0(),X) = X + 5 >= 0 = nil() first(s(X),cons(Y,Z)) = 1X + Z + 5 >= X + Z + 5 = cons(Y,n__first(X,activate(Z))) from(X) = 6 >= 6 = cons(X,n__from(n__s(X))) first(X1,X2) = X1 + X2 + 0 >= X1 + X2 = n__first(X1,X2) from(X) = 6 >= 6 = n__from(X) s(X) = 1X + 5 >= 1X + 5 = n__s(X) activate(n__first(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = first(activate(X1),activate(X2)) activate(n__from(X)) = 6 >= 6 = from(activate(X)) activate(n__s(X)) = 1X + 5 >= 1X + 5 = s(activate(X)) activate(X) = X + 1 >= X = X problem: DPs: activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Restore Modifier: DPs: activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) -> activate#(Z) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Arctic Interpretation Processor: dimension: 1 usable rules: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X interpretation: [activate#](x0) = x0 + 0, [first#](x0, x1) = x0 + x1, [n__from](x0) = 2x0 + 2, [n__s](x0) = x0 + 0, [from](x0) = 2x0 + 2, [n__first](x0, x1) = 4x0 + 2x1 + 0, [activate](x0) = x0, [cons](x0, x1) = x1 + 0, [s](x0) = x0 + 0, [nil] = 1, [first](x0, x1) = 4x0 + 2x1 + 0, [0] = 3 orientation: activate#(n__first(X1,X2)) = 4X1 + 2X2 + 0 >= X1 + X2 = first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) = X + Z + 0 >= Z + 0 = activate#(Z) first(0(),X) = 2X + 7 >= 1 = nil() first(s(X),cons(Y,Z)) = 4X + 2Z + 4 >= 4X + 2Z + 0 = cons(Y,n__first(X,activate(Z))) from(X) = 2X + 2 >= 2X + 2 = cons(X,n__from(n__s(X))) first(X1,X2) = 4X1 + 2X2 + 0 >= 4X1 + 2X2 + 0 = n__first(X1,X2) from(X) = 2X + 2 >= 2X + 2 = n__from(X) s(X) = X + 0 >= X + 0 = n__s(X) activate(n__first(X1,X2)) = 4X1 + 2X2 + 0 >= 4X1 + 2X2 + 0 = first(activate(X1),activate(X2)) activate(n__from(X)) = 2X + 2 >= 2X + 2 = from(activate(X)) activate(n__s(X)) = X + 0 >= X + 0 = s(activate(X)) activate(X) = X >= X = X problem: DPs: first#(s(X),cons(Y,Z)) -> activate#(Z) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Restore Modifier: DPs: first#(s(X),cons(Y,Z)) -> activate#(Z) TRS: first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) from(X) -> cons(X,n__from(n__s(X))) first(X1,X2) -> n__first(X1,X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X SCC Processor: #sccs: 0 #rules: 0 #arcs: 26/1