YES Problem: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X Proof: DP Processor: DPs: first#(s(X),cons(Y,Z)) -> activate#(Z) sel#(s(X),cons(Y,Z)) -> activate#(Z) sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) 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)) activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) TRS: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X TDG Processor: DPs: first#(s(X),cons(Y,Z)) -> activate#(Z) sel#(s(X),cons(Y,Z)) -> activate#(Z) sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) 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)) activate#(n__first(X1,X2)) -> activate#(X2) activate#(n__first(X1,X2)) -> activate#(X1) activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) TRS: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X graph: sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) -> sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) -> sel#(s(X),cons(Y,Z)) -> activate#(Z) sel#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2)) sel#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__first(X1,X2)) -> activate#(X1) sel#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__first(X1,X2)) -> activate#(X2) sel#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__s(X)) -> s#(activate(X)) sel#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__s(X)) -> activate#(X) sel#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__from(X)) -> from#(activate(X)) sel#(s(X),cons(Y,Z)) -> activate#(Z) -> 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#(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#(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)) -> 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)) -> first#(activate(X1),activate(X2)) -> first#(s(X),cons(Y,Z)) -> activate#(Z) 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__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__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__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) 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) 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) SCC Processor: #sccs: 2 #rules: 7 #arcs: 45/100 DPs: sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) TRS: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X Subterm Criterion Processor: simple projection: pi(sel#) = 0 problem: DPs: TRS: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X Qed DPs: activate#(n__from(X)) -> activate#(X) activate#(n__s(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) TRS: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X Usable Rule Processor: DPs: activate#(n__from(X)) -> activate#(X) activate#(n__s(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) TRS: activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(X1,X2) -> n__first(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(X1,X2) -> n__first(X1,X2) interpretation: [activate#](x0) = x0 + 1, [first#](x0, x1) = x0 + x1 + 0, [n__first](x0, x1) = x0 + x1, [activate](x0) = x0 + 1, [s](x0) = x0 + 1, [nil] = 1, [first](x0, x1) = x0 + x1 + 0, [0] = 4, [cons](x0, x1) = x0 + x1 + 1, [n__from](x0) = 5x0 + 7, [n__s](x0) = x0 + 0, [from](x0) = 5x0 + 7 orientation: activate#(n__from(X)) = 5X + 7 >= X + 1 = activate#(X) activate#(n__s(X)) = X + 1 >= X + 1 = activate#(X) activate#(n__first(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = activate#(X2) activate#(n__first(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = activate#(X1) activate#(n__first(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) = X + Y + Z + 1 >= Z + 1 = activate#(Z) activate(n__from(X)) = 5X + 7 >= 5X + 7 = from(activate(X)) activate(n__s(X)) = X + 1 >= X + 1 = s(activate(X)) activate(n__first(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = first(activate(X1),activate(X2)) activate(X) = X + 1 >= X = X from(X) = 5X + 7 >= 5X + 7 = cons(X,n__from(n__s(X))) from(X) = 5X + 7 >= 5X + 7 = n__from(X) s(X) = X + 1 >= X + 0 = n__s(X) first(0(),Z) = Z + 4 >= 1 = nil() first(s(X),cons(Y,Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = cons(Y,n__first(X,activate(Z))) first(X1,X2) = X1 + X2 + 0 >= X1 + X2 = n__first(X1,X2) problem: DPs: activate#(n__s(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) TRS: activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(X1,X2) -> n__first(X1,X2) Restore Modifier: DPs: activate#(n__s(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) TRS: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X Usable Rule Processor: DPs: activate#(n__s(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) TRS: activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(X1,X2) -> n__first(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(X1,X2) -> n__first(X1,X2) interpretation: [activate#](x0) = x0, [first#](x0, x1) = 7x0 + x1 + 0, [n__first](x0, x1) = 7x0 + x1 + 7, [activate](x0) = x0 + 0, [s](x0) = x0 + 0, [nil] = 0, [first](x0, x1) = 7x0 + x1 + 7, [0] = 0, [cons](x0, x1) = x1 + 0, [n__from](x0) = x0, [n__s](x0) = x0 + 0, [from](x0) = x0 + 0 orientation: activate#(n__s(X)) = X + 0 >= X = activate#(X) activate#(n__first(X1,X2)) = 7X1 + X2 + 7 >= X2 = activate#(X2) activate#(n__first(X1,X2)) = 7X1 + X2 + 7 >= X1 = activate#(X1) activate#(n__first(X1,X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) = 7X + Z + 7 >= Z = activate#(Z) activate(n__from(X)) = X + 0 >= X + 0 = from(activate(X)) activate(n__s(X)) = X + 0 >= X + 0 = s(activate(X)) activate(n__first(X1,X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = first(activate(X1),activate(X2)) activate(X) = X + 0 >= X = X from(X) = X + 0 >= X + 0 = cons(X,n__from(n__s(X))) from(X) = X + 0 >= X = n__from(X) s(X) = X + 0 >= X + 0 = n__s(X) first(0(),Z) = Z + 7 >= 0 = nil() first(s(X),cons(Y,Z)) = 7X + Z + 7 >= 7X + Z + 7 = cons(Y,n__first(X,activate(Z))) first(X1,X2) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = n__first(X1,X2) problem: DPs: activate#(n__s(X)) -> activate#(X) 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) TRS: activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(X1,X2) -> n__first(X1,X2) Restore Modifier: DPs: activate#(n__s(X)) -> activate#(X) 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) TRS: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X Usable Rule Processor: DPs: activate#(n__s(X)) -> activate#(X) 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) TRS: activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(X1,X2) -> n__first(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(X1,X2) -> n__first(X1,X2) interpretation: [activate#](x0) = 1x0, [first#](x0, x1) = 4x1 + 0, [n__first](x0, x1) = 4x1 + 0, [activate](x0) = x0, [s](x0) = x0, [nil] = 0, [first](x0, x1) = 4x1 + 0, [0] = 0, [cons](x0, x1) = x1, [n__from](x0) = 2, [n__s](x0) = x0, [from](x0) = 2 orientation: activate#(n__s(X)) = 1X >= 1X = activate#(X) activate#(n__first(X1,X2)) = 5X2 + 1 >= 1X2 = activate#(X2) activate#(n__first(X1,X2)) = 5X2 + 1 >= 4X2 + 0 = first#(activate(X1),activate(X2)) first#(s(X),cons(Y,Z)) = 4Z + 0 >= 1Z = activate#(Z) activate(n__from(X)) = 2 >= 2 = from(activate(X)) activate(n__s(X)) = X >= X = s(activate(X)) activate(n__first(X1,X2)) = 4X2 + 0 >= 4X2 + 0 = first(activate(X1),activate(X2)) activate(X) = X >= X = X from(X) = 2 >= 2 = cons(X,n__from(n__s(X))) from(X) = 2 >= 2 = n__from(X) s(X) = X >= X = n__s(X) first(0(),Z) = 4Z + 0 >= 0 = nil() first(s(X),cons(Y,Z)) = 4Z + 0 >= 4Z + 0 = cons(Y,n__first(X,activate(Z))) first(X1,X2) = 4X2 + 0 >= 4X2 + 0 = n__first(X1,X2) problem: DPs: activate#(n__s(X)) -> activate#(X) TRS: activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(X1,X2) -> n__first(X1,X2) Restore Modifier: DPs: activate#(n__s(X)) -> activate#(X) TRS: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X Subterm Criterion Processor: simple projection: pi(activate#) = 0 problem: DPs: TRS: from(X) -> cons(X,n__from(n__s(X))) first(0(),Z) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) sel(0(),cons(X,Z)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) first(X1,X2) -> n__first(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(X) -> X Qed