WORST_CASE(?,O(n^1)) * Step 1: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(X1,X2) activate(n__from(X)) -> from(X) activate(n__fst(X1,X2)) -> fst(X1,X2) activate(n__len(X)) -> len(X) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> X add(s(X),Y) -> s(n__add(activate(X),Y)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) fst(X1,X2) -> n__fst(X1,X2) fst(0(),Z) -> nil() fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) len(X) -> n__len(X) len(cons(X,Z)) -> s(n__len(activate(Z))) len(nil()) -> 0() - Signature: {activate/1,add/2,from/1,fst/2,len/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,from,fst,len} and constructors {0,cons ,n__add,n__from,n__fst,n__len,nil,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(cons) = {2}, uargs(n__add) = {1}, uargs(n__fst) = {1,2}, uargs(n__len) = {1}, uargs(s) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [1] p(activate) = [10] x1 + [0] p(add) = [10] x1 + [10] x2 + [4] p(cons) = [1] x2 + [0] p(from) = [0] p(fst) = [10] x1 + [10] x2 + [0] p(len) = [10] x1 + [0] p(n__add) = [1] x1 + [1] x2 + [0] p(n__from) = [0] p(n__fst) = [1] x1 + [1] x2 + [1] p(n__len) = [1] x1 + [0] p(nil) = [0] p(s) = [1] x1 + [1] Following rules are strictly oriented: activate(n__fst(X1,X2)) = [10] X1 + [10] X2 + [10] > [10] X1 + [10] X2 + [0] = fst(X1,X2) add(X1,X2) = [10] X1 + [10] X2 + [4] > [1] X1 + [1] X2 + [0] = n__add(X1,X2) add(0(),X) = [10] X + [14] > [1] X + [0] = X add(s(X),Y) = [10] X + [10] Y + [14] > [10] X + [1] Y + [1] = s(n__add(activate(X),Y)) fst(0(),Z) = [10] Z + [10] > [0] = nil() fst(s(X),cons(Y,Z)) = [10] X + [10] Z + [10] > [10] X + [10] Z + [1] = cons(Y,n__fst(activate(X),activate(Z))) Following rules are (at-least) weakly oriented: activate(X) = [10] X + [0] >= [1] X + [0] = X activate(n__add(X1,X2)) = [10] X1 + [10] X2 + [0] >= [10] X1 + [10] X2 + [4] = add(X1,X2) activate(n__from(X)) = [0] >= [0] = from(X) activate(n__len(X)) = [10] X + [0] >= [10] X + [0] = len(X) from(X) = [0] >= [0] = cons(X,n__from(s(X))) from(X) = [0] >= [0] = n__from(X) fst(X1,X2) = [10] X1 + [10] X2 + [0] >= [1] X1 + [1] X2 + [1] = n__fst(X1,X2) len(X) = [10] X + [0] >= [1] X + [0] = n__len(X) len(cons(X,Z)) = [10] Z + [0] >= [10] Z + [1] = s(n__len(activate(Z))) len(nil()) = [0] >= [1] = 0() Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(X1,X2) activate(n__from(X)) -> from(X) activate(n__len(X)) -> len(X) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) fst(X1,X2) -> n__fst(X1,X2) len(X) -> n__len(X) len(cons(X,Z)) -> s(n__len(activate(Z))) len(nil()) -> 0() - Weak TRS: activate(n__fst(X1,X2)) -> fst(X1,X2) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> X add(s(X),Y) -> s(n__add(activate(X),Y)) fst(0(),Z) -> nil() fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) - Signature: {activate/1,add/2,from/1,fst/2,len/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,from,fst,len} and constructors {0,cons ,n__add,n__from,n__fst,n__len,nil,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(cons) = {2}, uargs(n__add) = {1}, uargs(n__fst) = {1,2}, uargs(n__len) = {1}, uargs(s) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [4] p(activate) = [1] x1 + [0] p(add) = [1] x1 + [1] x2 + [4] p(cons) = [1] x2 + [0] p(from) = [0] p(fst) = [1] x1 + [1] x2 + [7] p(len) = [1] x1 + [3] p(n__add) = [1] x1 + [1] x2 + [2] p(n__from) = [0] p(n__fst) = [1] x1 + [1] x2 + [7] p(n__len) = [1] x1 + [5] p(nil) = [0] p(s) = [1] x1 + [0] Following rules are strictly oriented: activate(n__len(X)) = [1] X + [5] > [1] X + [3] = len(X) Following rules are (at-least) weakly oriented: activate(X) = [1] X + [0] >= [1] X + [0] = X activate(n__add(X1,X2)) = [1] X1 + [1] X2 + [2] >= [1] X1 + [1] X2 + [4] = add(X1,X2) activate(n__from(X)) = [0] >= [0] = from(X) activate(n__fst(X1,X2)) = [1] X1 + [1] X2 + [7] >= [1] X1 + [1] X2 + [7] = fst(X1,X2) add(X1,X2) = [1] X1 + [1] X2 + [4] >= [1] X1 + [1] X2 + [2] = n__add(X1,X2) add(0(),X) = [1] X + [8] >= [1] X + [0] = X add(s(X),Y) = [1] X + [1] Y + [4] >= [1] X + [1] Y + [2] = s(n__add(activate(X),Y)) from(X) = [0] >= [0] = cons(X,n__from(s(X))) from(X) = [0] >= [0] = n__from(X) fst(X1,X2) = [1] X1 + [1] X2 + [7] >= [1] X1 + [1] X2 + [7] = n__fst(X1,X2) fst(0(),Z) = [1] Z + [11] >= [0] = nil() fst(s(X),cons(Y,Z)) = [1] X + [1] Z + [7] >= [1] X + [1] Z + [7] = cons(Y,n__fst(activate(X),activate(Z))) len(X) = [1] X + [3] >= [1] X + [5] = n__len(X) len(cons(X,Z)) = [1] Z + [3] >= [1] Z + [5] = s(n__len(activate(Z))) len(nil()) = [3] >= [4] = 0() Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 3: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(X1,X2) activate(n__from(X)) -> from(X) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) fst(X1,X2) -> n__fst(X1,X2) len(X) -> n__len(X) len(cons(X,Z)) -> s(n__len(activate(Z))) len(nil()) -> 0() - Weak TRS: activate(n__fst(X1,X2)) -> fst(X1,X2) activate(n__len(X)) -> len(X) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> X add(s(X),Y) -> s(n__add(activate(X),Y)) fst(0(),Z) -> nil() fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) - Signature: {activate/1,add/2,from/1,fst/2,len/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,from,fst,len} and constructors {0,cons ,n__add,n__from,n__fst,n__len,nil,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(cons) = {2}, uargs(n__add) = {1}, uargs(n__fst) = {1,2}, uargs(n__len) = {1}, uargs(s) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [2] p(activate) = [2] x1 + [2] p(add) = [2] x1 + [1] x2 + [1] p(cons) = [1] x1 + [1] x2 + [0] p(from) = [2] x1 + [0] p(fst) = [2] x1 + [2] x2 + [2] p(len) = [2] x1 + [0] p(n__add) = [1] x1 + [1] x2 + [0] p(n__from) = [1] x1 + [0] p(n__fst) = [1] x1 + [1] x2 + [0] p(n__len) = [1] x1 + [0] p(nil) = [0] p(s) = [1] x1 + [1] Following rules are strictly oriented: activate(X) = [2] X + [2] > [1] X + [0] = X activate(n__add(X1,X2)) = [2] X1 + [2] X2 + [2] > [2] X1 + [1] X2 + [1] = add(X1,X2) activate(n__from(X)) = [2] X + [2] > [2] X + [0] = from(X) fst(X1,X2) = [2] X1 + [2] X2 + [2] > [1] X1 + [1] X2 + [0] = n__fst(X1,X2) Following rules are (at-least) weakly oriented: activate(n__fst(X1,X2)) = [2] X1 + [2] X2 + [2] >= [2] X1 + [2] X2 + [2] = fst(X1,X2) activate(n__len(X)) = [2] X + [2] >= [2] X + [0] = len(X) add(X1,X2) = [2] X1 + [1] X2 + [1] >= [1] X1 + [1] X2 + [0] = n__add(X1,X2) add(0(),X) = [1] X + [5] >= [1] X + [0] = X add(s(X),Y) = [2] X + [1] Y + [3] >= [2] X + [1] Y + [3] = s(n__add(activate(X),Y)) from(X) = [2] X + [0] >= [2] X + [1] = cons(X,n__from(s(X))) from(X) = [2] X + [0] >= [1] X + [0] = n__from(X) fst(0(),Z) = [2] Z + [6] >= [0] = nil() fst(s(X),cons(Y,Z)) = [2] X + [2] Y + [2] Z + [4] >= [2] X + [1] Y + [2] Z + [4] = cons(Y,n__fst(activate(X),activate(Z))) len(X) = [2] X + [0] >= [1] X + [0] = n__len(X) len(cons(X,Z)) = [2] X + [2] Z + [0] >= [2] Z + [3] = s(n__len(activate(Z))) len(nil()) = [0] >= [2] = 0() Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 4: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) len(X) -> n__len(X) len(cons(X,Z)) -> s(n__len(activate(Z))) len(nil()) -> 0() - Weak TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(X1,X2) activate(n__from(X)) -> from(X) activate(n__fst(X1,X2)) -> fst(X1,X2) activate(n__len(X)) -> len(X) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> X add(s(X),Y) -> s(n__add(activate(X),Y)) fst(X1,X2) -> n__fst(X1,X2) fst(0(),Z) -> nil() fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) - Signature: {activate/1,add/2,from/1,fst/2,len/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,from,fst,len} and constructors {0,cons ,n__add,n__from,n__fst,n__len,nil,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(cons) = {2}, uargs(n__add) = {1}, uargs(n__fst) = {1,2}, uargs(n__len) = {1}, uargs(s) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [2] p(activate) = [2] x1 + [0] p(add) = [2] x1 + [1] x2 + [3] p(cons) = [1] x2 + [1] p(from) = [7] p(fst) = [2] x1 + [2] x2 + [0] p(len) = [2] x1 + [0] p(n__add) = [1] x1 + [1] x2 + [2] p(n__from) = [4] p(n__fst) = [1] x1 + [1] x2 + [0] p(n__len) = [1] x1 + [3] p(nil) = [4] p(s) = [1] x1 + [2] Following rules are strictly oriented: from(X) = [7] > [5] = cons(X,n__from(s(X))) from(X) = [7] > [4] = n__from(X) len(nil()) = [8] > [2] = 0() Following rules are (at-least) weakly oriented: activate(X) = [2] X + [0] >= [1] X + [0] = X activate(n__add(X1,X2)) = [2] X1 + [2] X2 + [4] >= [2] X1 + [1] X2 + [3] = add(X1,X2) activate(n__from(X)) = [8] >= [7] = from(X) activate(n__fst(X1,X2)) = [2] X1 + [2] X2 + [0] >= [2] X1 + [2] X2 + [0] = fst(X1,X2) activate(n__len(X)) = [2] X + [6] >= [2] X + [0] = len(X) add(X1,X2) = [2] X1 + [1] X2 + [3] >= [1] X1 + [1] X2 + [2] = n__add(X1,X2) add(0(),X) = [1] X + [7] >= [1] X + [0] = X add(s(X),Y) = [2] X + [1] Y + [7] >= [2] X + [1] Y + [4] = s(n__add(activate(X),Y)) fst(X1,X2) = [2] X1 + [2] X2 + [0] >= [1] X1 + [1] X2 + [0] = n__fst(X1,X2) fst(0(),Z) = [2] Z + [4] >= [4] = nil() fst(s(X),cons(Y,Z)) = [2] X + [2] Z + [6] >= [2] X + [2] Z + [1] = cons(Y,n__fst(activate(X),activate(Z))) len(X) = [2] X + [0] >= [1] X + [3] = n__len(X) len(cons(X,Z)) = [2] Z + [2] >= [2] Z + [5] = s(n__len(activate(Z))) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 5: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: len(X) -> n__len(X) len(cons(X,Z)) -> s(n__len(activate(Z))) - Weak TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(X1,X2) activate(n__from(X)) -> from(X) activate(n__fst(X1,X2)) -> fst(X1,X2) activate(n__len(X)) -> len(X) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> X add(s(X),Y) -> s(n__add(activate(X),Y)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) fst(X1,X2) -> n__fst(X1,X2) fst(0(),Z) -> nil() fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) len(nil()) -> 0() - Signature: {activate/1,add/2,from/1,fst/2,len/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,from,fst,len} and constructors {0,cons ,n__add,n__from,n__fst,n__len,nil,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(cons) = {2}, uargs(n__add) = {1}, uargs(n__fst) = {1,2}, uargs(n__len) = {1}, uargs(s) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [6] p(activate) = [1] x1 + [1] p(add) = [1] x1 + [1] x2 + [1] p(cons) = [1] x2 + [0] p(from) = [1] p(fst) = [1] x1 + [1] x2 + [0] p(len) = [1] x1 + [7] p(n__add) = [1] x1 + [1] x2 + [0] p(n__from) = [1] p(n__fst) = [1] x1 + [1] x2 + [0] p(n__len) = [1] x1 + [6] p(nil) = [0] p(s) = [1] x1 + [2] Following rules are strictly oriented: len(X) = [1] X + [7] > [1] X + [6] = n__len(X) Following rules are (at-least) weakly oriented: activate(X) = [1] X + [1] >= [1] X + [0] = X activate(n__add(X1,X2)) = [1] X1 + [1] X2 + [1] >= [1] X1 + [1] X2 + [1] = add(X1,X2) activate(n__from(X)) = [2] >= [1] = from(X) activate(n__fst(X1,X2)) = [1] X1 + [1] X2 + [1] >= [1] X1 + [1] X2 + [0] = fst(X1,X2) activate(n__len(X)) = [1] X + [7] >= [1] X + [7] = len(X) add(X1,X2) = [1] X1 + [1] X2 + [1] >= [1] X1 + [1] X2 + [0] = n__add(X1,X2) add(0(),X) = [1] X + [7] >= [1] X + [0] = X add(s(X),Y) = [1] X + [1] Y + [3] >= [1] X + [1] Y + [3] = s(n__add(activate(X),Y)) from(X) = [1] >= [1] = cons(X,n__from(s(X))) from(X) = [1] >= [1] = n__from(X) fst(X1,X2) = [1] X1 + [1] X2 + [0] >= [1] X1 + [1] X2 + [0] = n__fst(X1,X2) fst(0(),Z) = [1] Z + [6] >= [0] = nil() fst(s(X),cons(Y,Z)) = [1] X + [1] Z + [2] >= [1] X + [1] Z + [2] = cons(Y,n__fst(activate(X),activate(Z))) len(cons(X,Z)) = [1] Z + [7] >= [1] Z + [9] = s(n__len(activate(Z))) len(nil()) = [7] >= [6] = 0() Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 6: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: len(cons(X,Z)) -> s(n__len(activate(Z))) - Weak TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(X1,X2) activate(n__from(X)) -> from(X) activate(n__fst(X1,X2)) -> fst(X1,X2) activate(n__len(X)) -> len(X) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> X add(s(X),Y) -> s(n__add(activate(X),Y)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) fst(X1,X2) -> n__fst(X1,X2) fst(0(),Z) -> nil() fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) len(X) -> n__len(X) len(nil()) -> 0() - Signature: {activate/1,add/2,from/1,fst/2,len/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,from,fst,len} and constructors {0,cons ,n__add,n__from,n__fst,n__len,nil,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(cons) = {2}, uargs(n__add) = {1}, uargs(n__fst) = {1,2}, uargs(n__len) = {1}, uargs(s) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [0] p(activate) = [4] x1 + [0] p(add) = [4] x1 + [4] x2 + [0] p(cons) = [1] x2 + [0] p(from) = [0] p(fst) = [4] x1 + [4] x2 + [5] p(len) = [4] x1 + [4] p(n__add) = [1] x1 + [1] x2 + [0] p(n__from) = [0] p(n__fst) = [1] x1 + [1] x2 + [2] p(n__len) = [1] x1 + [1] p(nil) = [2] p(s) = [1] x1 + [2] Following rules are strictly oriented: len(cons(X,Z)) = [4] Z + [4] > [4] Z + [3] = s(n__len(activate(Z))) Following rules are (at-least) weakly oriented: activate(X) = [4] X + [0] >= [1] X + [0] = X activate(n__add(X1,X2)) = [4] X1 + [4] X2 + [0] >= [4] X1 + [4] X2 + [0] = add(X1,X2) activate(n__from(X)) = [0] >= [0] = from(X) activate(n__fst(X1,X2)) = [4] X1 + [4] X2 + [8] >= [4] X1 + [4] X2 + [5] = fst(X1,X2) activate(n__len(X)) = [4] X + [4] >= [4] X + [4] = len(X) add(X1,X2) = [4] X1 + [4] X2 + [0] >= [1] X1 + [1] X2 + [0] = n__add(X1,X2) add(0(),X) = [4] X + [0] >= [1] X + [0] = X add(s(X),Y) = [4] X + [4] Y + [8] >= [4] X + [1] Y + [2] = s(n__add(activate(X),Y)) from(X) = [0] >= [0] = cons(X,n__from(s(X))) from(X) = [0] >= [0] = n__from(X) fst(X1,X2) = [4] X1 + [4] X2 + [5] >= [1] X1 + [1] X2 + [2] = n__fst(X1,X2) fst(0(),Z) = [4] Z + [5] >= [2] = nil() fst(s(X),cons(Y,Z)) = [4] X + [4] Z + [13] >= [4] X + [4] Z + [2] = cons(Y,n__fst(activate(X),activate(Z))) len(X) = [4] X + [4] >= [1] X + [1] = n__len(X) len(nil()) = [12] >= [0] = 0() Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 7: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(X1,X2) activate(n__from(X)) -> from(X) activate(n__fst(X1,X2)) -> fst(X1,X2) activate(n__len(X)) -> len(X) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> X add(s(X),Y) -> s(n__add(activate(X),Y)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) fst(X1,X2) -> n__fst(X1,X2) fst(0(),Z) -> nil() fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) len(X) -> n__len(X) len(cons(X,Z)) -> s(n__len(activate(Z))) len(nil()) -> 0() - Signature: {activate/1,add/2,from/1,fst/2,len/1} / {0/0,cons/2,n__add/2,n__from/1,n__fst/2,n__len/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,from,fst,len} and constructors {0,cons ,n__add,n__from,n__fst,n__len,nil,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))