MAYBE * Step 1: DependencyPairs MAYBE + Considered Problem: - Strict TRS: U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() length(cons(N,L)) -> U11(tt(),activate(L)) length(nil()) -> 0() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0 ,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,U21,U22,U23,activate,length,take ,zeros} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) activate#(X) -> c_6() activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) activate#(n__zeros()) -> c_8(zeros#()) length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) length#(nil()) -> c_10() take#(X1,X2) -> c_11() take#(0(),IL) -> c_12() take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) zeros#() -> c_14() zeros#() -> c_15() Weak DPs and mark the set of starting terms. * Step 2: UsableRules MAYBE + Considered Problem: - Strict DPs: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) activate#(X) -> c_6() activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) activate#(n__zeros()) -> c_8(zeros#()) length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) length#(nil()) -> c_10() take#(X1,X2) -> c_11() take#(0(),IL) -> c_12() take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) zeros#() -> c_14() zeros#() -> c_15() - Weak TRS: U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() length(cons(N,L)) -> U11(tt(),activate(L)) length(nil()) -> 0() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0,U11#/2,U12#/2,U21#/4,U22#/4,U23#/4 ,activate#/1,length#/1,take#/2,zeros#/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/4 ,c_4/4,c_5/3,c_6/0,c_7/1,c_8/1,c_9/2,c_10/0,c_11/0,c_12/0,c_13/2,c_14/0,c_15/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,U23#,activate#,length#,take# ,zeros#} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) activate#(X) -> c_6() activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) activate#(n__zeros()) -> c_8(zeros#()) length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) length#(nil()) -> c_10() take#(X1,X2) -> c_11() take#(0(),IL) -> c_12() take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) zeros#() -> c_14() zeros#() -> c_15() * Step 3: PredecessorEstimation MAYBE + Considered Problem: - Strict DPs: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) activate#(X) -> c_6() activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) activate#(n__zeros()) -> c_8(zeros#()) length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) length#(nil()) -> c_10() take#(X1,X2) -> c_11() take#(0(),IL) -> c_12() take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) zeros#() -> c_14() zeros#() -> c_15() - Weak TRS: U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0,U11#/2,U12#/2,U21#/4,U22#/4,U23#/4 ,activate#/1,length#/1,take#/2,zeros#/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/4 ,c_4/4,c_5/3,c_6/0,c_7/1,c_8/1,c_9/2,c_10/0,c_11/0,c_12/0,c_13/2,c_14/0,c_15/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,U23#,activate#,length#,take# ,zeros#} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {6,10,11,12,14,15} by application of Pre({6,10,11,12,14,15}) = {1,2,3,4,5,7,8,9,13}. Here rules are labelled as follows: 1: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) 2: U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) 3: U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) 4: U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) 5: U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) 6: activate#(X) -> c_6() 7: activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) 8: activate#(n__zeros()) -> c_8(zeros#()) 9: length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) 10: length#(nil()) -> c_10() 11: take#(X1,X2) -> c_11() 12: take#(0(),IL) -> c_12() 13: take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) 14: zeros#() -> c_14() 15: zeros#() -> c_15() * Step 4: PredecessorEstimation MAYBE + Considered Problem: - Strict DPs: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) activate#(n__zeros()) -> c_8(zeros#()) length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) - Weak DPs: activate#(X) -> c_6() length#(nil()) -> c_10() take#(X1,X2) -> c_11() take#(0(),IL) -> c_12() zeros#() -> c_14() zeros#() -> c_15() - Weak TRS: U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0,U11#/2,U12#/2,U21#/4,U22#/4,U23#/4 ,activate#/1,length#/1,take#/2,zeros#/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/4 ,c_4/4,c_5/3,c_6/0,c_7/1,c_8/1,c_9/2,c_10/0,c_11/0,c_12/0,c_13/2,c_14/0,c_15/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,U23#,activate#,length#,take# ,zeros#} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {7} by application of Pre({7}) = {1,2,3,4,5,8,9}. Here rules are labelled as follows: 1: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) 2: U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) 3: U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) 4: U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) 5: U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) 6: activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) 7: activate#(n__zeros()) -> c_8(zeros#()) 8: length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) 9: take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) 10: activate#(X) -> c_6() 11: length#(nil()) -> c_10() 12: take#(X1,X2) -> c_11() 13: take#(0(),IL) -> c_12() 14: zeros#() -> c_14() 15: zeros#() -> c_15() * Step 5: RemoveWeakSuffixes MAYBE + Considered Problem: - Strict DPs: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) - Weak DPs: activate#(X) -> c_6() activate#(n__zeros()) -> c_8(zeros#()) length#(nil()) -> c_10() take#(X1,X2) -> c_11() take#(0(),IL) -> c_12() zeros#() -> c_14() zeros#() -> c_15() - Weak TRS: U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0,U11#/2,U12#/2,U21#/4,U22#/4,U23#/4 ,activate#/1,length#/1,take#/2,zeros#/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/4 ,c_4/4,c_5/3,c_6/0,c_7/1,c_8/1,c_9/2,c_10/0,c_11/0,c_12/0,c_13/2,c_14/0,c_15/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,U23#,activate#,length#,take# ,zeros#} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: RemoveWeakSuffixes + Details: Consider the dependency graph 1:S:U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) -->_2 activate#(n__zeros()) -> c_8(zeros#()):10 -->_2 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_1 U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)):2 -->_2 activate#(X) -> c_6():9 2:S:U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) -->_2 activate#(n__zeros()) -> c_8(zeros#()):10 -->_1 length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)):7 -->_2 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_1 length#(nil()) -> c_10():11 -->_2 activate#(X) -> c_6():9 3:S:U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) -->_4 activate#(n__zeros()) -> c_8(zeros#()):10 -->_3 activate#(n__zeros()) -> c_8(zeros#()):10 -->_2 activate#(n__zeros()) -> c_8(zeros#()):10 -->_4 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_3 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_2 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_1 U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)):4 -->_4 activate#(X) -> c_6():9 -->_3 activate#(X) -> c_6():9 -->_2 activate#(X) -> c_6():9 4:S:U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) -->_4 activate#(n__zeros()) -> c_8(zeros#()):10 -->_3 activate#(n__zeros()) -> c_8(zeros#()):10 -->_2 activate#(n__zeros()) -> c_8(zeros#()):10 -->_4 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_3 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_2 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_1 U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)):5 -->_4 activate#(X) -> c_6():9 -->_3 activate#(X) -> c_6():9 -->_2 activate#(X) -> c_6():9 5:S:U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) -->_3 activate#(n__zeros()) -> c_8(zeros#()):10 -->_2 activate#(n__zeros()) -> c_8(zeros#()):10 -->_1 activate#(n__zeros()) -> c_8(zeros#()):10 -->_3 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_2 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_1 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_3 activate#(X) -> c_6():9 -->_2 activate#(X) -> c_6():9 -->_1 activate#(X) -> c_6():9 6:S:activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) -->_1 take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)):8 -->_1 take#(0(),IL) -> c_12():13 -->_1 take#(X1,X2) -> c_11():12 7:S:length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) -->_2 activate#(n__zeros()) -> c_8(zeros#()):10 -->_2 activate#(X) -> c_6():9 -->_2 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_1 U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)):1 8:S:take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) -->_2 activate#(n__zeros()) -> c_8(zeros#()):10 -->_2 activate#(X) -> c_6():9 -->_2 activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)):6 -->_1 U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)):3 9:W:activate#(X) -> c_6() 10:W:activate#(n__zeros()) -> c_8(zeros#()) -->_1 zeros#() -> c_15():15 -->_1 zeros#() -> c_14():14 11:W:length#(nil()) -> c_10() 12:W:take#(X1,X2) -> c_11() 13:W:take#(0(),IL) -> c_12() 14:W:zeros#() -> c_14() 15:W:zeros#() -> c_15() The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 11: length#(nil()) -> c_10() 12: take#(X1,X2) -> c_11() 13: take#(0(),IL) -> c_12() 9: activate#(X) -> c_6() 10: activate#(n__zeros()) -> c_8(zeros#()) 14: zeros#() -> c_14() 15: zeros#() -> c_15() * Step 6: Failure MAYBE + Considered Problem: - Strict DPs: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)) U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)) U21#(tt(),IL,M,N) -> c_3(U22#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U22#(tt(),IL,M,N) -> c_4(U23#(tt(),activate(IL),activate(M),activate(N)) ,activate#(IL) ,activate#(M) ,activate#(N)) U23#(tt(),IL,M,N) -> c_5(activate#(N),activate#(M),activate#(IL)) activate#(n__take(X1,X2)) -> c_7(take#(X1,X2)) length#(cons(N,L)) -> c_9(U11#(tt(),activate(L)),activate#(L)) take#(s(M),cons(N,IL)) -> c_13(U21#(tt(),activate(IL),M,N),activate#(IL)) - Weak TRS: U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0,U11#/2,U12#/2,U21#/4,U22#/4,U23#/4 ,activate#/1,length#/1,take#/2,zeros#/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/4 ,c_4/4,c_5/3,c_6/0,c_7/1,c_8/1,c_9/2,c_10/0,c_11/0,c_12/0,c_13/2,c_14/0,c_15/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,U23#,activate#,length#,take# ,zeros#} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE