MAYBE * Step 1: InnermostRuleRemoval MAYBE + Considered Problem: - Strict TRS: activate(X) -> X activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__incr(X)) -> incr(X) activate(n__repItems(X)) -> repItems(X) activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zip(X1,X2)) -> zip(X1,X2) cons(X1,X2) -> n__cons(X1,X2) incr(X) -> n__incr(X) incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS))) oddNs() -> incr(pairNs()) pairNs() -> cons(0(),n__incr(oddNs())) repItems(X) -> n__repItems(X) repItems(cons(X,XS)) -> cons(X,n__cons(X,n__repItems(activate(XS)))) repItems(nil()) -> nil() tail(cons(X,XS)) -> activate(XS) take(X1,X2) -> n__take(X1,X2) take(0(),XS) -> nil() take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS))) zip(X,nil()) -> nil() zip(X1,X2) -> n__zip(X1,X2) zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),n__zip(activate(XS),activate(YS))) zip(nil(),XS) -> nil() - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2} / {0/0,n__cons/2,n__incr/1 ,n__repItems/1,n__take/2,n__zip/2,nil/0,pair/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,cons,incr,oddNs,pairNs,repItems,tail,take ,zip} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: InnermostRuleRemoval + Details: Arguments of following rules are not normal-forms. incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS))) repItems(cons(X,XS)) -> cons(X,n__cons(X,n__repItems(activate(XS)))) tail(cons(X,XS)) -> activate(XS) take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS))) zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),n__zip(activate(XS),activate(YS))) All above mentioned rules can be savely removed. * Step 2: DependencyPairs MAYBE + Considered Problem: - Strict TRS: activate(X) -> X activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__incr(X)) -> incr(X) activate(n__repItems(X)) -> repItems(X) activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zip(X1,X2)) -> zip(X1,X2) cons(X1,X2) -> n__cons(X1,X2) incr(X) -> n__incr(X) oddNs() -> incr(pairNs()) pairNs() -> cons(0(),n__incr(oddNs())) repItems(X) -> n__repItems(X) repItems(nil()) -> nil() take(X1,X2) -> n__take(X1,X2) take(0(),XS) -> nil() zip(X,nil()) -> nil() zip(X1,X2) -> n__zip(X1,X2) zip(nil(),XS) -> nil() - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2} / {0/0,n__cons/2,n__incr/1 ,n__repItems/1,n__take/2,n__zip/2,nil/0,pair/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,cons,incr,oddNs,pairNs,repItems,tail,take ,zip} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs activate#(X) -> c_1() activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) activate#(n__incr(X)) -> c_3(incr#(X)) activate#(n__repItems(X)) -> c_4(repItems#(X)) activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) cons#(X1,X2) -> c_7() incr#(X) -> c_8() oddNs#() -> c_9(incr#(pairNs()),pairNs#()) pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) repItems#(X) -> c_11() repItems#(nil()) -> c_12() take#(X1,X2) -> c_13() take#(0(),XS) -> c_14() zip#(X,nil()) -> c_15() zip#(X1,X2) -> c_16() zip#(nil(),XS) -> c_17() Weak DPs and mark the set of starting terms. * Step 3: UsableRules MAYBE + Considered Problem: - Strict DPs: activate#(X) -> c_1() activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) activate#(n__incr(X)) -> c_3(incr#(X)) activate#(n__repItems(X)) -> c_4(repItems#(X)) activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) cons#(X1,X2) -> c_7() incr#(X) -> c_8() oddNs#() -> c_9(incr#(pairNs()),pairNs#()) pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) repItems#(X) -> c_11() repItems#(nil()) -> c_12() take#(X1,X2) -> c_13() take#(0(),XS) -> c_14() zip#(X,nil()) -> c_15() zip#(X1,X2) -> c_16() zip#(nil(),XS) -> c_17() - Weak TRS: activate(X) -> X activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__incr(X)) -> incr(X) activate(n__repItems(X)) -> repItems(X) activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zip(X1,X2)) -> zip(X1,X2) cons(X1,X2) -> n__cons(X1,X2) incr(X) -> n__incr(X) oddNs() -> incr(pairNs()) pairNs() -> cons(0(),n__incr(oddNs())) repItems(X) -> n__repItems(X) repItems(nil()) -> nil() take(X1,X2) -> n__take(X1,X2) take(0(),XS) -> nil() zip(X,nil()) -> nil() zip(X1,X2) -> n__zip(X1,X2) zip(nil(),XS) -> nil() - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1 ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2 ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0 ,c_14/0,c_15/0,c_16/0,c_17/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail# ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: cons(X1,X2) -> n__cons(X1,X2) incr(X) -> n__incr(X) oddNs() -> incr(pairNs()) pairNs() -> cons(0(),n__incr(oddNs())) activate#(X) -> c_1() activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) activate#(n__incr(X)) -> c_3(incr#(X)) activate#(n__repItems(X)) -> c_4(repItems#(X)) activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) cons#(X1,X2) -> c_7() incr#(X) -> c_8() oddNs#() -> c_9(incr#(pairNs()),pairNs#()) pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) repItems#(X) -> c_11() repItems#(nil()) -> c_12() take#(X1,X2) -> c_13() take#(0(),XS) -> c_14() zip#(X,nil()) -> c_15() zip#(X1,X2) -> c_16() zip#(nil(),XS) -> c_17() * Step 4: PredecessorEstimation MAYBE + Considered Problem: - Strict DPs: activate#(X) -> c_1() activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) activate#(n__incr(X)) -> c_3(incr#(X)) activate#(n__repItems(X)) -> c_4(repItems#(X)) activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) cons#(X1,X2) -> c_7() incr#(X) -> c_8() oddNs#() -> c_9(incr#(pairNs()),pairNs#()) pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) repItems#(X) -> c_11() repItems#(nil()) -> c_12() take#(X1,X2) -> c_13() take#(0(),XS) -> c_14() zip#(X,nil()) -> c_15() zip#(X1,X2) -> c_16() zip#(nil(),XS) -> c_17() - Weak TRS: cons(X1,X2) -> n__cons(X1,X2) incr(X) -> n__incr(X) oddNs() -> incr(pairNs()) pairNs() -> cons(0(),n__incr(oddNs())) - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1 ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2 ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0 ,c_14/0,c_15/0,c_16/0,c_17/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail# ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {1,7,8,11,12,13,14,15,16,17} by application of Pre({1,7,8,11,12,13,14,15,16,17}) = {2,3,4,5,6,9,10}. Here rules are labelled as follows: 1: activate#(X) -> c_1() 2: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) 3: activate#(n__incr(X)) -> c_3(incr#(X)) 4: activate#(n__repItems(X)) -> c_4(repItems#(X)) 5: activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) 6: activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) 7: cons#(X1,X2) -> c_7() 8: incr#(X) -> c_8() 9: oddNs#() -> c_9(incr#(pairNs()),pairNs#()) 10: pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) 11: repItems#(X) -> c_11() 12: repItems#(nil()) -> c_12() 13: take#(X1,X2) -> c_13() 14: take#(0(),XS) -> c_14() 15: zip#(X,nil()) -> c_15() 16: zip#(X1,X2) -> c_16() 17: zip#(nil(),XS) -> c_17() * Step 5: PredecessorEstimation MAYBE + Considered Problem: - Strict DPs: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) activate#(n__incr(X)) -> c_3(incr#(X)) activate#(n__repItems(X)) -> c_4(repItems#(X)) activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) oddNs#() -> c_9(incr#(pairNs()),pairNs#()) pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) - Weak DPs: activate#(X) -> c_1() cons#(X1,X2) -> c_7() incr#(X) -> c_8() repItems#(X) -> c_11() repItems#(nil()) -> c_12() take#(X1,X2) -> c_13() take#(0(),XS) -> c_14() zip#(X,nil()) -> c_15() zip#(X1,X2) -> c_16() zip#(nil(),XS) -> c_17() - Weak TRS: cons(X1,X2) -> n__cons(X1,X2) incr(X) -> n__incr(X) oddNs() -> incr(pairNs()) pairNs() -> cons(0(),n__incr(oddNs())) - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1 ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2 ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0 ,c_14/0,c_15/0,c_16/0,c_17/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail# ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {1,2,3,4,5} by application of Pre({1,2,3,4,5}) = {}. Here rules are labelled as follows: 1: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) 2: activate#(n__incr(X)) -> c_3(incr#(X)) 3: activate#(n__repItems(X)) -> c_4(repItems#(X)) 4: activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) 5: activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) 6: oddNs#() -> c_9(incr#(pairNs()),pairNs#()) 7: pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) 8: activate#(X) -> c_1() 9: cons#(X1,X2) -> c_7() 10: incr#(X) -> c_8() 11: repItems#(X) -> c_11() 12: repItems#(nil()) -> c_12() 13: take#(X1,X2) -> c_13() 14: take#(0(),XS) -> c_14() 15: zip#(X,nil()) -> c_15() 16: zip#(X1,X2) -> c_16() 17: zip#(nil(),XS) -> c_17() * Step 6: RemoveWeakSuffixes MAYBE + Considered Problem: - Strict DPs: oddNs#() -> c_9(incr#(pairNs()),pairNs#()) pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) - Weak DPs: activate#(X) -> c_1() activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) activate#(n__incr(X)) -> c_3(incr#(X)) activate#(n__repItems(X)) -> c_4(repItems#(X)) activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) cons#(X1,X2) -> c_7() incr#(X) -> c_8() repItems#(X) -> c_11() repItems#(nil()) -> c_12() take#(X1,X2) -> c_13() take#(0(),XS) -> c_14() zip#(X,nil()) -> c_15() zip#(X1,X2) -> c_16() zip#(nil(),XS) -> c_17() - Weak TRS: cons(X1,X2) -> n__cons(X1,X2) incr(X) -> n__incr(X) oddNs() -> incr(pairNs()) pairNs() -> cons(0(),n__incr(oddNs())) - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1 ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2 ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0 ,c_14/0,c_15/0,c_16/0,c_17/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail# ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: RemoveWeakSuffixes + Details: Consider the dependency graph 1:S:oddNs#() -> c_9(incr#(pairNs()),pairNs#()) -->_2 pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()):2 -->_1 incr#(X) -> c_8():10 2:S:pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) -->_1 cons#(X1,X2) -> c_7():9 -->_2 oddNs#() -> c_9(incr#(pairNs()),pairNs#()):1 3:W:activate#(X) -> c_1() 4:W:activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) -->_1 cons#(X1,X2) -> c_7():9 5:W:activate#(n__incr(X)) -> c_3(incr#(X)) -->_1 incr#(X) -> c_8():10 6:W:activate#(n__repItems(X)) -> c_4(repItems#(X)) -->_1 repItems#(nil()) -> c_12():12 -->_1 repItems#(X) -> c_11():11 7:W:activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) -->_1 take#(0(),XS) -> c_14():14 -->_1 take#(X1,X2) -> c_13():13 8:W:activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) -->_1 zip#(nil(),XS) -> c_17():17 -->_1 zip#(X1,X2) -> c_16():16 -->_1 zip#(X,nil()) -> c_15():15 9:W:cons#(X1,X2) -> c_7() 10:W:incr#(X) -> c_8() 11:W:repItems#(X) -> c_11() 12:W:repItems#(nil()) -> c_12() 13:W:take#(X1,X2) -> c_13() 14:W:take#(0(),XS) -> c_14() 15:W:zip#(X,nil()) -> c_15() 16:W:zip#(X1,X2) -> c_16() 17:W:zip#(nil(),XS) -> c_17() The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 8: activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2)) 15: zip#(X,nil()) -> c_15() 16: zip#(X1,X2) -> c_16() 17: zip#(nil(),XS) -> c_17() 7: activate#(n__take(X1,X2)) -> c_5(take#(X1,X2)) 13: take#(X1,X2) -> c_13() 14: take#(0(),XS) -> c_14() 6: activate#(n__repItems(X)) -> c_4(repItems#(X)) 11: repItems#(X) -> c_11() 12: repItems#(nil()) -> c_12() 5: activate#(n__incr(X)) -> c_3(incr#(X)) 4: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)) 3: activate#(X) -> c_1() 10: incr#(X) -> c_8() 9: cons#(X1,X2) -> c_7() * Step 7: SimplifyRHS MAYBE + Considered Problem: - Strict DPs: oddNs#() -> c_9(incr#(pairNs()),pairNs#()) pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) - Weak TRS: cons(X1,X2) -> n__cons(X1,X2) incr(X) -> n__incr(X) oddNs() -> incr(pairNs()) pairNs() -> cons(0(),n__incr(oddNs())) - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1 ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2 ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0 ,c_14/0,c_15/0,c_16/0,c_17/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail# ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: SimplifyRHS + Details: Consider the dependency graph 1:S:oddNs#() -> c_9(incr#(pairNs()),pairNs#()) -->_2 pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()):2 2:S:pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()) -->_2 oddNs#() -> c_9(incr#(pairNs()),pairNs#()):1 Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified: oddNs#() -> c_9(pairNs#()) pairNs#() -> c_10(oddNs#()) * Step 8: UsableRules MAYBE + Considered Problem: - Strict DPs: oddNs#() -> c_9(pairNs#()) pairNs#() -> c_10(oddNs#()) - Weak TRS: cons(X1,X2) -> n__cons(X1,X2) incr(X) -> n__incr(X) oddNs() -> incr(pairNs()) pairNs() -> cons(0(),n__incr(oddNs())) - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1 ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2 ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/1,c_10/1,c_11/0,c_12/0,c_13/0 ,c_14/0,c_15/0,c_16/0,c_17/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail# ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: oddNs#() -> c_9(pairNs#()) pairNs#() -> c_10(oddNs#()) * Step 9: WeightGap MAYBE + Considered Problem: - Strict DPs: oddNs#() -> c_9(pairNs#()) pairNs#() -> c_10(oddNs#()) - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1 ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2 ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/1,c_10/1,c_11/0,c_12/0,c_13/0 ,c_14/0,c_15/0,c_16/0,c_17/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail# ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following constant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: uargs(c_9) = {1}, uargs(c_10) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [0] p(activate) = [0] p(cons) = [0] p(incr) = [0] p(n__cons) = [0] p(n__incr) = [0] p(n__repItems) = [0] p(n__take) = [0] p(n__zip) = [0] p(nil) = [0] p(oddNs) = [0] p(pair) = [0] p(pairNs) = [0] p(repItems) = [0] p(s) = [0] p(tail) = [0] p(take) = [0] p(zip) = [0] p(activate#) = [0] p(cons#) = [0] p(incr#) = [0] p(oddNs#) = [0] p(pairNs#) = [3] p(repItems#) = [0] p(tail#) = [0] p(take#) = [0] p(zip#) = [0] p(c_1) = [0] p(c_2) = [0] p(c_3) = [0] p(c_4) = [0] p(c_5) = [0] p(c_6) = [0] p(c_7) = [0] p(c_8) = [0] p(c_9) = [1] x1 + [0] p(c_10) = [1] x1 + [0] p(c_11) = [0] p(c_12) = [0] p(c_13) = [0] p(c_14) = [0] p(c_15) = [0] p(c_16) = [0] p(c_17) = [0] Following rules are strictly oriented: pairNs#() = [3] > [0] = c_10(oddNs#()) Following rules are (at-least) weakly oriented: oddNs#() = [0] >= [3] = c_9(pairNs#()) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 10: Failure MAYBE + Considered Problem: - Strict DPs: oddNs#() -> c_9(pairNs#()) - Weak DPs: pairNs#() -> c_10(oddNs#()) - Signature: {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1 ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2 ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/1,c_10/1,c_11/0,c_12/0,c_13/0 ,c_14/0,c_15/0,c_16/0,c_17/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail# ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE