MAYBE * Step 1: DependencyPairs MAYBE + Considered Problem: - Strict TRS: a__and(X1,X2) -> and(X1,X2) a__and(tt(),X) -> mark(X) a__length(X) -> length(X) a__length(cons(N,L)) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> nil() a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL)) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__and/2,a__length/1,a__take/2,a__zeros/0,mark/1} / {0/0,and/2,cons/2,length/1,nil/0,s/1,take/2,tt/0 ,zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__and,a__length,a__take,a__zeros ,mark} and constructors {0,and,cons,length,nil,s,take,tt,zeros} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs a__and#(X1,X2) -> c_1() a__and#(tt(),X) -> c_2(mark#(X)) a__length#(X) -> c_3() a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)) a__length#(nil()) -> c_5() a__take#(X1,X2) -> c_6() a__take#(0(),IL) -> c_7() a__take#(s(M),cons(N,IL)) -> c_8(mark#(N)) a__zeros#() -> c_9() a__zeros#() -> c_10() mark#(0()) -> c_11() mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)) mark#(cons(X1,X2)) -> c_13(mark#(X1)) mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)) mark#(nil()) -> c_15() mark#(s(X)) -> c_16(mark#(X)) mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)) mark#(tt()) -> c_18() mark#(zeros()) -> c_19(a__zeros#()) Weak DPs and mark the set of starting terms. * Step 2: PredecessorEstimation MAYBE + Considered Problem: - Strict DPs: a__and#(X1,X2) -> c_1() a__and#(tt(),X) -> c_2(mark#(X)) a__length#(X) -> c_3() a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)) a__length#(nil()) -> c_5() a__take#(X1,X2) -> c_6() a__take#(0(),IL) -> c_7() a__take#(s(M),cons(N,IL)) -> c_8(mark#(N)) a__zeros#() -> c_9() a__zeros#() -> c_10() mark#(0()) -> c_11() mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)) mark#(cons(X1,X2)) -> c_13(mark#(X1)) mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)) mark#(nil()) -> c_15() mark#(s(X)) -> c_16(mark#(X)) mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)) mark#(tt()) -> c_18() mark#(zeros()) -> c_19(a__zeros#()) - Weak TRS: a__and(X1,X2) -> and(X1,X2) a__and(tt(),X) -> mark(X) a__length(X) -> length(X) a__length(cons(N,L)) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> nil() a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL)) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__and/2,a__length/1,a__take/2,a__zeros/0,mark/1,a__and#/2,a__length#/1,a__take#/2,a__zeros#/0 ,mark#/1} / {0/0,and/2,cons/2,length/1,nil/0,s/1,take/2,tt/0,zeros/0,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/0 ,c_7/0,c_8/1,c_9/0,c_10/0,c_11/0,c_12/2,c_13/1,c_14/2,c_15/0,c_16/1,c_17/3,c_18/0,c_19/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__and#,a__length#,a__take#,a__zeros# ,mark#} and constructors {0,and,cons,length,nil,s,take,tt,zeros} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {1,3,5,6,7,9,10,11,15,18} by application of Pre({1,3,5,6,7,9,10,11,15,18}) = {2,4,8,12,13,14,16,17,19}. Here rules are labelled as follows: 1: a__and#(X1,X2) -> c_1() 2: a__and#(tt(),X) -> c_2(mark#(X)) 3: a__length#(X) -> c_3() 4: a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)) 5: a__length#(nil()) -> c_5() 6: a__take#(X1,X2) -> c_6() 7: a__take#(0(),IL) -> c_7() 8: a__take#(s(M),cons(N,IL)) -> c_8(mark#(N)) 9: a__zeros#() -> c_9() 10: a__zeros#() -> c_10() 11: mark#(0()) -> c_11() 12: mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)) 13: mark#(cons(X1,X2)) -> c_13(mark#(X1)) 14: mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)) 15: mark#(nil()) -> c_15() 16: mark#(s(X)) -> c_16(mark#(X)) 17: mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)) 18: mark#(tt()) -> c_18() 19: mark#(zeros()) -> c_19(a__zeros#()) * Step 3: PredecessorEstimation MAYBE + Considered Problem: - Strict DPs: a__and#(tt(),X) -> c_2(mark#(X)) a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)) a__take#(s(M),cons(N,IL)) -> c_8(mark#(N)) mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)) mark#(cons(X1,X2)) -> c_13(mark#(X1)) mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)) mark#(s(X)) -> c_16(mark#(X)) mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)) mark#(zeros()) -> c_19(a__zeros#()) - Weak DPs: a__and#(X1,X2) -> c_1() a__length#(X) -> c_3() a__length#(nil()) -> c_5() a__take#(X1,X2) -> c_6() a__take#(0(),IL) -> c_7() a__zeros#() -> c_9() a__zeros#() -> c_10() mark#(0()) -> c_11() mark#(nil()) -> c_15() mark#(tt()) -> c_18() - Weak TRS: a__and(X1,X2) -> and(X1,X2) a__and(tt(),X) -> mark(X) a__length(X) -> length(X) a__length(cons(N,L)) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> nil() a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL)) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__and/2,a__length/1,a__take/2,a__zeros/0,mark/1,a__and#/2,a__length#/1,a__take#/2,a__zeros#/0 ,mark#/1} / {0/0,and/2,cons/2,length/1,nil/0,s/1,take/2,tt/0,zeros/0,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/0 ,c_7/0,c_8/1,c_9/0,c_10/0,c_11/0,c_12/2,c_13/1,c_14/2,c_15/0,c_16/1,c_17/3,c_18/0,c_19/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__and#,a__length#,a__take#,a__zeros# ,mark#} and constructors {0,and,cons,length,nil,s,take,tt,zeros} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {9} by application of Pre({9}) = {1,2,3,4,5,6,7,8}. Here rules are labelled as follows: 1: a__and#(tt(),X) -> c_2(mark#(X)) 2: a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)) 3: a__take#(s(M),cons(N,IL)) -> c_8(mark#(N)) 4: mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)) 5: mark#(cons(X1,X2)) -> c_13(mark#(X1)) 6: mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)) 7: mark#(s(X)) -> c_16(mark#(X)) 8: mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)) 9: mark#(zeros()) -> c_19(a__zeros#()) 10: a__and#(X1,X2) -> c_1() 11: a__length#(X) -> c_3() 12: a__length#(nil()) -> c_5() 13: a__take#(X1,X2) -> c_6() 14: a__take#(0(),IL) -> c_7() 15: a__zeros#() -> c_9() 16: a__zeros#() -> c_10() 17: mark#(0()) -> c_11() 18: mark#(nil()) -> c_15() 19: mark#(tt()) -> c_18() * Step 4: RemoveWeakSuffixes MAYBE + Considered Problem: - Strict DPs: a__and#(tt(),X) -> c_2(mark#(X)) a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)) a__take#(s(M),cons(N,IL)) -> c_8(mark#(N)) mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)) mark#(cons(X1,X2)) -> c_13(mark#(X1)) mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)) mark#(s(X)) -> c_16(mark#(X)) mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)) - Weak DPs: a__and#(X1,X2) -> c_1() a__length#(X) -> c_3() a__length#(nil()) -> c_5() a__take#(X1,X2) -> c_6() a__take#(0(),IL) -> c_7() a__zeros#() -> c_9() a__zeros#() -> c_10() mark#(0()) -> c_11() mark#(nil()) -> c_15() mark#(tt()) -> c_18() mark#(zeros()) -> c_19(a__zeros#()) - Weak TRS: a__and(X1,X2) -> and(X1,X2) a__and(tt(),X) -> mark(X) a__length(X) -> length(X) a__length(cons(N,L)) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> nil() a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL)) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__and/2,a__length/1,a__take/2,a__zeros/0,mark/1,a__and#/2,a__length#/1,a__take#/2,a__zeros#/0 ,mark#/1} / {0/0,and/2,cons/2,length/1,nil/0,s/1,take/2,tt/0,zeros/0,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/0 ,c_7/0,c_8/1,c_9/0,c_10/0,c_11/0,c_12/2,c_13/1,c_14/2,c_15/0,c_16/1,c_17/3,c_18/0,c_19/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__and#,a__length#,a__take#,a__zeros# ,mark#} and constructors {0,and,cons,length,nil,s,take,tt,zeros} + Applied Processor: RemoveWeakSuffixes + Details: Consider the dependency graph 1:S:a__and#(tt(),X) -> c_2(mark#(X)) -->_1 mark#(zeros()) -> c_19(a__zeros#()):19 -->_1 mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):8 -->_1 mark#(s(X)) -> c_16(mark#(X)):7 -->_1 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):6 -->_1 mark#(cons(X1,X2)) -> c_13(mark#(X1)):5 -->_1 mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)):4 -->_1 mark#(tt()) -> c_18():18 -->_1 mark#(nil()) -> c_15():17 -->_1 mark#(0()) -> c_11():16 2:S:a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)) -->_2 mark#(zeros()) -> c_19(a__zeros#()):19 -->_2 mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):8 -->_2 mark#(s(X)) -> c_16(mark#(X)):7 -->_2 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):6 -->_2 mark#(cons(X1,X2)) -> c_13(mark#(X1)):5 -->_2 mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)):4 -->_2 mark#(tt()) -> c_18():18 -->_2 mark#(nil()) -> c_15():17 -->_2 mark#(0()) -> c_11():16 -->_1 a__length#(nil()) -> c_5():11 -->_1 a__length#(X) -> c_3():10 -->_1 a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)):2 3:S:a__take#(s(M),cons(N,IL)) -> c_8(mark#(N)) -->_1 mark#(zeros()) -> c_19(a__zeros#()):19 -->_1 mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):8 -->_1 mark#(s(X)) -> c_16(mark#(X)):7 -->_1 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):6 -->_1 mark#(cons(X1,X2)) -> c_13(mark#(X1)):5 -->_1 mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)):4 -->_1 mark#(tt()) -> c_18():18 -->_1 mark#(nil()) -> c_15():17 -->_1 mark#(0()) -> c_11():16 4:S:mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)) -->_2 mark#(zeros()) -> c_19(a__zeros#()):19 -->_2 mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):8 -->_2 mark#(s(X)) -> c_16(mark#(X)):7 -->_2 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):6 -->_2 mark#(cons(X1,X2)) -> c_13(mark#(X1)):5 -->_2 mark#(tt()) -> c_18():18 -->_2 mark#(nil()) -> c_15():17 -->_2 mark#(0()) -> c_11():16 -->_1 a__and#(X1,X2) -> c_1():9 -->_2 mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)):4 -->_1 a__and#(tt(),X) -> c_2(mark#(X)):1 5:S:mark#(cons(X1,X2)) -> c_13(mark#(X1)) -->_1 mark#(zeros()) -> c_19(a__zeros#()):19 -->_1 mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):8 -->_1 mark#(s(X)) -> c_16(mark#(X)):7 -->_1 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):6 -->_1 mark#(tt()) -> c_18():18 -->_1 mark#(nil()) -> c_15():17 -->_1 mark#(0()) -> c_11():16 -->_1 mark#(cons(X1,X2)) -> c_13(mark#(X1)):5 -->_1 mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)):4 6:S:mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)) -->_2 mark#(zeros()) -> c_19(a__zeros#()):19 -->_2 mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):8 -->_2 mark#(s(X)) -> c_16(mark#(X)):7 -->_2 mark#(tt()) -> c_18():18 -->_2 mark#(nil()) -> c_15():17 -->_2 mark#(0()) -> c_11():16 -->_1 a__length#(nil()) -> c_5():11 -->_1 a__length#(X) -> c_3():10 -->_2 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):6 -->_2 mark#(cons(X1,X2)) -> c_13(mark#(X1)):5 -->_2 mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)):4 -->_1 a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)):2 7:S:mark#(s(X)) -> c_16(mark#(X)) -->_1 mark#(zeros()) -> c_19(a__zeros#()):19 -->_1 mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):8 -->_1 mark#(tt()) -> c_18():18 -->_1 mark#(nil()) -> c_15():17 -->_1 mark#(0()) -> c_11():16 -->_1 mark#(s(X)) -> c_16(mark#(X)):7 -->_1 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):6 -->_1 mark#(cons(X1,X2)) -> c_13(mark#(X1)):5 -->_1 mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)):4 8:S:mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)) -->_3 mark#(zeros()) -> c_19(a__zeros#()):19 -->_2 mark#(zeros()) -> c_19(a__zeros#()):19 -->_3 mark#(tt()) -> c_18():18 -->_2 mark#(tt()) -> c_18():18 -->_3 mark#(nil()) -> c_15():17 -->_2 mark#(nil()) -> c_15():17 -->_3 mark#(0()) -> c_11():16 -->_2 mark#(0()) -> c_11():16 -->_1 a__take#(0(),IL) -> c_7():13 -->_1 a__take#(X1,X2) -> c_6():12 -->_3 mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):8 -->_2 mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):8 -->_3 mark#(s(X)) -> c_16(mark#(X)):7 -->_2 mark#(s(X)) -> c_16(mark#(X)):7 -->_3 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):6 -->_2 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):6 -->_3 mark#(cons(X1,X2)) -> c_13(mark#(X1)):5 -->_2 mark#(cons(X1,X2)) -> c_13(mark#(X1)):5 -->_3 mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)):4 -->_2 mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)):4 -->_1 a__take#(s(M),cons(N,IL)) -> c_8(mark#(N)):3 9:W:a__and#(X1,X2) -> c_1() 10:W:a__length#(X) -> c_3() 11:W:a__length#(nil()) -> c_5() 12:W:a__take#(X1,X2) -> c_6() 13:W:a__take#(0(),IL) -> c_7() 14:W:a__zeros#() -> c_9() 15:W:a__zeros#() -> c_10() 16:W:mark#(0()) -> c_11() 17:W:mark#(nil()) -> c_15() 18:W:mark#(tt()) -> c_18() 19:W:mark#(zeros()) -> c_19(a__zeros#()) -->_1 a__zeros#() -> c_10():15 -->_1 a__zeros#() -> c_9():14 The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 9: a__and#(X1,X2) -> c_1() 10: a__length#(X) -> c_3() 11: a__length#(nil()) -> c_5() 12: a__take#(X1,X2) -> c_6() 13: a__take#(0(),IL) -> c_7() 16: mark#(0()) -> c_11() 17: mark#(nil()) -> c_15() 18: mark#(tt()) -> c_18() 19: mark#(zeros()) -> c_19(a__zeros#()) 14: a__zeros#() -> c_9() 15: a__zeros#() -> c_10() * Step 5: Failure MAYBE + Considered Problem: - Strict DPs: a__and#(tt(),X) -> c_2(mark#(X)) a__length#(cons(N,L)) -> c_4(a__length#(mark(L)),mark#(L)) a__take#(s(M),cons(N,IL)) -> c_8(mark#(N)) mark#(and(X1,X2)) -> c_12(a__and#(mark(X1),X2),mark#(X1)) mark#(cons(X1,X2)) -> c_13(mark#(X1)) mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)) mark#(s(X)) -> c_16(mark#(X)) mark#(take(X1,X2)) -> c_17(a__take#(mark(X1),mark(X2)),mark#(X1),mark#(X2)) - Weak TRS: a__and(X1,X2) -> and(X1,X2) a__and(tt(),X) -> mark(X) a__length(X) -> length(X) a__length(cons(N,L)) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> nil() a__take(s(M),cons(N,IL)) -> cons(mark(N),take(M,IL)) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__and/2,a__length/1,a__take/2,a__zeros/0,mark/1,a__and#/2,a__length#/1,a__take#/2,a__zeros#/0 ,mark#/1} / {0/0,and/2,cons/2,length/1,nil/0,s/1,take/2,tt/0,zeros/0,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/0 ,c_7/0,c_8/1,c_9/0,c_10/0,c_11/0,c_12/2,c_13/1,c_14/2,c_15/0,c_16/1,c_17/3,c_18/0,c_19/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__and#,a__length#,a__take#,a__zeros# ,mark#} and constructors {0,and,cons,length,nil,s,take,tt,zeros} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE