MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a__zeros() -> cons(0(), zeros()) , a__zeros() -> zeros() , a__U11(X1, X2) -> U11(X1, X2) , a__U11(tt(), L) -> a__U12(tt(), L) , a__U12(X1, X2) -> U12(X1, X2) , a__U12(tt(), L) -> s(a__length(mark(L))) , a__length(X) -> length(X) , a__length(cons(N, L)) -> a__U11(tt(), L) , a__length(nil()) -> 0() , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(0()) -> 0() , mark(zeros()) -> a__zeros() , mark(tt()) -> tt() , mark(s(X)) -> s(mark(X)) , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) , mark(nil()) -> nil() , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) , mark(U12(X1, X2)) -> a__U12(mark(X1), X2) , mark(length(X)) -> a__length(mark(X)) , mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) , mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) , mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) , a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) , a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N) , a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) , a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N) , a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) , a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL)) , a__take(X1, X2) -> take(X1, X2) , a__take(0(), IL) -> nil() , a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N) } Obligation: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { a__zeros^#() -> c_1() , a__zeros^#() -> c_2() , a__U11^#(X1, X2) -> c_3() , a__U11^#(tt(), L) -> c_4(a__U12^#(tt(), L)) , a__U12^#(X1, X2) -> c_5() , a__U12^#(tt(), L) -> c_6(a__length^#(mark(L)), mark^#(L)) , a__length^#(X) -> c_7() , a__length^#(cons(N, L)) -> c_8(a__U11^#(tt(), L)) , a__length^#(nil()) -> c_9() , mark^#(cons(X1, X2)) -> c_10(mark^#(X1)) , mark^#(0()) -> c_11() , mark^#(zeros()) -> c_12(a__zeros^#()) , mark^#(tt()) -> c_13() , mark^#(s(X)) -> c_14(mark^#(X)) , mark^#(take(X1, X2)) -> c_15(a__take^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , mark^#(nil()) -> c_16() , mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2), mark^#(X1)) , mark^#(U12(X1, X2)) -> c_18(a__U12^#(mark(X1), X2), mark^#(X1)) , mark^#(length(X)) -> c_19(a__length^#(mark(X)), mark^#(X)) , mark^#(U21(X1, X2, X3, X4)) -> c_20(a__U21^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U22(X1, X2, X3, X4)) -> c_21(a__U22^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U23(X1, X2, X3, X4)) -> c_22(a__U23^#(mark(X1), X2, X3, X4), mark^#(X1)) , a__take^#(X1, X2) -> c_29() , a__take^#(0(), IL) -> c_30() , a__take^#(s(M), cons(N, IL)) -> c_31(a__U21^#(tt(), IL, M, N)) , a__U21^#(X1, X2, X3, X4) -> c_23() , a__U21^#(tt(), IL, M, N) -> c_24(a__U22^#(tt(), IL, M, N)) , a__U22^#(X1, X2, X3, X4) -> c_25() , a__U22^#(tt(), IL, M, N) -> c_26(a__U23^#(tt(), IL, M, N)) , a__U23^#(X1, X2, X3, X4) -> c_27() , a__U23^#(tt(), IL, M, N) -> c_28(mark^#(N)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__zeros^#() -> c_1() , a__zeros^#() -> c_2() , a__U11^#(X1, X2) -> c_3() , a__U11^#(tt(), L) -> c_4(a__U12^#(tt(), L)) , a__U12^#(X1, X2) -> c_5() , a__U12^#(tt(), L) -> c_6(a__length^#(mark(L)), mark^#(L)) , a__length^#(X) -> c_7() , a__length^#(cons(N, L)) -> c_8(a__U11^#(tt(), L)) , a__length^#(nil()) -> c_9() , mark^#(cons(X1, X2)) -> c_10(mark^#(X1)) , mark^#(0()) -> c_11() , mark^#(zeros()) -> c_12(a__zeros^#()) , mark^#(tt()) -> c_13() , mark^#(s(X)) -> c_14(mark^#(X)) , mark^#(take(X1, X2)) -> c_15(a__take^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , mark^#(nil()) -> c_16() , mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2), mark^#(X1)) , mark^#(U12(X1, X2)) -> c_18(a__U12^#(mark(X1), X2), mark^#(X1)) , mark^#(length(X)) -> c_19(a__length^#(mark(X)), mark^#(X)) , mark^#(U21(X1, X2, X3, X4)) -> c_20(a__U21^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U22(X1, X2, X3, X4)) -> c_21(a__U22^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U23(X1, X2, X3, X4)) -> c_22(a__U23^#(mark(X1), X2, X3, X4), mark^#(X1)) , a__take^#(X1, X2) -> c_29() , a__take^#(0(), IL) -> c_30() , a__take^#(s(M), cons(N, IL)) -> c_31(a__U21^#(tt(), IL, M, N)) , a__U21^#(X1, X2, X3, X4) -> c_23() , a__U21^#(tt(), IL, M, N) -> c_24(a__U22^#(tt(), IL, M, N)) , a__U22^#(X1, X2, X3, X4) -> c_25() , a__U22^#(tt(), IL, M, N) -> c_26(a__U23^#(tt(), IL, M, N)) , a__U23^#(X1, X2, X3, X4) -> c_27() , a__U23^#(tt(), IL, M, N) -> c_28(mark^#(N)) } Weak Trs: { a__zeros() -> cons(0(), zeros()) , a__zeros() -> zeros() , a__U11(X1, X2) -> U11(X1, X2) , a__U11(tt(), L) -> a__U12(tt(), L) , a__U12(X1, X2) -> U12(X1, X2) , a__U12(tt(), L) -> s(a__length(mark(L))) , a__length(X) -> length(X) , a__length(cons(N, L)) -> a__U11(tt(), L) , a__length(nil()) -> 0() , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(0()) -> 0() , mark(zeros()) -> a__zeros() , mark(tt()) -> tt() , mark(s(X)) -> s(mark(X)) , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) , mark(nil()) -> nil() , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) , mark(U12(X1, X2)) -> a__U12(mark(X1), X2) , mark(length(X)) -> a__length(mark(X)) , mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) , mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) , mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) , a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) , a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N) , a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) , a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N) , a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) , a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL)) , a__take(X1, X2) -> take(X1, X2) , a__take(0(), IL) -> nil() , a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1,2,3,5,7,9,11,13,16,23,24,26,28,30} by applications of Pre({1,2,3,5,7,9,11,13,16,23,24,26,28,30}) = {4,6,8,10,12,14,15,17,18,19,20,21,22,25,27,29,31}. Here rules are labeled as follows: DPs: { 1: a__zeros^#() -> c_1() , 2: a__zeros^#() -> c_2() , 3: a__U11^#(X1, X2) -> c_3() , 4: a__U11^#(tt(), L) -> c_4(a__U12^#(tt(), L)) , 5: a__U12^#(X1, X2) -> c_5() , 6: a__U12^#(tt(), L) -> c_6(a__length^#(mark(L)), mark^#(L)) , 7: a__length^#(X) -> c_7() , 8: a__length^#(cons(N, L)) -> c_8(a__U11^#(tt(), L)) , 9: a__length^#(nil()) -> c_9() , 10: mark^#(cons(X1, X2)) -> c_10(mark^#(X1)) , 11: mark^#(0()) -> c_11() , 12: mark^#(zeros()) -> c_12(a__zeros^#()) , 13: mark^#(tt()) -> c_13() , 14: mark^#(s(X)) -> c_14(mark^#(X)) , 15: mark^#(take(X1, X2)) -> c_15(a__take^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , 16: mark^#(nil()) -> c_16() , 17: mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2), mark^#(X1)) , 18: mark^#(U12(X1, X2)) -> c_18(a__U12^#(mark(X1), X2), mark^#(X1)) , 19: mark^#(length(X)) -> c_19(a__length^#(mark(X)), mark^#(X)) , 20: mark^#(U21(X1, X2, X3, X4)) -> c_20(a__U21^#(mark(X1), X2, X3, X4), mark^#(X1)) , 21: mark^#(U22(X1, X2, X3, X4)) -> c_21(a__U22^#(mark(X1), X2, X3, X4), mark^#(X1)) , 22: mark^#(U23(X1, X2, X3, X4)) -> c_22(a__U23^#(mark(X1), X2, X3, X4), mark^#(X1)) , 23: a__take^#(X1, X2) -> c_29() , 24: a__take^#(0(), IL) -> c_30() , 25: a__take^#(s(M), cons(N, IL)) -> c_31(a__U21^#(tt(), IL, M, N)) , 26: a__U21^#(X1, X2, X3, X4) -> c_23() , 27: a__U21^#(tt(), IL, M, N) -> c_24(a__U22^#(tt(), IL, M, N)) , 28: a__U22^#(X1, X2, X3, X4) -> c_25() , 29: a__U22^#(tt(), IL, M, N) -> c_26(a__U23^#(tt(), IL, M, N)) , 30: a__U23^#(X1, X2, X3, X4) -> c_27() , 31: a__U23^#(tt(), IL, M, N) -> c_28(mark^#(N)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__U11^#(tt(), L) -> c_4(a__U12^#(tt(), L)) , a__U12^#(tt(), L) -> c_6(a__length^#(mark(L)), mark^#(L)) , a__length^#(cons(N, L)) -> c_8(a__U11^#(tt(), L)) , mark^#(cons(X1, X2)) -> c_10(mark^#(X1)) , mark^#(zeros()) -> c_12(a__zeros^#()) , mark^#(s(X)) -> c_14(mark^#(X)) , mark^#(take(X1, X2)) -> c_15(a__take^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2), mark^#(X1)) , mark^#(U12(X1, X2)) -> c_18(a__U12^#(mark(X1), X2), mark^#(X1)) , mark^#(length(X)) -> c_19(a__length^#(mark(X)), mark^#(X)) , mark^#(U21(X1, X2, X3, X4)) -> c_20(a__U21^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U22(X1, X2, X3, X4)) -> c_21(a__U22^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U23(X1, X2, X3, X4)) -> c_22(a__U23^#(mark(X1), X2, X3, X4), mark^#(X1)) , a__take^#(s(M), cons(N, IL)) -> c_31(a__U21^#(tt(), IL, M, N)) , a__U21^#(tt(), IL, M, N) -> c_24(a__U22^#(tt(), IL, M, N)) , a__U22^#(tt(), IL, M, N) -> c_26(a__U23^#(tt(), IL, M, N)) , a__U23^#(tt(), IL, M, N) -> c_28(mark^#(N)) } Weak DPs: { a__zeros^#() -> c_1() , a__zeros^#() -> c_2() , a__U11^#(X1, X2) -> c_3() , a__U12^#(X1, X2) -> c_5() , a__length^#(X) -> c_7() , a__length^#(nil()) -> c_9() , mark^#(0()) -> c_11() , mark^#(tt()) -> c_13() , mark^#(nil()) -> c_16() , a__take^#(X1, X2) -> c_29() , a__take^#(0(), IL) -> c_30() , a__U21^#(X1, X2, X3, X4) -> c_23() , a__U22^#(X1, X2, X3, X4) -> c_25() , a__U23^#(X1, X2, X3, X4) -> c_27() } Weak Trs: { a__zeros() -> cons(0(), zeros()) , a__zeros() -> zeros() , a__U11(X1, X2) -> U11(X1, X2) , a__U11(tt(), L) -> a__U12(tt(), L) , a__U12(X1, X2) -> U12(X1, X2) , a__U12(tt(), L) -> s(a__length(mark(L))) , a__length(X) -> length(X) , a__length(cons(N, L)) -> a__U11(tt(), L) , a__length(nil()) -> 0() , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(0()) -> 0() , mark(zeros()) -> a__zeros() , mark(tt()) -> tt() , mark(s(X)) -> s(mark(X)) , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) , mark(nil()) -> nil() , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) , mark(U12(X1, X2)) -> a__U12(mark(X1), X2) , mark(length(X)) -> a__length(mark(X)) , mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) , mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) , mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) , a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) , a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N) , a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) , a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N) , a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) , a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL)) , a__take(X1, X2) -> take(X1, X2) , a__take(0(), IL) -> nil() , a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N) } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {5} by applications of Pre({5}) = {2,4,6,7,8,9,10,11,12,13,17}. Here rules are labeled as follows: DPs: { 1: a__U11^#(tt(), L) -> c_4(a__U12^#(tt(), L)) , 2: a__U12^#(tt(), L) -> c_6(a__length^#(mark(L)), mark^#(L)) , 3: a__length^#(cons(N, L)) -> c_8(a__U11^#(tt(), L)) , 4: mark^#(cons(X1, X2)) -> c_10(mark^#(X1)) , 5: mark^#(zeros()) -> c_12(a__zeros^#()) , 6: mark^#(s(X)) -> c_14(mark^#(X)) , 7: mark^#(take(X1, X2)) -> c_15(a__take^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , 8: mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2), mark^#(X1)) , 9: mark^#(U12(X1, X2)) -> c_18(a__U12^#(mark(X1), X2), mark^#(X1)) , 10: mark^#(length(X)) -> c_19(a__length^#(mark(X)), mark^#(X)) , 11: mark^#(U21(X1, X2, X3, X4)) -> c_20(a__U21^#(mark(X1), X2, X3, X4), mark^#(X1)) , 12: mark^#(U22(X1, X2, X3, X4)) -> c_21(a__U22^#(mark(X1), X2, X3, X4), mark^#(X1)) , 13: mark^#(U23(X1, X2, X3, X4)) -> c_22(a__U23^#(mark(X1), X2, X3, X4), mark^#(X1)) , 14: a__take^#(s(M), cons(N, IL)) -> c_31(a__U21^#(tt(), IL, M, N)) , 15: a__U21^#(tt(), IL, M, N) -> c_24(a__U22^#(tt(), IL, M, N)) , 16: a__U22^#(tt(), IL, M, N) -> c_26(a__U23^#(tt(), IL, M, N)) , 17: a__U23^#(tt(), IL, M, N) -> c_28(mark^#(N)) , 18: a__zeros^#() -> c_1() , 19: a__zeros^#() -> c_2() , 20: a__U11^#(X1, X2) -> c_3() , 21: a__U12^#(X1, X2) -> c_5() , 22: a__length^#(X) -> c_7() , 23: a__length^#(nil()) -> c_9() , 24: mark^#(0()) -> c_11() , 25: mark^#(tt()) -> c_13() , 26: mark^#(nil()) -> c_16() , 27: a__take^#(X1, X2) -> c_29() , 28: a__take^#(0(), IL) -> c_30() , 29: a__U21^#(X1, X2, X3, X4) -> c_23() , 30: a__U22^#(X1, X2, X3, X4) -> c_25() , 31: a__U23^#(X1, X2, X3, X4) -> c_27() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__U11^#(tt(), L) -> c_4(a__U12^#(tt(), L)) , a__U12^#(tt(), L) -> c_6(a__length^#(mark(L)), mark^#(L)) , a__length^#(cons(N, L)) -> c_8(a__U11^#(tt(), L)) , mark^#(cons(X1, X2)) -> c_10(mark^#(X1)) , mark^#(s(X)) -> c_14(mark^#(X)) , mark^#(take(X1, X2)) -> c_15(a__take^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2), mark^#(X1)) , mark^#(U12(X1, X2)) -> c_18(a__U12^#(mark(X1), X2), mark^#(X1)) , mark^#(length(X)) -> c_19(a__length^#(mark(X)), mark^#(X)) , mark^#(U21(X1, X2, X3, X4)) -> c_20(a__U21^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U22(X1, X2, X3, X4)) -> c_21(a__U22^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U23(X1, X2, X3, X4)) -> c_22(a__U23^#(mark(X1), X2, X3, X4), mark^#(X1)) , a__take^#(s(M), cons(N, IL)) -> c_31(a__U21^#(tt(), IL, M, N)) , a__U21^#(tt(), IL, M, N) -> c_24(a__U22^#(tt(), IL, M, N)) , a__U22^#(tt(), IL, M, N) -> c_26(a__U23^#(tt(), IL, M, N)) , a__U23^#(tt(), IL, M, N) -> c_28(mark^#(N)) } Weak DPs: { a__zeros^#() -> c_1() , a__zeros^#() -> c_2() , a__U11^#(X1, X2) -> c_3() , a__U12^#(X1, X2) -> c_5() , a__length^#(X) -> c_7() , a__length^#(nil()) -> c_9() , mark^#(0()) -> c_11() , mark^#(zeros()) -> c_12(a__zeros^#()) , mark^#(tt()) -> c_13() , mark^#(nil()) -> c_16() , a__take^#(X1, X2) -> c_29() , a__take^#(0(), IL) -> c_30() , a__U21^#(X1, X2, X3, X4) -> c_23() , a__U22^#(X1, X2, X3, X4) -> c_25() , a__U23^#(X1, X2, X3, X4) -> c_27() } Weak Trs: { a__zeros() -> cons(0(), zeros()) , a__zeros() -> zeros() , a__U11(X1, X2) -> U11(X1, X2) , a__U11(tt(), L) -> a__U12(tt(), L) , a__U12(X1, X2) -> U12(X1, X2) , a__U12(tt(), L) -> s(a__length(mark(L))) , a__length(X) -> length(X) , a__length(cons(N, L)) -> a__U11(tt(), L) , a__length(nil()) -> 0() , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(0()) -> 0() , mark(zeros()) -> a__zeros() , mark(tt()) -> tt() , mark(s(X)) -> s(mark(X)) , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) , mark(nil()) -> nil() , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) , mark(U12(X1, X2)) -> a__U12(mark(X1), X2) , mark(length(X)) -> a__length(mark(X)) , mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) , mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) , mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) , a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) , a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N) , a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) , a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N) , a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) , a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL)) , a__take(X1, X2) -> take(X1, X2) , a__take(0(), IL) -> nil() , a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N) } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { a__zeros^#() -> c_1() , a__zeros^#() -> c_2() , a__U11^#(X1, X2) -> c_3() , a__U12^#(X1, X2) -> c_5() , a__length^#(X) -> c_7() , a__length^#(nil()) -> c_9() , mark^#(0()) -> c_11() , mark^#(zeros()) -> c_12(a__zeros^#()) , mark^#(tt()) -> c_13() , mark^#(nil()) -> c_16() , a__take^#(X1, X2) -> c_29() , a__take^#(0(), IL) -> c_30() , a__U21^#(X1, X2, X3, X4) -> c_23() , a__U22^#(X1, X2, X3, X4) -> c_25() , a__U23^#(X1, X2, X3, X4) -> c_27() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__U11^#(tt(), L) -> c_4(a__U12^#(tt(), L)) , a__U12^#(tt(), L) -> c_6(a__length^#(mark(L)), mark^#(L)) , a__length^#(cons(N, L)) -> c_8(a__U11^#(tt(), L)) , mark^#(cons(X1, X2)) -> c_10(mark^#(X1)) , mark^#(s(X)) -> c_14(mark^#(X)) , mark^#(take(X1, X2)) -> c_15(a__take^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2)) , mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2), mark^#(X1)) , mark^#(U12(X1, X2)) -> c_18(a__U12^#(mark(X1), X2), mark^#(X1)) , mark^#(length(X)) -> c_19(a__length^#(mark(X)), mark^#(X)) , mark^#(U21(X1, X2, X3, X4)) -> c_20(a__U21^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U22(X1, X2, X3, X4)) -> c_21(a__U22^#(mark(X1), X2, X3, X4), mark^#(X1)) , mark^#(U23(X1, X2, X3, X4)) -> c_22(a__U23^#(mark(X1), X2, X3, X4), mark^#(X1)) , a__take^#(s(M), cons(N, IL)) -> c_31(a__U21^#(tt(), IL, M, N)) , a__U21^#(tt(), IL, M, N) -> c_24(a__U22^#(tt(), IL, M, N)) , a__U22^#(tt(), IL, M, N) -> c_26(a__U23^#(tt(), IL, M, N)) , a__U23^#(tt(), IL, M, N) -> c_28(mark^#(N)) } Weak Trs: { a__zeros() -> cons(0(), zeros()) , a__zeros() -> zeros() , a__U11(X1, X2) -> U11(X1, X2) , a__U11(tt(), L) -> a__U12(tt(), L) , a__U12(X1, X2) -> U12(X1, X2) , a__U12(tt(), L) -> s(a__length(mark(L))) , a__length(X) -> length(X) , a__length(cons(N, L)) -> a__U11(tt(), L) , a__length(nil()) -> 0() , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(0()) -> 0() , mark(zeros()) -> a__zeros() , mark(tt()) -> tt() , mark(s(X)) -> s(mark(X)) , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) , mark(nil()) -> nil() , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) , mark(U12(X1, X2)) -> a__U12(mark(X1), X2) , mark(length(X)) -> a__length(mark(X)) , mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) , mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) , mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) , a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) , a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N) , a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) , a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N) , a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) , a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL)) , a__take(X1, X2) -> take(X1, X2) , a__take(0(), IL) -> nil() , a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..