*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        active(and(X1,X2)) -> and(active(X1),X2)
        active(and(tt(),X)) -> mark(X)
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(length(X)) -> length(active(X))
        active(length(cons(N,L))) -> mark(s(length(L)))
        active(length(nil())) -> mark(0())
        active(s(X)) -> s(active(X))
        active(take(X1,X2)) -> take(X1,active(X2))
        active(take(X1,X2)) -> take(active(X1),X2)
        active(take(0(),IL)) -> mark(nil())
        active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL)))
        active(zeros()) -> mark(cons(0(),zeros()))
        and(mark(X1),X2) -> mark(and(X1,X2))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        length(mark(X)) -> mark(length(X))
        length(ok(X)) -> ok(length(X))
        proper(0()) -> ok(0())
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(s(X)) -> s(proper(X))
        proper(take(X1,X2)) -> take(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(zeros()) -> ok(zeros())
        s(mark(X)) -> mark(s(X))
        s(ok(X)) -> ok(s(X))
        take(X1,mark(X2)) -> mark(take(X1,X2))
        take(mark(X1),X2) -> mark(take(X1,X2))
        take(ok(X1),ok(X2)) -> ok(take(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {active/1,and/2,cons/2,length/1,proper/1,s/1,take/2,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
      Obligation:
        Full
        basic terms: {active,and,cons,length,proper,s,take,top}/{0,mark,nil,ok,tt,zeros}
    Applied Processor:
      Bounds {initialAutomaton = perSymbol, enrichment = match}
    Proof:
      The problem is match-bounded by 5.
      The enriched problem is compatible with follwoing automaton.
        0_0() -> 1
        0_1() -> 16
        0_2() -> 26
        0_3() -> 37
        active_0(1) -> 2
        active_0(6) -> 2
        active_0(7) -> 2
        active_0(8) -> 2
        active_0(13) -> 2
        active_0(14) -> 2
        active_1(1) -> 23
        active_1(6) -> 23
        active_1(7) -> 23
        active_1(8) -> 23
        active_1(13) -> 23
        active_1(14) -> 23
        active_2(16) -> 24
        active_2(17) -> 24
        active_3(32) -> 31
        active_4(26) -> 36
        active_4(30) -> 36
        active_4(38) -> 39
        active_5(37) -> 40
        and_0(1,1) -> 3
        and_0(1,6) -> 3
        and_0(1,7) -> 3
        and_0(1,8) -> 3
        and_0(1,13) -> 3
        and_0(1,14) -> 3
        and_0(6,1) -> 3
        and_0(6,6) -> 3
        and_0(6,7) -> 3
        and_0(6,8) -> 3
        and_0(6,13) -> 3
        and_0(6,14) -> 3
        and_0(7,1) -> 3
        and_0(7,6) -> 3
        and_0(7,7) -> 3
        and_0(7,8) -> 3
        and_0(7,13) -> 3
        and_0(7,14) -> 3
        and_0(8,1) -> 3
        and_0(8,6) -> 3
        and_0(8,7) -> 3
        and_0(8,8) -> 3
        and_0(8,13) -> 3
        and_0(8,14) -> 3
        and_0(13,1) -> 3
        and_0(13,6) -> 3
        and_0(13,7) -> 3
        and_0(13,8) -> 3
        and_0(13,13) -> 3
        and_0(13,14) -> 3
        and_0(14,1) -> 3
        and_0(14,6) -> 3
        and_0(14,7) -> 3
        and_0(14,8) -> 3
        and_0(14,13) -> 3
        and_0(14,14) -> 3
        and_1(1,1) -> 18
        and_1(1,6) -> 18
        and_1(1,7) -> 18
        and_1(1,8) -> 18
        and_1(1,13) -> 18
        and_1(1,14) -> 18
        and_1(6,1) -> 18
        and_1(6,6) -> 18
        and_1(6,7) -> 18
        and_1(6,8) -> 18
        and_1(6,13) -> 18
        and_1(6,14) -> 18
        and_1(7,1) -> 18
        and_1(7,6) -> 18
        and_1(7,7) -> 18
        and_1(7,8) -> 18
        and_1(7,13) -> 18
        and_1(7,14) -> 18
        and_1(8,1) -> 18
        and_1(8,6) -> 18
        and_1(8,7) -> 18
        and_1(8,8) -> 18
        and_1(8,13) -> 18
        and_1(8,14) -> 18
        and_1(13,1) -> 18
        and_1(13,6) -> 18
        and_1(13,7) -> 18
        and_1(13,8) -> 18
        and_1(13,13) -> 18
        and_1(13,14) -> 18
        and_1(14,1) -> 18
        and_1(14,6) -> 18
        and_1(14,7) -> 18
        and_1(14,8) -> 18
        and_1(14,13) -> 18
        and_1(14,14) -> 18
        cons_0(1,1) -> 4
        cons_0(1,6) -> 4
        cons_0(1,7) -> 4
        cons_0(1,8) -> 4
        cons_0(1,13) -> 4
        cons_0(1,14) -> 4
        cons_0(6,1) -> 4
        cons_0(6,6) -> 4
        cons_0(6,7) -> 4
        cons_0(6,8) -> 4
        cons_0(6,13) -> 4
        cons_0(6,14) -> 4
        cons_0(7,1) -> 4
        cons_0(7,6) -> 4
        cons_0(7,7) -> 4
        cons_0(7,8) -> 4
        cons_0(7,13) -> 4
        cons_0(7,14) -> 4
        cons_0(8,1) -> 4
        cons_0(8,6) -> 4
        cons_0(8,7) -> 4
        cons_0(8,8) -> 4
        cons_0(8,13) -> 4
        cons_0(8,14) -> 4
        cons_0(13,1) -> 4
        cons_0(13,6) -> 4
        cons_0(13,7) -> 4
        cons_0(13,8) -> 4
        cons_0(13,13) -> 4
        cons_0(13,14) -> 4
        cons_0(14,1) -> 4
        cons_0(14,6) -> 4
        cons_0(14,7) -> 4
        cons_0(14,8) -> 4
        cons_0(14,13) -> 4
        cons_0(14,14) -> 4
        cons_1(1,1) -> 19
        cons_1(1,6) -> 19
        cons_1(1,7) -> 19
        cons_1(1,8) -> 19
        cons_1(1,13) -> 19
        cons_1(1,14) -> 19
        cons_1(6,1) -> 19
        cons_1(6,6) -> 19
        cons_1(6,7) -> 19
        cons_1(6,8) -> 19
        cons_1(6,13) -> 19
        cons_1(6,14) -> 19
        cons_1(7,1) -> 19
        cons_1(7,6) -> 19
        cons_1(7,7) -> 19
        cons_1(7,8) -> 19
        cons_1(7,13) -> 19
        cons_1(7,14) -> 19
        cons_1(8,1) -> 19
        cons_1(8,6) -> 19
        cons_1(8,7) -> 19
        cons_1(8,8) -> 19
        cons_1(8,13) -> 19
        cons_1(8,14) -> 19
        cons_1(13,1) -> 19
        cons_1(13,6) -> 19
        cons_1(13,7) -> 19
        cons_1(13,8) -> 19
        cons_1(13,13) -> 19
        cons_1(13,14) -> 19
        cons_1(14,1) -> 19
        cons_1(14,6) -> 19
        cons_1(14,7) -> 19
        cons_1(14,8) -> 19
        cons_1(14,13) -> 19
        cons_1(14,14) -> 19
        cons_1(16,17) -> 15
        cons_2(26,27) -> 25
        cons_2(28,29) -> 24
        cons_3(26,27) -> 32
        cons_3(30,27) -> 32
        cons_3(33,34) -> 31
        cons_4(36,27) -> 31
        cons_4(37,35) -> 38
        cons_5(40,35) -> 39
        length_0(1) -> 5
        length_0(6) -> 5
        length_0(7) -> 5
        length_0(8) -> 5
        length_0(13) -> 5
        length_0(14) -> 5
        length_1(1) -> 20
        length_1(6) -> 20
        length_1(7) -> 20
        length_1(8) -> 20
        length_1(13) -> 20
        length_1(14) -> 20
        mark_0(1) -> 6
        mark_0(6) -> 6
        mark_0(7) -> 6
        mark_0(8) -> 6
        mark_0(13) -> 6
        mark_0(14) -> 6
        mark_1(15) -> 2
        mark_1(15) -> 23
        mark_1(18) -> 3
        mark_1(18) -> 18
        mark_1(19) -> 4
        mark_1(19) -> 19
        mark_1(20) -> 5
        mark_1(20) -> 20
        mark_1(21) -> 10
        mark_1(21) -> 21
        mark_1(22) -> 11
        mark_1(22) -> 22
        mark_2(25) -> 24
        nil_0() -> 7
        nil_1() -> 16
        nil_2() -> 30
        ok_0(1) -> 8
        ok_0(6) -> 8
        ok_0(7) -> 8
        ok_0(8) -> 8
        ok_0(13) -> 8
        ok_0(14) -> 8
        ok_1(16) -> 9
        ok_1(16) -> 23
        ok_1(17) -> 9
        ok_1(17) -> 23
        ok_1(18) -> 3
        ok_1(18) -> 18
        ok_1(19) -> 4
        ok_1(19) -> 19
        ok_1(20) -> 5
        ok_1(20) -> 20
        ok_1(21) -> 10
        ok_1(21) -> 21
        ok_1(22) -> 11
        ok_1(22) -> 22
        ok_2(26) -> 28
        ok_2(27) -> 29
        ok_2(30) -> 28
        ok_3(32) -> 24
        ok_3(35) -> 34
        ok_3(37) -> 33
        ok_4(38) -> 31
        proper_0(1) -> 9
        proper_0(6) -> 9
        proper_0(7) -> 9
        proper_0(8) -> 9
        proper_0(13) -> 9
        proper_0(14) -> 9
        proper_1(1) -> 23
        proper_1(6) -> 23
        proper_1(7) -> 23
        proper_1(8) -> 23
        proper_1(13) -> 23
        proper_1(14) -> 23
        proper_2(15) -> 24
        proper_2(16) -> 28
        proper_2(17) -> 29
        proper_3(25) -> 31
        proper_3(26) -> 33
        proper_3(27) -> 34
        s_0(1) -> 10
        s_0(6) -> 10
        s_0(7) -> 10
        s_0(8) -> 10
        s_0(13) -> 10
        s_0(14) -> 10
        s_1(1) -> 21
        s_1(6) -> 21
        s_1(7) -> 21
        s_1(8) -> 21
        s_1(13) -> 21
        s_1(14) -> 21
        take_0(1,1) -> 11
        take_0(1,6) -> 11
        take_0(1,7) -> 11
        take_0(1,8) -> 11
        take_0(1,13) -> 11
        take_0(1,14) -> 11
        take_0(6,1) -> 11
        take_0(6,6) -> 11
        take_0(6,7) -> 11
        take_0(6,8) -> 11
        take_0(6,13) -> 11
        take_0(6,14) -> 11
        take_0(7,1) -> 11
        take_0(7,6) -> 11
        take_0(7,7) -> 11
        take_0(7,8) -> 11
        take_0(7,13) -> 11
        take_0(7,14) -> 11
        take_0(8,1) -> 11
        take_0(8,6) -> 11
        take_0(8,7) -> 11
        take_0(8,8) -> 11
        take_0(8,13) -> 11
        take_0(8,14) -> 11
        take_0(13,1) -> 11
        take_0(13,6) -> 11
        take_0(13,7) -> 11
        take_0(13,8) -> 11
        take_0(13,13) -> 11
        take_0(13,14) -> 11
        take_0(14,1) -> 11
        take_0(14,6) -> 11
        take_0(14,7) -> 11
        take_0(14,8) -> 11
        take_0(14,13) -> 11
        take_0(14,14) -> 11
        take_1(1,1) -> 22
        take_1(1,6) -> 22
        take_1(1,7) -> 22
        take_1(1,8) -> 22
        take_1(1,13) -> 22
        take_1(1,14) -> 22
        take_1(6,1) -> 22
        take_1(6,6) -> 22
        take_1(6,7) -> 22
        take_1(6,8) -> 22
        take_1(6,13) -> 22
        take_1(6,14) -> 22
        take_1(7,1) -> 22
        take_1(7,6) -> 22
        take_1(7,7) -> 22
        take_1(7,8) -> 22
        take_1(7,13) -> 22
        take_1(7,14) -> 22
        take_1(8,1) -> 22
        take_1(8,6) -> 22
        take_1(8,7) -> 22
        take_1(8,8) -> 22
        take_1(8,13) -> 22
        take_1(8,14) -> 22
        take_1(13,1) -> 22
        take_1(13,6) -> 22
        take_1(13,7) -> 22
        take_1(13,8) -> 22
        take_1(13,13) -> 22
        take_1(13,14) -> 22
        take_1(14,1) -> 22
        take_1(14,6) -> 22
        take_1(14,7) -> 22
        take_1(14,8) -> 22
        take_1(14,13) -> 22
        take_1(14,14) -> 22
        top_0(1) -> 12
        top_0(6) -> 12
        top_0(7) -> 12
        top_0(8) -> 12
        top_0(13) -> 12
        top_0(14) -> 12
        top_1(23) -> 12
        top_2(24) -> 12
        top_3(31) -> 12
        top_4(39) -> 12
        tt_0() -> 13
        tt_1() -> 16
        tt_2() -> 30
        zeros_0() -> 14
        zeros_1() -> 17
        zeros_2() -> 27
        zeros_3() -> 35
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        active(and(X1,X2)) -> and(active(X1),X2)
        active(and(tt(),X)) -> mark(X)
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(length(X)) -> length(active(X))
        active(length(cons(N,L))) -> mark(s(length(L)))
        active(length(nil())) -> mark(0())
        active(s(X)) -> s(active(X))
        active(take(X1,X2)) -> take(X1,active(X2))
        active(take(X1,X2)) -> take(active(X1),X2)
        active(take(0(),IL)) -> mark(nil())
        active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL)))
        active(zeros()) -> mark(cons(0(),zeros()))
        and(mark(X1),X2) -> mark(and(X1,X2))
        and(ok(X1),ok(X2)) -> ok(and(X1,X2))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        length(mark(X)) -> mark(length(X))
        length(ok(X)) -> ok(length(X))
        proper(0()) -> ok(0())
        proper(and(X1,X2)) -> and(proper(X1),proper(X2))
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(length(X)) -> length(proper(X))
        proper(nil()) -> ok(nil())
        proper(s(X)) -> s(proper(X))
        proper(take(X1,X2)) -> take(proper(X1),proper(X2))
        proper(tt()) -> ok(tt())
        proper(zeros()) -> ok(zeros())
        s(mark(X)) -> mark(s(X))
        s(ok(X)) -> ok(s(X))
        take(X1,mark(X2)) -> mark(take(X1,X2))
        take(mark(X1),X2) -> mark(take(X1,X2))
        take(ok(X1),ok(X2)) -> ok(take(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Signature:
        {active/1,and/2,cons/2,length/1,proper/1,s/1,take/2,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
      Obligation:
        Full
        basic terms: {active,and,cons,length,proper,s,take,top}/{0,mark,nil,ok,tt,zeros}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).