*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(tail(X)) -> tail(active(X))
        active(tail(cons(X,XS))) -> mark(XS)
        active(zeros()) -> mark(cons(0(),zeros()))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(tail(X)) -> tail(proper(X))
        proper(zeros()) -> ok(zeros())
        tail(mark(X)) -> mark(tail(X))
        tail(ok(X)) -> ok(tail(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0}
      Obligation:
        Full
        basic terms: {active,cons,proper,tail,top}/{0,mark,ok,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() -> 11
        0_2() -> 18
        0_3() -> 27
        active_0(1) -> 2
        active_0(4) -> 2
        active_0(5) -> 2
        active_0(9) -> 2
        active_1(1) -> 15
        active_1(4) -> 15
        active_1(5) -> 15
        active_1(9) -> 15
        active_2(11) -> 16
        active_2(12) -> 16
        active_3(26) -> 22
        active_4(18) -> 28
        active_4(29) -> 30
        active_5(27) -> 31
        cons_0(1,1) -> 3
        cons_0(1,4) -> 3
        cons_0(1,5) -> 3
        cons_0(1,9) -> 3
        cons_0(4,1) -> 3
        cons_0(4,4) -> 3
        cons_0(4,5) -> 3
        cons_0(4,9) -> 3
        cons_0(5,1) -> 3
        cons_0(5,4) -> 3
        cons_0(5,5) -> 3
        cons_0(5,9) -> 3
        cons_0(9,1) -> 3
        cons_0(9,4) -> 3
        cons_0(9,5) -> 3
        cons_0(9,9) -> 3
        cons_1(1,1) -> 13
        cons_1(1,4) -> 13
        cons_1(1,5) -> 13
        cons_1(1,9) -> 13
        cons_1(4,1) -> 13
        cons_1(4,4) -> 13
        cons_1(4,5) -> 13
        cons_1(4,9) -> 13
        cons_1(5,1) -> 13
        cons_1(5,4) -> 13
        cons_1(5,5) -> 13
        cons_1(5,9) -> 13
        cons_1(9,1) -> 13
        cons_1(9,4) -> 13
        cons_1(9,5) -> 13
        cons_1(9,9) -> 13
        cons_1(11,12) -> 10
        cons_2(18,19) -> 17
        cons_2(20,21) -> 16
        cons_3(18,19) -> 26
        cons_3(23,24) -> 22
        cons_4(27,25) -> 29
        cons_4(28,19) -> 22
        cons_5(31,25) -> 30
        mark_0(1) -> 4
        mark_0(4) -> 4
        mark_0(5) -> 4
        mark_0(9) -> 4
        mark_1(10) -> 2
        mark_1(10) -> 15
        mark_1(13) -> 3
        mark_1(13) -> 13
        mark_1(14) -> 7
        mark_1(14) -> 14
        mark_2(17) -> 16
        ok_0(1) -> 5
        ok_0(4) -> 5
        ok_0(5) -> 5
        ok_0(9) -> 5
        ok_1(11) -> 6
        ok_1(11) -> 15
        ok_1(12) -> 6
        ok_1(12) -> 15
        ok_1(13) -> 3
        ok_1(13) -> 13
        ok_1(14) -> 7
        ok_1(14) -> 14
        ok_2(18) -> 20
        ok_2(19) -> 21
        ok_3(25) -> 24
        ok_3(26) -> 16
        ok_3(27) -> 23
        ok_4(29) -> 22
        proper_0(1) -> 6
        proper_0(4) -> 6
        proper_0(5) -> 6
        proper_0(9) -> 6
        proper_1(1) -> 15
        proper_1(4) -> 15
        proper_1(5) -> 15
        proper_1(9) -> 15
        proper_2(10) -> 16
        proper_2(11) -> 20
        proper_2(12) -> 21
        proper_3(17) -> 22
        proper_3(18) -> 23
        proper_3(19) -> 24
        tail_0(1) -> 7
        tail_0(4) -> 7
        tail_0(5) -> 7
        tail_0(9) -> 7
        tail_1(1) -> 14
        tail_1(4) -> 14
        tail_1(5) -> 14
        tail_1(9) -> 14
        top_0(1) -> 8
        top_0(4) -> 8
        top_0(5) -> 8
        top_0(9) -> 8
        top_1(15) -> 8
        top_2(16) -> 8
        top_3(22) -> 8
        top_4(30) -> 8
        zeros_0() -> 9
        zeros_1() -> 12
        zeros_2() -> 19
        zeros_3() -> 25
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(tail(X)) -> tail(active(X))
        active(tail(cons(X,XS))) -> mark(XS)
        active(zeros()) -> mark(cons(0(),zeros()))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(tail(X)) -> tail(proper(X))
        proper(zeros()) -> ok(zeros())
        tail(mark(X)) -> mark(tail(X))
        tail(ok(X)) -> ok(tail(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Signature:
        {active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0}
      Obligation:
        Full
        basic terms: {active,cons,proper,tail,top}/{0,mark,ok,zeros}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).