*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        deeprev(C(x1,x2)) -> deeprevapp(C(x1,x2),N())
        deeprev(N()) -> N()
        deeprev(V(n)) -> V(n)
        deeprevapp(C(x1,x2),rest) -> deeprevapp(x2,C(x1,rest))
        deeprevapp(N(),rest) -> rest
        deeprevapp(V(n),rest) -> revconsapp(rest,V(n))
        first(C(x1,x2)) -> x1
        first(V(n)) -> N()
        goal(x) -> deeprev(x)
        isEmptyT(C(x1,x2)) -> False()
        isEmptyT(N()) -> True()
        isEmptyT(V(n)) -> False()
        isNotEmptyT(C(x1,x2)) -> True()
        isNotEmptyT(N()) -> False()
        isNotEmptyT(V(n)) -> False()
        isVal(C(x1,x2)) -> False()
        isVal(N()) -> False()
        isVal(V(n)) -> True()
        revconsapp(C(x1,x2),r) -> revconsapp(x2,C(x1,r))
        revconsapp(N(),r) -> r
        revconsapp(V(n),r) -> r
        second(C(x1,x2)) -> x2
        second(V(n)) -> N()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {deeprev/1,deeprevapp/2,first/1,goal/1,isEmptyT/1,isNotEmptyT/1,isVal/1,revconsapp/2,second/1} / {C/2,False/0,N/0,True/0,V/1}
      Obligation:
        Innermost
        basic terms: {deeprev,deeprevapp,first,goal,isEmptyT,isNotEmptyT,isVal,revconsapp,second}/{C,False,N,True,V}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 3.
      The enriched problem is compatible with follwoing automaton.
        C_0(2,2) -> 1
        C_0(2,2) -> 2
        C_1(2,1) -> 1
        C_1(2,2) -> 1
        C_1(2,2) -> 3
        C_1(2,3) -> 1
        C_1(2,3) -> 3
        C_1(2,5) -> 1
        C_1(2,5) -> 3
        C_1(2,6) -> 1
        C_2(2,1) -> 1
        C_2(2,1) -> 6
        C_2(2,4) -> 1
        C_2(2,4) -> 5
        C_2(2,5) -> 1
        C_2(2,5) -> 5
        C_2(2,6) -> 1
        C_2(2,6) -> 6
        C_3(2,5) -> 1
        C_3(2,5) -> 8
        C_3(2,6) -> 1
        C_3(2,6) -> 7
        C_3(2,7) -> 1
        C_3(2,7) -> 7
        C_3(2,8) -> 1
        C_3(2,8) -> 8
        False_0() -> 1
        False_0() -> 2
        False_1() -> 1
        N_0() -> 1
        N_0() -> 2
        N_1() -> 1
        N_1() -> 4
        True_0() -> 1
        True_0() -> 2
        True_1() -> 1
        V_0(2) -> 1
        V_0(2) -> 2
        V_1(2) -> 1
        deeprev_0(2) -> 1
        deeprev_1(2) -> 1
        deeprevapp_0(2,2) -> 1
        deeprevapp_1(2,3) -> 1
        deeprevapp_1(3,4) -> 1
        deeprevapp_2(2,5) -> 1
        deeprevapp_2(3,5) -> 1
        deeprevapp_2(5,5) -> 1
        deeprevapp_3(4,8) -> 1
        deeprevapp_3(5,8) -> 1
        first_0(2) -> 1
        goal_0(2) -> 1
        isEmptyT_0(2) -> 1
        isNotEmptyT_0(2) -> 1
        isVal_0(2) -> 1
        revconsapp_0(2,2) -> 1
        revconsapp_1(2,1) -> 1
        revconsapp_1(3,1) -> 1
        revconsapp_1(5,1) -> 1
        revconsapp_2(2,6) -> 1
        revconsapp_2(3,6) -> 1
        revconsapp_2(4,6) -> 1
        revconsapp_2(5,6) -> 1
        revconsapp_3(4,7) -> 1
        revconsapp_3(5,7) -> 1
        second_0(2) -> 1
        2 -> 1
        3 -> 1
        5 -> 1
        6 -> 1
        7 -> 1
        8 -> 1
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        deeprev(C(x1,x2)) -> deeprevapp(C(x1,x2),N())
        deeprev(N()) -> N()
        deeprev(V(n)) -> V(n)
        deeprevapp(C(x1,x2),rest) -> deeprevapp(x2,C(x1,rest))
        deeprevapp(N(),rest) -> rest
        deeprevapp(V(n),rest) -> revconsapp(rest,V(n))
        first(C(x1,x2)) -> x1
        first(V(n)) -> N()
        goal(x) -> deeprev(x)
        isEmptyT(C(x1,x2)) -> False()
        isEmptyT(N()) -> True()
        isEmptyT(V(n)) -> False()
        isNotEmptyT(C(x1,x2)) -> True()
        isNotEmptyT(N()) -> False()
        isNotEmptyT(V(n)) -> False()
        isVal(C(x1,x2)) -> False()
        isVal(N()) -> False()
        isVal(V(n)) -> True()
        revconsapp(C(x1,x2),r) -> revconsapp(x2,C(x1,r))
        revconsapp(N(),r) -> r
        revconsapp(V(n),r) -> r
        second(C(x1,x2)) -> x2
        second(V(n)) -> N()
      Signature:
        {deeprev/1,deeprevapp/2,first/1,goal/1,isEmptyT/1,isNotEmptyT/1,isVal/1,revconsapp/2,second/1} / {C/2,False/0,N/0,True/0,V/1}
      Obligation:
        Innermost
        basic terms: {deeprev,deeprevapp,first,goal,isEmptyT,isNotEmptyT,isVal,revconsapp,second}/{C,False,N,True,V}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).