(STRATEGY
    INNERMOST)

(VAR
    I P V V1 V2 X X1 X2 X3 Y Z)
(DATATYPES
    A = µX.< mark(X), nil, tt, a, e, i, o, u, ok(X) >)
(SIGNATURES
    active :: [A] -> A
    __ :: [A x A] -> A
    U11 :: [A x A] -> A
    U12 :: [A] -> A
    U21 :: [A x A x A] -> A
    U22 :: [A x A] -> A
    U23 :: [A] -> A
    U31 :: [A x A] -> A
    U32 :: [A] -> A
    U41 :: [A x A x A] -> A
    U42 :: [A x A] -> A
    U43 :: [A] -> A
    U51 :: [A x A x A] -> A
    U52 :: [A x A] -> A
    U53 :: [A] -> A
    U61 :: [A x A] -> A
    U62 :: [A] -> A
    U71 :: [A x A] -> A
    U72 :: [A] -> A
    and :: [A x A] -> A
    proper :: [A] -> A
    isNeList :: [A] -> A
    isList :: [A] -> A
    isQid :: [A] -> A
    isNePal :: [A] -> A
    isPalListKind :: [A] -> A
    isPal :: [A] -> A
    top :: [A] -> A)
(RULES
    active(__(__(X,Y),Z)) ->
      mark(__(X,__(Y,Z)))
    active(__(X,nil())) -> mark(X)
    active(__(nil(),X)) -> mark(X)
    active(U11(tt(),V)) ->
      mark(U12(isNeList(V)))
    active(U12(tt())) -> mark(tt())
    active(U21(tt(),V1,V2)) ->
      mark(U22(isList(V1),V2))
    active(U22(tt(),V2)) ->
      mark(U23(isList(V2)))
    active(U23(tt())) -> mark(tt())
    active(U31(tt(),V)) ->
      mark(U32(isQid(V)))
    active(U32(tt())) -> mark(tt())
    active(U41(tt(),V1,V2)) ->
      mark(U42(isList(V1),V2))
    active(U42(tt(),V2)) ->
      mark(U43(isNeList(V2)))
    active(U43(tt())) -> mark(tt())
    active(U51(tt(),V1,V2)) ->
      mark(U52(isNeList(V1),V2))
    active(U52(tt(),V2)) ->
      mark(U53(isList(V2)))
    active(U53(tt())) -> mark(tt())
    active(U61(tt(),V)) ->
      mark(U62(isQid(V)))
    active(U62(tt())) -> mark(tt())
    active(U71(tt(),V)) ->
      mark(U72(isNePal(V)))
    active(U72(tt())) -> mark(tt())
    active(and(tt(),X)) -> mark(X)
    active(isList(V)) ->
      mark(U11(isPalListKind(V),V))
    active(isList(nil())) ->
      mark(tt())
    active(isList(__(V1,V2))) ->
      mark(U21(and(isPalListKind(V1)
                  ,isPalListKind(V2))
              ,V1
              ,V2))
    active(isNeList(V)) ->
      mark(U31(isPalListKind(V),V))
    active(isNeList(__(V1,V2))) ->
      mark(U41(and(isPalListKind(V1)
                  ,isPalListKind(V2))
              ,V1
              ,V2))
    active(isNeList(__(V1,V2))) ->
      mark(U51(and(isPalListKind(V1)
                  ,isPalListKind(V2))
              ,V1
              ,V2))
    active(isNePal(V)) ->
      mark(U61(isPalListKind(V),V))
    active(isNePal(__(I
                     ,__(P,I)))) ->
      mark(and(and(isQid(I)
                  ,isPalListKind(I))
              ,and(isPal(P)
                  ,isPalListKind(P))))
    active(isPal(V)) ->
      mark(U71(isPalListKind(V),V))
    active(isPal(nil())) ->
      mark(tt())
    active(isPalListKind(a())) ->
      mark(tt())
    active(isPalListKind(e())) ->
      mark(tt())
    active(isPalListKind(i())) ->
      mark(tt())
    active(isPalListKind(nil())) ->
      mark(tt())
    active(isPalListKind(o())) ->
      mark(tt())
    active(isPalListKind(u())) ->
      mark(tt())
    active(isPalListKind(__(V1
                           ,V2))) ->
      mark(and(isPalListKind(V1)
              ,isPalListKind(V2)))
    active(isQid(a())) -> mark(tt())
    active(isQid(e())) -> mark(tt())
    active(isQid(i())) -> mark(tt())
    active(isQid(o())) -> mark(tt())
    active(isQid(u())) -> mark(tt())
    active(__(X1,X2)) ->
      __(active(X1),X2)
    active(__(X1,X2)) -> __(X1
                           ,active(X2))
    active(U11(X1,X2)) ->
      U11(active(X1),X2)
    active(U12(X)) -> U12(active(X))
    active(U21(X1,X2,X3)) ->
      U21(active(X1),X2,X3)
    active(U22(X1,X2)) ->
      U22(active(X1),X2)
    active(U23(X)) -> U23(active(X))
    active(U31(X1,X2)) ->
      U31(active(X1),X2)
    active(U32(X)) -> U32(active(X))
    active(U41(X1,X2,X3)) ->
      U41(active(X1),X2,X3)
    active(U42(X1,X2)) ->
      U42(active(X1),X2)
    active(U43(X)) -> U43(active(X))
    active(U51(X1,X2,X3)) ->
      U51(active(X1),X2,X3)
    active(U52(X1,X2)) ->
      U52(active(X1),X2)
    active(U53(X)) -> U53(active(X))
    active(U61(X1,X2)) ->
      U61(active(X1),X2)
    active(U62(X)) -> U62(active(X))
    active(U71(X1,X2)) ->
      U71(active(X1),X2)
    active(U72(X)) -> U72(active(X))
    active(and(X1,X2)) ->
      and(active(X1),X2)
    __(mark(X1),X2) -> mark(__(X1
                              ,X2))
    __(X1,mark(X2)) -> mark(__(X1
                              ,X2))
    U11(mark(X1),X2) -> mark(U11(X1
                                ,X2))
    U12(mark(X)) -> mark(U12(X))
    U21(mark(X1),X2,X3) ->
      mark(U21(X1,X2,X3))
    U22(mark(X1),X2) -> mark(U22(X1
                                ,X2))
    U23(mark(X)) -> mark(U23(X))
    U31(mark(X1),X2) -> mark(U31(X1
                                ,X2))
    U32(mark(X)) -> mark(U32(X))
    U41(mark(X1),X2,X3) ->
      mark(U41(X1,X2,X3))
    U42(mark(X1),X2) -> mark(U42(X1
                                ,X2))
    U43(mark(X)) -> mark(U43(X))
    U51(mark(X1),X2,X3) ->
      mark(U51(X1,X2,X3))
    U52(mark(X1),X2) -> mark(U52(X1
                                ,X2))
    U53(mark(X)) -> mark(U53(X))
    U61(mark(X1),X2) -> mark(U61(X1
                                ,X2))
    U62(mark(X)) -> mark(U62(X))
    U71(mark(X1),X2) -> mark(U71(X1
                                ,X2))
    U72(mark(X)) -> mark(U72(X))
    and(mark(X1),X2) -> mark(and(X1
                                ,X2))
    proper(__(X1,X2)) ->
      __(proper(X1),proper(X2))
    proper(nil()) -> ok(nil())
    proper(U11(X1,X2)) ->
      U11(proper(X1),proper(X2))
    proper(tt()) -> ok(tt())
    proper(U12(X)) -> U12(proper(X))
    proper(isNeList(X)) ->
      isNeList(proper(X))
    proper(U21(X1,X2,X3)) ->
      U21(proper(X1)
         ,proper(X2)
         ,proper(X3))
    proper(U22(X1,X2)) ->
      U22(proper(X1),proper(X2))
    proper(isList(X)) ->
      isList(proper(X))
    proper(U23(X)) -> U23(proper(X))
    proper(U31(X1,X2)) ->
      U31(proper(X1),proper(X2))
    proper(U32(X)) -> U32(proper(X))
    proper(isQid(X)) ->
      isQid(proper(X))
    proper(U41(X1,X2,X3)) ->
      U41(proper(X1)
         ,proper(X2)
         ,proper(X3))
    proper(U42(X1,X2)) ->
      U42(proper(X1),proper(X2))
    proper(U43(X)) -> U43(proper(X))
    proper(U51(X1,X2,X3)) ->
      U51(proper(X1)
         ,proper(X2)
         ,proper(X3))
    proper(U52(X1,X2)) ->
      U52(proper(X1),proper(X2))
    proper(U53(X)) -> U53(proper(X))
    proper(U61(X1,X2)) ->
      U61(proper(X1),proper(X2))
    proper(U62(X)) -> U62(proper(X))
    proper(U71(X1,X2)) ->
      U71(proper(X1),proper(X2))
    proper(U72(X)) -> U72(proper(X))
    proper(isNePal(X)) ->
      isNePal(proper(X))
    proper(and(X1,X2)) ->
      and(proper(X1),proper(X2))
    proper(isPalListKind(X)) ->
      isPalListKind(proper(X))
    proper(isPal(X)) ->
      isPal(proper(X))
    proper(a()) -> ok(a())
    proper(e()) -> ok(e())
    proper(i()) -> ok(i())
    proper(o()) -> ok(o())
    proper(u()) -> ok(u())
    __(ok(X1),ok(X2)) -> ok(__(X1
                              ,X2))
    U11(ok(X1),ok(X2)) -> ok(U11(X1
                                ,X2))
    U12(ok(X)) -> ok(U12(X))
    isNeList(ok(X)) ->
      ok(isNeList(X))
    U21(ok(X1),ok(X2),ok(X3)) ->
      ok(U21(X1,X2,X3))
    U22(ok(X1),ok(X2)) -> ok(U22(X1
                                ,X2))
    isList(ok(X)) -> ok(isList(X))
    U23(ok(X)) -> ok(U23(X))
    U31(ok(X1),ok(X2)) -> ok(U31(X1
                                ,X2))
    U32(ok(X)) -> ok(U32(X))
    isQid(ok(X)) -> ok(isQid(X))
    U41(ok(X1),ok(X2),ok(X3)) ->
      ok(U41(X1,X2,X3))
    U42(ok(X1),ok(X2)) -> ok(U42(X1
                                ,X2))
    U43(ok(X)) -> ok(U43(X))
    U51(ok(X1),ok(X2),ok(X3)) ->
      ok(U51(X1,X2,X3))
    U52(ok(X1),ok(X2)) -> ok(U52(X1
                                ,X2))
    U53(ok(X)) -> ok(U53(X))
    U61(ok(X1),ok(X2)) -> ok(U61(X1
                                ,X2))
    U62(ok(X)) -> ok(U62(X))
    U71(ok(X1),ok(X2)) -> ok(U71(X1
                                ,X2))
    U72(ok(X)) -> ok(U72(X))
    isNePal(ok(X)) -> ok(isNePal(X))
    and(ok(X1),ok(X2)) -> ok(and(X1
                                ,X2))
    isPalListKind(ok(X)) ->
      ok(isPalListKind(X))
    isPal(ok(X)) -> ok(isPal(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X)))