(STRATEGY
    INNERMOST)

(VAR
    I P V V1 V2 X X1 X2 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] -> A
    U21 :: [A x A] -> A
    U22 :: [A] -> A
    U31 :: [A] -> A
    U41 :: [A x A] -> A
    U42 :: [A] -> A
    U51 :: [A x A] -> A
    U52 :: [A] -> A
    U61 :: [A] -> A
    U71 :: [A x A] -> A
    U72 :: [A] -> A
    U81 :: [A] -> A
    proper :: [A] -> A
    isList :: [A] -> A
    isNeList :: [A] -> A
    isPal :: [A] -> A
    isQid :: [A] -> A
    isNePal :: [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())) -> mark(tt())
    active(U21(tt(),V2)) ->
      mark(U22(isList(V2)))
    active(U22(tt())) -> mark(tt())
    active(U31(tt())) -> mark(tt())
    active(U41(tt(),V2)) ->
      mark(U42(isNeList(V2)))
    active(U42(tt())) -> mark(tt())
    active(U51(tt(),V2)) ->
      mark(U52(isList(V2)))
    active(U52(tt())) -> mark(tt())
    active(U61(tt())) -> mark(tt())
    active(U71(tt(),P)) ->
      mark(U72(isPal(P)))
    active(U72(tt())) -> mark(tt())
    active(U81(tt())) -> mark(tt())
    active(isList(V)) ->
      mark(U11(isNeList(V)))
    active(isList(nil())) ->
      mark(tt())
    active(isList(__(V1,V2))) ->
      mark(U21(isList(V1),V2))
    active(isNeList(V)) ->
      mark(U31(isQid(V)))
    active(isNeList(__(V1,V2))) ->
      mark(U41(isList(V1),V2))
    active(isNeList(__(V1,V2))) ->
      mark(U51(isNeList(V1),V2))
    active(isNePal(V)) ->
      mark(U61(isQid(V)))
    active(isNePal(__(I
                     ,__(P,I)))) -> mark(U71(isQid(I)
                                            ,P))
    active(isPal(V)) ->
      mark(U81(isNePal(V)))
    active(isPal(nil())) ->
      mark(tt())
    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(X)) -> U11(active(X))
    active(U21(X1,X2)) ->
      U21(active(X1),X2)
    active(U22(X)) -> U22(active(X))
    active(U31(X)) -> U31(active(X))
    active(U41(X1,X2)) ->
      U41(active(X1),X2)
    active(U42(X)) -> U42(active(X))
    active(U51(X1,X2)) ->
      U51(active(X1),X2)
    active(U52(X)) -> U52(active(X))
    active(U61(X)) -> U61(active(X))
    active(U71(X1,X2)) ->
      U71(active(X1),X2)
    active(U72(X)) -> U72(active(X))
    active(U81(X)) -> U81(active(X))
    __(mark(X1),X2) -> mark(__(X1
                              ,X2))
    __(X1,mark(X2)) -> mark(__(X1
                              ,X2))
    U11(mark(X)) -> mark(U11(X))
    U21(mark(X1),X2) -> mark(U21(X1
                                ,X2))
    U22(mark(X)) -> mark(U22(X))
    U31(mark(X)) -> mark(U31(X))
    U41(mark(X1),X2) -> mark(U41(X1
                                ,X2))
    U42(mark(X)) -> mark(U42(X))
    U51(mark(X1),X2) -> mark(U51(X1
                                ,X2))
    U52(mark(X)) -> mark(U52(X))
    U61(mark(X)) -> mark(U61(X))
    U71(mark(X1),X2) -> mark(U71(X1
                                ,X2))
    U72(mark(X)) -> mark(U72(X))
    U81(mark(X)) -> mark(U81(X))
    proper(__(X1,X2)) ->
      __(proper(X1),proper(X2))
    proper(nil()) -> ok(nil())
    proper(U11(X)) -> U11(proper(X))
    proper(tt()) -> ok(tt())
    proper(U21(X1,X2)) ->
      U21(proper(X1),proper(X2))
    proper(U22(X)) -> U22(proper(X))
    proper(isList(X)) ->
      isList(proper(X))
    proper(U31(X)) -> U31(proper(X))
    proper(U41(X1,X2)) ->
      U41(proper(X1),proper(X2))
    proper(U42(X)) -> U42(proper(X))
    proper(isNeList(X)) ->
      isNeList(proper(X))
    proper(U51(X1,X2)) ->
      U51(proper(X1),proper(X2))
    proper(U52(X)) -> U52(proper(X))
    proper(U61(X)) -> U61(proper(X))
    proper(U71(X1,X2)) ->
      U71(proper(X1),proper(X2))
    proper(U72(X)) -> U72(proper(X))
    proper(isPal(X)) ->
      isPal(proper(X))
    proper(U81(X)) -> U81(proper(X))
    proper(isQid(X)) ->
      isQid(proper(X))
    proper(isNePal(X)) ->
      isNePal(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(X)) -> ok(U11(X))
    U21(ok(X1),ok(X2)) -> ok(U21(X1
                                ,X2))
    U22(ok(X)) -> ok(U22(X))
    isList(ok(X)) -> ok(isList(X))
    U31(ok(X)) -> ok(U31(X))
    U41(ok(X1),ok(X2)) -> ok(U41(X1
                                ,X2))
    U42(ok(X)) -> ok(U42(X))
    isNeList(ok(X)) ->
      ok(isNeList(X))
    U51(ok(X1),ok(X2)) -> ok(U51(X1
                                ,X2))
    U52(ok(X)) -> ok(U52(X))
    U61(ok(X)) -> ok(U61(X))
    U71(ok(X1),ok(X2)) -> ok(U71(X1
                                ,X2))
    U72(ok(X)) -> ok(U72(X))
    isPal(ok(X)) -> ok(isPal(X))
    U81(ok(X)) -> ok(U81(X))
    isQid(ok(X)) -> ok(isQid(X))
    isNePal(ok(X)) -> ok(isNePal(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X)))