(STRATEGY
    INNERMOST)

(VAR
    IL L M N V V1 V2 X X1 X2 X3 X4)
(DATATYPES
    A = µX.< cons(X, X), 0, zeros, tt, s(X), nil, take(X, X), length(X), U101(X, X, X), U102(X, X, X), isNatKind(X), U103(X, X, X), isNatIListKind(X), U104(X, X, X), U105(X, X), isNat(X), U106(X), isNatIList(X), U11(X, X), U12(X, X), U111(X, X, X), U112(X, X, X), U113(X, X, X), U114(X, X), U13(X), isNatList(X), U121(X, X), U122(X), U131(X, X, X, X), U132(X, X, X, X), U133(X, X, X, X), U134(X, X, X, X), U135(X, X, X, X), U136(X, X, X, X), U21(X, X), U22(X, X), U23(X), U31(X, X), U32(X, X), U33(X), U41(X, X, X), U42(X, X, X), U43(X, X, X), U44(X, X, X), U45(X, X), U46(X), U51(X, X), U52(X), U61(X, X), U62(X), U71(X), U81(X), U91(X, X, X), U92(X, X, X), U93(X, X, X), U94(X, X, X), U95(X, X), U96(X) >)
(SIGNATURES
    a__zeros :: [] -> A
    a__U101 :: [A x A x A] -> A
    a__U102 :: [A x A x A] -> A
    a__U103 :: [A x A x A] -> A
    a__U104 :: [A x A x A] -> A
    a__U105 :: [A x A] -> A
    a__U106 :: [A] -> A
    a__U11 :: [A x A] -> A
    a__U111 :: [A x A x A] -> A
    a__U112 :: [A x A x A] -> A
    a__U113 :: [A x A x A] -> A
    a__U114 :: [A x A] -> A
    a__U12 :: [A x A] -> A
    a__U121 :: [A x A] -> A
    a__U122 :: [A] -> A
    a__U13 :: [A] -> A
    a__U131 :: [A x A x A x A] -> A
    a__U132 :: [A x A x A x A] -> A
    a__U133 :: [A x A x A x A] -> A
    a__U134 :: [A x A x A x A] -> A
    a__U135 :: [A x A x A x A] -> A
    a__U136 :: [A x A x A x A] -> A
    a__U21 :: [A x A] -> A
    a__U22 :: [A x A] -> A
    a__U23 :: [A] -> A
    a__U31 :: [A x A] -> A
    a__U32 :: [A x A] -> A
    a__U33 :: [A] -> A
    a__U41 :: [A x A x A] -> A
    a__U42 :: [A x A x A] -> A
    a__U43 :: [A x A x A] -> A
    a__U44 :: [A x A x A] -> A
    a__U45 :: [A x A] -> A
    a__U46 :: [A] -> A
    a__U51 :: [A x A] -> A
    a__U52 :: [A] -> A
    a__U61 :: [A x A] -> A
    a__U62 :: [A] -> A
    a__U71 :: [A] -> A
    a__U81 :: [A] -> A
    a__U91 :: [A x A x A] -> A
    a__U92 :: [A x A x A] -> A
    a__U93 :: [A x A x A] -> A
    a__U94 :: [A x A x A] -> A
    a__U95 :: [A x A] -> A
    a__U96 :: [A] -> A
    a__isNat :: [A] -> A
    a__isNatIList :: [A] -> A
    a__isNatIListKind :: [A] -> A
    a__isNatKind :: [A] -> A
    a__isNatList :: [A] -> A
    a__length :: [A] -> A
    a__take :: [A x A] -> A
    mark :: [A] -> A)
(RULES
    a__zeros() -> cons(0(),zeros())
    a__U101(tt(),V1,V2) ->
      a__U102(a__isNatKind(V1),V1,V2)
    a__U102(tt(),V1,V2) ->
      a__U103(a__isNatIListKind(V2)
             ,V1
             ,V2)
    a__U103(tt(),V1,V2) ->
      a__U104(a__isNatIListKind(V2)
             ,V1
             ,V2)
    a__U104(tt(),V1,V2) ->
      a__U105(a__isNat(V1),V2)
    a__U105(tt(),V2) ->
      a__U106(a__isNatIList(V2))
    a__U106(tt()) -> tt()
    a__U11(tt(),V1) ->
      a__U12(a__isNatIListKind(V1),V1)
    a__U111(tt(),L,N) ->
      a__U112(a__isNatIListKind(L)
             ,L
             ,N)
    a__U112(tt(),L,N) ->
      a__U113(a__isNat(N),L,N)
    a__U113(tt(),L,N) ->
      a__U114(a__isNatKind(N),L)
    a__U114(tt(),L) ->
      s(a__length(mark(L)))
    a__U12(tt(),V1) ->
      a__U13(a__isNatList(V1))
    a__U121(tt(),IL) ->
      a__U122(a__isNatIListKind(IL))
    a__U122(tt()) -> nil()
    a__U13(tt()) -> tt()
    a__U131(tt(),IL,M,N) ->
      a__U132(a__isNatIListKind(IL)
             ,IL
             ,M
             ,N)
    a__U132(tt(),IL,M,N) ->
      a__U133(a__isNat(M),IL,M,N)
    a__U133(tt(),IL,M,N) ->
      a__U134(a__isNatKind(M),IL,M,N)
    a__U134(tt(),IL,M,N) ->
      a__U135(a__isNat(N),IL,M,N)
    a__U135(tt(),IL,M,N) ->
      a__U136(a__isNatKind(N),IL,M,N)
    a__U136(tt(),IL,M,N) ->
      cons(mark(N),take(M,IL))
    a__U21(tt(),V1) ->
      a__U22(a__isNatKind(V1),V1)
    a__U22(tt(),V1) ->
      a__U23(a__isNat(V1))
    a__U23(tt()) -> tt()
    a__U31(tt(),V) ->
      a__U32(a__isNatIListKind(V),V)
    a__U32(tt(),V) ->
      a__U33(a__isNatList(V))
    a__U33(tt()) -> tt()
    a__U41(tt(),V1,V2) ->
      a__U42(a__isNatKind(V1),V1,V2)
    a__U42(tt(),V1,V2) ->
      a__U43(a__isNatIListKind(V2)
            ,V1
            ,V2)
    a__U43(tt(),V1,V2) ->
      a__U44(a__isNatIListKind(V2)
            ,V1
            ,V2)
    a__U44(tt(),V1,V2) ->
      a__U45(a__isNat(V1),V2)
    a__U45(tt(),V2) ->
      a__U46(a__isNatIList(V2))
    a__U46(tt()) -> tt()
    a__U51(tt(),V2) ->
      a__U52(a__isNatIListKind(V2))
    a__U52(tt()) -> tt()
    a__U61(tt(),V2) ->
      a__U62(a__isNatIListKind(V2))
    a__U62(tt()) -> tt()
    a__U71(tt()) -> tt()
    a__U81(tt()) -> tt()
    a__U91(tt(),V1,V2) ->
      a__U92(a__isNatKind(V1),V1,V2)
    a__U92(tt(),V1,V2) ->
      a__U93(a__isNatIListKind(V2)
            ,V1
            ,V2)
    a__U93(tt(),V1,V2) ->
      a__U94(a__isNatIListKind(V2)
            ,V1
            ,V2)
    a__U94(tt(),V1,V2) ->
      a__U95(a__isNat(V1),V2)
    a__U95(tt(),V2) ->
      a__U96(a__isNatList(V2))
    a__U96(tt()) -> tt()
    a__isNat(0()) -> tt()
    a__isNat(length(V1)) ->
      a__U11(a__isNatIListKind(V1),V1)
    a__isNat(s(V1)) ->
      a__U21(a__isNatKind(V1),V1)
    a__isNatIList(V) ->
      a__U31(a__isNatIListKind(V),V)
    a__isNatIList(zeros()) -> tt()
    a__isNatIList(cons(V1,V2)) ->
      a__U41(a__isNatKind(V1),V1,V2)
    a__isNatIListKind(nil()) -> tt()
    a__isNatIListKind(zeros()) ->
      tt()
    a__isNatIListKind(cons(V1
                          ,V2)) -> a__U51(a__isNatKind(V1)
                                         ,V2)
    a__isNatIListKind(take(V1
                          ,V2)) -> a__U61(a__isNatKind(V1)
                                         ,V2)
    a__isNatKind(0()) -> tt()
    a__isNatKind(length(V1)) ->
      a__U71(a__isNatIListKind(V1))
    a__isNatKind(s(V1)) ->
      a__U81(a__isNatKind(V1))
    a__isNatList(nil()) -> tt()
    a__isNatList(cons(V1,V2)) ->
      a__U91(a__isNatKind(V1),V1,V2)
    a__isNatList(take(V1,V2)) ->
      a__U101(a__isNatKind(V1),V1,V2)
    a__length(nil()) -> 0()
    a__length(cons(N,L)) ->
      a__U111(a__isNatList(L),L,N)
    a__take(0(),IL) ->
      a__U121(a__isNatIList(IL),IL)
    a__take(s(M),cons(N,IL)) ->
      a__U131(a__isNatIList(IL)
             ,IL
             ,M
             ,N)
    mark(zeros()) -> a__zeros()
    mark(U101(X1,X2,X3)) ->
      a__U101(mark(X1),X2,X3)
    mark(U102(X1,X2,X3)) ->
      a__U102(mark(X1),X2,X3)
    mark(isNatKind(X)) ->
      a__isNatKind(X)
    mark(U103(X1,X2,X3)) ->
      a__U103(mark(X1),X2,X3)
    mark(isNatIListKind(X)) ->
      a__isNatIListKind(X)
    mark(U104(X1,X2,X3)) ->
      a__U104(mark(X1),X2,X3)
    mark(U105(X1,X2)) ->
      a__U105(mark(X1),X2)
    mark(isNat(X)) -> a__isNat(X)
    mark(U106(X)) ->
      a__U106(mark(X))
    mark(isNatIList(X)) ->
      a__isNatIList(X)
    mark(U11(X1,X2)) ->
      a__U11(mark(X1),X2)
    mark(U12(X1,X2)) ->
      a__U12(mark(X1),X2)
    mark(U111(X1,X2,X3)) ->
      a__U111(mark(X1),X2,X3)
    mark(U112(X1,X2,X3)) ->
      a__U112(mark(X1),X2,X3)
    mark(U113(X1,X2,X3)) ->
      a__U113(mark(X1),X2,X3)
    mark(U114(X1,X2)) ->
      a__U114(mark(X1),X2)
    mark(length(X)) ->
      a__length(mark(X))
    mark(U13(X)) -> a__U13(mark(X))
    mark(isNatList(X)) ->
      a__isNatList(X)
    mark(U121(X1,X2)) ->
      a__U121(mark(X1),X2)
    mark(U122(X)) ->
      a__U122(mark(X))
    mark(U131(X1,X2,X3,X4)) ->
      a__U131(mark(X1),X2,X3,X4)
    mark(U132(X1,X2,X3,X4)) ->
      a__U132(mark(X1),X2,X3,X4)
    mark(U133(X1,X2,X3,X4)) ->
      a__U133(mark(X1),X2,X3,X4)
    mark(U134(X1,X2,X3,X4)) ->
      a__U134(mark(X1),X2,X3,X4)
    mark(U135(X1,X2,X3,X4)) ->
      a__U135(mark(X1),X2,X3,X4)
    mark(U136(X1,X2,X3,X4)) ->
      a__U136(mark(X1),X2,X3,X4)
    mark(take(X1,X2)) ->
      a__take(mark(X1),mark(X2))
    mark(U21(X1,X2)) ->
      a__U21(mark(X1),X2)
    mark(U22(X1,X2)) ->
      a__U22(mark(X1),X2)
    mark(U23(X)) -> a__U23(mark(X))
    mark(U31(X1,X2)) ->
      a__U31(mark(X1),X2)
    mark(U32(X1,X2)) ->
      a__U32(mark(X1),X2)
    mark(U33(X)) -> a__U33(mark(X))
    mark(U41(X1,X2,X3)) ->
      a__U41(mark(X1),X2,X3)
    mark(U42(X1,X2,X3)) ->
      a__U42(mark(X1),X2,X3)
    mark(U43(X1,X2,X3)) ->
      a__U43(mark(X1),X2,X3)
    mark(U44(X1,X2,X3)) ->
      a__U44(mark(X1),X2,X3)
    mark(U45(X1,X2)) ->
      a__U45(mark(X1),X2)
    mark(U46(X)) -> a__U46(mark(X))
    mark(U51(X1,X2)) ->
      a__U51(mark(X1),X2)
    mark(U52(X)) -> a__U52(mark(X))
    mark(U61(X1,X2)) ->
      a__U61(mark(X1),X2)
    mark(U62(X)) -> a__U62(mark(X))
    mark(U71(X)) -> a__U71(mark(X))
    mark(U81(X)) -> a__U81(mark(X))
    mark(U91(X1,X2,X3)) ->
      a__U91(mark(X1),X2,X3)
    mark(U92(X1,X2,X3)) ->
      a__U92(mark(X1),X2,X3)
    mark(U93(X1,X2,X3)) ->
      a__U93(mark(X1),X2,X3)
    mark(U94(X1,X2,X3)) ->
      a__U94(mark(X1),X2,X3)
    mark(U95(X1,X2)) ->
      a__U95(mark(X1),X2)
    mark(U96(X)) -> a__U96(mark(X))
    mark(cons(X1,X2)) ->
      cons(mark(X1),X2)
    mark(0()) -> 0()
    mark(tt()) -> tt()
    mark(s(X)) -> s(mark(X))
    mark(nil()) -> nil()
    a__zeros() -> zeros()
    a__U101(X1,X2,X3) -> U101(X1
                             ,X2
                             ,X3)
    a__U102(X1,X2,X3) -> U102(X1
                             ,X2
                             ,X3)
    a__isNatKind(X) -> isNatKind(X)
    a__U103(X1,X2,X3) -> U103(X1
                             ,X2
                             ,X3)
    a__isNatIListKind(X) ->
      isNatIListKind(X)
    a__U104(X1,X2,X3) -> U104(X1
                             ,X2
                             ,X3)
    a__U105(X1,X2) -> U105(X1,X2)
    a__isNat(X) -> isNat(X)
    a__U106(X) -> U106(X)
    a__isNatIList(X) ->
      isNatIList(X)
    a__U11(X1,X2) -> U11(X1,X2)
    a__U12(X1,X2) -> U12(X1,X2)
    a__U111(X1,X2,X3) -> U111(X1
                             ,X2
                             ,X3)
    a__U112(X1,X2,X3) -> U112(X1
                             ,X2
                             ,X3)
    a__U113(X1,X2,X3) -> U113(X1
                             ,X2
                             ,X3)
    a__U114(X1,X2) -> U114(X1,X2)
    a__length(X) -> length(X)
    a__U13(X) -> U13(X)
    a__isNatList(X) -> isNatList(X)
    a__U121(X1,X2) -> U121(X1,X2)
    a__U122(X) -> U122(X)
    a__U131(X1,X2,X3,X4) -> U131(X1
                                ,X2
                                ,X3
                                ,X4)
    a__U132(X1,X2,X3,X4) -> U132(X1
                                ,X2
                                ,X3
                                ,X4)
    a__U133(X1,X2,X3,X4) -> U133(X1
                                ,X2
                                ,X3
                                ,X4)
    a__U134(X1,X2,X3,X4) -> U134(X1
                                ,X2
                                ,X3
                                ,X4)
    a__U135(X1,X2,X3,X4) -> U135(X1
                                ,X2
                                ,X3
                                ,X4)
    a__U136(X1,X2,X3,X4) -> U136(X1
                                ,X2
                                ,X3
                                ,X4)
    a__take(X1,X2) -> take(X1,X2)
    a__U21(X1,X2) -> U21(X1,X2)
    a__U22(X1,X2) -> U22(X1,X2)
    a__U23(X) -> U23(X)
    a__U31(X1,X2) -> U31(X1,X2)
    a__U32(X1,X2) -> U32(X1,X2)
    a__U33(X) -> U33(X)
    a__U41(X1,X2,X3) -> U41(X1
                           ,X2
                           ,X3)
    a__U42(X1,X2,X3) -> U42(X1
                           ,X2
                           ,X3)
    a__U43(X1,X2,X3) -> U43(X1
                           ,X2
                           ,X3)
    a__U44(X1,X2,X3) -> U44(X1
                           ,X2
                           ,X3)
    a__U45(X1,X2) -> U45(X1,X2)
    a__U46(X) -> U46(X)
    a__U51(X1,X2) -> U51(X1,X2)
    a__U52(X) -> U52(X)
    a__U61(X1,X2) -> U61(X1,X2)
    a__U62(X) -> U62(X)
    a__U71(X) -> U71(X)
    a__U81(X) -> U81(X)
    a__U91(X1,X2,X3) -> U91(X1
                           ,X2
                           ,X3)
    a__U92(X1,X2,X3) -> U92(X1
                           ,X2
                           ,X3)
    a__U93(X1,X2,X3) -> U93(X1
                           ,X2
                           ,X3)
    a__U94(X1,X2,X3) -> U94(X1
                           ,X2
                           ,X3)
    a__U95(X1,X2) -> U95(X1,X2)
    a__U96(X) -> U96(X))