(STRATEGY
    INNERMOST)

(VAR
    IL L M N V V1 V2 X X1 X2)
(DATATYPES
    A = µX.< n__zeros, tt, n__take(X, X), n__0, n__length(X), n__s(X), n__cons(X, X), n__nil >)
(SIGNATURES
    zeros :: [] -> A
    U101 :: [A x A x A] -> A
    U102 :: [A x A x A] -> A
    U103 :: [A x A x A] -> A
    U104 :: [A x A x A] -> A
    U105 :: [A x A] -> A
    U106 :: [A] -> A
    U11 :: [A x A] -> A
    U111 :: [A x A x A] -> A
    U112 :: [A x A x A] -> A
    U113 :: [A x A x A] -> A
    U114 :: [A x A] -> A
    U12 :: [A x A] -> A
    U121 :: [A x A] -> A
    U122 :: [A] -> A
    U13 :: [A] -> A
    U131 :: [A x A x A x A] -> A
    U132 :: [A x A x A x A] -> A
    U133 :: [A x A x A x A] -> A
    U134 :: [A x A x A x A] -> A
    U135 :: [A x A x A x A] -> A
    U136 :: [A x A x A x A] -> A
    U21 :: [A x A] -> A
    U22 :: [A x A] -> A
    U23 :: [A] -> A
    U31 :: [A x A] -> A
    U32 :: [A x A] -> A
    U33 :: [A] -> A
    U41 :: [A x A x A] -> A
    U42 :: [A x A x A] -> A
    U43 :: [A x A x A] -> A
    U44 :: [A x A x A] -> A
    U45 :: [A x A] -> A
    U46 :: [A] -> A
    U51 :: [A x A] -> A
    U52 :: [A] -> A
    U61 :: [A x A] -> A
    U62 :: [A] -> A
    U71 :: [A] -> A
    U81 :: [A] -> A
    U91 :: [A x A x A] -> A
    U92 :: [A x A x A] -> A
    U93 :: [A x A x A] -> A
    U94 :: [A x A x A] -> A
    U95 :: [A x A] -> A
    U96 :: [A] -> A
    isNat :: [A] -> A
    isNatIList :: [A] -> A
    isNatIListKind :: [A] -> A
    isNatKind :: [A] -> A
    isNatList :: [A] -> A
    length :: [A] -> A
    take :: [A x A] -> A
    0 :: [] -> A
    s :: [A] -> A
    cons :: [A x A] -> A
    nil :: [] -> A
    activate :: [A] -> A)
(RULES
    zeros() -> cons(0(),n__zeros())
    U101(tt(),V1,V2) ->
      U102(isNatKind(activate(V1))
          ,activate(V1)
          ,activate(V2))
    U102(tt(),V1,V2) ->
      U103(isNatIListKind(activate(V2))
          ,activate(V1)
          ,activate(V2))
    U103(tt(),V1,V2) ->
      U104(isNatIListKind(activate(V2))
          ,activate(V1)
          ,activate(V2))
    U104(tt(),V1,V2) ->
      U105(isNat(activate(V1))
          ,activate(V2))
    U105(tt(),V2) ->
      U106(isNatIList(activate(V2)))
    U106(tt()) -> tt()
    U11(tt(),V1) ->
      U12(isNatIListKind(activate(V1))
         ,activate(V1))
    U111(tt(),L,N) ->
      U112(isNatIListKind(activate(L))
          ,activate(L)
          ,activate(N))
    U112(tt(),L,N) ->
      U113(isNat(activate(N))
          ,activate(L)
          ,activate(N))
    U113(tt(),L,N) ->
      U114(isNatKind(activate(N))
          ,activate(L))
    U114(tt(),L) ->
      s(length(activate(L)))
    U12(tt(),V1) ->
      U13(isNatList(activate(V1)))
    U121(tt(),IL) ->
      U122(isNatIListKind(activate(IL)))
    U122(tt()) -> nil()
    U13(tt()) -> tt()
    U131(tt(),IL,M,N) ->
      U132(isNatIListKind(activate(IL))
          ,activate(IL)
          ,activate(M)
          ,activate(N))
    U132(tt(),IL,M,N) ->
      U133(isNat(activate(M))
          ,activate(IL)
          ,activate(M)
          ,activate(N))
    U133(tt(),IL,M,N) ->
      U134(isNatKind(activate(M))
          ,activate(IL)
          ,activate(M)
          ,activate(N))
    U134(tt(),IL,M,N) ->
      U135(isNat(activate(N))
          ,activate(IL)
          ,activate(M)
          ,activate(N))
    U135(tt(),IL,M,N) ->
      U136(isNatKind(activate(N))
          ,activate(IL)
          ,activate(M)
          ,activate(N))
    U136(tt(),IL,M,N) ->
      cons(activate(N)
          ,n__take(activate(M)
                  ,activate(IL)))
    U21(tt(),V1) ->
      U22(isNatKind(activate(V1))
         ,activate(V1))
    U22(tt(),V1) ->
      U23(isNat(activate(V1)))
    U23(tt()) -> tt()
    U31(tt(),V) ->
      U32(isNatIListKind(activate(V))
         ,activate(V))
    U32(tt(),V) ->
      U33(isNatList(activate(V)))
    U33(tt()) -> tt()
    U41(tt(),V1,V2) ->
      U42(isNatKind(activate(V1))
         ,activate(V1)
         ,activate(V2))
    U42(tt(),V1,V2) ->
      U43(isNatIListKind(activate(V2))
         ,activate(V1)
         ,activate(V2))
    U43(tt(),V1,V2) ->
      U44(isNatIListKind(activate(V2))
         ,activate(V1)
         ,activate(V2))
    U44(tt(),V1,V2) ->
      U45(isNat(activate(V1))
         ,activate(V2))
    U45(tt(),V2) ->
      U46(isNatIList(activate(V2)))
    U46(tt()) -> tt()
    U51(tt(),V2) ->
      U52(isNatIListKind(activate(V2)))
    U52(tt()) -> tt()
    U61(tt(),V2) ->
      U62(isNatIListKind(activate(V2)))
    U62(tt()) -> tt()
    U71(tt()) -> tt()
    U81(tt()) -> tt()
    U91(tt(),V1,V2) ->
      U92(isNatKind(activate(V1))
         ,activate(V1)
         ,activate(V2))
    U92(tt(),V1,V2) ->
      U93(isNatIListKind(activate(V2))
         ,activate(V1)
         ,activate(V2))
    U93(tt(),V1,V2) ->
      U94(isNatIListKind(activate(V2))
         ,activate(V1)
         ,activate(V2))
    U94(tt(),V1,V2) ->
      U95(isNat(activate(V1))
         ,activate(V2))
    U95(tt(),V2) ->
      U96(isNatList(activate(V2)))
    U96(tt()) -> tt()
    isNat(n__0()) -> tt()
    isNat(n__length(V1)) ->
      U11(isNatIListKind(activate(V1))
         ,activate(V1))
    isNat(n__s(V1)) ->
      U21(isNatKind(activate(V1))
         ,activate(V1))
    isNatIList(V) ->
      U31(isNatIListKind(activate(V))
         ,activate(V))
    isNatIList(n__zeros()) -> tt()
    isNatIList(n__cons(V1,V2)) ->
      U41(isNatKind(activate(V1))
         ,activate(V1)
         ,activate(V2))
    isNatIListKind(n__nil()) -> tt()
    isNatIListKind(n__zeros()) ->
      tt()
    isNatIListKind(n__cons(V1
                          ,V2)) ->
      U51(isNatKind(activate(V1))
         ,activate(V2))
    isNatIListKind(n__take(V1
                          ,V2)) ->
      U61(isNatKind(activate(V1))
         ,activate(V2))
    isNatKind(n__0()) -> tt()
    isNatKind(n__length(V1)) ->
      U71(isNatIListKind(activate(V1)))
    isNatKind(n__s(V1)) ->
      U81(isNatKind(activate(V1)))
    isNatList(n__nil()) -> tt()
    isNatList(n__cons(V1,V2)) ->
      U91(isNatKind(activate(V1))
         ,activate(V1)
         ,activate(V2))
    isNatList(n__take(V1,V2)) ->
      U101(isNatKind(activate(V1))
          ,activate(V1)
          ,activate(V2))
    length(nil()) -> 0()
    length(cons(N,L)) ->
      U111(isNatList(activate(L))
          ,activate(L)
          ,N)
    take(0(),IL) ->
      U121(isNatIList(IL),IL)
    take(s(M),cons(N,IL)) ->
      U131(isNatIList(activate(IL))
          ,activate(IL)
          ,M
          ,N)
    zeros() -> n__zeros()
    take(X1,X2) -> n__take(X1,X2)
    0() -> n__0()
    length(X) -> n__length(X)
    s(X) -> n__s(X)
    cons(X1,X2) -> n__cons(X1,X2)
    nil() -> n__nil()
    activate(n__zeros()) -> zeros()
    activate(n__take(X1,X2)) ->
      take(X1,X2)
    activate(n__0()) -> 0()
    activate(n__length(X)) ->
      length(X)
    activate(n__s(X)) -> s(X)
    activate(n__cons(X1,X2)) ->
      cons(X1,X2)
    activate(n__nil()) -> nil()
    activate(X) -> X)