(STRATEGY
    INNERMOST)

(VAR
    L N V V1 V2 X X1 X2)
(DATATYPES
    A = µX.< n__zeros, tt, n__0, n__length(X), n__s(X), n__cons(X, X), n__nil >)
(SIGNATURES
    zeros :: [] -> A
    U11 :: [A x A] -> A
    U12 :: [A x A] -> A
    U13 :: [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] -> A
    U71 :: [A] -> A
    U81 :: [A x A x A] -> A
    U82 :: [A x A x A] -> A
    U83 :: [A x A x A] -> A
    U84 :: [A x A x A] -> A
    U85 :: [A x A] -> A
    U86 :: [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] -> A
    isNat :: [A] -> A
    isNatIList :: [A] -> A
    isNatIListKind :: [A] -> A
    isNatKind :: [A] -> A
    isNatList :: [A] -> A
    length :: [A] -> A
    0 :: [] -> A
    s :: [A] -> A
    cons :: [A x A] -> A
    nil :: [] -> A
    activate :: [A] -> A)
(RULES
    zeros() -> cons(0(),n__zeros())
    U11(tt(),V1) ->
      U12(isNatIListKind(activate(V1))
         ,activate(V1))
    U12(tt(),V1) ->
      U13(isNatList(activate(V1)))
    U13(tt()) -> tt()
    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()) -> tt()
    U71(tt()) -> tt()
    U81(tt(),V1,V2) ->
      U82(isNatKind(activate(V1))
         ,activate(V1)
         ,activate(V2))
    U82(tt(),V1,V2) ->
      U83(isNatIListKind(activate(V2))
         ,activate(V1)
         ,activate(V2))
    U83(tt(),V1,V2) ->
      U84(isNatIListKind(activate(V2))
         ,activate(V1)
         ,activate(V2))
    U84(tt(),V1,V2) ->
      U85(isNat(activate(V1))
         ,activate(V2))
    U85(tt(),V2) ->
      U86(isNatList(activate(V2)))
    U86(tt()) -> tt()
    U91(tt(),L,N) ->
      U92(isNatIListKind(activate(L))
         ,activate(L)
         ,activate(N))
    U92(tt(),L,N) ->
      U93(isNat(activate(N))
         ,activate(L)
         ,activate(N))
    U93(tt(),L,N) ->
      U94(isNatKind(activate(N))
         ,activate(L))
    U94(tt(),L) ->
      s(length(activate(L)))
    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))
    isNatKind(n__0()) -> tt()
    isNatKind(n__length(V1)) ->
      U61(isNatIListKind(activate(V1)))
    isNatKind(n__s(V1)) ->
      U71(isNatKind(activate(V1)))
    isNatList(n__nil()) -> tt()
    isNatList(n__cons(V1,V2)) ->
      U81(isNatKind(activate(V1))
         ,activate(V1)
         ,activate(V2))
    length(nil()) -> 0()
    length(cons(N,L)) ->
      U91(isNatList(activate(L))
         ,activate(L)
         ,N)
    zeros() -> n__zeros()
    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__0()) -> 0()
    activate(n__length(X)) ->
      length(activate(X))
    activate(n__s(X)) ->
      s(activate(X))
    activate(n__cons(X1,X2)) ->
      cons(activate(X1),X2)
    activate(n__nil()) -> nil()
    activate(X) -> X)