(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), U11(X), U21(X), U31(X), U41(X, X), U42(X), isNatIList(X), U51(X, X), U52(X), isNatList(X), U61(X, X), U62(X), U71(X, X, X), U72(X, X), isNat(X), U81(X), U91(X, X, X, X), U92(X, X, X, X), U93(X, X, X, X) >)
(SIGNATURES
    a__zeros :: [] -> A
    a__U11 :: [A] -> A
    a__U21 :: [A] -> A
    a__U31 :: [A] -> A
    a__U41 :: [A x A] -> A
    a__U42 :: [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 x A x A] -> A
    a__U72 :: [A x A] -> A
    a__U81 :: [A] -> A
    a__U91 :: [A x A x A x A] -> A
    a__U92 :: [A x A x A x A] -> A
    a__U93 :: [A x A x A x A] -> A
    a__isNat :: [A] -> A
    a__isNatIList :: [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__U11(tt()) -> tt()
    a__U21(tt()) -> tt()
    a__U31(tt()) -> tt()
    a__U41(tt(),V2) ->
      a__U42(a__isNatIList(V2))
    a__U42(tt()) -> tt()
    a__U51(tt(),V2) ->
      a__U52(a__isNatList(V2))
    a__U52(tt()) -> tt()
    a__U61(tt(),V2) ->
      a__U62(a__isNatIList(V2))
    a__U62(tt()) -> tt()
    a__U71(tt(),L,N) ->
      a__U72(a__isNat(N),L)
    a__U72(tt(),L) ->
      s(a__length(mark(L)))
    a__U81(tt()) -> nil()
    a__U91(tt(),IL,M,N) ->
      a__U92(a__isNat(M),IL,M,N)
    a__U92(tt(),IL,M,N) ->
      a__U93(a__isNat(N),IL,M,N)
    a__U93(tt(),IL,M,N) ->
      cons(mark(N),take(M,IL))
    a__isNat(0()) -> tt()
    a__isNat(length(V1)) ->
      a__U11(a__isNatList(V1))
    a__isNat(s(V1)) ->
      a__U21(a__isNat(V1))
    a__isNatIList(V) ->
      a__U31(a__isNatList(V))
    a__isNatIList(zeros()) -> tt()
    a__isNatIList(cons(V1,V2)) ->
      a__U41(a__isNat(V1),V2)
    a__isNatList(nil()) -> tt()
    a__isNatList(cons(V1,V2)) ->
      a__U51(a__isNat(V1),V2)
    a__isNatList(take(V1,V2)) ->
      a__U61(a__isNat(V1),V2)
    a__length(nil()) -> 0()
    a__length(cons(N,L)) ->
      a__U71(a__isNatList(L),L,N)
    a__take(0(),IL) ->
      a__U81(a__isNatIList(IL))
    a__take(s(M),cons(N,IL)) ->
      a__U91(a__isNatIList(IL),IL,M,N)
    mark(zeros()) -> a__zeros()
    mark(U11(X)) -> a__U11(mark(X))
    mark(U21(X)) -> a__U21(mark(X))
    mark(U31(X)) -> a__U31(mark(X))
    mark(U41(X1,X2)) ->
      a__U41(mark(X1),X2)
    mark(U42(X)) -> a__U42(mark(X))
    mark(isNatIList(X)) ->
      a__isNatIList(X)
    mark(U51(X1,X2)) ->
      a__U51(mark(X1),X2)
    mark(U52(X)) -> a__U52(mark(X))
    mark(isNatList(X)) ->
      a__isNatList(X)
    mark(U61(X1,X2)) ->
      a__U61(mark(X1),X2)
    mark(U62(X)) -> a__U62(mark(X))
    mark(U71(X1,X2,X3)) ->
      a__U71(mark(X1),X2,X3)
    mark(U72(X1,X2)) ->
      a__U72(mark(X1),X2)
    mark(isNat(X)) -> a__isNat(X)
    mark(length(X)) ->
      a__length(mark(X))
    mark(U81(X)) -> a__U81(mark(X))
    mark(U91(X1,X2,X3,X4)) ->
      a__U91(mark(X1),X2,X3,X4)
    mark(U92(X1,X2,X3,X4)) ->
      a__U92(mark(X1),X2,X3,X4)
    mark(U93(X1,X2,X3,X4)) ->
      a__U93(mark(X1),X2,X3,X4)
    mark(take(X1,X2)) ->
      a__take(mark(X1),mark(X2))
    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__U11(X) -> U11(X)
    a__U21(X) -> U21(X)
    a__U31(X) -> U31(X)
    a__U41(X1,X2) -> U41(X1,X2)
    a__U42(X) -> U42(X)
    a__isNatIList(X) ->
      isNatIList(X)
    a__U51(X1,X2) -> U51(X1,X2)
    a__U52(X) -> U52(X)
    a__isNatList(X) -> isNatList(X)
    a__U61(X1,X2) -> U61(X1,X2)
    a__U62(X) -> U62(X)
    a__U71(X1,X2,X3) -> U71(X1
                           ,X2
                           ,X3)
    a__U72(X1,X2) -> U72(X1,X2)
    a__isNat(X) -> isNat(X)
    a__length(X) -> length(X)
    a__U81(X) -> U81(X)
    a__U91(X1,X2,X3,X4) -> U91(X1
                              ,X2
                              ,X3
                              ,X4)
    a__U92(X1,X2,X3,X4) -> U92(X1
                              ,X2
                              ,X3
                              ,X4)
    a__U93(X1,X2,X3,X4) -> U93(X1
                              ,X2
                              ,X3
                              ,X4)
    a__take(X1,X2) -> take(X1,X2))