(STRATEGY
    INNERMOST)

(VAR
    N X X1 X2 X3 X4 XS Y YS ZS)
(DATATYPES
    A = µX.< tt, pair(X, X), cons(X, X), natsFrom(X), s(X), 0, nil, U11(X, X, X), U12(X, X, X), snd(X), splitAt(X, X), U21(X, X), U22(X, X), U31(X, X), U32(X, X), U41(X, X, X), U42(X, X, X), head(X), afterNth(X, X), U51(X, X), U52(X, X), U61(X, X, X, X), U62(X, X, X, X), U63(X, X, X, X), U64(X, X), U71(X, X), U72(X, X), U81(X, X, X), U82(X, X, X), fst(X), sel(X, X), tail(X), take(X, X) >)
(SIGNATURES
    a__U11 :: [A x A x A] -> A
    a__U12 :: [A x A x A] -> A
    a__U21 :: [A x A] -> A
    a__U22 :: [A x A] -> A
    a__U31 :: [A x A] -> A
    a__U32 :: [A x A] -> A
    a__U41 :: [A x A x A] -> A
    a__U42 :: [A x A x A] -> A
    a__U51 :: [A x A] -> A
    a__U52 :: [A x A] -> A
    a__U61 :: [A x A x A x A] -> A
    a__U62 :: [A x A x A x A] -> A
    a__U63 :: [A x A x A x A] -> A
    a__U64 :: [A x A] -> A
    a__U71 :: [A x A] -> A
    a__U72 :: [A x A] -> A
    a__U81 :: [A x A x A] -> A
    a__U82 :: [A x A x A] -> A
    a__afterNth :: [A x A] -> A
    a__fst :: [A] -> A
    a__head :: [A] -> A
    a__natsFrom :: [A] -> A
    a__sel :: [A x A] -> A
    a__snd :: [A] -> A
    a__splitAt :: [A x A] -> A
    a__tail :: [A] -> A
    a__take :: [A x A] -> A
    mark :: [A] -> A)
(RULES
    a__U11(tt(),N,XS) -> a__U12(tt()
                               ,N
                               ,XS)
    a__U12(tt(),N,XS) ->
      a__snd(a__splitAt(mark(N)
                       ,mark(XS)))
    a__U21(tt(),X) -> a__U22(tt(),X)
    a__U22(tt(),X) -> mark(X)
    a__U31(tt(),N) -> a__U32(tt(),N)
    a__U32(tt(),N) -> mark(N)
    a__U41(tt(),N,XS) -> a__U42(tt()
                               ,N
                               ,XS)
    a__U42(tt(),N,XS) ->
      a__head(a__afterNth(mark(N)
                         ,mark(XS)))
    a__U51(tt(),Y) -> a__U52(tt(),Y)
    a__U52(tt(),Y) -> mark(Y)
    a__U61(tt(),N,X,XS) ->
      a__U62(tt(),N,X,XS)
    a__U62(tt(),N,X,XS) ->
      a__U63(tt(),N,X,XS)
    a__U63(tt(),N,X,XS) ->
      a__U64(a__splitAt(mark(N)
                       ,mark(XS))
            ,X)
    a__U64(pair(YS,ZS),X) ->
      pair(cons(mark(X),YS),mark(ZS))
    a__U71(tt(),XS) -> a__U72(tt()
                             ,XS)
    a__U72(tt(),XS) -> mark(XS)
    a__U81(tt(),N,XS) -> a__U82(tt()
                               ,N
                               ,XS)
    a__U82(tt(),N,XS) ->
      a__fst(a__splitAt(mark(N)
                       ,mark(XS)))
    a__afterNth(N,XS) -> a__U11(tt()
                               ,N
                               ,XS)
    a__fst(pair(X,Y)) -> a__U21(tt()
                               ,X)
    a__head(cons(N,XS)) ->
      a__U31(tt(),N)
    a__natsFrom(N) -> cons(mark(N)
                          ,natsFrom(s(N)))
    a__sel(N,XS) -> a__U41(tt()
                          ,N
                          ,XS)
    a__snd(pair(X,Y)) -> a__U51(tt()
                               ,Y)
    a__splitAt(0(),XS) -> pair(nil()
                              ,mark(XS))
    a__splitAt(s(N),cons(X,XS)) ->
      a__U61(tt(),N,X,XS)
    a__tail(cons(N,XS)) ->
      a__U71(tt(),XS)
    a__take(N,XS) -> a__U81(tt()
                           ,N
                           ,XS)
    mark(U11(X1,X2,X3)) ->
      a__U11(mark(X1),X2,X3)
    mark(U12(X1,X2,X3)) ->
      a__U12(mark(X1),X2,X3)
    mark(snd(X)) -> a__snd(mark(X))
    mark(splitAt(X1,X2)) ->
      a__splitAt(mark(X1),mark(X2))
    mark(U21(X1,X2)) ->
      a__U21(mark(X1),X2)
    mark(U22(X1,X2)) ->
      a__U22(mark(X1),X2)
    mark(U31(X1,X2)) ->
      a__U31(mark(X1),X2)
    mark(U32(X1,X2)) ->
      a__U32(mark(X1),X2)
    mark(U41(X1,X2,X3)) ->
      a__U41(mark(X1),X2,X3)
    mark(U42(X1,X2,X3)) ->
      a__U42(mark(X1),X2,X3)
    mark(head(X)) ->
      a__head(mark(X))
    mark(afterNth(X1,X2)) ->
      a__afterNth(mark(X1),mark(X2))
    mark(U51(X1,X2)) ->
      a__U51(mark(X1),X2)
    mark(U52(X1,X2)) ->
      a__U52(mark(X1),X2)
    mark(U61(X1,X2,X3,X4)) ->
      a__U61(mark(X1),X2,X3,X4)
    mark(U62(X1,X2,X3,X4)) ->
      a__U62(mark(X1),X2,X3,X4)
    mark(U63(X1,X2,X3,X4)) ->
      a__U63(mark(X1),X2,X3,X4)
    mark(U64(X1,X2)) ->
      a__U64(mark(X1),X2)
    mark(U71(X1,X2)) ->
      a__U71(mark(X1),X2)
    mark(U72(X1,X2)) ->
      a__U72(mark(X1),X2)
    mark(U81(X1,X2,X3)) ->
      a__U81(mark(X1),X2,X3)
    mark(U82(X1,X2,X3)) ->
      a__U82(mark(X1),X2,X3)
    mark(fst(X)) -> a__fst(mark(X))
    mark(natsFrom(X)) ->
      a__natsFrom(mark(X))
    mark(sel(X1,X2)) ->
      a__sel(mark(X1),mark(X2))
    mark(tail(X)) ->
      a__tail(mark(X))
    mark(take(X1,X2)) ->
      a__take(mark(X1),mark(X2))
    mark(tt()) -> tt()
    mark(pair(X1,X2)) ->
      pair(mark(X1),mark(X2))
    mark(cons(X1,X2)) ->
      cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    mark(0()) -> 0()
    mark(nil()) -> nil()
    a__U11(X1,X2,X3) -> U11(X1
                           ,X2
                           ,X3)
    a__U12(X1,X2,X3) -> U12(X1
                           ,X2
                           ,X3)
    a__snd(X) -> snd(X)
    a__splitAt(X1,X2) -> splitAt(X1
                                ,X2)
    a__U21(X1,X2) -> U21(X1,X2)
    a__U22(X1,X2) -> U22(X1,X2)
    a__U31(X1,X2) -> U31(X1,X2)
    a__U32(X1,X2) -> U32(X1,X2)
    a__U41(X1,X2,X3) -> U41(X1
                           ,X2
                           ,X3)
    a__U42(X1,X2,X3) -> U42(X1
                           ,X2
                           ,X3)
    a__head(X) -> head(X)
    a__afterNth(X1,X2) ->
      afterNth(X1,X2)
    a__U51(X1,X2) -> U51(X1,X2)
    a__U52(X1,X2) -> U52(X1,X2)
    a__U61(X1,X2,X3,X4) -> U61(X1
                              ,X2
                              ,X3
                              ,X4)
    a__U62(X1,X2,X3,X4) -> U62(X1
                              ,X2
                              ,X3
                              ,X4)
    a__U63(X1,X2,X3,X4) -> U63(X1
                              ,X2
                              ,X3
                              ,X4)
    a__U64(X1,X2) -> U64(X1,X2)
    a__U71(X1,X2) -> U71(X1,X2)
    a__U72(X1,X2) -> U72(X1,X2)
    a__U81(X1,X2,X3) -> U81(X1
                           ,X2
                           ,X3)
    a__U82(X1,X2,X3) -> U82(X1
                           ,X2
                           ,X3)
    a__fst(X) -> fst(X)
    a__natsFrom(X) -> natsFrom(X)
    a__sel(X1,X2) -> sel(X1,X2)
    a__tail(X) -> tail(X)
    a__take(X1,X2) -> take(X1,X2))