(STRATEGY
    INNERMOST)

(VAR
    @l @l1 @l2 @l3 @x @xs @y @ys @z
    @zs)
(DATATYPES
    A = µX.< ::(X, X), nil, tuple#3(X, X, X) >)
(SIGNATURES
    group3 :: [A] -> A
    group3#1 :: [A] -> A
    group3#2 :: [A x A] -> A
    group3#3 :: [A x A x A] -> A
    zip3 :: [A x A x A] -> A
    zip3#1 :: [A x A x A] -> A
    zip3#2 :: [A x A x A x A] -> A
    zip3#3 :: [A x A x A x A x A] -> A)
(RULES
    group3(@l) -> group3#1(@l)
    group3#1(::(@x,@xs)) ->
      group3#2(@xs,@x)
    group3#1(nil()) -> nil()
    group3#2(::(@y,@ys),@x) ->
      group3#3(@ys,@x,@y)
    group3#2(nil(),@x) -> nil()
    group3#3(::(@z,@zs),@x,@y) ->
      ::(tuple#3(@x,@y,@z)
        ,group3(@zs))
    group3#3(nil(),@x,@y) -> nil()
    zip3(@l1,@l2,@l3) -> zip3#1(@l1
                               ,@l2
                               ,@l3)
    zip3#1(::(@x,@xs),@l2,@l3) ->
      zip3#2(@l2,@l3,@x,@xs)
    zip3#1(nil(),@l2,@l3) -> nil()
    zip3#2(::(@y,@ys),@l3,@x,@xs) ->
      zip3#3(@l3,@x,@xs,@y,@ys)
    zip3#2(nil(),@l3,@x,@xs) ->
      nil()
    zip3#3(::(@z,@zs)
          ,@x
          ,@xs
          ,@y
          ,@ys) -> ::(tuple#3(@x,@y,@z)
                     ,zip3(@xs,@ys,@zs))
    zip3#3(nil(),@x,@xs,@y,@ys) ->
      nil())