(STRATEGY
    INNERMOST)

(VAR
    @acc @l @l1 @l2 @line @ls @m @m1
    @m2 @n @x @xs @y @ys)
(DATATYPES
    A = µX.< ::(X, X), nil, #0, #neg(X), #s(X), #pos(X) >)
(SIGNATURES
    * :: [A x A] -> A
    + :: [A x A] -> A
    computeLine :: [A x A x A] -> A
    computeLine#1 :: [A x A x A] -> A
    computeLine#2 :: [A x A x A x A] -> A
    lineMult :: [A x A x A] -> A
    lineMult#1 :: [A x A x A] -> A
    lineMult#2 :: [A x A x A x A] -> A
    matrixMult :: [A x A] -> A
    matrixMult#1 :: [A x A] -> A
    #add :: [A x A] -> A
    #mult :: [A x A] -> A
    #natmult :: [A x A] -> A
    #pred :: [A] -> A
    #succ :: [A] -> A)
(RULES
    *(@x,@y) -> #mult(@x,@y)
    +(@x,@y) -> #add(@x,@y)
    computeLine(@line,@m,@acc) ->
      computeLine#1(@line,@acc,@m)
    computeLine#1(::(@x,@xs)
                 ,@acc
                 ,@m) -> computeLine#2(@m
                                      ,@acc
                                      ,@x
                                      ,@xs)
    computeLine#1(nil(),@acc,@m) ->
      @acc
    computeLine#2(::(@l,@ls)
                 ,@acc
                 ,@x
                 ,@xs) -> computeLine(@xs
                                     ,@ls
                                     ,lineMult(@x,@l,@acc))
    computeLine#2(nil()
                 ,@acc
                 ,@x
                 ,@xs) -> nil()
    lineMult(@n,@l1,@l2) ->
      lineMult#1(@l1,@l2,@n)
    lineMult#1(::(@x,@xs),@l2,@n) ->
      lineMult#2(@l2,@n,@x,@xs)
    lineMult#1(nil(),@l2,@n) ->
      nil()
    lineMult#2(::(@y,@ys)
              ,@n
              ,@x
              ,@xs) -> ::(+(*(@x,@n),@y)
                         ,lineMult(@n,@xs,@ys))
    lineMult#2(nil(),@n,@x,@xs) ->
      ::(*(@x,@n)
        ,lineMult(@n,@xs,nil()))
    matrixMult(@m1,@m2) ->
      matrixMult#1(@m1,@m2)
    matrixMult#1(::(@l,@ls),@m2) ->
      ::(computeLine(@l,@m2,nil())
        ,matrixMult(@ls,@m2))
    matrixMult#1(nil(),@m2) -> nil()
    #add(#0(),@y) ->= @y
    #add(#neg(#s(#0())),@y) ->=
      #pred(@y)
    #add(#neg(#s(#s(@x))),@y) ->=
      #pred(#add(#pos(#s(@x)),@y))
    #add(#pos(#s(#0())),@y) ->=
      #succ(@y)
    #add(#pos(#s(#s(@x))),@y) ->=
      #succ(#add(#pos(#s(@x)),@y))
    #mult(#0(),#0()) ->= #0()
    #mult(#0(),#neg(@y)) ->= #0()
    #mult(#0(),#pos(@y)) ->= #0()
    #mult(#neg(@x),#0()) ->= #0()
    #mult(#neg(@x),#neg(@y)) ->=
      #pos(#natmult(@x,@y))
    #mult(#neg(@x),#pos(@y)) ->=
      #neg(#natmult(@x,@y))
    #mult(#pos(@x),#0()) ->= #0()
    #mult(#pos(@x),#neg(@y)) ->=
      #neg(#natmult(@x,@y))
    #mult(#pos(@x),#pos(@y)) ->=
      #pos(#natmult(@x,@y))
    #natmult(#0(),@y) ->= #0()
    #natmult(#s(@x),@y) ->=
      #add(#pos(@y),#natmult(@x,@y))
    #pred(#0()) ->= #neg(#s(#0()))
    #pred(#neg(#s(@x))) ->=
      #neg(#s(#s(@x)))
    #pred(#pos(#s(#0()))) ->= #0()
    #pred(#pos(#s(#s(@x)))) ->=
      #pos(#s(@x))
    #succ(#0()) ->= #pos(#s(#0()))
    #succ(#neg(#s(#0()))) ->= #0()
    #succ(#neg(#s(#s(@x)))) ->=
      #neg(#s(@x))
    #succ(#pos(#s(@x))) ->=
      #pos(#s(#s(@x))))