(STRATEGY
    INNERMOST)

(VAR
    u v x y z)
(DATATYPES
    A = µX.< 0, true, s(X), false, quotZeroErro >)
(SIGNATURES
    le :: [A x A] -> A
    quot :: [A x A] -> A
    quotIter :: [A x A x A x A x A] -> A
    if :: [A x A x A x A x A x A] -> A
    if2 :: [A x A x A x A x A x A] -> A)
(RULES
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    quot(x,0()) -> quotZeroErro()
    quot(x,s(y)) -> quotIter(x
                            ,s(y)
                            ,0()
                            ,0()
                            ,0())
    quotIter(x,s(y),z,u,v) ->
      if(le(x,z),x,s(y),z,u,v)
    if(true(),x,y,z,u,v) -> v
    if(false(),x,y,z,u,v) ->
      if2(le(y,s(u)),x,y,s(z),s(u),v)
    if2(false(),x,y,z,u,v) ->
      quotIter(x,y,z,u,v)
    if2(true(),x,y,z,u,v) ->
      quotIter(x,y,z,0(),s(v)))