== API ==
-- functions --
Empty, None :: RE Symbol
Star :: RE Symbol -> RE Symbol
(:+), (:.) :: RE Symbol -> RE Symbol -> RE Symbol

-- variables --
r1, r2, r3 :: RE Symbol

-- the following types are using non-standard equality --
RE Symbol

== Testing ==
Depth 1: 6 terms, 22 tests, 81 evaluations, 6 classes, 0 raw equations.
Depth 2: 61 terms, 1000 tests, 28370 evaluations, 24 classes, 37 raw equations.
Depth 3: 1087 terms, 2000 tests, 543254 evaluations, 532 classes, 555 raw equations.
555 raw equations; 532 terms in universe.

== Equations about Star ==
  1: Star Empty == Empty
  2: Star None == Empty
  3: Star (Star r1) == Star r1

== Equations about (:+) ==
  4: r1:+r2 == r2:+r1
  5: r1:+r1 == r1
  6: r1:+None == r1
  7: r1:+(r2:+r3) == r2:+(r1:+r3)

== Equations about (:.) ==
  8: r1:.Empty == r1
  9: r1:.None == None
 10: Empty:.r1 == r1
 11: None:.r1 == None
 12: (r1:.r2):.r3 == r1:.(r2:.r3)

== Equations about several functions ==
 13: r1:+Star r1 == Star r1
 14: Star r1:.r1 == r1:.Star r1
 15: (r1:.r2):+(r1:.r3) == r1:.(r2:+r3)
 16: (r1:.r2):+(r3:.r2) == (r1:+r3):.r2
 17: Star (r1:+Empty) == Star r1
 18: Star r1:+(r1:.r1) == Star r1
 19: Star r1:.Star r1 == Star r1
 20: (r1:.r1):.Star r1 == Star r1:.(r1:.r1)
 21: Star r1:.(r1:+Empty) == Star r1
 22: (r1:+Empty):.(r1:+Empty) == (r1:.r1):+(r1:+Empty)