algebraic-graphs-s4.out

max expr size  =    4
max  #-tests   = 1080
max  #-vars    =    2  (for inequational and conditional laws)

_ :: Bool  (holes: Bool)
_ :: Int  (holes: Int)
_ :: Nat3  (holes: Nat3)
_ :: Graph Nat3  (holes: Graph Nat3)
0 :: Nat3
0 :: Int
True :: Bool
empty :: Graph Nat3
vertex :: Nat3 -> Graph Nat3
(+) :: Graph Nat3 -> Graph Nat3 -> Graph Nat3
(*) :: Graph Nat3 -> Graph Nat3 -> Graph Nat3
overlay :: Graph Nat3 -> Graph Nat3 -> Graph Nat3
connect :: Graph Nat3 -> Graph Nat3 -> Graph Nat3
edge :: Nat3 -> Nat3 -> Graph Nat3
length :: Graph Nat3 -> Int
size :: Graph Nat3 -> Int

length (vertex i) == length (vertex j)
  size (vertex i) == length (vertex 0)
length (edge i j) == length (edge k i')
length (edge i j) == size (edge k i')
   length (x * y) == length (x + y)
     size (x * y) == size (x + y)
            x + x == x
        x + empty == x
        x * empty == x
        empty * x == x
            x + y == y + x
      overlay x y == x + y
      connect x y == x * y

                0 <= length x
                0 <= size x
         length x <= size x
       size empty <= size x
         length x <= length (x + y)
           size x <= size (x + y)
         length x <= size (y + x)
length (edge i i) <= size x
            empty <= x
                x <= x + y
                x <= x * y
                x <= y * x
         vertex i <= edge i j
         vertex i <= edge j i
            x + y <= x * y