test: More canonization tests

test_reg.py

 from lib.parsing.parser import Parser
+from lib.dfa import DFA
 
 def is_can(dfa: str) -> bool:
     parser = Parser()
-    return parser.str_to_dfa(dfa).is_canonical()
+    return parse(dfa).is_canonical()
     
+def parse(dfa: str) -> DFA:
+    parser = Parser()
+    return parser.str_to_dfa(dfa)
+
+def to_str(dfa: DFA) -> str:
+    parser = Parser()
+    return parser.dfa_to_str(dfa)
 
 def test_can() -> None:
-    assert is_can("init=1 (1,a)=1 (1,b)=2 (2,b)=1 (2,a)=1 final={2}")
+    ex1 = "init=1 (1,a)=1 (1,b)=2 (2,b)=1 (2,a)=1 final={2}"
+    assert is_can(ex1)
     assert is_can("init=1 (1,b)=3 (1,a)=2 (2,b)=1 (2,a)=1 (3,a)=2 (3,b)=2 final={2}")
     assert not is_can("init=1 (1,b)=3 (1,c)=2 (2,b)=1 (2,a)=1 (3,a)=2 (3,b)=2 final={2}")
     assert not is_can("init=1 (1,a)=1 (1,b)=2 (2,b)=1 (2,b)=1 (unreach,a)=1 (unreach,b)=unreach final={2}")
+
+    assert DFA.is_identical(parse(ex1).canonize(), parse(ex1))
+    auto_can = parse("init=x (x,a)=z (x,b)=y (y,a)=z (y,b)=z (z,a)=z (z,b)=z final={z}").canonize()
+    expect_can = parse("init=1 (1,a)=2 (1,b)=3 (2,a)=2 (2,b)=2 (3,a)=2 (3,b)=2 final={2}")
+    assert DFA.is_identical(auto_can, expect_can), f"{to_str(auto_can)} ≠ {to_str(expect_can)}"