------------------------------------------------------------------------------
Expression:
"a"

Tree:
-[a   ]

Labelled graph:
[(0,"a",[])]

Simplified tree:
-[0:a ]

------------------------------------------------------------------------------
Expression:
("+" "a" "a")

Tree:
-[+   ]-+-[a   ]
        |
        `-[a   ]

Labelled graph:
[(0,"+",[2,2]),
 (2,"a",[])]

Simplified tree:
-[0:+ ]-+-[2:a ]
        |
        `-[2:<>]

------------------------------------------------------------------------------
Expression:
("+" ("*" "a" "b") ("*" "a" "b"))

Tree:
-[+   ]-+-[*   ]-+-[a   ]
        |        |
        |        `-[b   ]
        |
        `-[*   ]-+-[a   ]
                 |
                 `-[b   ]

Labelled graph:
[(0,"+",[4,4]),
 (4,"*",[5,6]),
 (5,"a",[]),
 (6,"b",[])]

Simplified tree:
-[0:+ ]-+-[4:* ]-+-[5:a ]
        |        |
        |        `-[6:b ]
        |
        `-[4:<>]

------------------------------------------------------------------------------
Expression:
("+" ("*" ("+" "a" "b") "c") ("+" "a" "b"))

Tree:
-[+   ]-+-[*   ]-+-[+   ]-+-[a   ]
        |        |        |
        |        |        `-[b   ]
        |        |
        |        `-[c   ]
        |
        `-[+   ]-+-[a   ]
                 |
                 `-[b   ]

Labelled graph:
[(0,"+",[1,6]),
 (1,"*",[6,5]),
 (5,"c",[]),
 (6,"+",[7,8]),
 (7,"a",[]),
 (8,"b",[])]

Simplified tree:
-[0:+ ]-+-[1:* ]-+-[6:+ ]-+-[7:a ]
        |        |        |
        |        |        `-[8:b ]
        |        |
        |        `-[5:c ]
        |
        `-[6:<>]

------------------------------------------------------------------------------
Expression:
("X" "0" ("+" "0" "a") ("+" ("+" "0" "a") "b") ("+" ("+" ("+" "0" "a") "b") "c") ("+" ("+" ("+" ("+" "0" "a") "b") "c") "d"))

Tree:
-[X   ]-+-[0   ]
        |
        +-[+   ]-+-[0   ]
        |        |
        |        `-[a   ]
        |
        +-[+   ]-+-[+   ]-+-[0   ]
        |        |        |
        |        |        `-[a   ]
        |        |
        |        `-[b   ]
        |
        +-[+   ]-+-[+   ]-+-[+   ]-+-[0   ]
        |        |        |        |
        |        |        |        `-[a   ]
        |        |        |
        |        |        `-[b   ]
        |        |
        |        `-[c   ]
        |
        `-[+   ]-+-[+   ]-+-[+   ]-+-[+   ]-+-[0   ]
                 |        |        |        |
                 |        |        |        `-[a   ]
                 |        |        |
                 |        |        `-[b   ]
                 |        |
                 |        `-[c   ]
                 |
                 `-[d   ]

Labelled graph:
[(0,"X",[21,20,19,18,17]),
 (17,"+",[18,25]),
 (18,"+",[19,24]),
 (19,"+",[20,23]),
 (20,"+",[21,22]),
 (21,"0",[]),
 (22,"a",[]),
 (23,"b",[]),
 (24,"c",[]),
 (25,"d",[])]

Simplified tree:
-[0:X ]-+-[21:0]
        |
        +-[20:+]-+-[21:<]
        |        |
        |        `-[22:a]
        |
        +-[19:+]-+-[20:<]
        |        |
        |        `-[23:b]
        |
        +-[18:+]-+-[19:<]
        |        |
        |        `-[24:c]
        |
        `-[17:+]-+-[18:<]
                 |
                 `-[25:d]

------------------------------------------------------------------------------
Expression:
("X" ("+" "a" ("+" "b" ("+" "c" ("+" "d" "0")))) ("+" "b" ("+" "c" ("+" "d" "0"))) ("+" "c" ("+" "d" "0")) ("+" "d" "0") "0")

Tree:
-[X   ]-+-[+   ]-+-[a   ]
        |        |
        |        `-[+   ]-+-[b   ]
        |                 |
        |                 `-[+   ]-+-[c   ]
        |                          |
        |                          `-[+   ]-+-[d   ]
        |                                   |
        |                                   `-[0   ]
        |
        +-[+   ]-+-[b   ]
        |        |
        |        `-[+   ]-+-[c   ]
        |                 |
        |                 `-[+   ]-+-[d   ]
        |                          |
        |                          `-[0   ]
        |
        +-[+   ]-+-[c   ]
        |        |
        |        `-[+   ]-+-[d   ]
        |                 |
        |                 `-[0   ]
        |
        +-[+   ]-+-[d   ]
        |        |
        |        `-[0   ]
        |
        `-[0   ]

Labelled graph:
[(0,"X",[1,10,17,22,25]),
 (1,"+",[2,10]),
 (2,"a",[]),
 (10,"+",[11,17]),
 (11,"b",[]),
 (17,"+",[18,22]),
 (18,"c",[]),
 (22,"+",[23,25]),
 (23,"d",[]),
 (25,"0",[])]

Simplified tree:
-[0:X ]-+-[1:+ ]-+-[2:a ]
        |        |
        |        `-[10:+]-+-[11:b]
        |                 |
        |                 `-[17:+]-+-[18:c]
        |                          |
        |                          `-[22:+]-+-[23:d]
        |                                   |
        |                                   `-[25:0]
        |
        +-[10:<]
        |
        +-[17:<]
        |
        +-[22:<]
        |
        `-[25:<]