⟨a, b | abaaaabbba=1⟩

Up:

Monoids with two generators and one relation

Complete rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = deg(b) = 0, c < d < b; deg(a) = 1
Auxiliary generator: bbb=c
Auxiliary generator: aabaaaa=d

cd ⇒ 1
dc ⇒ 1
bc ⇒ cb
bd ⇒ db
b³ ⇒ c
ca²ba ⇒ aca²b
daca² ⇒ a²badb²
cba²ba ⇒ baca²b
dbaca² ⇒ ba²badb²
cb²a²ba ⇒ b²aca²b
db²aca² ⇒ b²a²badb²
da²ca² ⇒ a²ba²db²
ba⁴ ⇒ a²ca²db
dba²ca² ⇒ (ba²)²db²
b²a²ca² ⇒ ca⁴b²
b(ba²)² ⇒ a⁴c
da³ca² ⇒ a²ba³db²
dba³ca² ⇒ ba²ba³db²
b²a³ca² ⇒ ca⁴cadb²
a⁴ca² ⇒ db²

# ab:abaaaabbba=1 cdb/a bbb=c,aabaaaa=d magic:1 cd=1 dc=1 bc=cb bd=db bbb=c caaba=acaab dacaa=aabadbb cbaaba=bacaab dbacaa=baabadbb cbbaaba=bbacaab dbbacaa=bbaabadbb daacaa=aabaadbb baaaa=aacaadb dbaacaa=baabaadbb bbaacaa=caaaabb bbaabaa=aaaac daaacaa=aabaaadbb dbaaacaa=baabaaadbb bbaaacaa=caaaacadbb aaaacaa=dbb

Up:	Monoids with two generators and one relation
Prev:	#1481 ⟨a, b \| abaaaabbab=1⟩
Next:	#1487 ⟨a, b \| abaaabbaab=1⟩

#1482 ⟨a, b | abaaaabbba=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)