⟨a, b | aaabbbbbaba=1⟩

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Monoids with two generators and one relation

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(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaaa=c
2. bbbbbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[16]
2.	dc ⇒ 1	[19]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[20]
5.	a⁴ ⇒ c	[2]
6.	abcb ⇒ babc	[30]
7.	a³bab ⇒ (cb)²d	[32]
8.	a³b²ab ⇒ cbcb²d	[34]
9.	a³b³ab ⇒ cbcb³d	[36]
10.	cb⁵ ⇒ b⁴aba³	[24]
11.	db⁴ab ⇒ b⁵da	[21]
12.	cab⁵ ⇒ ab⁴aba³	[25]
13.	dab⁴ab ⇒ ab⁵da	[23]
14.	ca²b⁵ ⇒ a²b⁴aba³	[39]
15.	da²b⁴ab ⇒ a²b⁵da	[38]
16.	a³b⁵ ⇒ bcb⁴da³	[42]
17.	a³b⁴ab ⇒ cbcb⁴d	[40]
18.	b⁵ab ⇒ d	[3]

# ab:aaabbbbbaba=1 cda/b aaaa=c,bbbbbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaa=c abcb=babc aaabab=cbcbd aaabbab=cbcbbd aaabbbab=cbcbbbd cbbbbb=bbbbabaaa dbbbbab=bbbbbda cabbbbb=abbbbabaaa dabbbbab=abbbbbda caabbbbb=aabbbbabaaa daabbbbab=aabbbbbda aaabbbbb=bcbbbbdaaa aaabbbbab=cbcbbbbd bbbbbab=d

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