⟨a, b | aabbbbbabba=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. aaa=c
2. bbbbbabb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[9]
2.	dc ⇒ 1	[11]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[10]
5.	a³ ⇒ c	[2]
6.	ab²cb ⇒ bab²c	[26]
7.	a²bab² ⇒ cb²cbd	[28]
8.	a(ab²)² ⇒ (cb²)²d	[30]
9.	cb⁵ ⇒ b³ab²a²	[16]
10.	db³ab² ⇒ b⁵da	[12]
11.	cab⁵ ⇒ ab³ab²a²	[17]
12.	dab³ab² ⇒ ab⁵da	[15]
13.	a²b⁵ ⇒ b²cb³da²	[37]
14.	a²b³ab² ⇒ cb²cb³d	[33]
15.	db⁴ab² ⇒ b⁵abd	[13]
16.	dab⁴ab² ⇒ ab⁵abd	[35]
17.	a²b⁴ab² ⇒ cb²cb⁴d	[38]
18.	b⁵ab² ⇒ d	[3]

# ab:aabbbbbabba=1 cda/b aaa=c,bbbbbabb=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c abbcb=babbc aababb=cbbcbd aabbabb=cbbcbbd cbbbbb=bbbabbaa dbbbabb=bbbbbda cabbbbb=abbbabbaa dabbbabb=abbbbbda aabbbbb=bbcbbbdaa aabbbabb=cbbcbbbd dbbbbabb=bbbbbabd dabbbbabb=abbbbbabd aabbbbabb=cbbcbbbbd bbbbbabb=d

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#3163 ⟨a, b | aabbbbbabba=1⟩

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Rewriting system