⟨a, b | aaabbbbaba=1⟩

Up:

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. bbbbab=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	[28]
7.	a³bab ⇒ (cb)²d	[30]
8.	a³b²ab ⇒ cbcb²d	[32]
9.	cb⁴ ⇒ b³aba³	[24]
10.	db³ab ⇒ b⁴da	[21]
11.	cab⁴ ⇒ ab³aba³	[25]
12.	dab³ab ⇒ ab⁴da	[23]
13.	ca²b⁴ ⇒ a²b³aba³	[35]
14.	da²b³ab ⇒ a²b⁴da	[34]
15.	a³b⁴ ⇒ bcb³da³	[38]
16.	a³b³ab ⇒ cbcb³d	[36]
17.	b⁴ab ⇒ d	[3]

# ab:aaabbbbaba=1 cda/b aaaa=c,bbbbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaa=c abcb=babc aaabab=cbcbd aaabbab=cbcbbd cbbbb=bbbabaaa dbbbab=bbbbda cabbbb=abbbabaaa dabbbab=abbbbda caabbbb=aabbbabaaa daabbbab=aabbbbda aaabbbb=bcbbbdaaa aaabbbab=cbcbbbd bbbbab=d

Up:	Monoids with two generators and one relation
Prev:	#1385 ⟨a, b \| aaabbbbaab=1⟩
Next:	#1387 ⟨a, b \| aaabbbbabb=1⟩

#1386 ⟨a, b | aaabbbbaba=1⟩

Quick links

Properties

Rewriting system