⟨a, b | aabbbaaab=a⟩

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

Auxiliary generators:
1. c = aaa
Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²b³cb ⇒ cb³cbc	[12]
2.	c²bcb³cb ⇒ c²b⁴cbc	[16]
3.	(cb)³b²cb ⇒ cbcb⁴cbc	[15]
4.	cb(bc)²b³cb ⇒ cb²cb⁴cbc	[13]
5.	(cb³cb)² ⇒ c(b³cb)²c	[10]
6.	c²b⁴cbcb³cb ⇒ cbcb⁴cbcb³c	[18]
7.	cbcb⁴cbcb³cb ⇒ cb²cb⁴cbcb³c	[17]
8.	cb²cb⁴cbcb³cb ⇒ c(b³cb)²cb³c	[14]
9.	c(b³cb)²cb³cb ⇒ c	[11]
10.	a ⇒ c(b³cb)²	[9]

# ab:aabbbaaab=a bc/a aaa=c morph:3/0 ccbbbcb=cbbbcbc ccbcbbbcb=ccbbbbcbc cbcbcbbbcb=cbcbbbbcbc cbbcbcbbbcb=cbbcbbbbcbc cbbbcbcbbbcb=cbbbcbbbbcbc ccbbbbcbcbbbcb=cbcbbbbcbcbbbc cbcbbbbcbcbbbcb=cbbcbbbbcbcbbbc cbbcbbbbcbcbbbcb=cbbbcbbbbcbcbbbc cbbbcbbbbcbcbbbcb=c a=cbbbcbbbbcb

Up:	Monoids with two generators and one relation
Prev:	#1728 ⟨a, b \| aabbabbba=b⟩
Next:	#1730 ⟨a, b \| aabbbaaab=b⟩

#1729 ⟨a, b | aabbbaaab=a⟩

Quick links

Properties

Rewriting system