⟨a, b | ababbaab=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 = babbaa
Reduction order:
- Right-to-left recursive path with deg(c) = deg(b) = 0, c < b; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²b ⇒ c	[4]
2.	cab ⇒ cb²ac	[19]
3.	cac² ⇒ c³a	[11]
4.	cbac² ⇒ c²a	[18]
5.	cb²ac² ⇒ ca	[14]
6.	acb ⇒ a	[3]
7.	ca²b ⇒ cb²a²c	[24]
8.	cba²b ⇒ cbab²ac	[27]
9.	cb²a²b ⇒ bab²ac	[25]
10.	a²c² ⇒ ac²a	[15]
11.	abac² ⇒ aca	[17]
12.	bab²ac² ⇒ cb²a²	[7]
13.	ca³ ⇒ c⁵	[13]
14.	cba³ ⇒ c⁴	[23]
15.	cb²a³ ⇒ c³	[20]
16.	bab²a² ⇒ c	[2]
17.	a³b ⇒ a²b²ac	[16]
18.	aba²b ⇒ abab²ac	[26]
19.	a²b²ac² ⇒ a³	[8]
20.	a⁴ ⇒ ac⁴	[21]
21.	aba³ ⇒ ac³	[22]
22.	a²b²a² ⇒ ac²	[5]

# ab:ababbaab=a reversed:cb/a babbaa=c morph:6/1 ccb=c cab=cbbac cacc=ccca cbacc=cca cbbacc=ca acb=a caab=cbbaac cbaab=cbabbac cbbaab=babbac aacc=acca abacc=aca babbacc=cbbaa caaa=ccccc cbaaa=cccc cbbaaa=ccc babbaa=c aaab=aabbac abaab=ababbac aabbacc=aaa aaaa=acccc abaaa=accc aabbaa=acc

Up:	Monoids with two generators and one relation
Prev:	#850 ⟨a, b \| abababba=b⟩
Next:	#852 ⟨a, b \| ababbaab=b⟩

#851 ⟨a, b | ababbaab=a⟩

Quick links

Properties

Rewriting system