#3482 ⟨a, b | aaabbaaaab=a⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

Rewriting system

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) = 0; deg(b) = deg(a) = 1, b < a
Auxiliary generators:
1. aaaab=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c³bcb ⇒ (cbc)²	[9]
2.	acbc ⇒ cbca	[5]
3.	a² ⇒ cbc	[4]
4.	(cbc)²b ⇒ c	[6]
5.	c³bcab ⇒ cbc²bac	[15]
6.	ac(cb)² ⇒ abc²bc	[13]
7.	c²ab²c ⇒ cbc²ba	[10]
8.	(cbc)²ab ⇒ ac	[8]
9.	cbcab²c ⇒ a	[7]
10.	abc(cb)² ⇒ a	[11]
11.	ac²bcab ⇒ abc²bac	[17]
12.	acab²c ⇒ abc²ba	[14]
13.	abc²bcab ⇒ cbcab²ac	[16]
14.	abcab²c ⇒ cbcab²a	[12]

# ab:aaabbaaaab=a c/ba aaaab=c morph:5/0
cccbcb=cbccbc
acbc=cbca
aa=cbc
cbccbcb=c
cccbcab=cbccbac
accbcb=abccbc
ccabbc=cbccba
cbccbcab=ac
cbcabbc=a
abccbcb=a
accbcab=abccbac
acabbc=abccba
abccbcab=cbcabbac
abcabbc=cbcabba