#964 ⟨a, b | aabbbba=ab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ab⁴a = ab and a ⋅ b = ab, however ab⁴a ≠ b
Enveloping group: ⟨a, b | aaaaabb⟩

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

Auxiliary generators:
1. c = babbbba
Reduction order:
- Right-to-left 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.	cb² ⇒ c²	[8]
2.	cbc ⇒ c²b	[9]
3.	ab² ⇒ ac	[4]
4.	abc ⇒ acb	[7]
5.	bac²b ⇒ c³a	[16]
6.	cac²b ⇒ c³ba	[11]
7.	bac³ ⇒ c³ab	[19]
8.	cac³ ⇒ c³bab	[12]
9.	bac²a ⇒ c	[14]
10.	cac²a ⇒ cb	[10]
11.	a²c²b ⇒ ac²ba	[18]
12.	a²c³ ⇒ ac²bab	[20]
13.	a²c²a ⇒ ab	[13]

# ab:aabbbba=ab reversed:bc/a babbbba=c morph:7/0
cbb=cc
cbc=ccb
abb=ac
abc=acb
baccb=ccca
caccb=cccba
baccc=cccab
caccc=cccbab
bacca=c
cacca=cb
aaccb=accba
aaccc=accbab
aacca=ab