#1902 ⟨a, b | aaababba=ab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a²bab²a = ab and a ⋅ b = ab, however a²bab²a ≠ b
Enveloping group: ⟨a, b | aababbab^-1⟩

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 = ab
Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(a) = deg(b) = 1, a < b
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ab ⇒ c	[2]
2.	cb² ⇒ cac²bc	[7]
3.	cac²ba ⇒ cb	[6]
4.	a²c²bc ⇒ cb	[5]
5.	c(ac²)²bc ⇒ cbc²ba	[11]
6.	cac(cb)² ⇒ cbac²bc	[9]
7.	a²c²ba ⇒ c	[4]
8.	cbac²ba ⇒ cac²bc	[8]
9.	a(ac²)²bc ⇒ c³ba	[10]
10.	cb(ac²)²bc ⇒ cac²bc³ba	[13]
11.	cbac(cb)² ⇒ c(ac²bc)²	[12]

# ab:aaababba=ab reversed:c/ab ab=c magic:0
ab=c
cbb=caccbc
caccba=cb
aaccbc=cb
caccaccbc=cbccba
caccbcb=cbaccbc
aaccba=c
cbaccba=caccbc
aaccaccbc=cccba
cbaccaccbc=caccbcccba
cbaccbcb=caccbcaccbc