#437 ⟨a, b | aaabba=ab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 8
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a²b²a = ab and a ⋅ b = ab, however a²b²a ≠ b
Enveloping group: ⟨a, b | aabab^-1b^-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 ⇒ cacbc	[7]
3.	cacba ⇒ cb	[6]
4.	a²cbc ⇒ cb	[5]
5.	c(ac)²bc ⇒ (cb)²a	[11]
6.	ca(cb)² ⇒ cbacbc	[9]
7.	a²cba ⇒ c	[4]
8.	(cba)² ⇒ cacbc	[8]
9.	a(ac)²bc ⇒ c²ba	[10]
10.	cb(ac)²bc ⇒ cacbc²ba	[13]
11.	cba(cb)² ⇒ c(acbc)²	[12]

# ab:aaabba=ab reversed:c/ab ab=c magic:0
ab=c
cbb=cacbc
cacba=cb
aacbc=cb
cacacbc=cbcba
cacbcb=cbacbc
aacba=c
cbacba=cacbc
aacacbc=ccba
cbacacbc=cacbccba
cbacbcb=cacbcacbc