#1125 ⟨a, b | ababba=baa⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- abab² ⋅ a = ba² and ba ⋅ a = ba², however abab² ≠ ba
Enveloping group: ⟨a, b | aabba^-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 = baa
Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	(ab)²c ⇒ ca	[5]
2.	abab²c ⇒ bac	[6]
3.	ba² ⇒ c	[2]
4.	(ba)²c ⇒ cbab²c	[9]
5.	baca ⇒ cbabc	[7]
6.	cbab²a ⇒ bac	[13]
7.	cbab³ac ⇒ bacbab²c	[14]
8.	cbab²ca ⇒ bacbabc	[12]
9.	c(babc)² ⇒ bac²a	[10]
10.	(cbab)²bc ⇒ (bac)²	[11]
11.	abab²a ⇒ c	[3]
12.	abab³ac ⇒ cbab²c	[8]

# ab:ababba=baa bc/a baa=c magic:0
ababc=ca
ababbc=bac
baa=c
babac=cbabbc
baca=cbabc
cbabba=bac
cbabbbac=bacbabbc
cbabbca=bacbabc
cbabcbabc=bacca
cbabcbabbc=bacbac
ababba=c
ababbbac=cbabbc