#953 ⟨a, b | aabbaba=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 ⋅ ab(ba)² = ab and a ⋅ b = ab, however ab(ba)² ≠ 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 = abb
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	acaba ⇒ ab	[3]
2.	acabc ⇒ cb	[4]
3.	c²aba ⇒ cb	[7]
4.	ab² ⇒ c	[2]
5.	abcaba ⇒ c	[5]
6.	cb² ⇒ (abc)²	[6]
7.	c(ba)² ⇒ ac²	[8]
8.	cbcaba ⇒ (abc)²	[10]
9.	c²abcb ⇒ cbcabc	[11]
10.	(abc)²b ⇒ c²abc	[9]
11.	cbabcb ⇒ ac³abc	[12]
12.	cbcabcb ⇒ ab(cabc)²	[13]

# ab:aabbaba=ab ac/b abb=c morph:3/0
acaba=ab
acabc=cb
ccaba=cb
abb=c
abcaba=c
cbb=abcabc
cbaba=acc
cbcaba=abcabc
ccabcb=cbcabc
abcabcb=ccabc
cbabcb=acccabc
cbcabcb=abcabccabc