#1986 ⟨a, b | aabbaaba=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 ⋅ ab²a²ba = ab and a ⋅ b = ab, however ab²a²ba ≠ b
Enveloping group: ⟨a, b | aabab^-1abb⟩

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.	aca²ba ⇒ ab	[3]
2.	aca²bc ⇒ cb	[4]
3.	c²a²ba ⇒ cb	[7]
4.	ab² ⇒ c	[2]
5.	abca²ba ⇒ c	[5]
6.	cb² ⇒ abca²bc	[6]
7.	cba²ba ⇒ (ac)²	[8]
8.	cbca²ba ⇒ abca²bc	[10]
9.	c²a²bcb ⇒ cbca²bc	[11]
10.	abca²bcb ⇒ c²a²bc	[9]
11.	cba²bcb ⇒ acac²a²bc	[12]
12.	cbca²bcb ⇒ ab(ca²bc)²	[13]

# ab:aabbaaba=ab ac/b abb=c morph:3/0
acaaba=ab
acaabc=cb
ccaaba=cb
abb=c
abcaaba=c
cbb=abcaabc
cbaaba=acac
cbcaaba=abcaabc
ccaabcb=cbcaabc
abcaabcb=ccaabc
cbaabcb=acaccaabc
cbcaabcb=abcaabccaabc