⟨a, b | aabaabba=ab⟩

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Monoids with two generators and one relation

#1954 ⟨a, b | aabaabba=aa⟩

#1956 ⟨a, b | aabaabba=ba⟩

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(c) = 0; deg(a) = deg(b) = 1, a < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ab² ⇒ c	[2]
2.	cb³ ⇒ cabac²	[8]
3.	a²bac² ⇒ cb	[4]
4.	cabaca ⇒ cb	[7]
5.	c(ba)²c² ⇒ cabac²b	[12]
6.	cb²aca ⇒ cabacb	[14]
7.	a²baca ⇒ ab	[3]
8.	a²bacb ⇒ (ca)²	[10]
9.	a(ba)²c² ⇒ cb²	[6]
10.	c(ba)²ca ⇒ cb²	[9]
11.	c(ba)²cb ⇒ cabac(ca)²	[15]
12.	cb(ba)²c² ⇒ cabac²b²	[16]
13.	a(ba)²ca ⇒ c	[5]
14.	a(ba)²cb ⇒ cbaca	[11]
15.	cb(ba)²ca ⇒ cabac²	[13]
16.	cb(ba)²cb ⇒ cabac²baca	[17]

# ab:aabaabba=ab c/ab abb=c morph:3/0 abb=c cbbb=cabacc aabacc=cb cabaca=cb cbabacc=cabaccb cbbaca=cabacb aabaca=ab aabacb=caca ababacc=cbb cbabaca=cbb cbabacb=cabaccaca cbbabacc=cabaccbb ababaca=c ababacb=cbaca cbbabaca=cabacc cbbabacb=cabaccbaca

#1955 ⟨a, b | aabaabba=ab⟩

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