⟨a, b | aabba=ab⟩

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Monoids with two generators and one relation

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 = bbbabba
Reduction order:
- Right-to-left recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	cbc ⇒ c²b	[10]
2.	cb²c ⇒ c²b²	[11]
3.	cb⁴ ⇒ c²	[9]
4.	cb³c ⇒ c²b³	[12]
5.	cac ⇒ cb³ab	[27]
6.	cbac ⇒ c²ab	[23]
7.	b³ac ⇒ cb²ab	[29]
8.	cb²ac ⇒ c²bab	[26]
9.	abc ⇒ acb	[13]
10.	cab³ ⇒ cb³a	[19]
11.	cbab³ ⇒ c²a	[20]
12.	b³ab³ ⇒ cb²a	[17]
13.	cb²ab³ ⇒ c²ba	[21]
14.	ab²c ⇒ acb²	[14]
15.	ab⁴ ⇒ ac	[8]
16.	ab³c ⇒ acb³	[15]
17.	cab²a ⇒ cb	[4]
18.	cbab²a ⇒ cb²	[5]
19.	b(b²a)² ⇒ c	[2]
20.	c(b²a)² ⇒ cb³	[6]
21.	a²c ⇒ ab³ab	[28]
22.	abac ⇒ acab	[24]
23.	ab²ac ⇒ acbab	[25]
24.	a²b³ ⇒ ab³a	[16]
25.	abab³ ⇒ aca	[18]
26.	ab²ab³ ⇒ acba	[22]
27.	a²b²a ⇒ ab	[1]
28.	abab²a ⇒ ab²	[3]
29.	a(b²a)² ⇒ ab³	[7]

# ab:aabba=ab reversed:bc/a bbbabba=c morph:7/0 cbc=ccb cbbc=ccbb cbbbb=cc cbbbc=ccbbb cac=cbbbab cbac=ccab bbbac=cbbab cbbac=ccbab abc=acb cabbb=cbbba cbabbb=cca bbbabbb=cbba cbbabbb=ccba abbc=acbb abbbb=ac abbbc=acbbb cabba=cb cbabba=cbb bbbabba=c cbbabba=cbbb aac=abbbab abac=acab abbac=acbab aabbb=abbba ababbb=aca abbabbb=acba aabba=ab ababba=abb abbabba=abbb

Up:	Monoids with two generators and one relation
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Next:	#221 ⟨a, b \| aabba=ba⟩

#220 ⟨a, b | aabba=ab⟩

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