⟨a, b | aabbba=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 = bbabbba
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	[13]
2.	cb³ ⇒ c²	[8]
3.	cb²c ⇒ c²b²	[14]
4.	cacb ⇒ c²ba	[21]
5.	b²acb ⇒ c²a	[24]
6.	cbacb ⇒ c²b²a	[28]
7.	abc ⇒ acb	[22]
8.	cac² ⇒ c²bab²	[26]
9.	b²ac² ⇒ c²ab²	[27]
10.	cbac² ⇒ c²b²ab²	[31]
11.	ab³ ⇒ ac	[15]
12.	ab²c ⇒ acb²	[23]
13.	(ca)² ⇒ cb	[19]
14.	b²aca ⇒ c	[17]
15.	cbaca ⇒ cb²	[20]
16.	a²cb ⇒ acba	[25]
17.	abacb ⇒ acb²a	[29]
18.	a²c² ⇒ acbab²	[30]
19.	abac² ⇒ acb²ab²	[32]
20.	a²ca ⇒ ab	[16]
21.	abaca ⇒ ab²	[18]

# ab:aabbba=ab reversed:bc/a bbabbba=c morph:7/0 cbc=ccb cbbb=cc cbbc=ccbb cacb=ccba bbacb=cca cbacb=ccbba abc=acb cacc=ccbabb bbacc=ccabb cbacc=ccbbabb abbb=ac abbc=acbb caca=cb bbaca=c cbaca=cbb aacb=acba abacb=acbba aacc=acbabb abacc=acbbabb aaca=ab abaca=abb

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#462 ⟨a, b | aabbba=ab⟩

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Rewriting system