⟨a, b | abbaaab=aba⟩

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

#	Rule	Proof
1.	abcb ⇒ aba	[3]
2.	(cb)² ⇒ cba	[4]
3.	ba³ ⇒ c	[2]
4.	abacb ⇒ aba²	[6]
5.	ac²b ⇒ aca	[14]
6.	abc² ⇒ aca	[5]
7.	cbacb ⇒ cba²	[8]
8.	c³b ⇒ c²a	[16]
9.	cbc² ⇒ c²a	[7]
10.	aba²cb ⇒ ac	[11]
11.	aca² ⇒ abac²	[9]
12.	(ac)²b ⇒ abac²	[17]
13.	cba²cb ⇒ c²	[13]
14.	c²a² ⇒ cbac²	[10]
15.	c²acb ⇒ cbac²	[19]
16.	abac²a ⇒ aba²c²	[12]
17.	ac³a ⇒ acac²	[18]
18.	cbac²a ⇒ cba²c²	[21]
19.	c⁴a ⇒ c²ac²	[20]
20.	aba²c²a ⇒ ac³	[15]
21.	acac²a ⇒ abac⁴	[23]
22.	cba²c²a ⇒ c⁴	[22]
23.	(c²a)² ⇒ cbac⁴	[24]

# ab:abbaaab=aba b/ac baaa=c morph:4/2 abcb=aba cbcb=cba baaa=c abacb=abaa accb=aca abcc=aca cbacb=cbaa cccb=cca cbcc=cca abaacb=ac acaa=abacc acacb=abacc cbaacb=cc ccaa=cbacc ccacb=cbacc abacca=abaacc accca=acacc cbacca=cbaacc cccca=ccacc abaacca=accc acacca=abacccc cbaacca=cccc ccacca=cbacccc

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#2345 ⟨a, b | abbaaab=aba⟩

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