⟨a, b | abbabba=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 = abbbb
Reduction order:
- Left-to-right shortlex with c < b < a
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²a ⇒ cb	[35]
2.	cbc ⇒ c²b	[36]
3.	cac ⇒ cb	[20]
4.	cab ⇒ cba	[30]
5.	ca² ⇒ ab	[19]
6.	c²ba ⇒ cb²	[37]
7.	cb²c ⇒ c²b²	[40]
8.	cbac ⇒ cb²	[24]
9.	cbab ⇒ cb²a	[33]
10.	cba² ⇒ ab²	[26]
11.	ab²c ⇒ cb²a	[45]
12.	c²b²a ⇒ cb³	[41]
13.	cb³c ⇒ c²b³	[47]
14.	cb²ac ⇒ cb³	[18]
15.	cb²ab ⇒ cb³a	[31]
16.	cb²a² ⇒ ab³	[28]
17.	ab³c ⇒ cb³a	[44]
18.	ab⁴ ⇒ c	[2]
19.	ab²ab ⇒ ab³a	[3]
20.	c²b³a ⇒ cb⁴	[42]
21.	cb⁴c ⇒ c²b⁴	[48]
22.	cb⁵ ⇒ c³	[43]
23.	cb⁴a ⇒ c²	[34]
24.	cb³ac ⇒ cb⁴	[27]
25.	cb³ab ⇒ c²	[46]
26.	cb³a² ⇒ c	[29]
27.	ab³ab ⇒ ca	[11]

# ab:abbabba=ab cba abbbb=c morph:5/0 cca=cb cbc=ccb cac=cb cab=cba caa=ab ccba=cbb cbbc=ccbb cbac=cbb cbab=cbba cbaa=abb abbc=cbba ccbba=cbbb cbbbc=ccbbb cbbac=cbbb cbbab=cbbba cbbaa=abbb abbbc=cbbba abbbb=c abbab=abbba ccbbba=cbbbb cbbbbc=ccbbbb cbbbbb=ccc cbbbba=cc cbbbac=cbbbb cbbbab=cc cbbbaa=c abbbab=ca

Up:	Monoids with two generators and one relation
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#998 ⟨a, b | abbabba=ab⟩

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