⟨a, b | abaabbabaab=1⟩

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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

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

#	Rule	Proof
1.	bc ⇒ cb	[11]
2.	c²b ⇒ 1	[9]
3.	acb²ab ⇒ cb(ba)²	[22]
4.	abac ⇒ ca²b	[13]
5.	acb²ac ⇒ ba²	[18]
6.	a²cb ⇒ c²acb²a	[21]
7.	aba² ⇒ c³	[10]
8.	a²b²ab ⇒ c²ab³aba	[28]
9.	a²b³ab ⇒ cbacb³aba	[31]
10.	a²b²ac ⇒ c²acb³a²	[29]
11.	a²b³ac ⇒ cbab²a²	[27]

# ab:abaabbabaab=1 reversed:bc/a babaa=c morph:5/0 bc=cb ccb=1 acbbab=cbbaba abac=caab acbbac=baa aacb=ccacbba abaa=ccc aabbab=ccabbbaba aabbbab=cbacbbbaba aabbac=ccacbbbaa aabbbac=cbabbaa

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

Σ	#	Presentation	Mapping
11	3237	⟨a, b \| ababaabbaba=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3237

⟨a, b | ababaabbaba=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3215 ⟨a, b \| abaabbaabab=1⟩
Next:	#3219 ⟨a, b \| abaabbabbba=1⟩

#3217 ⟨a, b | abaabbabaab=1⟩

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Properties

Rewriting system

Isomorphic instances