⟨a, b | aabbabaabba=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. aabba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	bc ⇒ cb	[4]
2.	c²b ⇒ 1	[12]
3.	ab²ac ⇒ cba²b	[7]
4.	acbac ⇒ c⁴ab²a	[13]
5.	a²b² ⇒ cb²acba	[18]
6.	a²cb² ⇒ cab²a	[5]
7.	acba² ⇒ c⁴	[10]
8.	ab(ba)²c ⇒ b²ac³ab²a	[23]
9.	ab²aba² ⇒ b²ac³	[20]

# ab:aabbabaabba=1 reversed:bc/a aabba=c morph:5/0 bc=cb ccb=1 abbac=cbaab acbac=ccccabba aabb=cbbacba aacbb=cabba acbaa=cccc abbabac=bbacccabba abbabaa=bbaccc

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

Σ	#	Presentation	Mapping
11	3254	⟨a, b \| ababbaabbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

3254

⟨a, b | ababbaabbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#3118 ⟨a, b \| aabbabaabab=1⟩
Next:	#3120 ⟨a, b \| aabbababaab=1⟩

#3119 ⟨a, b | aabbabaabba=1⟩

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Properties

Rewriting system

Isomorphic instances