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

#	Rule	Proof
1.	bc ⇒ cb	[19]
2.	c²b ⇒ 1	[21]
3.	a²c ⇒ c⁴acbab	[23]
4.	ab²ac ⇒ cb²a²	[4]
5.	acbab² ⇒ cbab²a	[25]
6.	(acb)²b ⇒ b²a²	[26]
7.	ab²a² ⇒ c	[2]
8.	a²bab² ⇒ c³acb(b²a)²	[29]
9.	a²bacb² ⇒ c³ab⁴a²	[24]

# ab:ababbaaabba=1 reversed:bc/a abbaa=c morph:5/0 bc=cb ccb=1 aac=ccccacbab abbac=cbbaa acbabb=cbabba acbacbb=bbaa abbaa=c aababb=cccacbbbabba aabacbb=cccabbbbaa

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

Σ	#	Presentation	Mapping
11	3286	⟨a, b \| abbabaabbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

3286

⟨a, b | abbabaabbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#3244 ⟨a, b \| ababababbba=1⟩
Next:	#3253 ⟨a, b \| ababbaabaab=1⟩

#3252 ⟨a, b | ababbaaabba=1⟩

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Properties

Rewriting system

Isomorphic instances