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

#	Rule	Proof
1.	cb ⇒ bc	[4]
2.	bc² ⇒ 1	[5]
3.	bab²ca ⇒ abab²c	[17]
4.	caba ⇒ ba²c	[8]
5.	cab²ca ⇒ a²b	[13]
6.	bca² ⇒ ab²cac²	[18]
7.	a²ba ⇒ c³	[6]
8.	bab²a² ⇒ abab³ac²	[24]
9.	bab³a² ⇒ abab³cabc	[27]
10.	cab²a² ⇒ a²b³cac²	[25]
11.	cab³a² ⇒ a²b²abc	[23]

# ab:aababbaabab=1 bc/a aabab=c morph:5/0 cb=bc bcc=1 babbca=ababbc caba=baac cabbca=aab bcaa=abbcacc aaba=ccc babbaa=ababbbacc babbbaa=ababbbcabc cabbaa=aabbbcacc cabbbaa=aabbabc

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

Σ	#	Presentation	Mapping
11	3235	⟨a, b \| ababaababba=1⟩	φ(a) = a, φ(b) = b
11	3279	⟨a, b \| abbaababaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3235

⟨a, b | ababaababba=1⟩

φ(a) = a, φ(b) = b

3279

⟨a, b | abbaababaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3076 ⟨a, b \| aababbaaabb=1⟩
Next:	#3078 ⟨a, b \| aababbaabba=1⟩

#3077 ⟨a, b | aababbaabab=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances