⟨a, b | abaaabaabab=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(c) = deg(d) = 0, c < d; deg(a) = deg(b) = 1, a < b
Auxiliary generators:
1. ab=c
2. aaca=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dc ⇒ cd	[8]
2.	c³d ⇒ 1	[9]
3.	a² ⇒ dbcd	[10]
4.	aca ⇒ bc²d²	[11]
5.	ac³a ⇒ c²dbc²d	[23]
6.	ab ⇒ c	[2]
7.	ba ⇒ cac³bc²d²	[33]
8.	bca ⇒ c³ac²dbc²d	[30]
9.	bda ⇒ acbc²d²	[20]
10.	bc²a ⇒ cac²bc²d	[29]
11.	bcda ⇒ c³adbcd	[24]
12.	bc²da ⇒ 1	[15]
13.	bc²d²a ⇒ acdbcd	[19]
14.	bcdb ⇒ c³ac	[17]
15.	bc²db ⇒ cac⁴	[31]
16.	bc²d²b ⇒ ac²	[18]

# ab:abaaabaabab=1 cd/ab ab=c,aaca=d morph:2/0,4/0 dc=cd cccd=1 aa=dbcd aca=bccdd accca=ccdbccd ab=c ba=cacccbccdd bca=cccaccdbccd bda=acbccdd bcca=caccbccd bcda=cccadbcd bccda=1 bccdda=acdbcd bcdb=cccac bccdb=cacccc bccddb=acc

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

Σ	#	Presentation	Mapping
11	3230	⟨a, b \| ababaaabaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3230

⟨a, b | ababaaabaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3183 ⟨a, b \| abaaaabbbab=1⟩
Next:	#3188 ⟨a, b \| abaaabaabba=1⟩

#3187 ⟨a, b | abaaabaabab=1⟩

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Properties

Rewriting system

Isomorphic instances