⟨a, b | ababbba=bab⟩

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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

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

#	Rule	Proof
1.	a²bc³ ⇒ cb	[5]
2.	bab ⇒ abc	[3]
3.	ba²bc ⇒ abcab	[4]
4.	(abc)²c ⇒ bcb	[8]
5.	b²cb ⇒ (abc²)²	[9]
6.	ab³a ⇒ c	[2]
7.	abcb²a ⇒ bc	[6]
8.	abc²b²a ⇒ b²c	[7]
9.	b³c ⇒ abc³b²a	[10]
10.	b²cabc ⇒ ab(c²ab)²	[11]
11.	bcb³a ⇒ abcb²c	[12]
12.	abcab⁴a ⇒ ba³bcb²c	[13]
13.	b²a³bcb²c ⇒ abc²ab⁴a	[15]
14.	a(bc²a)²b⁴a ⇒ b²ca²bcb²c	[14]
15.	abcb²ca²bcb²c ⇒ bcabc³ab⁴a	[16]

# ab:ababbba=bab reversed:ac/b abbba=c morph:5/0 aabccc=cb bab=abc baabc=abcab abcabcc=bcb bbcb=abccabcc abbba=c abcbba=bc abccbba=bbc bbbc=abcccbba bbcabc=abccabccab bcbbba=abcbbc abcabbbba=baaabcbbc bbaaabcbbc=abccabbbba abccabccabbbba=bbcaabcbbc abcbbcaabcbbc=bcabcccabbbba

Other submonoids of same group

Σ	#	Presentation	Description	Related
8	400	⟨a, b \| abaabba=b⟩	Infinite cancellative non-commutative monoid
8	534	⟨a, b \| aabba=bab⟩	Infinite cancellative non-commutative monoid
10	1419	⟨a, b \| aababaabba=1⟩	Infinite non-Abelian group	5 iso
10	1758	⟨a, b \| abaaababa=b⟩	Infinite cancellative non-commutative monoid
10	2504	⟨a, b \| aababa=baab⟩	Infinite cancellative non-commutative monoid

Presentation

Description

400

⟨a, b | abaabba=b⟩

Infinite cancellative non-commutative monoid

534

⟨a, b | aabba=bab⟩

Infinite cancellative non-commutative monoid

1419

⟨a, b | aababaabba=1⟩

Infinite non-Abelian group

5 iso