⟨a, b | aababaabba=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

Auxiliary generators:
1. c = aaa
2. d = babaabb
Reduction order:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[10]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[9]
5.	a³ ⇒ c	[2]
6.	ba²b²c ⇒ a(ab)²a²b	[14]
7.	baba²bd ⇒ adba²b²	[11]
8.	ba²b²a ⇒ a²dbcbab	[30]
9.	b²cba ⇒ (ab)²a²b	[27]
10.	bc(ba)² ⇒ a²b²cb	[36]
11.	b(aba)² ⇒ dbcbabc	[19]
12.	baba²b² ⇒ d	[3]
13.	b²cb³c ⇒ a²dba(aba²b)²	[48]
14.	b(bc)²b²c ⇒ a(ba)²cbaba²b	[45]
15.	bcbabcb²c ⇒ a²b²a²cbaba²b	[47]
16.	b²cb²a²bd ⇒ adbcba²dba²b²	[37]
17.	bcbab²a²bd ⇒ (aba)²dba²b²	[50]
18.	(bcba)²abd ⇒ cbab²a²b²	[22]
19.	b²cb³a ⇒ a²d(ba²)²dbcbab	[49]
20.	b(bc)²b²a ⇒ (ab)³cbab	[44]
21.	bcbabcb²a ⇒ a²b²a²bcbab	[46]
22.	b²cb²a²ba ⇒ a(dbcba)²bc	[38]
23.	bcbab²a²ba ⇒ aba²bdbcbabc	[52]
24.	(bcba)²aba ⇒ cbaba²dbcbabc	[25]
25.	b²cb²a²b² ⇒ adbcbad	[26]
26.	bcbab²a²b² ⇒ aba²bd	[16]
27.	(bcba)²ab² ⇒ cbaba²d	[21]

# ab:aababaabba=1 reversed:cda/b aaa=c,babaabb=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c baabbc=aababaab babaabd=adbaabb baabba=aadbcbab bbcba=ababaab bcbaba=aabbcb babaaba=dbcbabc babaabb=d bbcbbbc=aadbaabaababaab bbcbcbbc=ababacbabaab bcbabcbbc=aabbaacbabaab bbcbbaabd=adbcbaadbaabb bcbabbaabd=abaabadbaabb bcbabcbaabd=cbabbaabb bbcbbba=aadbaabaadbcbab bbcbcbba=abababcbab bcbabcbba=aabbaabcbab bbcbbaaba=adbcbadbcbabc bcbabbaaba=abaabdbcbabc bcbabcbaaba=cbabaadbcbabc bbcbbaabb=adbcbad bcbabbaabb=abaabd bcbabcbaabb=cbabaad

Other submonoids of same group

Σ	#	Presentation	Description
8	400	⟨a, b \| abaabba=b⟩	Infinite cancellative non-commutative monoid
8	534	⟨a, b \| aabba=bab⟩	Infinite cancellative non-commutative monoid
10	1758	⟨a, b \| abaaababa=b⟩	Infinite cancellative non-commutative monoid
10	2340	⟨a, b \| ababbba=bab⟩	Infinite cancellative non-commutative monoid
10	2504	⟨a, b \| aababa=baab⟩	Infinite cancellative non-commutative monoid

Presentation

Description

400

⟨a, b | abaabba=b⟩