⟨a, b | aaaabaabbba=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(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaaaa=c
2. baabbb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[13]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[12]
5.	a⁵ ⇒ c	[2]
6.	bcba² ⇒ cba²b	[22]
7.	ba²ba³ ⇒ d(bc)²	[24]
8.	b³c ⇒ a³ba²b²	[17]
9.	ba²b²d ⇒ a²db³	[14]
10.	b³ac ⇒ a³ba²b²a	[19]
11.	ba²b²ad ⇒ a²db³a	[15]
12.	b³a²c ⇒ a³ba²b²a²	[26]
13.	ba²b²a²d ⇒ a²db³a²	[27]
14.	b³a³ ⇒ a³db²cb	[30]
15.	ba²b²a³ ⇒ db(bc)²	[28]
16.	ba²b³ ⇒ d	[3]

# ab:aaaabaabbba=1 reversed:cda/b aaaaa=c,baabbb=d magic:0 dc=1 cd=1 ca=ac da=ad aaaaa=c bcbaa=cbaab baabaaa=dbcbc bbbc=aaabaabb baabbd=aadbbb bbbac=aaabaabba baabbad=aadbbba bbbaac=aaabaabbaa baabbaad=aadbbbaa bbbaaa=aaadbbcb baabbaaa=dbbcbc baabbb=d

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

Σ	#	Presentation	Mapping
11	2924	⟨a, b \| aaabaabbbaa=1⟩	φ(a) = a, φ(b) = b
11	3134	⟨a, b \| aabbbaaaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2924

⟨a, b | aaabaabbbaa=1⟩

φ(a) = a, φ(b) = b

3134

⟨a, b | aabbbaaaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2852 ⟨a, b \| aaaabaabbab=1⟩
Next:	#2854 ⟨a, b \| aaaabaabbbb=1⟩

#2853 ⟨a, b | aaaabaabbba=1⟩

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Properties

Rewriting system

Isomorphic instances