#1175 ⟨a, b | aaaba=baba⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- a³b ⋅ a = (ba)² and bab ⋅ a = (ba)², however a³b ≠ bab
Enveloping group is isomorphic to ℤ

Rewriting system

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 = baba
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.

#	Rule	Proof
1.	a³c² ⇒ ca³c	[12]
2.	a⁶c ⇒ c²	[10]
3.	(a³c)² ⇒ c³	[13]
4.	cba ⇒ a³c	[6]
5.	a³ba ⇒ c	[2]
6.	cbc ⇒ a³ca²ba	[11]
7.	a³bc ⇒ ca²ba	[7]
8.	bac ⇒ a³c	[8]
9.	ba⁴c ⇒ c²	[9]
10.	(ba)² ⇒ c	[3]
11.	babc ⇒ ca²ba	[5]

# ab:aaaba=baba reversed:ac/b baba=c magic:0
aaacc=caaac
aaaaaac=cc
aaacaaac=ccc
cba=aaac
aaaba=c
cbc=aaacaaba
aaabc=caaba
bac=aaac
baaaac=cc
baba=c
babc=caaba

Up:	Monoids with two generators and one relation
Prev:	#1174 ⟨a, b \| aaaba=baab⟩
Next:	#1176 ⟨a, b \| aaaba=babb⟩