#2399 ⟨a, b | aaaaba=baba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- a⁴b ⋅ a = (ba)² and bab ⋅ a = (ba)², however a⁴b ≠ 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.	a⁴c² ⇒ ca⁴c	[11]
2.	a⁸c ⇒ c²	[8]
3.	(a⁴c)² ⇒ c³	[12]
4.	cba ⇒ a⁴c	[6]
5.	a⁴ba ⇒ c	[2]
6.	cbc ⇒ a⁴ca³ba	[10]
7.	a⁴bc ⇒ ca³ba	[7]
8.	bac ⇒ a⁴c	[13]
9.	ba⁵c ⇒ c²	[9]
10.	(ba)² ⇒ c	[3]
11.	babc ⇒ ca³ba	[5]

# ab:aaaaba=baba reversed:ac/b baba=c magic:0
aaaacc=caaaac
aaaaaaaac=cc
aaaacaaaac=ccc
cba=aaaac
aaaaba=c
cbc=aaaacaaaba
aaaabc=caaaba
bac=aaaac
baaaaac=cc
baba=c
babc=caaaba

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