#4872 ⟨a, b | abbabbba=aab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

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

Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(c) = deg(a) = 1, c < a
Auxiliary generators:
1. aab=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a²b ⇒ c	[2]
2.	c(ab)² ⇒ cb²ab³c	[9]
3.	cbab³a ⇒ ac	[6]
4.	cb²ab³a ⇒ cab	[5]
5.	acab ⇒ cbab³c	[7]
6.	ab²ab³c ⇒ cab	[13]
7.	ab²ab³a ⇒ c	[3]
8.	c(ab³)²c ⇒ cb²ab³cab	[14]
9.	ca(b³a)² ⇒ cb²ab³c	[8]
10.	acb²ab³c ⇒ cbab³cab	[12]
11.	c(bab³c)² ⇒ ac²ab	[11]
12.	cb(bab³c)² ⇒ (cab)²	[10]

# ab:abbabbba=aab b/ca aab=c magic:0
aab=c
cabab=cbbabbbc
cbabbba=ac
cbbabbba=cab
acab=cbabbbc
abbabbbc=cab
abbabbba=c
cabbbabbbc=cbbabbbcab
cabbbabbba=cbbabbbc
acbbabbbc=cbabbbcab
cbabbbcbabbbc=accab
cbbabbbcbabbbc=cabcab