#4875 ⟨a, b | abbabbba=baa⟩

Quick links

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) = deg(c) = 0, b < c; deg(a) = 1
Auxiliary generators:
1. baa=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	(ab²)²c ⇒ ca	[5]
2.	ab²ab³c ⇒ bac	[6]
3.	ba² ⇒ c	[2]
4.	(ba)²c ⇒ cb²ab³c	[9]
5.	baca ⇒ cb²ab²c	[7]
6.	cb²ab³a ⇒ bac	[13]
7.	cb²ab⁴ac ⇒ bacb²ab³c	[14]
8.	cb²ab³ca ⇒ bacb²ab²c	[12]
9.	c(b²ab²c)² ⇒ bac²a	[10]
10.	(cb²ab²)²bc ⇒ (bac)²	[11]
11.	ab²ab³a ⇒ c	[3]
12.	ab²ab⁴ac ⇒ cb²ab³c	[8]

# ab:abbabbba=baa bc/a baa=c magic:0
abbabbc=ca
abbabbbc=bac
baa=c
babac=cbbabbbc
baca=cbbabbc
cbbabbba=bac
cbbabbbbac=bacbbabbbc
cbbabbbca=bacbbabbc
cbbabbcbbabbc=bacca
cbbabbcbbabbbc=bacbac
abbabbba=c
abbabbbbac=cbbabbbc