#4349 ⟨a, b | abbabbbba=ba⟩

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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(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. bbbbbba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	b³a ⇒ ab²ac	[6]
2.	b³c ⇒ cb²ac	[8]
3.	ab²abc ⇒ bab²ac	[7]
4.	cb²abc ⇒ bcb²ac	[10]
5.	(ab²)²c ⇒ (b²a)²c	[9]
6.	a(b²ac)² ⇒ c	[14]
7.	cb²ab²c ⇒ b²cb²ac	[11]
8.	ab(ba)²b²ac ⇒ ba	[13]
9.	cb(ba)²b²ac ⇒ bc	[16]
10.	a(b²a)³c ⇒ b²a	[15]
11.	c(b²a)³c ⇒ b²c	[12]

# ab:abbabbbba=ba ac/b bbbbbba=c morph:7/2
bbba=abbac
bbbc=cbbac
abbabc=babbac
cbbabc=bcbbac
abbabbc=bbabbac
abbacbbac=c
cbbabbc=bbcbbac
abbababbac=ba
cbbababbac=bc
abbabbabbac=bba
cbbabbabbac=bbc