#4338 ⟨a, b | abbaabbba=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. bbbbba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	b³a ⇒ ab²a²c	[6]
2.	b³c ⇒ cb²a²c	[8]
3.	ab²a²bc ⇒ bab²a²c	[7]
4.	cb²a²bc ⇒ bcb²a²c	[11]
5.	(b²a)²ac ⇒ c	[14]
6.	ab²a²b²c ⇒ c	[9]
7.	(ab²a²)²c ⇒ ba	[15]
8.	a(b²a²c)² ⇒ bc	[10]
9.	cb²a²b²c ⇒ b²cb²a²c	[13]
10.	cb²a³b²a²c ⇒ bc	[17]
11.	ab²a²bab²a²c ⇒ b²a	[16]
12.	cb²a²bab²a²c ⇒ b²c	[12]

# ab:abbaabbba=ba ac/b bbbbba=c morph:6/2
bbba=abbaac
bbbc=cbbaac
abbaabc=babbaac
cbbaabc=bcbbaac
bbabbaac=c
abbaabbc=c
abbaaabbaac=ba
abbaacbbaac=bc
cbbaabbc=bbcbbaac
cbbaaabbaac=bc
abbaababbaac=bba
cbbaababbaac=bbc