#3977 ⟨a, b | aaabaabba=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. bbba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	b²a ⇒ a³ba²c	[3]
2.	b²c ⇒ ca²ba²c	[7]
3.	ba³ba²c ⇒ c	[11]
4.	a(a²b)²c ⇒ c	[5]
5.	(a³ba²)²c ⇒ ba	[10]
6.	a(a²ba²c)² ⇒ bc	[8]
7.	c(a²b)²c ⇒ bca²ba²c	[9]
8.	ca²ba⁵ba²c ⇒ bc	[4]

# ab:aaabaabba=ba ac/b bbba=c morph:4/2
bba=aaabaac
bbc=caabaac
baaabaac=c
aaabaabc=c
aaabaaaaabaac=ba
aaabaacaabaac=bc
caabaabc=bcaabaac
caabaaaaabaac=bc

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