#4129 ⟨a, b | aabababba=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. bbbba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	b³a ⇒ a²(ba)²c	[6]
2.	b³c ⇒ ca(ba)²c	[8]
3.	ba²(ba)²c ⇒ c	[14]
4.	a(ab)³c ⇒ c	[7]
5.	c(ab)³c ⇒ bca(ba)²c	[10]
6.	a(ab)³ba ⇒ ba	[1]
7.	a(ab)³bc ⇒ bc	[9]
8.	(a²(ba)²)²c ⇒ b²a	[15]
9.	a(a(ba)²c)² ⇒ b²c	[11]
10.	c(ab)³ba ⇒ bc	[4]
11.	c(ab)³bc ⇒ b²ca(ba)²c	[12]
12.	c(ab)²a³(ba)²c ⇒ b²c	[13]

# ab:aabababba=ba ac/b bbbba=c morph:5/2
bbba=aababac
bbbc=cababac
baababac=c
aabababc=c
cabababc=bcababac
aabababba=ba
aabababbc=bc
aababaaababac=bba
aababacababac=bbc
cabababba=bc
cabababbc=bbcababac
cababaaababac=bbc