#4304 ⟨a, b | abababbba=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 ⇒ a(ba)²c	[6]
2.	b³c ⇒ c(ba)²c	[8]
3.	(ab)³c ⇒ (ba)³c	[7]
4.	cb(ab)²c ⇒ bc(ba)²c	[11]
5.	b(ba)³c ⇒ c	[14]
6.	(ab)³bc ⇒ c	[9]
7.	(a(ba)²)²c ⇒ ba	[15]
8.	a((ba)²c)² ⇒ bc	[10]
9.	c(ba)²b²c ⇒ b²c(ba)²c	[13]
10.	cb(aba)²bac ⇒ bc	[17]
11.	a(ba)⁵c ⇒ b²a	[16]
12.	c(ba)⁵c ⇒ b²c	[12]

# ab:abababbba=ba ac/b bbbbba=c morph:6/2
bbba=ababac
bbbc=cbabac
abababc=bababac
cbababc=bcbabac
bbababac=c
abababbc=c
ababaababac=ba
ababacbabac=bc
cbababbc=bbcbabac
cbabaababac=bc
abababababac=bba
cbababababac=bbc