#4293 ⟨a, b | ababaabba=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 ⇒ (ab)²a²c	[6]
2.	b³c ⇒ cbaba²c	[8]
3.	(ba)³ac ⇒ c	[14]
4.	(ab)²a²bc ⇒ c	[7]
5.	cbaba²bc ⇒ bcbaba²c	[10]
6.	(ab)²a²b²a ⇒ ba	[1]
7.	(ab)²a²b²c ⇒ bc	[9]
8.	((ab)²a²)²c ⇒ b²a	[15]
9.	a(baba²c)² ⇒ b²c	[11]
10.	cbaba²b²a ⇒ bc	[4]
11.	cbaba²b²c ⇒ b²cbaba²c	[12]
12.	cbaba³baba²c ⇒ b²c	[13]

# ab:ababaabba=ba ac/b bbbba=c morph:5/2
bbba=ababaac
bbbc=cbabaac
bababaac=c
ababaabc=c
cbabaabc=bcbabaac
ababaabba=ba
ababaabbc=bc
ababaaababaac=bba
ababaacbabaac=bbc
cbabaabba=bc
cbabaabbc=bbcbabaac
cbabaaababaac=bbc