#4269 ⟨a, b | abaababba=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 ⇒ (aba)²c	[6]
2.	b³c ⇒ cba²bac	[8]
3.	b(aba)²c ⇒ c	[14]
4.	(aba)²bc ⇒ c	[7]
5.	cba(ab)²c ⇒ bcba²bac	[10]
6.	(aba)²b²a ⇒ ba	[1]
7.	(aba)²b²c ⇒ bc	[9]
8.	(aba)⁴c ⇒ b²a	[15]
9.	a(ba²bac)² ⇒ b²c	[11]
10.	cba²bab²a ⇒ bc	[4]
11.	cba²bab²c ⇒ b²cba²bac	[12]
12.	cb(a²b)³ac ⇒ b²c	[13]

# ab:abaababba=ba ac/b bbbba=c morph:5/2
bbba=abaabac
bbbc=cbaabac
babaabac=c
abaababc=c
cbaababc=bcbaabac
abaababba=ba
abaababbc=bc
abaabaabaabac=bba
abaabacbaabac=bbc
cbaababba=bc
cbaababbc=bbcbaabac
cbaabaabaabac=bbc