#4319 ⟨a, b | ababbbaba=ab⟩

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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(c) = 0; deg(a) = deg(b) = 1, a < b
Auxiliary generators:
1. abbb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²aba ⇒ c	[14]
2.	cbabc ⇒ abc²b	[8]
3.	cbcabc ⇒ c²abcb	[12]
4.	cb³ ⇒ c²abc	[11]
5.	(abc)² ⇒ cb	[4]
6.	ab³ ⇒ c	[2]
7.	c(ba)² ⇒ abcab	[7]
8.	cbcaba ⇒ cb	[15]
9.	cb²abc ⇒ ab²c²b	[9]
10.	cb²cabc ⇒ c²abcb²	[13]
11.	abcaba ⇒ ab	[3]
12.	ab²cabc ⇒ cb²	[6]
13.	cb(ba)² ⇒ ab²cab	[10]
14.	cb²caba ⇒ cb²	[16]
15.	ab²caba ⇒ ab²	[5]

# ab:ababbbaba=ab c/ab abbb=c morph:4/1
ccaba=c
cbabc=abccb
cbcabc=ccabcb
cbbb=ccabc
abcabc=cb
abbb=c
cbaba=abcab
cbcaba=cb
cbbabc=abbccb
cbbcabc=ccabcbb
abcaba=ab
abbcabc=cbb
cbbaba=abbcab
cbbcaba=cbb
abbcaba=abb