#4203 ⟨a, b | aabbbabba=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(a) = deg(c) = 0, a < c; deg(b) = 1
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.	acab²a ⇒ ab	[3]
2.	acab²c ⇒ cb	[4]
3.	c²ab²a ⇒ cb	[9]
4.	ab³ ⇒ c	[2]
5.	abcab²a ⇒ ab²	[5]
6.	abcab²c ⇒ cb²	[6]
7.	cbab²a ⇒ ac²	[14]
8.	cbcab²a ⇒ cb²	[10]
9.	ac²b³ ⇒ cbab²c	[17]
10.	c²ab²cb ⇒ cbcab²c	[12]
11.	ab²cab²a ⇒ c	[7]
12.	(ab²c)² ⇒ cb³	[8]
13.	cb⁴ ⇒ c²ab²c	[11]
14.	c(b²a)² ⇒ abc²	[16]
15.	cb²ab²c ⇒ abc²b³	[22]
16.	cb²cab²a ⇒ cb³	[13]
17.	cbab²cb ⇒ ac³ab²c	[18]
18.	cbcab²cb ⇒ cb²cab²c	[20]
19.	cb(b²a)² ⇒ ab²c²	[19]
20.	cb³ab²c ⇒ ab²c²b³	[23]
21.	cb³cab²a ⇒ c²ab²c	[15]
22.	cb²cab²cb ⇒ cb³cab²c	[21]
23.	cb³cab²cb ⇒ (c²ab²)²c	[24]

# ab:aabbbabba=ab ac/b abbb=c morph:4/0
acabba=ab
acabbc=cb
ccabba=cb
abbb=c
abcabba=abb
abcabbc=cbb
cbabba=acc
cbcabba=cbb
accbbb=cbabbc
ccabbcb=cbcabbc
abbcabba=c
abbcabbc=cbbb
cbbbb=ccabbc
cbbabba=abcc
cbbabbc=abccbbb
cbbcabba=cbbb
cbabbcb=acccabbc
cbcabbcb=cbbcabbc
cbbbabba=abbcc
cbbbabbc=abbccbbb
cbbbcabba=ccabbc
cbbcabbcb=cbbbcabbc
cbbbcabbcb=ccabbccabbc