#4187 ⟨a, b | aabbabbba=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.	a²b²c² ⇒ cb	[4]
2.	cab²ca ⇒ cb	[9]
3.	ab³ ⇒ c	[2]
4.	cbab²c² ⇒ cab²c²b	[15]
5.	cb³ca ⇒ cab²cb	[17]
6.	cb⁴ ⇒ cab²c²	[10]
7.	a²b²ca ⇒ ab	[3]
8.	a²b²cb ⇒ c²a	[11]
9.	abab²c² ⇒ cb²	[6]
10.	cbab²ca ⇒ cb²	[12]
11.	cbab²cb ⇒ cab²c³a	[19]
12.	cb²ab²c² ⇒ cab²c²b²	[16]
13.	abab²ca ⇒ ab²	[5]
14.	abab²cb ⇒ cbca	[13]
15.	(ab²)²c² ⇒ cb³	[7]
16.	cb²ab²ca ⇒ cb³	[14]
17.	cb²ab²cb ⇒ cab²c²bca	[22]
18.	cb³ab²c² ⇒ cab²c²b³	[21]
19.	(ab²)²ca ⇒ c	[8]
20.	(ab²)²cb ⇒ cb²ca	[18]
21.	cb³ab²ca ⇒ cab²c²	[20]
22.	cb³ab²cb ⇒ cab²c²b²ca	[23]

# ab:aabbabbba=ab c/ab abbb=c morph:4/0
aabbcc=cb
cabbca=cb
abbb=c
cbabbcc=cabbccb
cbbbca=cabbcb
cbbbb=cabbcc
aabbca=ab
aabbcb=cca
ababbcc=cbb
cbabbca=cbb
cbabbcb=cabbccca
cbbabbcc=cabbccbb
ababbca=abb
ababbcb=cbca
abbabbcc=cbbb
cbbabbca=cbbb
cbbabbcb=cabbccbca
cbbbabbcc=cabbccbbb
abbabbca=c
abbabbcb=cbbca
cbbbabbca=cabbcc
cbbbabbcb=cabbccbbca