#4211 ⟨a, b | aabbbbaba=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. abbbb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	acaba ⇒ ab	[3]
2.	acabc ⇒ cb	[4]
3.	c²aba ⇒ cb	[11]
4.	abcaba ⇒ ab²	[5]
5.	cb² ⇒ (abc)²	[6]
6.	cbcaba ⇒ (abc)²	[12]
7.	acab² ⇒ c(ba)²	[8]
8.	c²abcb ⇒ cbcabc	[15]
9.	ab²caba ⇒ ab³	[7]
10.	(abc)²b ⇒ ab²cabc	[9]
11.	cbcabcb ⇒ ab(cabc)²	[17]
12.	ab⁴ ⇒ c	[2]
13.	ab³caba ⇒ c	[10]
14.	ab²cabcb ⇒ ab³cabc	[13]
15.	c(ba)²b² ⇒ ac²	[16]
16.	ab³cabcb ⇒ c²abc	[14]

# ab:aabbbbaba=ab ac/b abbbb=c morph:5/0
acaba=ab
acabc=cb
ccaba=cb
abcaba=abb
cbb=abcabc
cbcaba=abcabc
acabb=cbaba
ccabcb=cbcabc
abbcaba=abbb
abcabcb=abbcabc
cbcabcb=abcabccabc
abbbb=c
abbbcaba=c
abbcabcb=abbbcabc
cbababb=acc
abbbcabcb=ccabc