#3784 ⟨a, b | ababbabaab=b⟩

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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. abaab=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ca²b ⇒ abac	[4]
2.	aba²b ⇒ c	[2]
3.	cab²c ⇒ (ab)²	[5]
4.	abab²c ⇒ b	[3]
5.	cab³ ⇒ ab³c	[14]
6.	cab²abc ⇒ ab²a²b	[11]
7.	cab(ba)²c ⇒ abc	[8]
8.	abab³ ⇒ bab(bc)²	[15]
9.	a(bab)²c ⇒ (bab)²ac	[10]
10.	a(bab)²ac ⇒ ba²b	[6]
11.	c(ab²)² ⇒ (ab²)²c	[13]
12.	cab²(ab)² ⇒ ab²	[9]
13.	ab(ab²)² ⇒ (bab)²ab	[12]
14.	a(bab)²ab ⇒ bab²c	[7]

# ab:ababbabaab=b ac/b abaab=c morph:5/0
caab=abac
abaab=c
cabbc=abab
ababbc=b
cabbb=abbbc
cabbabc=abbaab
cabbabac=abc
ababbb=babbcbc
ababbabc=babbabac
ababbabac=baab
cabbabb=abbabbc
cabbabab=abb
ababbabb=babbabab
ababbabab=babbc