#4836 ⟨a, b | ababbaab=bab⟩

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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:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. bba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ab(ac)² ⇒ bac	[5]
2.	cb(ac)² ⇒ bc²	[7]
3.	abac³ ⇒ bc²	[11]
4.	abacab ⇒ bab	[3]
5.	cbacab ⇒ bcb	[4]
6.	abac²b ⇒ bcb	[17]
7.	b²a ⇒ c	[2]
8.	a(bac)² ⇒ c²	[8]
9.	b²c² ⇒ c(bac)²	[10]
10.	(ab)²c² ⇒ c²ac	[14]
11.	abacbc² ⇒ c(bac)²	[15]
12.	bcbac³ ⇒ cbacbc²	[16]
13.	abacbab ⇒ cb	[6]
14.	b²cb ⇒ (cba)²b	[9]
15.	(ab)²cb ⇒ c²ab	[13]
16.	aba(cb)² ⇒ (cba)²b	[19]
17.	bcbac²b ⇒ cba(cb)²	[20]
18.	bc(bac)² ⇒ cbac³	[12]
19.	bcbabc² ⇒ cbac³ac	[21]
20.	bcbacbc² ⇒ (cbac)²bac	[23]
21.	b(cba)²b ⇒ cbac²b	[18]
22.	bcbabcb ⇒ cbac³ab	[22]
23.	bcba(cb)² ⇒ (cbac)²bab	[24]

# ab:ababbaab=bab reversed:ac/b bba=c morph:3/1
abacac=bac
cbacac=bcc
abaccc=bcc
abacab=bab
cbacab=bcb
abaccb=bcb
bba=c
abacbac=cc
bbcc=cbacbac
ababcc=ccac
abacbcc=cbacbac
bcbaccc=cbacbcc
abacbab=cb
bbcb=cbacbab
ababcb=ccab
abacbcb=cbacbab
bcbaccb=cbacbcb
bcbacbac=cbaccc
bcbabcc=cbacccac
bcbacbcc=cbaccbacbac
bcbacbab=cbaccb
bcbabcb=cbacccab
bcbacbcb=cbaccbacbab