#4855 ⟨a, b | abbaaaab=aba⟩

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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(b) = 0; deg(a) = deg(c) = 1, a < c
Auxiliary generators:
1. baaaa=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	abcb ⇒ aba	[3]
2.	(cb)² ⇒ cba	[4]
3.	abacb ⇒ aba²	[6]
4.	ac²b ⇒ aca	[18]
5.	abc² ⇒ aca	[5]
6.	cbacb ⇒ cba²	[8]
7.	c³b ⇒ c²a	[21]
8.	cbc² ⇒ c²a	[7]
9.	ba⁴ ⇒ c	[2]
10.	aba²cb ⇒ aba³	[11]
11.	aca² ⇒ abac²	[9]
12.	(ac)²b ⇒ abac²	[20]
13.	cba²cb ⇒ cba³	[13]
14.	c²a² ⇒ cbac²	[10]
15.	c²acb ⇒ cbac²	[23]
16.	aba³cb ⇒ ac	[14]
17.	abac²a ⇒ aba²c²	[12]
18.	ac³a ⇒ acac²	[22]
19.	cba³cb ⇒ c²	[16]
20.	cbac²a ⇒ cba²c²	[15]
21.	c⁴a ⇒ c²ac²	[24]
22.	aba²c²a ⇒ aba³c²	[17]
23.	acac²a ⇒ abac⁴	[27]
24.	cba²c²a ⇒ cba³c²	[25]
25.	(c²a)² ⇒ cbac⁴	[28]
26.	aba³c²a ⇒ ac³	[19]
27.	cba³c²a ⇒ c⁴	[26]

# ab:abbaaaab=aba b/ac baaaa=c morph:5/2
abcb=aba
cbcb=cba
abacb=abaa
accb=aca
abcc=aca
cbacb=cbaa
cccb=cca
cbcc=cca
baaaa=c
abaacb=abaaa
acaa=abacc
acacb=abacc
cbaacb=cbaaa
ccaa=cbacc
ccacb=cbacc
abaaacb=ac
abacca=abaacc
accca=acacc
cbaaacb=cc
cbacca=cbaacc
cccca=ccacc
abaacca=abaaacc
acacca=abacccc
cbaacca=cbaaacc
ccacca=cbacccc
abaaacca=accc
cbaaacca=cccc