#3772 ⟨a, b | abababbaab=a⟩

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

#	Rule	Proof
1.	c³b ⇒ c	[15]
2.	c²ab ⇒ cbac	[30]
3.	cacb ⇒ cabc	[21]
4.	cbacb ⇒ cbabc	[19]
5.	cac³ ⇒ c⁴a	[25]
6.	cbac³ ⇒ c²a	[26]
7.	cabc² ⇒ ca	[11]
8.	cbabc² ⇒ cba	[8]
9.	ab²c ⇒ cb²a	[4]
10.	ac²b ⇒ a	[14]
11.	cac²a ⇒ c⁸	[29]
12.	cbac²a ⇒ c⁶	[27]
13.	cabca ⇒ c⁵	[22]
14.	cbabca ⇒ c³	[13]
15.	ab²a ⇒ c	[2]
16.	ca²b ⇒ cabcbac	[34]
17.	cba²b ⇒ cbabcbac	[32]
18.	acab ⇒ abac	[37]
19.	a²cb ⇒ a²bc	[20]
20.	abacb ⇒ (ab)²c	[18]
21.	a²c³ ⇒ ac³a	[24]
22.	abac³ ⇒ aca	[36]
23.	a²bc² ⇒ a²	[10]
24.	(ab)²c² ⇒ aba	[6]
25.	a²c²a ⇒ ac⁷	[28]
26.	abac²a ⇒ ac⁵	[35]
27.	a²bca ⇒ ac⁴	[23]
28.	(ab)²ca ⇒ ac²	[12]
29.	a³b ⇒ a²bcbac	[33]
30.	aba²b ⇒ (ab)²cbac	[31]

# ab:abababbaab=a reversed:cb/a abba=c morph:4/0
cccb=c
ccab=cbac
cacb=cabc
cbacb=cbabc
caccc=cccca
cbaccc=cca
cabcc=ca
cbabcc=cba
abbc=cbba
accb=a
cacca=cccccccc
cbacca=cccccc
cabca=ccccc
cbabca=ccc
abba=c
caab=cabcbac
cbaab=cbabcbac
acab=abac
aacb=aabc
abacb=ababc
aaccc=accca
abaccc=aca
aabcc=aa
ababcc=aba
aacca=accccccc
abacca=accccc
aabca=acccc
ababca=acc
aaab=aabcbac
abaab=ababcbac