#3643 ⟨a, b | aabbabaaab=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:
- Left-to-right recursive path with deg(c) = deg(b) = deg(d) = 0, c < b < d; deg(a) = 1
Auxiliary generators:
1. baba=c
2. caa=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	d²c ⇒ cd²	[29]
2.	(db)² ⇒ cdc	[18]
3.	c(dc)² ⇒ d	[20]
4.	cdbdc ⇒ cdcbd	[34]
5.	dbcdc ⇒ (cd)²b	[30]
6.	d²bdc ⇒ cd²bd	[36]
7.	cdcbdb ⇒ c	[22]
8.	cdb²db ⇒ cdcbc	[27]
9.	d²b²db ⇒ cd²bc	[38]
10.	cdcbcdc ⇒ cdb	[31]
11.	cdb²cdc ⇒ cdcbcdb	[35]
12.	d²b²cdc ⇒ cd²bcdb	[42]
13.	adbdc ⇒ adcbd	[40]
14.	adcbdb ⇒ a	[21]
15.	adb²db ⇒ adcbc	[24]
16.	adcbcdc ⇒ adb	[32]
17.	adb²cdc ⇒ adcbcdb	[41]
18.	ca ⇒ cdc	[23]
19.	da ⇒ cd²	[37]
20.	cba ⇒ bac	[5]
21.	dba ⇒ dbdc	[16]
22.	cdb²a ⇒ cdb²dc	[33]
23.	d²b²a ⇒ d²b²dc	[43]
24.	a² ⇒ adc	[17]
25.	adb²a ⇒ adb²dc	[39]
26.	(ba)² ⇒ c	[2]

# ab:aabbabaaab=a cbd/a baba=c,caa=d morph:4/1,3/1
ddc=cdd
dbdb=cdc
cdcdc=d
cdbdc=cdcbd
dbcdc=cdcdb
ddbdc=cddbd
cdcbdb=c
cdbbdb=cdcbc
ddbbdb=cddbc
cdcbcdc=cdb
cdbbcdc=cdcbcdb
ddbbcdc=cddbcdb
adbdc=adcbd
adcbdb=a
adbbdb=adcbc
adcbcdc=adb
adbbcdc=adcbcdb
ca=cdc
da=cdd
cba=bac
dba=dbdc
cdbba=cdbbdc
ddbba=ddbbdc
aa=adc
adbba=adbbdc
baba=c