#3761 ⟨a, b | ababaabaab=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(e) = deg(d) = 0, e < d; deg(b) = deg(c) = deg(a) = 1, b < c < a
Auxiliary generators:
1. aa=c
2. ba=d
3. dad=e
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ece ⇒ e(de)²c	[27]
2.	dce ⇒ d(de)²c	[26]
3.	ecd ⇒ ed³ec	[30]
4.	dcd ⇒ d⁴ec	[31]
5.	eae ⇒ d²ec	[24]
6.	edae ⇒ dc	[13]
7.	ed²ae ⇒ ea	[16]
8.	d³ae ⇒ da	[15]
9.	ead ⇒ dae	[8]
10.	dad ⇒ e	[4]
11.	ecb ⇒ ed³ea	[35]
12.	dcb ⇒ d⁴ea	[34]
13.	e²ab ⇒ da	[11]
14.	edeab ⇒ e	[14]
15.	d²eab ⇒ d	[10]
16.	bc ⇒ da	[7]
17.	c²e ⇒ c(de)²c	[29]
18.	c²d ⇒ cd³ec	[28]
19.	ace ⇒ a(de)²c	[25]
20.	acd ⇒ ad³ec	[32]
21.	ba ⇒ d	[3]
22.	ca ⇒ ac	[6]
23.	cdae ⇒ adec	[20]
24.	cd²ae ⇒ ac	[17]
25.	a² ⇒ c	[2]
26.	ad²ae ⇒ c	[12]
27.	c²b ⇒ cd³ea	[36]
28.	acb ⇒ ad³ea	[33]
29.	ceab ⇒ adea	[19]
30.	cdeab ⇒ c	[9]
31.	daeab ⇒ d²ea	[23]
32.	adeab ⇒ a	[5]

# ab:ababaabaab=a reversed:ed/bca aa=c,ba=d,dad=e morph:2/0,2/0,3/0
ece=ededec
dce=ddedec
ecd=edddec
dcd=ddddec
eae=ddec
edae=dc
eddae=ea
dddae=da
ead=dae
dad=e
ecb=edddea
dcb=ddddea
eeab=da
edeab=e
ddeab=d
bc=da
cce=cdedec
ccd=cdddec
ace=adedec
acd=adddec
ba=d
ca=ac
cdae=adec
cddae=ac
aa=c
addae=c
ccb=cdddea
acb=adddea
ceab=adea
cdeab=c
daeab=ddea
adeab=a