#11071 ⟨a, b | baab=aaa, bbbb=1⟩

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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

Auxiliary generators:
1. c = bbb
2. d = cacaca
3. e = dadadad
Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(e) = 1; deg(d) = 2; deg(c) = deg(b) = 3, c < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ea³ ⇒ a²	[97]
2.	ae ⇒ ea	[109]
3.	e²a ⇒ e	[115]
4.	dea² ⇒ da	[101]
5.	a²dea ⇒ a²d	[132]
6.	a⁵d ⇒ da⁵	[57]
7.	ed ⇒ a⁴de⁵	[175]
8.	ead ⇒ dea	[125]
9.	ea²d ⇒ adea	[108]
10.	dadea ⇒ dad	[136]
11.	da³d ⇒ a²	[55]
12.	a²d² ⇒ dada³	[91]
13.	a³dad ⇒ d²a²	[58]
14.	d³a ⇒ a³de	[64]
15.	d³e ⇒ a³de³	[180]
16.	dad²ea ⇒ dad²	[148]
17.	d(ad)² ⇒ a²de³	[158]
18.	dad³ ⇒ da⁴de²	[165]
19.	ca² ⇒ a³de	[70]
20.	ce ⇒ a³de⁴	[181]
21.	cda ⇒ a(a²d)²e⁴	[171]
22.	cde ⇒ a(a²d)²e⁶	[172]
23.	cada ⇒ ea²	[129]
24.	cade ⇒ e	[84]
25.	cd²a ⇒ (ad)²a⁴de	[176]
26.	cd²e ⇒ (ad)²a⁴de³	[177]
27.	cad²a ⇒ da	[79]
28.	cad²e ⇒ de	[87]
29.	a²c ⇒ da²	[32]
30.	ec ⇒ a²de³	[159]
31.	eac ⇒ a³de³	[179]
32.	dca ⇒ cad	[16]
33.	dac ⇒ da⁴de³	[169]
34.	a²dc ⇒ ea²	[130]
35.	dadc ⇒ dea	[138]
36.	dad²c ⇒ dade	[157]
37.	ba² ⇒ ada²	[38]
38.	be ⇒ ade	[85]
39.	bda ⇒ ad²a	[72]
40.	bde ⇒ ad²e	[88]
41.	bada ⇒ a(da)²	[78]
42.	bade ⇒ (ad)²e	[147]
43.	bd²a ⇒ a⁴de	[80]
44.	bd²e ⇒ a⁴de³	[178]
45.	bad²a ⇒ adad²a	[152]
46.	bad²e ⇒ adad²e	[168]
47.	abd ⇒ dada³	[37]
48.	a²b ⇒ a³d	[66]
49.	eb ⇒ dea	[112]
50.	eab ⇒ adea	[128]
51.	dbd ⇒ dad²	[151]
52.	dab ⇒ da²d	[23]
53.	a²db ⇒ a(ad)²	[146]
54.	dadb ⇒ a²de³	[160]
55.	dad²b ⇒ (dad)²	[156]
56.	a(ca)² ⇒ bd	[19]
57.	cb ⇒ 1	[6]
58.	bc ⇒ 1	[7]
59.	b² ⇒ c²	[8]
60.	c³ ⇒ b	[9]

# ab:baab=aaa,bbbb=1 a/e/d/cb bbb=c,cacaca=d,dadadad=e morph:3/0,6/0,7/0
eaaa=aa
ae=ea
eea=e
deaa=da
aadea=aad
aaaaad=daaaaa
ed=aaaadeeeee
ead=dea
eaad=adea
dadea=dad
daaad=aa
aadd=dadaaa
aaadad=ddaa
ddda=aaade
ddde=aaadeee
daddea=dadd
dadad=aadeee
daddd=daaaadee
caa=aaade
ce=aaadeeee
cda=aaadaadeeee
cde=aaadaadeeeeee
cada=eaa
cade=e
cdda=adadaaaade
cdde=adadaaaadeee
cadda=da
cadde=de
aac=daa
ec=aadeee
eac=aaadeee
dca=cad
dac=daaaadeee
aadc=eaa
dadc=dea
daddc=dade
baa=adaa
be=ade
bda=adda
bde=adde
bada=adada
bade=adade
bdda=aaaade
bdde=aaaadeee
badda=adadda
badde=adadde
abd=dadaaa
aab=aaad
eb=dea
eab=adea
dbd=dadd
dab=daad
aadb=aadad
dadb=aadeee
daddb=daddad
acaca=bd
cb=1
bc=1
bb=cc
ccc=b