#4987 ⟨a, b | aaaabba=baaa⟩

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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(d) = deg(a) = deg(e) = 0, d < a < e; deg(c) = deg(b) = 1, c < b
Auxiliary generators:
1. bb=c
2. aaca=d
3. aacd=e
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	da³e ⇒ ea²	[18]
2.	a⁴e ⇒ da²	[17]
3.	a²cd ⇒ e	[4]
4.	da³dacd ⇒ ead	[26]
5.	a⁴dacd ⇒ dad	[25]
6.	daca ⇒ e	[7]
7.	a²ca ⇒ d	[3]
8.	eaca ⇒ dacd	[9]
9.	dace ⇒ eacd	[10]
10.	a²ce ⇒ dacd	[8]
11.	cd² ⇒ a(ae)²ca	[28]
12.	cad ⇒ a²eca	[19]
13.	ced ⇒ a(ae)³ca	[40]
14.	cde ⇒ a(ae)²cd	[30]
15.	cae ⇒ a²ecd	[20]
16.	ce² ⇒ a(ae)³cd	[41]
17.	cdad ⇒ a²eadacd	[29]
18.	ca²d ⇒ a²dacd	[16]
19.	cead ⇒ a²(ea)²dacd	[39]
20.	cda² ⇒ a(ae)²	[23]
21.	ca³ ⇒ a²e	[13]
22.	cea² ⇒ a(ae)³	[32]
23.	cdae ⇒ a²(ea)²cd	[31]
24.	ca²e ⇒ a²eacd	[21]
25.	ceae ⇒ a²(ea)³cd	[42]
26.	bd² ⇒ a²daeca	[33]
27.	bad ⇒ a²dca	[12]
28.	bed ⇒ a²d(ae)²ca	[43]
29.	bde ⇒ a²daecd	[35]
30.	bae ⇒ a²dcd	[14]
31.	be² ⇒ a²d(ae)²cd	[44]
32.	bdad ⇒ a²(da)²cd	[34]
33.	ba²d ⇒ a²e	[27]
34.	bead ⇒ a²daeadacd	[38]
35.	bda² ⇒ a²dae	[22]
36.	ba³ ⇒ a²d	[5]
37.	bea² ⇒ a²d(ae)²	[37]
38.	bdae ⇒ a²daeacd	[36]
39.	ba²e ⇒ a²dacd	[15]
40.	beae ⇒ a²da(ea)²cd	[45]
41.	d(acd)² ⇒ eace	[24]
42.	cb ⇒ bc	[6]
43.	b² ⇒ c	[2]

# ab:aaaabba=baaa reversed:dae/cb bb=c,aaca=d,aacd=e morph:2/1,4/1,4/1
daaae=eaa
aaaae=daa
aacd=e
daaadacd=ead
aaaadacd=dad
daca=e
aaca=d
eaca=dacd
dace=eacd
aace=dacd
cdd=aaeaeca
cad=aaeca
ced=aaeaeaeca
cde=aaeaecd
cae=aaecd
cee=aaeaeaecd
cdad=aaeadacd
caad=aadacd
cead=aaeaeadacd
cdaa=aaeae
caaa=aae
ceaa=aaeaeae
cdae=aaeaeacd
caae=aaeacd
ceae=aaeaeaeacd
bdd=aadaeca
bad=aadca
bed=aadaeaeca
bde=aadaecd
bae=aadcd
bee=aadaeaecd
bdad=aadadacd
baad=aae
bead=aadaeadacd
bdaa=aadae
baaa=aad
beaa=aadaeae
bdae=aadaeacd
baae=aadacd
beae=aadaeaeacd
dacdacd=eace
cb=bc
bb=c