#3817 ⟨a, b | abbabbaaab=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(d) = 1; deg(e) = deg(a) = 2, e < a
Auxiliary generators:
1. ab=c
2. cba=d
3. daca=e
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	db ⇒ cbc	[6]
2.	cec ⇒ cb(dc)³be	[67]
3.	c²bec ⇒ cb(dc)²be	[53]
4.	c(cb)²ec ⇒ cbdcbe	[27]
5.	(cb)⁴ec ⇒ d	[44]
6.	dec ⇒ cbc(dc)³be	[69]
7.	dcbec ⇒ cbc(dc)²be	[72]
8.	d(cb)²ec ⇒ cbcdcbe	[73]
9.	d(cb)³ec ⇒ (cb)²e	[29]
10.	ceb ⇒ c(bc)²(dc)²be	[75]
11.	(cb)²eb ⇒ dc	[17]
12.	deb ⇒ (cbc)²(dc)²be	[77]
13.	dcbeb ⇒ (cb)²ec	[19]
14.	(cb)²ec² ⇒ eb	[23]
15.	(cb)³ecb ⇒ c	[37]
16.	ced ⇒ cb(dc)²e	[62]
17.	c²bed ⇒ cbdce	[56]
18.	c(cb)²ed ⇒ cbe	[51]
19.	(cb)³ed ⇒ c(cb)³ec	[26]
20.	ded ⇒ cbc(dc)²e	[65]
21.	dcbed ⇒ cbcdce	[70]
22.	d(cb)²ed ⇒ cbce	[71]
23.	a ⇒ (cb)³ec	[22]
24.	e²c ⇒ eb(dc)³be	[68]
25.	ebec ⇒ eb²(dc)³be	[66]
26.	ecbec ⇒ eb(dc)²be	[59]
27.	eb²ec ⇒ (cb)²ecb(dc)²be	[58]
28.	ebcbec ⇒ eb²(dc)²be	[52]
29.	e(cb)²ec ⇒ ebdcbe	[48]
30.	eb²cbec ⇒ (cb)²ecbdcbe	[50]
31.	eb(cb)²ec ⇒ eb²dcbe	[47]
32.	e(cb)³ec ⇒ eb²e	[31]
33.	eb²(cb)²ec ⇒ e	[28]
34.	eb²(cb)³ec ⇒ (cb)²ecd	[25]
35.	e²b ⇒ e(bc)²(dc)²be	[76]
36.	(eb)² ⇒ eb(bc)²(dc)²be	[74]
37.	ecbeb ⇒ (cb)²ecb(dc)²be	[64]
38.	eb²eb ⇒ ec	[32]
39.	eb²cbeb ⇒ (cb)²ecdc	[36]
40.	e²d ⇒ eb(dc)²e	[63]
41.	ebed ⇒ eb²(dc)²e	[61]
42.	ecbed ⇒ ebdce	[60]
43.	eb²ed ⇒ (cb)²ecbdce	[57]
44.	ebcbed ⇒ eb²dce	[55]
45.	e(cb)²ed ⇒ ebe	[54]
46.	eb²cbed ⇒ cb(cbe)²	[49]
47.	eb(cb)²ed ⇒ eb²e	[42]
48.	eb²(cb)²ed ⇒ eb(cb)³ec	[34]

# ab:abbabbaaab=a reversed:cb/d/ea ab=c,cba=d,daca=e morph:2/0,3/1,4/1
db=cbc
cec=cbdcdcdcbe
ccbec=cbdcdcbe
ccbcbec=cbdcbe
cbcbcbcbec=d
dec=cbcdcdcdcbe
dcbec=cbcdcdcbe
dcbcbec=cbcdcbe
dcbcbcbec=cbcbe
ceb=cbcbcdcdcbe
cbcbeb=dc
deb=cbccbcdcdcbe
dcbeb=cbcbec
cbcbecc=eb
cbcbcbecb=c
ced=cbdcdce
ccbed=cbdce
ccbcbed=cbe
cbcbcbed=ccbcbcbec
ded=cbcdcdce
dcbed=cbcdce
dcbcbed=cbce
a=cbcbcbec
eec=ebdcdcdcbe
ebec=ebbdcdcdcbe
ecbec=ebdcdcbe
ebbec=cbcbecbdcdcbe
ebcbec=ebbdcdcbe
ecbcbec=ebdcbe
ebbcbec=cbcbecbdcbe
ebcbcbec=ebbdcbe
ecbcbcbec=ebbe
ebbcbcbec=e
ebbcbcbcbec=cbcbecd
eeb=ebcbcdcdcbe
ebeb=ebbcbcdcdcbe
ecbeb=cbcbecbdcdcbe
ebbeb=ec
ebbcbeb=cbcbecdc
eed=ebdcdce
ebed=ebbdcdce
ecbed=ebdce
ebbed=cbcbecbdce
ebcbed=ebbdce
ecbcbed=ebe
ebbcbed=cbcbecbe
ebcbcbed=ebbe
ebbcbcbed=ebcbcbcbec