#3812 ⟨a, b | abbabaaaab=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(b) = deg(d) = deg(c) = deg(e) = 0, b < d < c < e; deg(f) = deg(a) = 1, f < a
Auxiliary generators:
1. ab=c
2. ac=d
3. ad=e
4. ebcaea=f
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dfb ⇒ c²f	[39]
2.	efb ⇒ dcf	[37]
3.	dcfb ⇒ dbcf	[36]
4.	c²fb ⇒ cbcf	[35]
5.	ecfb ⇒ ebcf	[34]
6.	fd ⇒ dbcecf	[44]
7.	fc ⇒ cbcecf	[43]
8.	fe ⇒ ebcecf	[45]
9.	dbcfb² ⇒ d	[28]
10.	cbcfb² ⇒ c	[25]
11.	ebcfb² ⇒ e	[21]
12.	dbcfbd ⇒ fb	[29]
13.	cbcfbd ⇒ e	[27]
14.	ebcfbd ⇒ cbcecf	[46]
15.	dbcfbc ⇒ e	[30]
16.	cbcfbc ⇒ d	[26]
17.	ebcfbc ⇒ fb	[24]
18.	dbcfbe ⇒ cbcecf	[48]
19.	cbcfbe ⇒ fb	[38]
20.	ebcfbe ⇒ dbcecf	[47]
21.	a ⇒ cbcfb	[17]
22.	f²b ⇒ fb²cecf	[41]
23.	(fb)² ⇒ ecf	[40]
24.	fbcfb ⇒ fb²cf	[33]
25.	fb²cfb ⇒ f	[32]

# ab:abbabaaaab=a reversed:bdce/fa ab=c,ac=d,ad=e,ebcaea=f morph:2/1,2/1,2/1,6/0
dfb=ccf
efb=dcf
dcfb=dbcf
ccfb=cbcf
ecfb=ebcf
fd=dbcecf
fc=cbcecf
fe=ebcecf
dbcfbb=d
cbcfbb=c
ebcfbb=e
dbcfbd=fb
cbcfbd=e
ebcfbd=cbcecf
dbcfbc=e
cbcfbc=d
ebcfbc=fb
dbcfbe=cbcecf
cbcfbe=fb
ebcfbe=dbcecf
a=cbcfb
ffb=fbbcecf
fbfb=ecf
fbcfb=fbbcf
fbbcfb=f