⟨a, b | abbabaaaab=a⟩

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Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Auxiliary generators:
1. c = ab
2. d = ac
3. e = ad
4. f = ebcaea
Reduction order:
- Right-to-left recursive path with deg(b) = deg(d) = deg(c) = 0, b < d < c; deg(e) = 1; deg(f) = 2; deg(a) = 3
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

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

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

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#3812 ⟨a, b | abbabaaaab=a⟩

Contents

Properties

Rewriting system