⟨a, b | abbbabaaab=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 = bcada
Reduction order:
- Right-to-left recursive path with deg(d) = deg(b) = 0, d < b; deg(c) = 1; deg(e) = deg(a) = 2, e < a
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ed ⇒ b(cd)²be	[42]
2.	deb ⇒ db²c²b²(cd)²be	[45]
3.	d²beb ⇒ c²dbe	[48]
4.	ceb ⇒ (cb²c)²dcdbe	[44]
5.	cbeb ⇒ d	[14]
6.	dcdbeb ⇒ dbcdbe	[38]
7.	dbcdbeb ⇒ db²cdbe	[30]
8.	db²cdbeb ⇒ cbe	[27]
9.	c²dbeb ⇒ cbcdbe	[41]
10.	cbcdbeb ⇒ cb²cdbe	[29]
11.	cb²cdbebd ⇒ dbeb	[25]
12.	cb²cdbeb² ⇒ c	[22]
13.	ec ⇒ bcdbebd	[32]
14.	bcdbebc ⇒ eb	[31]
15.	a ⇒ cb²cdbeb	[21]
16.	e²b ⇒ eb²c²b²(cd)²be	[46]
17.	(eb)² ⇒ eb³c²b²(cd)²be	[43]
18.	eb²eb ⇒ bcdbebd	[20]
19.	ebdbeb ⇒ bcdbeb²cdbe	[49]
20.	ebcdbeb ⇒ eb²cdbe	[47]
21.	eb²cdbeb ⇒ eb³cdbe	[28]
22.	eb³cdbeb ⇒ e	[26]

# ab:abbbabaaab=a reversed:db/c/ea ab=c,ac=d,bcada=e morph:2/0,2/1,5/2 ed=bcdcdbe deb=dbbccbbcdcdbe ddbeb=ccdbe ceb=cbbccbbcdcdbe cbeb=d dcdbeb=dbcdbe dbcdbeb=dbbcdbe dbbcdbeb=cbe ccdbeb=cbcdbe cbcdbeb=cbbcdbe cbbcdbebd=dbeb cbbcdbebb=c ec=bcdbebd bcdbebc=eb a=cbbcdbeb eeb=ebbccbbcdcdbe ebeb=ebbbccbbcdcdbe ebbeb=bcdbebd ebdbeb=bcdbebbcdbe ebcdbeb=ebbcdbe ebbcdbeb=ebbbcdbe ebbbcdbeb=e

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#3827 ⟨a, b | abbbabaaab=a⟩

Contents

Properties

Rewriting system