⟨a, b | aabbbbba=baa⟩

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

#	Rule	Proof
1.	a²e⁵ ⇒ ea	[13]
2.	a²e⁴d ⇒ e	[8]
3.	da ⇒ e	[4]
4.	de ⇒ eae⁴d	[10]
5.	ca ⇒ a²d	[7]
6.	ce ⇒ ead	[9]
7.	a²e⁴cd ⇒ ec	[14]
8.	dc ⇒ cd	[6]
9.	a²e⁴c²d ⇒ ec²	[15]
10.	a²e⁴c³d ⇒ ec³	[16]
11.	a²e⁴c⁴d ⇒ ec⁴	[17]
12.	c⁵ ⇒ d	[3]
13.	be ⇒ a²ea(eae⁴)³d²	[11]
14.	ba² ⇒ a²c	[5]
15.	bae ⇒ a⁴(eae⁴)⁴d²	[12]
16.	b⁵a ⇒ c	[2]

# ab:aabbbbba=baa reversed:ae/dc/b bbbbba=c,ccccc=d,da=e morph:6/2,5/0,2/0 aaeeeee=ea aaeeeed=e da=e de=eaeeeed ca=aad ce=ead aaeeeecd=ec dc=cd aaeeeeccd=ecc aaeeeecccd=eccc aaeeeeccccd=ecccc ccccc=d be=aaeaeaeeeeeaeeeeeaeeeedd baa=aac bae=aaaaeaeeeeeaeeeeeaeeeeeaeeeedd bbbbba=c

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#4749 ⟨a, b | aabbbbba=baa⟩

Contents

Properties

Rewriting system