⟨a, b | abbbbbbba=ab⟩

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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 = bbb
2. d = acccc
Reduction order:
- Left-to-right shortlex with a < d < c < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	bc ⇒ cb	[5]
2.	ac² ⇒ da	[14]
3.	d²a ⇒ d	[15]
4.	dca ⇒ dac	[32]
5.	dcd ⇒ d²c	[34]
6.	dc² ⇒ d²	[23]
7.	dba ⇒ dab	[30]
8.	dbd ⇒ d²b	[24]
9.	b³ ⇒ c	[2]
10.	daca ⇒ ac	[21]
11.	dacd ⇒ dc	[26]
12.	daba ⇒ ab	[16]
13.	dabd ⇒ db	[18]
14.	dcba ⇒ dacb	[33]
15.	dcbd ⇒ d²cb	[35]
16.	db²a ⇒ dab²	[31]
17.	db²d ⇒ d²b²	[36]
18.	dacba ⇒ acb	[27]
19.	dacbd ⇒ dcb	[29]
20.	dab²a ⇒ ab²	[19]
21.	dab²d ⇒ db²	[25]
22.	dcb²a ⇒ dacb²	[37]
23.	dcb²d ⇒ d²cb²	[38]
24.	dacb²a ⇒ acb²	[28]
25.	dacb²d ⇒ dcb²	[39]

# ab:abbbbbbba=ab adcb bbb=c,acccc=d morph:3/0,5/0 bc=cb acc=da dda=d dca=dac dcd=ddc dcc=dd dba=dab dbd=ddb bbb=c daca=ac dacd=dc daba=ab dabd=db dcba=dacb dcbd=ddcb dbba=dabb dbbd=ddbb dacba=acb dacbd=dcb dabba=abb dabbd=dbb dcbba=dacbb dcbbd=ddcbb dacbba=acbb dacbbd=dcbb

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#4359 ⟨a, b | abbbbbbba=ab⟩

Contents

Properties

Rewriting system