#4359 ⟨a, b | abbbbbbba=ab⟩

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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:
- Left-to-right shortlex with a < d < c < b
Auxiliary generators:
1. bbb=c
2. acccc=d
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