#3064 ⟨a, b | aabababaaba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = dc²b
- b^-1 = adc²
- c^-1 = dc²
- d^-1 = c³

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:
- Right-to-left recursive path with deg(c) = deg(d) = 0, c < d; deg(a) = deg(b) = 1, a < b
Auxiliary generators:
1. ba=c
2. acaa=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	cd ⇒ dc	[27]
2.	dc³ ⇒ 1	[28]
3.	a² ⇒ dcbd	[29]
4.	aca ⇒ d²c²b	[21]
5.	ac³a ⇒ dc²bdc²	[40]
6.	ba ⇒ c	[2]
7.	ab ⇒ d²c²bc³ac	[45]
8.	acb ⇒ dc²bdc²ac³	[46]
9.	adb ⇒ d²c²bca	[35]
10.	ac²b ⇒ dc²bc²ac	[41]
11.	adcb ⇒ dcbdac³	[42]
12.	adc²b ⇒ 1	[37]
13.	ad²c²b ⇒ dcbdca	[34]
14.	bdcb ⇒ cac³	[32]
15.	bdc²b ⇒ c⁴ac	[24]
16.	bd²c²b ⇒ c²a	[33]

# ab:aabababaaba=1 reversed:cd/ab ba=c,acaa=d morph:2/0,4/0
cd=dc
dccc=1
aa=dcbd
aca=ddccb
accca=dccbdcc
ba=c
ab=ddccbcccac
acb=dccbdccaccc
adb=ddccbca
accb=dccbccac
adcb=dcbdaccc
adccb=1
addccb=dcbdca
bdcb=caccc
bdccb=ccccac
bddccb=cca