#3063 ⟨a, b | aabababaaab=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = acac³
- b^-1 = dc²a
- 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:
- Left-to-right recursive path with deg(d) = deg(c) = 0, d < c; deg(a) = 1; deg(b) = 2
Auxiliary generators:
1. ab=c
2. aaca=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	cd ⇒ dc	[18]
2.	dc³ ⇒ 1	[16]
3.	daca ⇒ a²dc	[20]
4.	cac³a ⇒ acac³	[27]
5.	d(ca)² ⇒ ca²dc	[21]
6.	c²a² ⇒ ac³adc²	[25]
7.	dc(ca)² ⇒ ac³ad	[24]
8.	a²ca ⇒ d	[3]
9.	(cac)²a ⇒ acac⁶ad	[30]
10.	b ⇒ acac⁴	[29]

# ab:aabababaaab=1 dc/a/b ab=c,aaca=d morph:2/0,4/1
cd=dc
dccc=1
daca=aadc
caccca=acaccc
dcaca=caadc
ccaa=acccadcc
dccaca=acccad
aaca=d
caccaca=acaccccccad
b=acacccc