#1523 ⟨a, b | ababbbabba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Inverses of generators:
- a^-1 = dc
- b^-1 = abca
- c^-1 = ad
- d^-1 = ca

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(a) = deg(c) = deg(d) = 0, a < c < d; deg(b) = 1
Auxiliary generators:
1. bbabba=c
2. bab=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	adc ⇒ 1	[4]
2.	cad ⇒ 1	[19]
3.	dca ⇒ 1	[14]
4.	cb ⇒ bd²	[7]
5.	db ⇒ abcacdc	[23]
6.	a²b ⇒ bcaca³d²	[24]
7.	cab ⇒ abc	[21]
8.	dab ⇒ bad	[6]
9.	bab ⇒ d	[3]

# ab:ababbbabba=1 acd/b bbabba=c,bab=d morph:6/0,3/0
adc=1
cad=1
dca=1
cb=bdd
db=abcacdc
aab=bcacaaadd
cab=abc
dab=bad
bab=d