#708 ⟨a, b | abaabbaba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 9
Infinite non-Abelian group
Inverses of generators:
- a^-1 = d³ada
- b^-1 = ada
- c^-1 = d
- d^-1 = c

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

#	Rule	Proof
1.	cd ⇒ 1	[17]
2.	dc ⇒ 1	[4]
3.	b ⇒ ad³	[21]
4.	ad³ad ⇒ d³ada	[23]
5.	adac ⇒ c³ad³a	[37]
6.	ad³ac ⇒ da²d	[33]
7.	a²d² ⇒ cad³a	[41]
8.	ada² ⇒ c³	[28]
9.	a(dad)² ⇒ c³ad⁶ada	[44]
10.	adad²ac ⇒ c³ad⁴a²d	[40]

# ab:abaabbaba=1 reversed:dc/ab aba=c,cabb=d morph:3/0,4/0
cd=1
dc=1
b=addd
adddad=dddada
adac=cccaddda
adddac=daad
aadd=caddda
adaa=ccc
adaddad=cccaddddddada
adaddac=cccaddddaad