#1498 ⟨a, b | abaabbaaab=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-Abelian group
Inverses of generators:
- a^-1 = a²d²adc
- b^-1 = da²
- c^-1 = da²d²a²
- d^-1 = a²d²a²c

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) = 0; deg(a) = 1; deg(c) = 2; deg(b) = 3
Auxiliary generators:
1. baabb=c
2. aca=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	da²d²ad ⇒ a	[16]
2.	a³d²ad ⇒ da²d²a²	[18]
3.	da²d²a²c ⇒ 1	[15]
4.	a³d²a²c ⇒ da²d²a	[17]
5.	cd ⇒ d(da)²(d²ad)²c	[24]
6.	ca ⇒ a(a(d²ad)²)²c	[25]
7.	b ⇒ d²a²c	[9]

# ab:abaabbaaab=1 reversed:d/a/c/b baabb=c,aca=d morph:5/0,3/0
daaddad=a
aaaddad=daaddaa
daaddaac=1
aaaddaac=daadda
cd=ddadaddadddadc
ca=aaddadddadaddadddadc
b=ddaac

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