#3210 ⟨a, b | abaabababba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = acd
- b^-1 = (ca)²c²
- c^-1 = acac³acd
- d^-1 = a²c

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

#	Rule	Proof
1.	(ca)²c²a ⇒ a²cac³	[19]
2.	(ca)²c³ ⇒ a	[18]
3.	a²cac⁴ac²a ⇒ (ca)³acac³	[22]
4.	a²(cac³)² ⇒ (ca)³	[21]
5.	a²cd ⇒ 1	[11]
6.	a²cac³acd ⇒ (ca)²c²	[20]
7.	da ⇒ acac⁴d	[14]
8.	dc ⇒ ac⁴ac⁷d	[25]
9.	b ⇒ cacd	[7]

# ab:abaabababba=1 reversed:a/c/db ba=c,accbb=d morph:2/0,5/2
cacacca=aacaccc
cacaccc=a
aacaccccacca=cacacaacaccc
aacaccccaccc=cacaca
aacd=1
aacacccacd=cacacc
da=acaccccd
dc=accccacccccccd
b=cacd