#2930 ⟨a, b | aaababaabaa=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = ca⁴
- b^-1 = aba²ba⁵
- c^-1 = a⁵

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

#	Rule	Proof
1.	ac ⇒ ca	[9]
2.	ca⁵ ⇒ 1	[10]
3.	aba⁵b ⇒ ba²ba⁴	[19]
4.	caba²b ⇒ babca²	[11]
5.	c(a²b)² ⇒ (ab)²ca²	[13]
6.	a³bab ⇒ ba⁵bca⁴	[24]
7.	ca(a²b)² ⇒ a(ab)²ca²	[12]
8.	ca⁴ba²b ⇒ ba⁵bca	[25]
9.	baba²b ⇒ c	[2]
10.	aba⁴ba²b ⇒ ba²ba⁹bca	[28]
11.	a³b²a²b ⇒ ba(a⁴b)²ca	[26]

# ab:aaababaabaa=1 ca/b babaab=c morph:6/0
ac=ca
caaaaa=1
abaaaaab=baabaaaa
cabaab=babcaa
caabaab=ababcaa
aaabab=baaaaabcaaaa
caaabaab=aababcaa
caaaabaab=baaaaabca
babaab=c
abaaaabaab=baabaaaaaaaaabca
aaabbaab=baaaaabaaaabca