#2857 ⟨a, b | aaaababaaba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = bc²a³
- b^-1 = c²a⁴
- c^-1 = baca³

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. aba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²a³c ⇒ a	[26]
2.	aca³c ⇒ c²a⁴	[28]
3.	c²a²c²a⁴ ⇒ a⁴c	[29]
4.	aca²c²a⁴ ⇒ c²a⁷c	[30]
5.	bc²a⁴ ⇒ 1	[15]
6.	baca⁴ ⇒ ca³c	[27]
7.	cb ⇒ bc⁴a²	[17]
8.	ab ⇒ bc⁴a²c²a³	[22]

# ab:aaaababaaba=1 ca/b aba=c morph:3/0
ccaaac=a
acaaac=ccaaaa
ccaaccaaaa=aaaac
acaaccaaaa=ccaaaaaaac
bccaaaa=1
bacaaaa=caaac
cb=bccccaa
ab=bccccaaccaaa