#3211 ⟨a, b | abaababbaab=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = bacb²a
- b^-1 = c²
- c^-1 = cb

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

#	Rule	Proof
1.	bc ⇒ cb	[24]
2.	c²b ⇒ 1	[20]
3.	a²b ⇒ cacb²a	[28]
4.	a²c ⇒ c³aba	[23]
5.	acb²ac ⇒ c²(ab)²	[29]
6.	abacb ⇒ cb²a²	[25]
7.	acb²a² ⇒ c²	[19]
8.	abab²ac ⇒ cb²ac²(ab)²	[37]
9.	abab³ac ⇒ bacb(ab)²	[38]
10.	abab²a² ⇒ cb²ac²	[35]
11.	abab³a² ⇒ bacb	[34]

# ab:abaababbaab=1 reversed:bc/a baaba=c morph:5/0
bc=cb
ccb=1
aab=cacbba
aac=cccaba
acbbac=ccabab
abacb=cbbaa
acbbaa=cc
ababbac=cbbaccabab
ababbbac=bacbabab
ababbaa=cbbacc
ababbbaa=bacb