#3044 ⟨a, b | aabaabbabaa=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = a²d
- b^-1 = a²ca⁴
- c^-1 = a⁴ba²
- d^-1 = a³

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

#	Rule	Proof
1.	da ⇒ ad	[7]
2.	a³d ⇒ 1	[12]
3.	ca⁴b ⇒ ad	[20]
4.	ba²c ⇒ a²d²	[9]
5.	ca²c ⇒ b²d	[8]
6.	ca⁴c ⇒ adbab	[21]
7.	ca⁵c ⇒ a²(ba²)²d²	[30]
8.	ca⁶c ⇒ a²dba⁴bad	[41]
9.	ba²b² ⇒ adca³	[16]
10.	b²ab ⇒ c	[2]
11.	ba⁴ba²b ⇒ aca⁴	[35]
12.	baba⁴b ⇒ a²ca²	[23]
13.	ba²bc ⇒ adca³bab	[18]
14.	ba⁴bc ⇒ aca⁶b²d	[38]
15.	b²ac ⇒ cbab	[6]
16.	ba²bac ⇒ adca⁷(ba²)²d²	[33]
17.	ba²badc ⇒ adca⁵b²d	[31]
18.	b²a²dc ⇒ ca²b²d	[10]
19.	b²a³c ⇒ caba⁴bad	[26]
20.	ba⁴ba³c ⇒ aca⁸(ba²)²d²	[39]
21.	baba⁴c ⇒ a²ca(ab)²	[25]
22.	(ba⁴)²c ⇒ aca(a⁴b)²ad	[40]
23.	baba⁵c ⇒ a²ca⁶(ba²)²d²	[34]
24.	baba⁶c ⇒ a²c(a³ba)²d	[42]

# ab:aabaabbabaa=1 reversed:da/bc bbab=c,abaac=d morph:4/0,5/0
da=ad
aaad=1
caaaab=ad
baac=aadd
caac=bbd
caaaac=adbab
caaaaac=aabaabaadd
caaaaaac=aadbaaaabad
baabb=adcaaa
bbab=c
baaaabaab=acaaaa
babaaaab=aacaa
baabc=adcaaabab
baaaabc=acaaaaaabbd
bbac=cbab
baabac=adcaaaaaaabaabaadd
baabadc=adcaaaaabbd
bbaadc=caabbd
bbaaac=cabaaaabad
baaaabaaac=acaaaaaaaabaabaadd
babaaaac=aacaabab
baaaabaaaac=acaaaaabaaaabad
babaaaaac=aacaaaaaabaabaadd
babaaaaaac=aacaaabaaaabad