#3180 ⟨a, b | abaaaababba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = ad
- b^-1 = a²ca²
- c^-1 = a²ba²
- d^-1 = a²

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

#	Rule	Proof
1.	da ⇒ ad	[12]
2.	a²d ⇒ 1	[16]
3.	ca²b ⇒ d	[3]
4.	ba²c ⇒ d	[17]
5.	c² ⇒ adb²	[22]
6.	ca²c ⇒ a(ab)²d	[19]
7.	ca³c ⇒ d(ba²)²	[32]
8.	ca⁴c ⇒ ba⁴bad	[31]
9.	bab² ⇒ dc	[14]
10.	ba⁴bab ⇒ ca²	[29]
11.	b²a²b ⇒ acd	[21]
12.	ba²ba⁴b ⇒ a²ca	[38]
13.	b²c ⇒ acadb²	[24]
14.	babc ⇒ dca⁴babd	[26]
15.	babdc ⇒ dcab²	[15]
16.	(ba)²c ⇒ dc(ba²)²	[43]
17.	ba⁴bac ⇒ ca⁶babd	[40]
18.	ba⁴badc ⇒ ca³b²	[30]
19.	b²a³c ⇒ acd(ba²)²	[44]
20.	ba⁴ba³c ⇒ c(a⁴b)²ad	[41]
21.	b²a⁴c ⇒ acba⁴bad	[45]
22.	ba²ba⁴c ⇒ a²ca⁵babd	[47]
23.	ba²ba⁵c ⇒ a²ca(ba²)²	[46]
24.	ba²ba⁶c ⇒ a²c(a³ba)²d	[48]

# ab:abaaaababba=1 reversed:da/bc aababb=c,caab=d morph:6/0,4/0
da=ad
aad=1
caab=d
baac=d
cc=adbb
caac=aababd
caaac=dbaabaa
caaaac=baaaabad
babb=dc
baaaabab=caa
bbaab=acd
baabaaaab=aaca
bbc=acadbb
babc=dcaaaababd
babdc=dcabb
babac=dcbaabaa
baaaabac=caaaaaababd
baaaabadc=caaabb
bbaaac=acdbaabaa
baaaabaaac=caaaabaaaabad
bbaaaac=acbaaaabad
baabaaaac=aacaaaaababd
baabaaaaac=aacabaabaa
baabaaaaaac=aacaaabaaaabad