#3115 ⟨a, b | aabbabaaaab=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = da
- b^-1 = a²ca³
- c^-1 = a³ba²
- 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:
- Left-to-right recursive path with deg(d) = deg(a) = 0, d < a; deg(b) = deg(c) = 1, b < c
Auxiliary generators:
1. bbaba=c
2. baaca=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ad ⇒ da	[17]
2.	da² ⇒ 1	[19]
3.	ba²c ⇒ d²a	[20]
4.	ca³b ⇒ d	[8]
5.	cac ⇒ b²d	[21]
6.	ca³c ⇒ d(ba)²	[10]
7.	ca⁴c ⇒ (a²b)²d²a	[49]
8.	ca⁵c ⇒ daba⁴bda	[38]
9.	b²ab ⇒ cda	[25]
10.	baba⁴b ⇒ a²ca	[31]
11.	ba²b² ⇒ dca²	[23]
12.	ba⁴ba²b ⇒ aca³	[37]
13.	cba⁴b ⇒ b²a³ca	[33]
14.	cab² ⇒ b²daca²	[24]
15.	c(ab)² ⇒ dbaba⁴cda	[30]
16.	cd(ab)² ⇒ b²acda	[27]
17.	ca(ab)² ⇒ (a²b)²cda	[50]
18.	ca²ba⁴b ⇒ dbaba⁶ca	[34]
19.	ca⁴b² ⇒ (a²b)²dca²	[51]
20.	c(a⁴b)² ⇒ da(ba⁴)²ca	[36]
21.	ca⁵b² ⇒ daba⁴bca²	[39]
22.	ca⁵ba²b ⇒ dbaba⁵ca³	[41]
23.	ca⁶ba²b ⇒ (a²b)²aca³	[45]
24.	ca⁷ba²b ⇒ d(aba³)²ca³	[42]

# ab:aabbabaaaab=1 da/bc bbaba=c,baaca=d morph:5/0,5/0
ad=da
daa=1
baac=dda
caaab=d
cac=bbd
caaac=dbaba
caaaac=aabaabdda
caaaaac=dabaaaabda
bbab=cda
babaaaab=aaca
baabb=dcaa
baaaabaab=acaaa
cbaaaab=bbaaaca
cabb=bbdacaa
cabab=dbabaaaacda
cdabab=bbacda
caabab=aabaabcda
caabaaaab=dbabaaaaaaca
caaaabb=aabaabdcaa
caaaabaaaab=dabaaaabaaaaca
caaaaabb=dabaaaabcaa
caaaaabaab=dbabaaaaacaaa
caaaaaabaab=aabaabacaaa
caaaaaaabaab=dabaaaabaaacaaa