#3062 ⟨a, b | aababaabbba=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 = cbaba²b²
- c^-1 = d
- d^-1 = c

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(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaa=c
2. babaabbb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[10]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[9]
5.	a³ ⇒ c	[2]
6.	b(aba)² ⇒ dbcbabc	[23]
7.	bcbaba² ⇒ cbaba²b	[20]
8.	ba²b³c ⇒ a(ab)²a²b²	[14]
9.	baba²b²d ⇒ adba²b³	[11]
10.	ba²b³a ⇒ a²db²cbab	[38]
11.	baba²b²a ⇒ db²cbabc	[36]
12.	b³cba ⇒ (ab)²a²b²	[43]
13.	b²c(ba)² ⇒ a²b³cb	[47]
14.	baba²b³ ⇒ d	[3]
15.	(bcba)²aba ⇒ cbaba²dbcbabc	[27]
16.	bc(ba)²cb³c ⇒ (c(ba)²)²ab²	[26]
17.	(bcba)²ab²d ⇒ cbab²a²b³	[25]
18.	bc(ba)²cb³a ⇒ c(ba)²b²cbab	[35]
19.	(bcba)²ab²a ⇒ cbaba²db²cbabc	[59]
20.	b³cb²a²ba ⇒ adb²cbadbcbabc	[49]
21.	b²cbab²a²ba ⇒ aba²b²dbcbabc	[34]
22.	(bcba)²ab³ ⇒ cbaba²d	[24]
23.	b³cb⁴c ⇒ a²d(ba²b)²aba²b²	[61]
24.	b³cbcb³c ⇒ adb(c(ba)²)²ab²	[56]
25.	b²cbabcb³c ⇒ a²b³a²cbaba²b²	[58]
26.	b³cb²a²b²d ⇒ adb²cba²dba²b³	[48]
27.	b²cbab²a²b²d ⇒ aba²b²adba²b³	[32]
28.	b³cb⁴a ⇒ a²dba²b²a²db²cbab	[63]
29.	b³cbcb³a ⇒ adbc(ba)²b²cbab	[55]
30.	b²cbabcb³a ⇒ a²b³a²b²cbab	[57]
31.	b³cb²a²b²a ⇒ a(db²cba)²bc	[50]
32.	b²cb(ab²a)² ⇒ aba²b²db²cbabc	[40]
33.	b³cb²a²b³ ⇒ adb²cbad	[42]
34.	b²cbab²a²b³ ⇒ aba²b²d	[31]

# ab:aababaabbba=1 reversed:cda/b aaa=c,babaabbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
babaaba=dbcbabc
bcbabaa=cbabaab
baabbbc=aababaabb
babaabbd=adbaabbb
baabbba=aadbbcbab
babaabba=dbbcbabc
bbbcba=ababaabb
bbcbaba=aabbbcb
babaabbb=d
bcbabcbaaba=cbabaadbcbabc
bcbabacbbbc=cbabacbabaabb
bcbabcbaabbd=cbabbaabbb
bcbabacbbba=cbababbcbab
bcbabcbaabba=cbabaadbbcbabc
bbbcbbaaba=adbbcbadbcbabc
bbcbabbaaba=abaabbdbcbabc
bcbabcbaabbb=cbabaad
bbbcbbbbc=aadbaabbaababaabb
bbbcbcbbbc=adbcbabacbabaabb
bbcbabcbbbc=aabbbaacbabaabb
bbbcbbaabbd=adbbcbaadbaabbb
bbcbabbaabbd=abaabbadbaabbb
bbbcbbbba=aadbaabbaadbbcbab
bbbcbcbbba=adbcbababbcbab
bbcbabcbbba=aabbbaabbcbab
bbbcbbaabba=adbbcbadbbcbabc
bbcbabbaabba=abaabbdbbcbabc
bbbcbbaabbb=adbbcbad
bbcbabbaabbb=abaabbd