#3224 ⟨a, b | abaabbbbaab=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 = b³cbabc
- 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:
- Left-to-right recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aa=c
2. bbbbaabab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[11]
2.	dc ⇒ 1	[20]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[21]
5.	a² ⇒ c	[2]
6.	cbabcb ⇒ bcbabc	[29]
7.	dbcbab ⇒ babcbd	[33]
8.	c(ab)²cb ⇒ abcbabc	[30]
9.	dabcbab ⇒ (ab)²cbd	[35]
10.	db²cbab ⇒ babcb²d	[37]
11.	ab³cb ⇒ cbcb³da	[27]
12.	abcb³ ⇒ b³cba	[23]
13.	dab²cbab ⇒ (ab)²cb²d	[38]
14.	cb⁴cb ⇒ b³c(ba)²	[15]
15.	cbab²cbab ⇒ bcb(abc)²bd	[49]
16.	db³cbab ⇒ b⁴cbda	[28]
17.	ab⁴cb ⇒ bcb⁴a	[47]
18.	cabab²cbab ⇒ abcb(abc)²bd	[51]
19.	b⁴cbab ⇒ d	[3]
20.	(cb)³b³ ⇒ bcb(abc)²b²d	[55]
21.	d(bc)³b³ ⇒ babcbdb²cba	[57]
22.	ca(bc)²b⁴ ⇒ abcb(abc)²b²d	[56]
23.	da(bc)³b³ ⇒ (ab)²cbdb²cba	[58]
24.	db(bc)³b³ ⇒ babcb²db²cba	[59]
25.	dbcb²cb⁴ ⇒ babcbdb³cbda	[43]
26.	dab(bc)³b³ ⇒ (ab)²cb²db²cba	[60]
27.	dabcb²cb⁴ ⇒ (ab)²cbdb³cbda	[44]
28.	cbab(bc)³b³ ⇒ bcb(abc)²bdb²cba	[62]
29.	db²(bc)³b³ ⇒ b⁴cbdab²cba	[61]
30.	d(b²c)²b⁴ ⇒ babcb²db³cbda	[45]
31.	c(ab)²(bc)³b³ ⇒ abcb(abc)²bdb²cba	[63]
32.	da(b²c)²b⁴ ⇒ (ab)²cb²db³cbda	[46]
33.	b³(bc)³b³ ⇒ db²cba	[25]
34.	cba(b²c)²b⁴ ⇒ bcb(abc)²bdb³cbda	[65]
35.	db(b²c)²b⁴ ⇒ b⁴cb²cb³d	[54]
36.	caba(b²c)²b⁴ ⇒ abcb(abc)²bdb³cbda	[66]
37.	b⁴cb²cb⁴ ⇒ db³cbda	[42]

# ab:abaabbbbaab=1 cda/b aa=c,bbbbaabab=d magic:0
cd=1
dc=1
ac=ca
ad=da
aa=c
cbabcb=bcbabc
dbcbab=babcbd
cababcb=abcbabc
dabcbab=ababcbd
dbbcbab=babcbbd
abbbcb=cbcbbbda
abcbbb=bbbcba
dabbcbab=ababcbbd
cbbbbcb=bbbcbaba
cbabbcbab=bcbabcabcbd
dbbbcbab=bbbbcbda
abbbbcb=bcbbbba
cababbcbab=abcbabcabcbd
bbbbcbab=d
cbcbcbbbb=bcbabcabcbbd
dbcbcbcbbb=babcbdbbcba
cabcbcbbbb=abcbabcabcbbd
dabcbcbcbbb=ababcbdbbcba
dbbcbcbcbbb=babcbbdbbcba
dbcbbcbbbb=babcbdbbbcbda
dabbcbcbcbbb=ababcbbdbbcba
dabcbbcbbbb=ababcbdbbbcbda
cbabbcbcbcbbb=bcbabcabcbdbbcba
dbbbcbcbcbbb=bbbbcbdabbcba
dbbcbbcbbbb=babcbbdbbbcbda
cababbcbcbcbbb=abcbabcabcbdbbcba
dabbcbbcbbbb=ababcbbdbbbcbda
bbbbcbcbcbbb=dbbcba
cbabbcbbcbbbb=bcbabcabcbdbbbcbda
dbbbcbbcbbbb=bbbbcbbcbbbd
cababbcbbcbbbb=abcbabcabcbdbbbcbda
bbbbcbbcbbbb=dbbbcbda