#3238 ⟨a, b | ababaabbbba=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 = cbabcb³
- 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. aa=c
2. bbbbaabab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[16]
2.	cd ⇒ 1	[26]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[23]
5.	a² ⇒ c	[2]
6.	bcbabc ⇒ cbabcb	[29]
7.	babcbd ⇒ dbcbab	[17]
8.	bc(ba)²c ⇒ cbabcba	[31]
9.	babcbad ⇒ dbc(ba)²	[28]
10.	babcb²d ⇒ db²cbab	[18]
11.	bcb³a ⇒ adb³cbc	[45]
12.	b³cba ⇒ abcb³	[38]
13.	babcb²ad ⇒ db²c(ba)²	[33]
14.	bcb⁴c ⇒ (ab)²cb³	[11]
15.	babcb²abc ⇒ db(cba)²bcb	[30]
16.	babcb³d ⇒ adbcb⁴	[25]
17.	bcb⁴a ⇒ ab⁴cb	[46]
18.	babcb(ba)²c ⇒ db(cba)²bcba	[32]
19.	babcb⁴ ⇒ d	[15]
20.	b³(bc)³ ⇒ db²(cba)²bcb	[56]
21.	b³(cb)³d ⇒ abcb²dbcbab	[42]
22.	b⁴(cb)²ac ⇒ db²(cba)²bcba	[57]
23.	b³(cb)³ad ⇒ abcb²dbc(ba)²	[44]
24.	b³(cb)³bd ⇒ abcb²db²cbab	[43]
25.	b³(bcb)²d ⇒ adbcb³dbcbab	[48]
26.	b³(cb)³bad ⇒ abcb²db²c(ba)²	[51]
27.	b³(bcb)²ad ⇒ adbcb³dbc(ba)²	[50]
28.	b³(cb)³babc ⇒ abcb²db(cba)²bcb	[59]
29.	b²(bc)³b³d ⇒ abcb²adbcb⁴	[37]
30.	b⁴(cb²)²d ⇒ adbcb³db²cbab	[49]
31.	b³(cb)³(ba)²c ⇒ abcb²db(cba)²bcba	[60]
32.	b⁴(cb²)²ad ⇒ adbcb³db²c(ba)²	[58]
33.	b²(bc)³b⁴ ⇒ abcb²d	[36]
34.	b⁴(cb²)²abc ⇒ adbcb³db(cba)²bcb	[62]
35.	b⁴cb²cb³d ⇒ db(b²c)²b⁴	[55]
36.	b⁴(cb²)²abac ⇒ adbcb³db(cba)²bcba	[63]
37.	b⁴cb²cb⁴ ⇒ adbcb³d	[47]

# ab:ababaabbbba=1 reversed:cda/b aa=c,bbbbaabab=d magic:0
dc=1
cd=1
ca=ac
da=ad
aa=c
bcbabc=cbabcb
babcbd=dbcbab
bcbabac=cbabcba
babcbad=dbcbaba
babcbbd=dbbcbab
bcbbba=adbbbcbc
bbbcba=abcbbb
babcbbad=dbbcbaba
bcbbbbc=ababcbbb
babcbbabc=dbcbacbabcb
babcbbbd=adbcbbbb
bcbbbba=abbbbcb
babcbbabac=dbcbacbabcba
babcbbbb=d
bbbbcbcbc=dbbcbacbabcb
bbbcbcbcbd=abcbbdbcbab
bbbbcbcbac=dbbcbacbabcba
bbbcbcbcbad=abcbbdbcbaba
bbbcbcbcbbd=abcbbdbbcbab
bbbbcbbcbd=adbcbbbdbcbab
bbbcbcbcbbad=abcbbdbbcbaba
bbbbcbbcbad=adbcbbbdbcbaba
bbbcbcbcbbabc=abcbbdbcbacbabcb
bbbcbcbcbbbd=abcbbadbcbbbb
bbbbcbbcbbd=adbcbbbdbbcbab
bbbcbcbcbbabac=abcbbdbcbacbabcba
bbbbcbbcbbad=adbcbbbdbbcbaba
bbbcbcbcbbbb=abcbbd
bbbbcbbcbbabc=adbcbbbdbcbacbabcb
bbbbcbbcbbbd=dbbbcbbcbbbb
bbbbcbbcbbabac=adbcbbbdbcbacbabcba
bbbbcbbcbbbb=adbcbbbd