#2932 ⟨a, b | aaababaabba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = a³d
- b^-1 = cbaba²b
- 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(a) = 0, c < a; deg(d) = 1; deg(b) = 2
Auxiliary generators:
1. aaaa=c
2. babaabb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ca ⇒ ac	[5]
2.	a⁴ ⇒ c	[2]
3.	cd ⇒ 1	[8]
4.	dc ⇒ 1	[11]
5.	da ⇒ ad	[13]
6.	ba²b²c ⇒ a³baba²b	[17]
7.	b²cba ⇒ a(ab)²a²b	[28]
8.	bc(ba)² ⇒ a²b²cb	[31]
9.	ba²b²ac ⇒ a³b(aba)²	[19]
10.	ba²b²a² ⇒ a³dbcbab	[36]
11.	ba(ba²)² ⇒ dbcbabc	[22]
12.	baba²bd ⇒ adba²b²	[14]
13.	b(aba)²d ⇒ adba²b²a	[16]
14.	baba²b² ⇒ d	[3]
15.	bcbab³c ⇒ ab(a²ba)²ba²b	[43]
16.	bcbabcb²c ⇒ (c(ba)²)²ab	[24]
17.	b(aba)²b²c ⇒ a²db²a³cbaba²b	[50]
18.	bcbab³ac ⇒ aba²ba³b(aba)²	[44]
19.	bcbabcb²ac ⇒ (c(ba)²)²aba	[41]
20.	b(aba)²b²ac ⇒ a²db²a³cb(aba)²	[51]
21.	bcbab³a² ⇒ aba²ba³dbcbab	[52]
22.	bcbabcb²a² ⇒ cb(ab)²cbab	[40]
23.	b(aba)²b²a² ⇒ a²db²a³bcbab	[48]
24.	b²cb(ba²)² ⇒ a²(dbcba)²bc	[34]
25.	b²cb²a²bd ⇒ a²dbcba²dba²b²	[33]
26.	b²cb²a²bad ⇒ a²dbcba²dba²b²a	[46]
27.	b²cb²a²b² ⇒ a²dbcbad	[27]
28.	b²cb²a²bab²c ⇒ a²dbcba³db²a³cbaba²b	[55]
29.	b²cb²a²bab²ac ⇒ a²dbcba³db²a³cb(aba)²	[56]
30.	b²cb²a²bab²a² ⇒ a²dbcba³db²a³bcbab	[54]

# ab:aaababaabba=1 reversed:ca/d/b aaaa=c,babaabb=d magic:0
ca=ac
aaaa=c
cd=1
dc=1
da=ad
baabbc=aaababaab
bbcba=aababaab
bcbaba=aabbcb
baabbac=aaababaaba
baabbaa=aaadbcbab
babaabaa=dbcbabc
babaabd=adbaabb
babaabad=adbaabba
babaabb=d
bcbabbbc=abaabaaababaab
bcbabcbbc=cbabacbabaab
babaababbc=aadbbaaacbabaab
bcbabbbac=abaabaaababaaba
bcbabcbbac=cbabacbabaaba
babaababbac=aadbbaaacbabaaba
bcbabbbaa=abaabaaadbcbab
bcbabcbbaa=cbababcbab
babaababbaa=aadbbaaabcbab
bbcbbaabaa=aadbcbadbcbabc
bbcbbaabd=aadbcbaadbaabb
bbcbbaabad=aadbcbaadbaabba
bbcbbaabb=aadbcbad
bbcbbaababbc=aadbcbaaadbbaaacbabaab
bbcbbaababbac=aadbcbaaadbbaaacbabaaba
bbcbbaababbaa=aadbcbaaadbbaaabcbab