⟨a, b | aabbbababa=1⟩

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Monoids with two generators and one relation

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. bbbabab=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(ab)²c ⇒ (ab)²cb	[17]
7.	babcbd ⇒ a²db(ab)²	[26]
8.	b³a ⇒ adbcb²	[33]
9.	(ba)³c ⇒ (ab)²cba	[23]
10.	babcbad ⇒ a²d(ba)³	[27]
11.	bcb²a² ⇒ a²b³c	[37]
12.	(ba)³ac ⇒ (ab)²cba²	[28]
13.	babcba²d ⇒ a²d(ba)³a	[38]
14.	babcb²d ⇒ a²db²(ab)²	[39]
15.	babcb²ad ⇒ a²db(ba)³	[41]
16.	b(ba)³a ⇒ abcb³	[22]
17.	babcb³ ⇒ a²d	[21]
18.	bcb³cbd ⇒ a²b²a²db(ab)²	[43]
19.	bcb³cbad ⇒ a²b²a²d(ba)³	[44]
20.	bcb³cba²d ⇒ a²b²a²d(ba)³a	[45]
21.	(bcb²)²d ⇒ a²b²a²db²(ab)²	[46]
22.	(bcb²)²ad ⇒ a²b²a²db(ba)³	[47]
23.	b(cb³)² ⇒ a²b²a²d	[42]

# ab:aabbbababa=1 reversed:cda/b aaa=c,bbbabab=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c bababc=ababcb babcbd=aadbabab bbba=adbcbb bababac=ababcba babcbad=aadbababa bcbbaa=aabbbc bababaac=ababcbaa babcbaad=aadbababaa babcbbd=aadbbabab babcbbad=aadbbababa bbababaa=abcbbb babcbbb=aad bcbbbcbd=aabbaadbabab bcbbbcbad=aabbaadbababa bcbbbcbaad=aabbaadbababaa bcbbbcbbd=aabbaadbbabab bcbbbcbbad=aabbaadbbababa bcbbbcbbb=aabbaad

Up:	Monoids with two generators and one relation
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#1463 ⟨a, b | aabbbababa=1⟩

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