⟨a, b | aabbababbba=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. bbababbb=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.	bab³c ⇒ a²b²(ab)²	[15]
7.	b²(ab)²d ⇒ adbab³	[11]
8.	b²cb²a ⇒ ab³cb	[36]
9.	bcb(ba)² ⇒ cb²(ab)²	[22]
10.	bab³ac ⇒ a²b(ba)³	[17]
11.	b(ba)³d ⇒ adbab³a	[13]
12.	bab³a² ⇒ a²dbcb²ab	[32]
13.	b³cba² ⇒ a²d(b²c)²	[42]
14.	b(ba)³a ⇒ dbcb²abc	[25]
15.	b(ba)²b²d ⇒ d(ba)²b³	[12]
16.	b(ba)²b²ad ⇒ d(ba)²b³a	[33]
17.	b(ba)²b²a² ⇒ adb(b²c)²	[41]
18.	b(ba)²b³ ⇒ d	[3]
19.	b³cb⁴c ⇒ a²db²cba²b²(ab)²	[44]
20.	b³cb⁴ac ⇒ a²db²cba²b(ba)³	[45]
21.	b³cb⁴a² ⇒ a²db²cba²dbcb²ab	[47]

# ab:aabbababbba=1 reversed:cda/b aaa=c,bbababbb=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c babbbc=aabbabab bbababd=adbabbb bbcbba=abbbcb bcbbaba=cbbabab babbbac=aabbababa bbababad=adbabbba babbbaa=aadbcbbab bbbcbaa=aadbbcbbc bbababaa=dbcbbabc bbababbd=dbababbb bbababbad=dbababbba bbababbaa=adbbbcbbc bbababbb=d bbbcbbbbc=aadbbcbaabbabab bbbcbbbbac=aadbbcbaabbababa bbbcbbbbaa=aadbbcbaadbcbbab

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

Σ	#	Presentation	Mapping
11	3140	⟨a, b \| aabbbaababa=1⟩	φ(a) = b, φ(b) = a
11	3197	⟨a, b \| abaaabbbaab=1⟩	φ(a) = b, φ(b) = a
11	3232	⟨a, b \| ababaaabbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

3140

⟨a, b | aabbbaababa=1⟩

φ(a) = b, φ(b) = a

3197

⟨a, b | abaaabbbaab=1⟩

φ(a) = b, φ(b) = a

3232

⟨a, b | ababaaabbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#3123 ⟨a, b \| aabbababbab=1⟩
Next:	#3125 ⟨a, b \| aabbabbaaab=1⟩

#3124 ⟨a, b | aabbababbba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances