⟨a, b | aaabbabaaab=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. bbabaaab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[16]
2.	cd ⇒ 1	[4]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[19]
5.	a³ ⇒ c	[2]
6.	b²a ⇒ dbabc	[11]
7.	baba² ⇒ cb²	[23]
8.	ba(bc)² ⇒ ab(cb)²	[12]
9.	b(cb)²d ⇒ a²dbabcb	[28]
10.	babcbac ⇒ ab(cb)²a	[25]
11.	b(cb)²ad ⇒ a²dbabcba	[29]
12.	b(cb)²a² ⇒ a²bcb²c	[32]
13.	babcba² ⇒ cbcb²	[26]
14.	(bc)²b² ⇒ a²d	[21]

# ab:aaabbabaaab=1 reversed:cda/b aaa=c,bbabaaab=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c bba=dbabc babaa=cbb babcbc=abcbcb bcbcbd=aadbabcb babcbac=abcbcba bcbcbad=aadbabcba bcbcbaa=aabcbbc babcbaa=cbcbb bcbcbb=aad

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

Σ	#	Presentation	Mapping
11	3024	⟨a, b \| aabaaabbaba=1⟩	φ(a) = a, φ(b) = b
11	3116	⟨a, b \| aabbabaaaba=1⟩	φ(a) = a, φ(b) = b
11	3263	⟨a, b \| ababbbabbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

3024

⟨a, b | aabaaabbaba=1⟩

φ(a) = a, φ(b) = b

3116

⟨a, b | aabbabaaaba=1⟩

φ(a) = a, φ(b) = b

3263

⟨a, b | ababbbabbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#2966 ⟨a, b \| aaabbaabbba=1⟩
Next:	#2968 ⟨a, b \| aaabbabaaba=1⟩

#2967 ⟨a, b | aaabbabaaab=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances