⟨a, b | aaa=1, abbba=bb⟩

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Monoids with two generators and two relations

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:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	b³² ⇒ b²	[22]
2.	b²ab³⁰ ⇒ b²a	[28]
3.	b⁵a ⇒ ab⁵	[5]
4.	a²b² ⇒ b³a	[3]
5.	abab² ⇒ b²ab²⁹	[23]
6.	ab³a ⇒ b²	[2]
7.	b²a² ⇒ ab³	[4]
8.	b(ba)² ⇒ b⁴ab²⁷	[29]
9.	(b²a)² ⇒ ab⁴ab³	[8]
10.	b³ab⁴a ⇒ (ab²)²	[10]
11.	a³ ⇒ 1	[1]
12.	bab²ab⁴a ⇒ ab²ab⁴ab¹⁹	[26]

# ab:aaa=1,abbba=bb b/a bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bb bbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bba bbbbba=abbbbb aabb=bbba ababb=bbabbbbbbbbbbbbbbbbbbbbbbbbbbbbb abbba=bb bbaa=abbb bbaba=bbbbabbbbbbbbbbbbbbbbbbbbbbbbbbb bbabba=abbbbabbb bbbabbbba=abbabb aaa=1 babbabbbba=abbabbbbabbbbbbbbbbbbbbbbbbb

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

Σ	#	Presentation	Mapping
11	23316	⟨a, b \| aaa=1, bbaa=abbb⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

23316

⟨a, b | aaa=1, bbaa=abbb⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
Prev:	#7796 ⟨a, b \| aaa=1, abbab=bb⟩
Next:	#7802 ⟨a, b \| aaa=1, abbbb=ba⟩

#7799 ⟨a, b | aaa=1, abbba=bb⟩

Quick links

Properties

Rewriting system

Isomorphic instances