#22841 ⟨a, b | aaa=1, babab=abb⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

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:
- 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.	b⁷ ⇒ b⁴	[14]
2.	bab⁶ ⇒ bab³	[9]
3.	b²ab⁵ ⇒ b²ab²	[12]
4.	b³ab ⇒ ab⁴	[7]
5.	abab³ ⇒ b²ab⁴	[13]
6.	ba²b² ⇒ ab²ab	[3]
7.	b(ab)² ⇒ ab²	[2]
8.	(b²a)²b ⇒ a²b⁵	[10]
9.	a³ ⇒ 1	[1]
10.	a(ab²)² ⇒ bab⁴	[15]
11.	ab(ab²)² ⇒ bab²ab⁴	[16]
12.	ba²bab² ⇒ a(bab)²	[4]

# ab:aaa=1,babab=abb b/a
bbbbbbb=bbbb
babbbbbb=babbb
bbabbbbb=bbabb
bbbab=abbbb
ababbb=bbabbbb
baabb=abbab
babab=abb
bbabbab=aabbbbb
aaa=1
aabbabb=babbbb
ababbabb=babbabbbb
baababb=ababbab