#15435 ⟨a, b | aaa=aa, babbb=a⟩

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

#	Rule	Proof
1.	a³ ⇒ a²	[1]
2.	aba² ⇒ ba²	[8]
3.	a(ba)² ⇒ (ba)²	[6]
4.	ba²ba ⇒ (ba)²	[16]
5.	ab²a² ⇒ b²a²	[12]
6.	bab²a ⇒ a²b³	[3]
7.	ba²b²a ⇒ a²b³	[15]
8.	ab(ba)² ⇒ b(ba)²	[10]
9.	b³a² ⇒ a²b³a	[13]
10.	bab³ ⇒ a	[2]
11.	ba²b³a ⇒ a²	[14]
12.	b³aba ⇒ a²b⁴a	[9]
13.	a²b⁵a ⇒ b²a²b³	[17]
14.	ba²b⁴a ⇒ a²ba	[18]
15.	a²b⁶ ⇒ (ba)²	[4]

# ab:aaa=aa,babbb=a reversed:a/b
aaa=aa
abaa=baa
ababa=baba
baaba=baba
abbaa=bbaa
babba=aabbb
baabba=aabbb
abbaba=bbaba
bbbaa=aabbba
babbb=a
baabbba=aa
bbbaba=aabbbba
aabbbbba=bbaabbb
baabbbba=aaba
aabbbbbb=baba