#17660 ⟨a, b | aaaa=1, abbab=bb⟩

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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:
- 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.	b¹⁵ ⇒ b³	[15]
2.	bab¹⁴ ⇒ bab²	[17]
3.	b³ab ⇒ ab⁴	[4]
4.	ab²ab ⇒ b²	[2]
5.	ba²b² ⇒ abab⁴	[6]
6.	b²(ab)² ⇒ a²b²	[5]
7.	a³b² ⇒ b²ab	[3]
8.	(ab)³b ⇒ bab¹²	[18]
9.	ba²bab² ⇒ a²bab⁷	[16]
10.	a⁴ ⇒ 1	[1]
11.	a³bab² ⇒ (ba)²b⁴	[11]

# ab:aaaa=1,abbab=bb b/a
bbbbbbbbbbbbbbb=bbb
babbbbbbbbbbbbbb=babb
bbbab=abbbb
abbab=bb
baabb=ababbbb
bbabab=aabb
aaabb=bbab
abababb=babbbbbbbbbbbb
baababb=aababbbbbbb
aaaa=1
aaababb=bababbbb

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