#5830 ⟨a, b | abaaab=babab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by b is not injective:
- aba³ ⋅ b = b(ab)² and (ba)² ⋅ b = b(ab)², however aba³ ≠ (ba)²
Enveloping group: ⟨a, b | aabab^-1b^-1⟩

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

Auxiliary generators:
1. c = babab
Reduction order:
- Right-to-left recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	bac ⇒ cab	[4]
2.	b(ab)² ⇒ c	[2]
3.	(bab)²c ⇒ ca²c	[8]
4.	ca³b ⇒ babc	[7]
5.	ca³c ⇒ babc(ab)²	[9]
6.	aba²c ⇒ babc	[10]
7.	ca(ab)²c ⇒ babca²c	[12]
8.	aba³b ⇒ c	[3]
9.	aba³c ⇒ c(ab)²	[6]
10.	(aba)²bc ⇒ ca²c	[11]

# ab:abaaab=babab reversed:bc/a babab=c magic:0
bac=cab
babab=c
babbabc=caac
caaab=babc
caaac=babcabab
abaac=babc
caababc=babcaac
abaaab=c
abaaac=cabab
abaababc=caac

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