#5933 ⟨a, b | abbbba=abaab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b⁴a = aba²b and a ⋅ ba²b = aba²b, however b⁴a ≠ ba²b
Enveloping group: ⟨a, b | aaabba^-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 = abaab
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ca²b ⇒ abac	[4]
2.	aba²b ⇒ c	[2]
3.	cb³a ⇒ abac	[7]
4.	cb³c ⇒ abacba²b	[8]
5.	ab⁴a ⇒ c	[3]
6.	ab⁴c ⇒ cba²b	[6]
7.	cb⁴a ⇒ cba²b	[10]
8.	c(ba²b)² ⇒ cb⁴c	[9]
9.	cba²b⁵a ⇒ cb⁴c	[11]
10.	cba²b⁵c ⇒ cb⁴cba²b	[12]

# ab:abbbba=abaab ac/b abaab=c magic:0
caab=abac
abaab=c
cbbba=abac
cbbbc=abacbaab
abbbba=c
abbbbc=cbaab
cbbbba=cbaab
cbaabbaab=cbbbbc
cbaabbbbba=cbbbbc
cbaabbbbbc=cbbbbcbaab

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