#5834 ⟨a, b | abaaab=bbaab⟩

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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 = b²a²b and b²a² ⋅ b = b²a²b, however aba³ ≠ b²a²
Enveloping group: ⟨a, b | aaabb⟩

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 = bbaab
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.	b²a²b ⇒ c	[2]
2.	b²a²c ⇒ cba²b	[4]
3.	(b²a)²c ⇒ ca²c	[8]
4.	ca³b ⇒ b²ac	[7]
5.	ca³c ⇒ b²acba²b	[9]
6.	aba²c ⇒ b²ac	[10]
7.	ca²b²ac ⇒ b²aca²c	[12]
8.	aba³b ⇒ c	[3]
9.	aba³c ⇒ cba²b	[6]
10.	aba²b²ac ⇒ ca²c	[11]

# ab:abaaab=bbaab reversed:bc/a bbaab=c magic:0
bbaab=c
bbaac=cbaab
bbabbac=caac
caaab=bbac
caaac=bbacbaab
abaac=bbac
caabbac=bbacaac
abaaab=c
abaaac=cbaab
abaabbac=caac

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