#5838 ⟨a, b | abaaab=bbbab⟩

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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 = b³ab and b³a ⋅ b = b³ab, however aba³ ≠ b³a
Enveloping group: ⟨a, b | aaabba^-1b⟩

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 = bbbab
Reduction order:
- Right-to-left 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.	aba²c ⇒ ca³b	[7]
2.	aba³b ⇒ c	[2]
3.	cb²c ⇒ aba³ca³b	[8]
4.	(aba³)²c ⇒ cb²ac	[11]
5.	cb²ab ⇒ aba³c	[6]
6.	b³c ⇒ ca³b	[5]
7.	b³ac ⇒ aba³c	[9]
8.	cb²a²ba³c ⇒ aba³cb²ac	[12]
9.	b³ab ⇒ c	[3]
10.	b³a²ba³c ⇒ cb²ac	[10]

# ab:abaaab=bbbab reversed:ac/b bbbab=c magic:0
abaac=caaab
abaaab=c
cbbc=abaaacaaab
abaaaabaaac=cbbac
cbbab=abaaac
bbbc=caaab
bbbac=abaaac
cbbaabaaac=abaaacbbac
bbbab=c
bbbaabaaac=cbbac

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