#3031 ⟨a, b, c | aba=b, aca=c⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order

Rewriting system

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Reduction order:
- Left-to-right shortlex with a < b < c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	aba ⇒ b	[1]
2.	aca ⇒ c	[2]
3.	b²a ⇒ ab²	[3]
4.	bca ⇒ abc	[4]
5.	cba ⇒ acb	[5]
6.	c²a ⇒ ac²	[6]

# abc:aba=b,aca=c abc - -
aba=b
aca=c
bba=abb
bca=abc
cba=acb
cca=acc