#4137 ⟨a, b, c | aaa=1, bacb=c⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 8
Infinite non-commutative monoid
Element ba² 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.	a³ ⇒ 1	[1]
2.	bacb ⇒ c	[2]
3.	cacb ⇒ bac²	[3]

# abc:aaa=1,bacb=c abc - -
aaa=1
bacb=c
cacb=bacc