#7226 ⟨a, b, c | aa=1, bacb=ca⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 8
Infinite non-commutative monoid
Element ab 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 < c < b
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	bac² ⇒ c²ba	[4]
3.	bacb ⇒ ca	[2]

# abc:aa=1,bacb=ca acb - -
aa=1
bacc=ccba
bacb=ca