#1566 ⟨a, b, c | aaa=ab, ccb=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ cbc = c and c ⋅ 1 = c, however cbc ≠ 1
Not right cancellative, because right multiplication by cb is not injective:
- cbc ⋅ cb = cb and 1 ⋅ cb = cb, however cbc ≠ 1

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 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.	ab ⇒ a³	[1]
2.	c²b ⇒ 1	[2]

# abc:aaa=ab,ccb=1 ac/b - -
ab=aaa
ccb=1