#2452 ⟨a, b, c | aab=b, caab=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 ⋅ bc = c and c ⋅ 1 = c, however bc ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- bc ⋅ b = b and 1 ⋅ b = b, however bc ≠ 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

#	Rule	Proof
1.	cb ⇒ 1	[2]
2.	a²b ⇒ b	[1]

# abc:aab=b,caab=1 abc - -
cb=1
aab=b

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ	#	Presentation	Mapping
8	6896	⟨a, b, c \| ab=1, abccb=b⟩	φ(a) = c, φ(b) = b, φ(c) = a