#3303 ⟨a, b, c | bb=ac, caca=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 ⋅ (ac)² = c and c ⋅ 1 = c, however (ac)² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- (ac)²b ⋅ a = ba and b ⋅ a = ba, however (ac)²b ≠ b

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

# abc:bb=ac,caca=1 abc - -
bb=ac
bac=acb
caca=1
acacba=ba

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

1 total

Σ	#	Presentation	Mapping
8	3305	⟨a, b, c \| bb=ac, cbba=1⟩	φ(a) = a, φ(b) = b, φ(c) = c