#3516 ⟨a, b, c | bb=ac, aca=a⟩

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 b is not injective:
- b ⋅ b³ = b² and b ⋅ b = b², however b³ ≠ b
Not right cancellative, because right multiplication by a is not injective:
- b² ⋅ a = a and 1 ⋅ a = a, however b² ≠ 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

# abc:bb=ac,aca=a bac - -
ac=bb
bba=a
bbbb=bb

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

1 total

Σ	#	Presentation	Mapping
8	3528	⟨a, b, c \| bb=ac, bba=a⟩	φ(a) = a, φ(b) = b, φ(c) = c