#7179 ⟨a, b | ab=aa, bbb=aaa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a² and a ⋅ a = a², however b ≠ a
Not right cancellative, because right multiplication by a is not injective:
- ba² ⋅ a = a⁴ and a³ ⋅ a = a⁴, however ba² ≠ a³

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

# ab:ab=aa,bbb=aaa ab - -
ab=aa
bbb=aaa
baaa=aaaa

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

3 total

Σ	#	Presentation	Mapping
10	7180	⟨a, b \| ab=aa, bbb=aab⟩	φ(a) = a, φ(b) = b
10	7181	⟨a, b \| ab=aa, bbb=aba⟩	φ(a) = a, φ(b) = b
10	7182	⟨a, b \| ab=aa, bbb=abb⟩	φ(a) = a, φ(b) = b