#660 ⟨a, b | ab=aa, bb=aa⟩

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 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:
- ba ⋅ a = a³ and a² ⋅ a = a³, however ba ≠ a²

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,bb=aa ab - -
ab=aa
bb=aa
baa=aaa

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

1 total

Σ	#	Presentation	Mapping
8	661	⟨a, b \| ab=aa, bb=ab⟩	φ(a) = a, φ(b) = b