#2066 ⟨a, b | aab=b, abbb=a⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a² = a and a ⋅ 1 = a, however a² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a² ⋅ a = a and 1 ⋅ a = a, however a² ≠ 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

# ab:aab=b,abbb=a ab - -
aaa=a
aab=b
baa=b
bbb=aa

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

3 total

Σ	#	Presentation	Mapping
11	18974	⟨a, b \| aab=b, aaabbb=a⟩	φ(a) = a, φ(b) = b
11	18998	⟨a, b \| aab=b, abaabb=a⟩	φ(a) = a, φ(b) = b
11	19010	⟨a, b \| aab=b, abbaab=a⟩	φ(a) = a, φ(b) = b