#19532 ⟨a, b | aab=b, aabbb=aa⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ a² = b and b ⋅ 1 = b, however a² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- a² ⋅ b = b and 1 ⋅ b = b, 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,aabbb=aa ab - -
aab=b
baa=b
bbb=aa
aaaa=aa

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

2 total

Σ	#	Presentation	Mapping
11	19580	⟨a, b \| aab=b, baabb=aa⟩	φ(a) = a, φ(b) = b
11	19604	⟨a, b \| aab=b, bbaab=aa⟩	φ(a) = a, φ(b) = b