#5373 ⟨a, b | aab=ab, aba=aa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element ab² has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a² = a² and a ⋅ a = a², however a² ≠ a
Not right cancellative, because right multiplication by a is not injective:
- a² ⋅ a = a² and a ⋅ a = a², however a² ≠ a

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=ab,aba=aa ab - -
aaa=aa
aab=ab
aba=aa

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

2 total

Σ	#	Presentation	Mapping
11	16153	⟨a, b \| aab=ab, aaba=aa⟩	φ(a) = a, φ(b) = b
11	16353	⟨a, b \| aba=aa, abab=ab⟩	φ(a) = a, φ(b) = b