#16503 ⟨a, b | aab=ab, bab=aaa⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a³ = a³ and a ⋅ a² = a³, however a³ ≠ a²
Not right cancellative, because right multiplication by a is not injective:
- a³ ⋅ a = a³ and a² ⋅ a = a³, however a³ ≠ 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:aab=ab,bab=aaa a/b - -
aaaa=aaa
ab=baaa
bbaaa=aaa

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

1 total

Σ	#	Presentation	Mapping
11	16538	⟨a, b \| aba=ab, bab=aaa⟩	φ(a) = a, φ(b) = b