#5394 ⟨a, b | aab=ba, abb=aa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b² = a² and a ⋅ a = a², however b² ≠ a
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=ba,abb=aa reversed:a/b - -
aaaa=aaa
ba=aab
abb=aa

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

1 total

Σ	#	Presentation	Mapping
11	16279	⟨a, b \| aab=bb, aaab=ba⟩	φ(a) = b, φ(b) = a