#7198 ⟨a, b | bb=aa, aba=aaa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba = a³ and a ⋅ a² = a³, however ba ≠ a²
Not right cancellative, because right multiplication by a is not injective:
- ab ⋅ a = a³ and a² ⋅ a = a³, however ab ≠ 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:bb=aa,aba=aaa ab - -
bb=aa
aba=aaa
baa=aab
aaab=aaaa

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

1 total

Σ	#	Presentation	Mapping
10	7202	⟨a, b \| bb=aa, abb=aba⟩	φ(a) = a, φ(b) = b