#9368 ⟨a, b | ab=a, bbba=aaa⟩

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 ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a³ ⋅ a = a² and a ⋅ a = a², however a³ ≠ 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:ab=a,bbba=aaa ab - -
ab=a
aaaa=aa
bbba=aaa

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

4 total

Σ	#	Presentation	Mapping
11	25636	⟨a, b \| ab=a, bbbab=aaa⟩	φ(a) = a, φ(b) = b
11	25884	⟨a, b \| ab=a, bbba=aaab⟩	φ(a) = a, φ(b) = b
11	25885	⟨a, b \| ab=a, bbba=aaba⟩	φ(a) = a, φ(b) = b
11	25887	⟨a, b \| ab=a, bbba=abaa⟩	φ(a) = a, φ(b) = b