#14467 ⟨a, b | aaab=a, bbbab=a⟩

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 ⋅ a⁸ = a and a ⋅ 1 = a, however a⁸ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- b³ ⋅ a = a³ and a² ⋅ a = a³, however b³ ≠ 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:aaab=a,bbbab=a a/b - -
aaaaaaaaa=a
ab=aaaaaaa
bbba=aaa

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

1 total

Σ	#	Presentation	Mapping
11	14595	⟨a, b \| aaba=a, bbbab=a⟩	φ(a) = a, φ(b) = b

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

1 total

Σ	#	Presentation	Mapping
11	14583	⟨a, b \| aaba=a, babbb=a⟩	φ(a) = a, φ(b) = b