#5068 ⟨a, b | aaa=ab, bbab=a⟩

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 = a³ and a ⋅ a² = a³, however b ≠ a²
Not right cancellative, because right multiplication by a is not injective:
- a⁶ ⋅ a = a and 1 ⋅ a = a, however a⁶ ≠ 1

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:aaa=ab,bbab=a a/b - -
aaaaaaa=a
ab=aaa
bba=aaaaa

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

8 total

Σ	#	Presentation	Mapping
11	14616	⟨a, b \| aaba=b, aabbb=b⟩	φ(a) = b, φ(b) = a
11	14640	⟨a, b \| aaba=b, baabb=b⟩	φ(a) = b, φ(b) = a
11	14644	⟨a, b \| aaba=b, babab=b⟩	φ(a) = b, φ(b) = a
11	14646	⟨a, b \| aaba=b, babba=b⟩	φ(a) = b, φ(b) = a
11	14652	⟨a, b \| aaba=b, bbaab=b⟩	φ(a) = b, φ(b) = a
11	14654	⟨a, b \| aaba=b, bbaba=b⟩	φ(a) = b, φ(b) = a
11	14658	⟨a, b \| aaba=b, bbbaa=b⟩	φ(a) = b, φ(b) = a
11	15489	⟨a, b \| aaa=ab, bbaaa=a⟩	φ(a) = a, φ(b) = b