#19733 ⟨a, b | aba=b, aabbb=bb⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b² = b² and b ⋅ b = b², however b² ≠ b
Not right cancellative, because right multiplication by b is not injective:
- b² ⋅ b = b² and b ⋅ b = b², however b² ≠ b

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:aba=b,aabbb=bb ab - -
aba=b
bba=abb
bbb=bb
aabb=bb
babb=abb

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

6 total

Σ	#	Presentation	Mapping
11	19744	⟨a, b \| aba=b, ababb=bb⟩	φ(a) = a, φ(b) = b
11	19748	⟨a, b \| aba=b, abbab=bb⟩	φ(a) = a, φ(b) = b
11	19751	⟨a, b \| aba=b, abbba=bb⟩	φ(a) = a, φ(b) = b
11	19762	⟨a, b \| aba=b, baabb=bb⟩	φ(a) = a, φ(b) = b
11	19765	⟨a, b \| aba=b, babab=bb⟩	φ(a) = a, φ(b) = b
11	20285	⟨a, b \| aba=b, abab=bbb⟩	φ(a) = a, φ(b) = b