#20295 ⟨a, b | aba=b, abbb=abb⟩

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 a is not injective:
- a ⋅ b³ = ab² and a ⋅ b² = ab², however b³ ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- a²b ⋅ b = b³ and b² ⋅ b = b³, however a²b ≠ b²

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,abbb=abb ab - -
aba=b
bba=abb
aabb=bbb
abbb=abb
babb=abb
bbbb=bbb

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

3 total

Σ	#	Presentation	Mapping
11	20298	⟨a, b \| aba=b, abbb=bba⟩	φ(a) = a, φ(b) = b
11	20309	⟨a, b \| aba=b, babb=abb⟩	φ(a) = a, φ(b) = b
11	20312	⟨a, b \| aba=b, babb=bba⟩	φ(a) = a, φ(b) = b