#20273 ⟨a, b | aba=b, aabb=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 ⋅ ab² = ab² and a ⋅ b² = ab², however ab² ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- a²b ⋅ b = ab² and ab ⋅ b = ab², however a²b ≠ ab

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

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

2 total

Σ	#	Presentation	Mapping
11	20276	⟨a, b \| aba=b, aabb=bba⟩	φ(a) = a, φ(b) = b
11	20289	⟨a, b \| aba=b, abba=abb⟩	φ(a) = a, φ(b) = b