#5308 ⟨a, b | aaa=aa, bbb=aa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b²a = b³ and b ⋅ b² = b³, however b²a ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- ab² ⋅ b = b³ and b² ⋅ b = b³, however ab² ≠ 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:aaa=aa,bbb=aa b/a - -
bbbbbb=bbb
abbb=bbb
bbba=bbb
aa=bbb

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

3 total

Σ	#	Presentation	Mapping
11	16051	⟨a, b \| aaa=bb, aaab=bb⟩	φ(a) = b, φ(b) = a
11	16477	⟨a, b \| aaa=aa, bbb=aaa⟩	φ(a) = a, φ(b) = b
11	16489	⟨a, b \| aaa=bb, bbb=aaa⟩	φ(a) = b, φ(b) = a