#2270 ⟨a, b | bb=aa, aaa=aa⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ba = b² and b ⋅ b = b², however ba ≠ b
Not right cancellative, because right multiplication by b is not injective:
- ab ⋅ b = b² and b ⋅ b = b², however ab ≠ 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:bb=aa,aaa=aa ba - -
aa=bb
bba=bb
abb=bb
bbbb=bb

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

6 total

Σ	#	Presentation	Mapping
9	2272	⟨a, b \| bb=aa, aaa=bb⟩	φ(a) = a, φ(b) = b
9	2273	⟨a, b \| bb=aa, aab=aa⟩	φ(a) = b, φ(b) = a
9	2276	⟨a, b \| bb=aa, aab=bb⟩	φ(a) = b, φ(b) = a
11	15947	⟨a, b \| aaa=aa, aaaa=bb⟩	φ(a) = a, φ(b) = b
11	16096	⟨a, b \| aab=aa, aabb=bb⟩	φ(a) = b, φ(b) = a
11	16108	⟨a, b \| aab=aa, abba=bb⟩	φ(a) = b, φ(b) = a