#652 ⟨a, b | bb=aa, aaa=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b² = a and a ⋅ 1 = a, however b² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- b² ⋅ a = a and 1 ⋅ a = a, however b² ≠ 1

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=a ba - -
aa=bb
bba=a
abb=a
bbbb=bb

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

4 total

Σ	#	Presentation	Mapping
8	655	⟨a, b \| bb=aa, aab=b⟩	φ(a) = b, φ(b) = a
10	6528	⟨a, b \| aaa=a, aaaa=bb⟩	φ(a) = a, φ(b) = b
10	6674	⟨a, b \| aab=b, aabb=aa⟩	φ(a) = b, φ(b) = a
10	6698	⟨a, b \| aab=b, baab=aa⟩	φ(a) = b, φ(b) = a