#20616 ⟨a, b | ab=aa, bbaaaa=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a² and a ⋅ a = a², however b ≠ a
Not right cancellative, because right multiplication by a is not injective:
- a⁵ ⋅ a = a and 1 ⋅ a = a, however a⁵ ≠ 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:ab=aa,bbaaaa=a ab - -
ab=aa
bba=aaa
aaaaaa=a

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

7 total

Σ	#	Presentation	Mapping
11	20618	⟨a, b \| ab=aa, bbaaab=a⟩	φ(a) = a, φ(b) = b
11	20620	⟨a, b \| ab=aa, bbaaba=a⟩	φ(a) = a, φ(b) = b
11	20622	⟨a, b \| ab=aa, bbaabb=a⟩	φ(a) = a, φ(b) = b
11	20624	⟨a, b \| ab=aa, bbabaa=a⟩	φ(a) = a, φ(b) = b
11	20626	⟨a, b \| ab=aa, bbabab=a⟩	φ(a) = a, φ(b) = b
11	20628	⟨a, b \| ab=aa, bbabba=a⟩	φ(a) = a, φ(b) = b
11	20630	⟨a, b \| ab=aa, bbabbb=a⟩	φ(a) = a, φ(b) = b