#20632 ⟨a, b | ab=aa, bbbaaa=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,bbbaaa=a ab - -
ab=aa
bbba=aaaa
aaaaaa=a

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

3 total

Σ	#	Presentation	Mapping
11	20634	⟨a, b \| ab=aa, bbbaab=a⟩	φ(a) = a, φ(b) = b
11	20636	⟨a, b \| ab=aa, bbbaba=a⟩	φ(a) = a, φ(b) = b
11	20638	⟨a, b \| ab=aa, bbbabb=a⟩	φ(a) = a, φ(b) = b