#2992 ⟨a, b | ab=a, bbbaa=a⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a ⋅ a = a and 1 ⋅ a = a, however a ≠ 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=a,bbbaa=a ab - -
aa=a
ab=a
bbba=a

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

14 total

Σ	#	Presentation	Mapping
10	8826	⟨a, b \| ab=a, bbbaab=a⟩	φ(a) = a, φ(b) = b
10	8828	⟨a, b \| ab=a, bbbaba=a⟩	φ(a) = a, φ(b) = b
10	9097	⟨a, b \| ab=a, bbbaa=ab⟩	φ(a) = a, φ(b) = b
11	14785	⟨a, b \| abab=a, bbbaa=a⟩	φ(a) = a, φ(b) = b
11	15601	⟨a, b \| aab=aa, bbbaa=a⟩	φ(a) = a, φ(b) = b
11	18944	⟨a, b \| aab=a, bbbaaa=a⟩	φ(a) = a, φ(b) = b
11	19489	⟨a, b \| aab=a, bbbaa=ab⟩	φ(a) = a, φ(b) = b
11	20035	⟨a, b \| aab=a, bbba=abb⟩	φ(a) = a, φ(b) = b
11	24562	⟨a, b \| ab=a, bbbaabb=a⟩	φ(a) = a, φ(b) = b
11	24566	⟨a, b \| ab=a, bbbabab=a⟩	φ(a) = a, φ(b) = b
11	24568	⟨a, b \| ab=a, bbbabba=a⟩	φ(a) = a, φ(b) = b
11	25089	⟨a, b \| ab=a, bbbaab=ab⟩	φ(a) = a, φ(b) = b
11	25093	⟨a, b \| ab=a, bbbaba=ab⟩	φ(a) = a, φ(b) = b
11	25631	⟨a, b \| ab=a, bbbaa=abb⟩	φ(a) = a, φ(b) = b

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

1 total

Σ	#	Presentation	Mapping
11	19660	⟨a, b \| aba=a, aabbb=ba⟩	φ(a) = a, φ(b) = b