#3122 ⟨a, b | ab=a, bbaa=ba⟩

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 ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a² ⋅ a = a² and a ⋅ a = a², however a² ≠ a

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,bbaa=ba ab - -
ab=a
aaa=aa
baa=ba
bba=ba

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

9 total

Σ	#	Presentation	Mapping
10	9086	⟨a, b \| ab=a, bbaab=ba⟩	φ(a) = a, φ(b) = b
10	9090	⟨a, b \| ab=a, bbaba=ba⟩	φ(a) = a, φ(b) = b
10	9357	⟨a, b \| ab=a, bbaa=bab⟩	φ(a) = a, φ(b) = b
11	25066	⟨a, b \| ab=a, bbaabb=ba⟩	φ(a) = a, φ(b) = b
11	25074	⟨a, b \| ab=a, bbabab=ba⟩	φ(a) = a, φ(b) = b
11	25078	⟨a, b \| ab=a, bbabba=ba⟩	φ(a) = a, φ(b) = b
11	25609	⟨a, b \| ab=a, bbaab=bab⟩	φ(a) = a, φ(b) = b
11	25617	⟨a, b \| ab=a, bbaba=bab⟩	φ(a) = a, φ(b) = b
11	25869	⟨a, b \| ab=a, bbaa=babb⟩	φ(a) = a, φ(b) = b