#8886 ⟨a, b | aa=a, abbba=ab⟩

Properties

Sum of relation sides is 10
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:aa=a,abbba=ab ab - -
aa=a
aba=ab
abba=abb
abbb=ab

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

3 total

Σ	#	Presentation	Mapping
11	24639	⟨a, b \| aa=a, aabbba=ab⟩	φ(a) = a, φ(b) = b
11	24662	⟨a, b \| aa=a, ababba=ab⟩	φ(a) = a, φ(b) = b
11	25207	⟨a, b \| aa=a, abbba=aab⟩	φ(a) = a, φ(b) = b

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

2 total

Σ	#	Presentation	Mapping
11	24640	⟨a, b \| aa=a, aabbba=ba⟩	φ(a) = a, φ(b) = b
11	24663	⟨a, b \| aa=a, ababba=ba⟩	φ(a) = a, φ(b) = b