#2048 ⟨a, b | aab=a, bbba=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 ⋅ a³ = a and a ⋅ 1 = a, however a³ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a³ ⋅ a = a and 1 ⋅ a = a, however a³ ≠ 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:aab=a,bbba=a a/b - -
aaaa=a
ab=aaa
bbba=a

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

6 total

Σ	#	Presentation	Mapping
11	18946	⟨a, b \| aab=a, bbbaab=a⟩	φ(a) = a, φ(b) = b
11	18948	⟨a, b \| aab=a, bbbaba=a⟩	φ(a) = a, φ(b) = b
11	19488	⟨a, b \| aab=a, bbbaa=aa⟩	φ(a) = a, φ(b) = b
11	19493	⟨a, b \| aab=a, bbbab=ab⟩	φ(a) = a, φ(b) = b
11	20033	⟨a, b \| aab=a, bbba=aab⟩	φ(a) = a, φ(b) = b
11	20034	⟨a, b \| aab=a, bbba=aba⟩	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	12587	⟨a, b \| abba=ba, baaa=b⟩	φ(a) = b, φ(b) = a
11	19146	⟨a, b \| aba=a, baabbb=a⟩	φ(a) = a, φ(b) = b