#6318 ⟨a, b | aab=a, aaaaa=a⟩

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 ⋅ a⁴ = a and a ⋅ 1 = a, however a⁴ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a⁴ ⋅ a = a and 1 ⋅ a = a, however a⁴ ≠ 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

#	Rule	Proof
1.	a⁵ ⇒ a	[2]
2.	ab ⇒ a⁴	[3]

# ab:aab=a,aaaaa=a a/b - -
aaaaa=a
ab=aaaa

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

5 total

Σ	#	Presentation	Mapping
10	6348	⟨a, b \| aab=a, abbbb=a⟩	φ(a) = a, φ(b) = b
10	6599	⟨a, b \| aab=a, aaaa=ab⟩	φ(a) = a, φ(b) = b
10	6626	⟨a, b \| aab=a, abbb=aa⟩	φ(a) = a, φ(b) = b
10	6727	⟨a, b \| aba=a, aaaa=ab⟩	φ(a) = a, φ(b) = b
10	6809	⟨a, b \| aab=a, abb=aaa⟩	φ(a) = a, φ(b) = b