#8984 ⟨a, b | ab=a, aaaaa=aa⟩

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 ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a⁴ ⋅ a = a² and a ⋅ a = a², however a⁴ ≠ 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

#	Rule	Proof
1.	ab ⇒ a	[1]
2.	a⁵ ⇒ a²	[2]

# ab:ab=a,aaaaa=aa ab - -
ab=a
aaaaa=aa

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

7 total

Σ	#	Presentation	Mapping
11	24864	⟨a, b \| ab=a, aaaaab=aa⟩	φ(a) = a, φ(b) = b
11	24868	⟨a, b \| ab=a, aaaaba=aa⟩	φ(a) = a, φ(b) = b
11	24876	⟨a, b \| ab=a, aaabaa=aa⟩	φ(a) = a, φ(b) = b
11	24892	⟨a, b \| ab=a, aabaaa=aa⟩	φ(a) = a, φ(b) = b
11	24924	⟨a, b \| ab=a, abaaaa=aa⟩	φ(a) = a, φ(b) = b
11	25405	⟨a, b \| ab=a, aaaaa=aab⟩	φ(a) = a, φ(b) = b
11	25406	⟨a, b \| ab=a, aaaaa=aba⟩	φ(a) = a, φ(b) = b