#8712 ⟨a, b | ab=a, aaaaaa=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 ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a⁵ ⋅ a = a and 1 ⋅ a = a, however a⁵ ≠ 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.	ab ⇒ a	[1]
2.	a⁶ ⇒ a	[2]

# ab:ab=a,aaaaaa=a ab - -
ab=a
aaaaaa=a

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

7 total

Σ	#	Presentation	Mapping
11	24334	⟨a, b \| ab=a, aaaaaab=a⟩	φ(a) = a, φ(b) = b
11	24336	⟨a, b \| ab=a, aaaaaba=a⟩	φ(a) = a, φ(b) = b
11	24340	⟨a, b \| ab=a, aaaabaa=a⟩	φ(a) = a, φ(b) = b
11	24348	⟨a, b \| ab=a, aaabaaa=a⟩	φ(a) = a, φ(b) = b
11	24364	⟨a, b \| ab=a, aabaaaa=a⟩	φ(a) = a, φ(b) = b
11	24396	⟨a, b \| ab=a, abaaaaa=a⟩	φ(a) = a, φ(b) = b
11	24861	⟨a, b \| ab=a, aaaaaa=ab⟩	φ(a) = a, φ(b) = b