#582 ⟨a, b | aab=a, aba=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ab = a and a ⋅ 1 = a, however ab ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- ab ⋅ a = a and 1 ⋅ a = a, however ab ≠ 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.	a²b ⇒ a	[1]
2.	aba ⇒ a	[2]

# ab:aab=a,aba=a ab - -
aab=a
aba=a

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

6 total

Σ	#	Presentation	Mapping
10	6330	⟨a, b \| aab=a, aabba=a⟩	φ(a) = a, φ(b) = b
10	6336	⟨a, b \| aab=a, abaab=a⟩	φ(a) = a, φ(b) = b
10	6456	⟨a, b \| aba=a, aabab=a⟩	φ(a) = a, φ(b) = b
10	6462	⟨a, b \| aba=a, abaab=a⟩	φ(a) = a, φ(b) = b
10	6614	⟨a, b \| aab=a, abaa=aa⟩	φ(a) = a, φ(b) = b
10	6808	⟨a, b \| aab=a, aba=aab⟩	φ(a) = a, φ(b) = b