#5392 ⟨a, b | aab=ba, aba=ba⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a²b = a²b and a ⋅ ab = a²b, however a²b ≠ ab
Not right cancellative, because right multiplication by b is not injective:
- a³ ⋅ b = a²b and a² ⋅ b = a²b, however a³ ≠ a²

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.	a³b ⇒ a²b	[2]
2.	ba ⇒ a²b	[1]

# ab:aab=ba,aba=ba reversed:a/b - -
aaab=aab
ba=aab

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

2 total

Σ	#	Presentation	Mapping
11	16215	⟨a, b \| aab=ba, aaab=ba⟩	φ(a) = a, φ(b) = b
11	16508	⟨a, b \| aab=ba, aba=aab⟩	φ(a) = a, φ(b) = b