#5391 ⟨a, b | aab=ba, aba=ab⟩

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 = ab and a ⋅ b = ab, however a²b ≠ b
Not right cancellative, because right multiplication by b is not injective:
- a³ ⋅ b = ab and a ⋅ b = ab, however a³ ≠ 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.	a³b ⇒ ab	[2]
2.	ba ⇒ a²b	[1]

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

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

2 total

Σ	#	Presentation	Mapping
11	16214	⟨a, b \| aab=ba, aaab=ab⟩	φ(a) = a, φ(b) = b
11	16383	⟨a, b \| aba=ab, aaba=ba⟩	φ(a) = a, φ(b) = b