#5396 ⟨a, b | aab=ba, baa=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 b is not injective:
- b ⋅ a⁴ = ba and b ⋅ a = ba, however a⁴ ≠ a
Not right cancellative, because right multiplication by a is not injective:
- ba³ ⋅ a = ba and b ⋅ a = ba, however ba³ ≠ b

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.	ba⁴ ⇒ ba	[3]
2.	ab ⇒ ba²	[2]

# ab:aab=ba,baa=ab a/b - -
baaaa=ba
ab=baa

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

1 total

Σ	#	Presentation	Mapping
11	16218	⟨a, b \| aab=ba, aaba=ab⟩	φ(a) = a, φ(b) = b