#7177 ⟨a, b | ab=aa, bba=baa⟩

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 ⋅ b = a² and a ⋅ a = a², however b ≠ a
Not right cancellative, because right multiplication by a is not injective:
- b² ⋅ a = ba² and ba ⋅ a = ba², however b² ≠ ba

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 ⇒ a²	[1]
2.	b²a ⇒ ba²	[2]

# ab:ab=aa,bba=baa ab - -
ab=aa
bba=baa

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

1 total

Σ	#	Presentation	Mapping
10	7178	⟨a, b \| ab=aa, bba=bab⟩	φ(a) = a, φ(b) = b