#16146 ⟨a, b | aab=ab, aaaa=ab⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a⁴ and a ⋅ a³ = a⁴, however b ≠ a³
Not right cancellative, because right multiplication by a is not injective:
- a⁴ ⋅ a = a⁴ and a³ ⋅ a = a⁴, however a⁴ ≠ a³

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.	a⁵ ⇒ a⁴	[4]
2.	ab ⇒ a⁴	[2]

# ab:aab=ab,aaaa=ab a/b - -
aaaaa=aaaa
ab=aaaa

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

1 total

Σ	#	Presentation	Mapping
11	16374	⟨a, b \| aba=ab, aaaa=ab⟩	φ(a) = a, φ(b) = b