#2052 ⟨a, b | aab=b, aaaa=a⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a³ = a and a ⋅ 1 = a, however a³ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- a ⋅ b = b and 1 ⋅ b = b, however a ≠ 1

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 ⇒ b	[3]
2.	a⁴ ⇒ a	[2]

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

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

1 total

Σ	#	Presentation	Mapping
11	14332	⟨a, b \| aaaa=a, aaaab=b⟩	φ(a) = a, φ(b) = b