#4618 ⟨a, b | aaaa=a, aabb=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a²ba 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 a is not injective:
- a³ ⋅ a = a and 1 ⋅ a = a, however a³ ≠ 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.	ab² ⇒ a³	[3]
2.	a⁴ ⇒ a	[1]

# ab:aaaa=a,aabb=a ab - -
abb=aaa
aaaa=a

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

3 total

Σ	#	Presentation	Mapping
11	12964	⟨a, b \| abb=aaa, aaaa=a⟩	φ(a) = a, φ(b) = b
11	12970	⟨a, b \| abb=aaa, aabb=a⟩	φ(a) = a, φ(b) = b
11	12976	⟨a, b \| abb=aaa, abba=a⟩	φ(a) = a, φ(b) = b