#5228 ⟨a, b | aba=aa, aabb=a⟩

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 ⋅ ab² = a and a ⋅ 1 = a, however ab² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- ab ⋅ a = a² and a ⋅ a = a², however ab ≠ a

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.	aba ⇒ a²	[1]
2.	a²b² ⇒ a	[2]

# ab:aba=aa,aabb=a ab - -
aba=aa
aabb=a

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

1 total

Σ	#	Presentation	Mapping
11	15821	⟨a, b \| aba=aa, ababb=a⟩	φ(a) = a, φ(b) = b