#1693 ⟨a, b | abb=bb, bbb=b⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b² = b and b ⋅ 1 = b, however b² ≠ 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.	b³ ⇒ b	[2]

# ab:abb=bb,bbb=b ab - -
ab=b
bbb=b

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

10 total

Σ	#	Presentation	Mapping
10	5141	⟨a, b \| aab=ab, abbb=b⟩	φ(a) = a, φ(b) = b
11	12254	⟨a, b \| aaab=ab, baaa=a⟩	φ(a) = b, φ(b) = a
11	12380	⟨a, b \| aaba=ba, abaa=a⟩	φ(a) = b, φ(b) = a
11	12388	⟨a, b \| aaba=ba, baaa=a⟩	φ(a) = b, φ(b) = a
11	12494	⟨a, b \| abaa=ba, baaa=a⟩	φ(a) = b, φ(b) = a
11	14573	⟨a, b \| aaba=a, baaba=a⟩	φ(a) = b, φ(b) = a
11	14577	⟨a, b \| aaba=a, babaa=a⟩	φ(a) = b, φ(b) = a
11	15624	⟨a, b \| aab=ab, aabbb=b⟩	φ(a) = a, φ(b) = b
11	15632	⟨a, b \| aab=ab, ababb=b⟩	φ(a) = a, φ(b) = b
11	15636	⟨a, b \| aab=ab, abbab=b⟩	φ(a) = a, φ(b) = b