#3540 ⟨a, b | aa=1, bbabb=bb⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bab² = b² and b ⋅ b = b², however bab² ≠ b
Not right cancellative, because right multiplication by b is not injective:
- b²ab ⋅ b = b² and b ⋅ b = b², however b²ab ≠ b

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.	a² ⇒ 1	[1]
2.	b²ab² ⇒ b²	[2]

# ab:aa=1,bbabb=bb ab - -
aa=1
bbabb=bb

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

6 total

Σ	#	Presentation	Mapping
11	27068	⟨a, b \| aa=1, aabbabb=bb⟩	φ(a) = a, φ(b) = b
11	27189	⟨a, b \| aa=1, baababb=bb⟩	φ(a) = a, φ(b) = b
11	27222	⟨a, b \| aa=1, bbaaabb=bb⟩	φ(a) = a, φ(b) = b
11	27669	⟨a, b \| aa=1, abbabb=abb⟩	φ(a) = a, φ(b) = b
11	28279	⟨a, b \| aa=1, bbabb=aabb⟩	φ(a) = a, φ(b) = b
11	28283	⟨a, b \| aa=1, bbabb=baab⟩	φ(a) = a, φ(b) = b