#3673 ⟨a, b | aa=1, babb=bbb⟩

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 ⋅ ab² = b³ and b ⋅ b² = b³, however ab² ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- bab ⋅ b = b³ and b² ⋅ b = b³, however bab ≠ b²

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.	bab² ⇒ b³	[2]

# ab:aa=1,babb=bbb ab - -
aa=1
babb=bbb

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

5 total

Σ	#	Presentation	Mapping
11	27581	⟨a, b \| aa=1, aababb=bbb⟩	φ(a) = a, φ(b) = b
11	27709	⟨a, b \| aa=1, baaabb=bbb⟩	φ(a) = a, φ(b) = b
11	28135	⟨a, b \| aa=1, aabbb=babb⟩	φ(a) = a, φ(b) = b
11	28173	⟨a, b \| aa=1, ababb=abbb⟩	φ(a) = a, φ(b) = b
11	28245	⟨a, b \| aa=1, baabb=babb⟩	φ(a) = a, φ(b) = b

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

5 total

Σ	#	Presentation	Mapping
11	27595	⟨a, b \| aa=1, aabbab=bbb⟩	φ(a) = a, φ(b) = b
11	27717	⟨a, b \| aa=1, baabab=bbb⟩	φ(a) = a, φ(b) = b
11	28137	⟨a, b \| aa=1, aabbb=bbab⟩	φ(a) = a, φ(b) = b
11	28189	⟨a, b \| aa=1, abbab=abbb⟩	φ(a) = a, φ(b) = b
11	28247	⟨a, b \| aa=1, baabb=bbab⟩	φ(a) = a, φ(b) = b