#3537 ⟨a, b | aa=1, babbb=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 ⋅ ab³ = b² and b ⋅ b = b², however ab³ ≠ b
Not right cancellative, because right multiplication by b is not injective:
- bab² ⋅ b = b² and b ⋅ b = b², however bab² ≠ 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.	bab³ ⇒ b²	[2]

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

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

7 total

Σ	#	Presentation	Mapping
11	27056	⟨a, b \| aa=1, aababbb=bb⟩	φ(a) = a, φ(b) = b
11	27182	⟨a, b \| aa=1, baaabbb=bb⟩	φ(a) = a, φ(b) = b
11	27201	⟨a, b \| aa=1, babaabb=bb⟩	φ(a) = a, φ(b) = b
11	27653	⟨a, b \| aa=1, ababbb=abb⟩	φ(a) = a, φ(b) = b
11	28263	⟨a, b \| aa=1, babbb=aabb⟩	φ(a) = a, φ(b) = b
11	28269	⟨a, b \| aa=1, babbb=baab⟩	φ(a) = a, φ(b) = b
11	28272	⟨a, b \| aa=1, babbb=bbaa⟩	φ(a) = a, φ(b) = b

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

3 total

Σ	#	Presentation	Mapping
11	27075	⟨a, b \| aa=1, aabbbab=bb⟩	φ(a) = a, φ(b) = b
11	27193	⟨a, b \| aa=1, baabbab=bb⟩	φ(a) = a, φ(b) = b
11	27677	⟨a, b \| aa=1, abbbab=abb⟩	φ(a) = a, φ(b) = b