#1131 ⟨a, b | aa=1, babbb=b⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab³ = b and b ⋅ 1 = b, however ab³ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- bab² ⋅ b = b and 1 ⋅ b = b, however bab² ≠ 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.	a² ⇒ 1	[1]
2.	bab³ ⇒ b	[2]

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

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

6 total

Σ	#	Presentation	Mapping
10	9701	⟨a, b \| aa=1, aababbb=b⟩	φ(a) = a, φ(b) = b
10	9767	⟨a, b \| aa=1, baaabbb=b⟩	φ(a) = a, φ(b) = b
10	9777	⟨a, b \| aa=1, babaabb=b⟩	φ(a) = a, φ(b) = b
10	10006	⟨a, b \| aa=1, ababbb=ab⟩	φ(a) = a, φ(b) = b
10	10325	⟨a, b \| aa=1, babbb=aab⟩	φ(a) = a, φ(b) = b
10	10328	⟨a, b \| aa=1, babbb=baa⟩	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
10	9711	⟨a, b \| aa=1, aabbbab=b⟩	φ(a) = a, φ(b) = b
10	9773	⟨a, b \| aa=1, baabbab=b⟩	φ(a) = a, φ(b) = b
10	10018	⟨a, b \| aa=1, abbbab=ab⟩	φ(a) = a, φ(b) = b