#3401 ⟨a, b | aa=1, babbbb=b⟩

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 ⋅ ab⁴ = b and b ⋅ 1 = b, however ab⁴ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- bab³ ⋅ b = b and 1 ⋅ b = b, however bab³ ≠ 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.	bab⁴ ⇒ b	[2]

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

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

7 total

Σ	#	Presentation	Mapping
11	26529	⟨a, b \| aa=1, aababbbb=b⟩	φ(a) = a, φ(b) = b
11	26655	⟨a, b \| aa=1, baaabbbb=b⟩	φ(a) = a, φ(b) = b
11	26675	⟨a, b \| aa=1, babaabbb=b⟩	φ(a) = a, φ(b) = b
11	26683	⟨a, b \| aa=1, babbaabb=b⟩	φ(a) = a, φ(b) = b
11	27127	⟨a, b \| aa=1, ababbbb=ab⟩	φ(a) = a, φ(b) = b
11	27741	⟨a, b \| aa=1, babbbb=aab⟩	φ(a) = a, φ(b) = b
11	27744	⟨a, b \| aa=1, babbbb=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
11	26551	⟨a, b \| aa=1, aabbbbab=b⟩	φ(a) = a, φ(b) = b
11	26667	⟨a, b \| aa=1, baabbbab=b⟩	φ(a) = a, φ(b) = b
11	27158	⟨a, b \| aa=1, abbbbab=ab⟩	φ(a) = a, φ(b) = b