#3405 ⟨a, b | aa=1, bbabbb=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

# ab:aa=1,bbabbb=b ab - -
aa=1
bbab=babb
babbbb=b

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

10 total

Σ	#	Presentation	Mapping
11	26541	⟨a, b \| aa=1, aabbabbb=b⟩	φ(a) = a, φ(b) = b
11	26547	⟨a, b \| aa=1, aabbbabb=b⟩	φ(a) = a, φ(b) = b
11	26661	⟨a, b \| aa=1, baababbb=b⟩	φ(a) = a, φ(b) = b
11	26665	⟨a, b \| aa=1, baabbabb=b⟩	φ(a) = a, φ(b) = b
11	26695	⟨a, b \| aa=1, bbaaabbb=b⟩	φ(a) = a, φ(b) = b
11	26697	⟨a, b \| aa=1, bbaababb=b⟩	φ(a) = a, φ(b) = b
11	27146	⟨a, b \| aa=1, abbabbb=ab⟩	φ(a) = a, φ(b) = b
11	27154	⟨a, b \| aa=1, abbbabb=ab⟩	φ(a) = a, φ(b) = b
11	27755	⟨a, b \| aa=1, bbabbb=aab⟩	φ(a) = a, φ(b) = b
11	27758	⟨a, b \| aa=1, bbabbb=baa⟩	φ(a) = a, φ(b) = b