#3383 ⟨a, b | aa=1, abbbab=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 ⋅ b³ = b and b ⋅ 1 = b, however b³ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b³ ⋅ b = b and 1 ⋅ b = b, however b³ ≠ 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,abbbab=b ab - -
aa=1
bbbb=b
bbbab=ab

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

8 total

Σ	#	Presentation	Mapping
11	26497	⟨a, b \| aa=1, aaabbbab=b⟩	φ(a) = a, φ(b) = b
11	26575	⟨a, b \| aa=1, abaabbab=b⟩	φ(a) = a, φ(b) = b
11	26607	⟨a, b \| aa=1, abbaabab=b⟩	φ(a) = a, φ(b) = b
11	26623	⟨a, b \| aa=1, abbbaaab=b⟩	φ(a) = a, φ(b) = b
11	27073	⟨a, b \| aa=1, aabbbab=ab⟩	φ(a) = a, φ(b) = b
11	27191	⟨a, b \| aa=1, baabbab=ab⟩	φ(a) = a, φ(b) = b
11	27675	⟨a, b \| aa=1, abbbab=aab⟩	φ(a) = a, φ(b) = b
11	27678	⟨a, b \| aa=1, abbbab=baa⟩	φ(a) = a, φ(b) = b

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

9 total

Σ	#	Presentation	Mapping
9	3536	⟨a, b \| aa=1, babbb=ba⟩	φ(a) = a, φ(b) = b
11	26527	⟨a, b \| aa=1, aababbba=b⟩	φ(a) = a, φ(b) = b
11	27055	⟨a, b \| aa=1, aababbb=ba⟩	φ(a) = a, φ(b) = b
11	27123	⟨a, b \| aa=1, ababbba=ab⟩	φ(a) = a, φ(b) = b
11	27181	⟨a, b \| aa=1, baaabbb=ba⟩	φ(a) = a, φ(b) = b
11	27200	⟨a, b \| aa=1, babaabb=ba⟩	φ(a) = a, φ(b) = b
11	27652	⟨a, b \| aa=1, ababbb=aba⟩	φ(a) = a, φ(b) = b
11	28262	⟨a, b \| aa=1, babbb=aaba⟩	φ(a) = a, φ(b) = b
11	28268	⟨a, b \| aa=1, babbb=baaa⟩	φ(a) = a, φ(b) = b