#8073 ⟨a, b | aaa=1, abbb=bab⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element aba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b¹⁴ = b⁸ and b ⋅ b⁷ = b⁸, however b¹⁴ ≠ b⁷
Not right cancellative, because right multiplication by b is not injective:
- ba ⋅ b = ab³ and ab² ⋅ b = ab³, however ba ≠ ab²

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:aaa=1,abbb=bab b/a - -
bbbbbbbbbbbbbbb=bbbbbbbb
bab=abbb
baabbb=aabbbbbbb
aaa=1

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

1 total

Σ	#	Presentation	Mapping
11	22763	⟨a, b \| aaa=1, aabab=bbb⟩	φ(a) = a, φ(b) = b