#13203 ⟨a, b | abb=aab, bbb=ab⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b⁴ = b⁴ and b ⋅ b³ = b⁴, however b⁴ ≠ b³
Not right cancellative, because right multiplication by b is not injective:
- a ⋅ b = b³ and b² ⋅ b = b³, however a ≠ b²

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.	b⁵ ⇒ b⁴	[4]
2.	ab ⇒ b³	[2]

# ab:abb=aab,bbb=ab b/a - -
bbbbb=bbbb
ab=bbb

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

1 total

Σ	#	Presentation	Mapping
11	13252	⟨a, b \| bab=aab, bbb=ab⟩	φ(a) = a, φ(b) = b