#993 ⟨a, b, c | ab=a, cbb=a⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ b³ = cb² and c ⋅ b² = cb², however b³ ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- cb² ⋅ b = cb² and cb ⋅ b = cb², however cb² ≠ cb

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

Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cb³ ⇒ cb²	[4]
2.	a ⇒ cb²	[2]

# abc:ab=a,cbb=a bc/a - -
cbbb=cbb
a=cbb

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

1 total

Σ	#	Presentation	Mapping
8	5943	⟨a, b, c \| ab=a, cbb=ab⟩	φ(a) = cbb, φ(b) = b, φ(c) = c