#5775 ⟨a, b, c | aa=b, ccc=cc⟩

Properties

Sum of relation sides is 8
Isomorphic to ℕ_{(3 = 2)} ∗ ℕ
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ c² = c² and c ⋅ c = c², however c² ≠ c
Not right cancellative, because right multiplication by c is not injective:
- c² ⋅ c = c² and c ⋅ c = c², however c² ≠ c

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(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	c³ ⇒ c²	[2]
2.	b ⇒ a²	[1]

# abc:aa=b,ccc=cc ac/b - -
ccc=cc
b=aa

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

1 total

Σ	#	Presentation	Mapping
8	5987	⟨a, b, c \| ab=c, aaa=aa⟩	φ(a) = c, φ(b) = a, φ(c) = ca