#1049 ⟨a, b, c | ab=c, ccc=c⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b(ab)² = ab and a ⋅ b = ab, however b(ab)² ≠ b
Not right cancellative, because right multiplication by b is not injective:
- a(ba)² ⋅ b = ab and a ⋅ b = ab, however a(ba)² ≠ a

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

#	Rule	Proof
1.	(ab)³ ⇒ ab	[2]
2.	c ⇒ ab	[1]

# abc:ab=c,ccc=c ab/c - -
ababab=ab
c=ab

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

3 total

Σ	#	Presentation	Mapping
8	5533	⟨a, b, c \| ab=c, abcc=c⟩	φ(a) = a, φ(b) = b, φ(c) = ab
8	5600	⟨a, b, c \| ab=c, cabc=c⟩	φ(a) = a, φ(b) = b, φ(c) = ab
8	6108	⟨a, b, c \| ab=c, ccc=ab⟩	φ(a) = a, φ(b) = b, φ(c) = ab