#1005 ⟨a, b, c | ab=a, ccc=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 ⋅ c²b = c³ and c ⋅ c² = c³, however c²b ≠ c²

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.	c³b ⇒ c³	[4]
2.	a ⇒ c³	[2]

# abc:ab=a,ccc=a bc/a - -
cccb=ccc
a=ccc

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

5 total

Σ	#	Presentation	Mapping
8	5687	⟨a, b, c \| aa=b, abc=ab⟩	φ(a) = c, φ(b) = cc, φ(c) = b
8	5689	⟨a, b, c \| aa=b, abc=ba⟩	φ(a) = c, φ(b) = cc, φ(c) = b
8	5723	⟨a, b, c \| aa=b, bac=ab⟩	φ(a) = c, φ(b) = cc, φ(c) = b
8	5725	⟨a, b, c \| aa=b, bac=ba⟩	φ(a) = c, φ(b) = cc, φ(c) = b
8	5979	⟨a, b, c \| ab=a, ccc=ab⟩	φ(a) = ccc, φ(b) = b, φ(c) = c