#561 ⟨a, b, c | bc=ac, cc=a⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not right cancellative, because right multiplication by c is not injective:
- b ⋅ c = c³ and c² ⋅ c = c³, however b ≠ 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(c) = 0; deg(a) = deg(b) = 1, a < b
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a ⇒ c²	[2]
2.	bc ⇒ c³	[3]

# abc:bc=ac,cc=a c/ab - -
a=cc
bc=ccc

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

1 total

Σ	#	Presentation	Mapping
7	563	⟨a, b, c \| ca=bc, cc=a⟩	φ(a) = cc, φ(b) = b, φ(c) = c

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

3 total

Σ	#	Presentation	Mapping
7	1010	⟨a, b, c \| ab=c, aaa=c⟩	φ(a) = c, φ(b) = b, φ(c) = ccc
8	5661	⟨a, b, c \| aa=b, aaa=ac⟩	φ(a) = c, φ(b) = cc, φ(c) = b
8	5988	⟨a, b, c \| ab=c, aaa=ab⟩	φ(a) = c, φ(b) = b, φ(c) = ccc