#517 ⟨a, b, c | ab=aa, cc=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 ⋅ cb = c⁴ and c ⋅ c³ = c⁴, however cb ≠ c³

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.	c²b ⇒ c⁴	[4]

# abc:ab=aa,cc=a c/ab - -
a=cc
ccb=cccc

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

3 total

Σ	#	Presentation	Mapping
8	5665	⟨a, b, c \| aa=b, aab=bc⟩	φ(a) = c, φ(b) = cc, φ(c) = b
8	5673	⟨a, b, c \| aa=b, aac=bb⟩	φ(a) = c, φ(b) = cc, φ(c) = b
8	5679	⟨a, b, c \| aa=b, aba=bc⟩	φ(a) = c, φ(b) = cc, φ(c) = b

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

1 total

Σ	#	Presentation	Mapping
8	5667	⟨a, b, c \| aa=b, aab=cb⟩	φ(a) = c, φ(b) = cc, φ(c) = b