#3364 ⟨a, b, c | ab=aa, cca=b⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ c²a = a² and a ⋅ a = a², however c²a ≠ a
Not right cancellative, because right multiplication by a is not injective:
- ac² ⋅ a = a² and a ⋅ a = a², however ac² ≠ 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(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ac²a ⇒ a²	[3]
2.	b ⇒ c²a	[2]

# abc:ab=aa,cca=b ac/b - -
acca=aa
b=cca

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

3 total

Σ	#	Presentation	Mapping
8	5209	⟨a, b, c \| aa=b, acca=b⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5769	⟨a, b, c \| aa=b, cbc=cc⟩	φ(a) = c, φ(b) = cc, φ(c) = a
8	6069	⟨a, b, c \| ab=c, bac=bb⟩	φ(a) = c, φ(b) = a, φ(c) = ca