#3073 ⟨a, b, c | ab=aa, aaac=1⟩

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 ⋅ b = a² and a ⋅ a = a², however b ≠ a
Not right cancellative, because right multiplication by a²c is not injective:
- a²ca ⋅ a²c = a²c and 1 ⋅ a²c = a²c, however a²ca ≠ 1

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

#	Rule	Proof
1.	ab ⇒ a²	[1]
2.	a³c ⇒ 1	[2]

# abc:ab=aa,aaac=1 abc - -
ab=aa
aaac=1

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

3 total

Σ	#	Presentation	Mapping
8	3074	⟨a, b, c \| ab=aa, aabc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	3078	⟨a, b, c \| ab=aa, abac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	3079	⟨a, b, c \| ab=aa, abbc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c