#4370 ⟨a, b, c | aba=1, aaac=c⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by c is not injective:
- b ⋅ c = ac and a ⋅ c = ac, however b ≠ 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

# abc:aba=1,aaac=c abc - -
ba=ab
bc=ac
aab=1
aaac=c

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

3 total

Σ	#	Presentation	Mapping
8	4393	⟨a, b, c \| aba=1, abbc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	4431	⟨a, b, c \| aba=1, babc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	4440	⟨a, b, c \| aba=1, bbac=c⟩	φ(a) = a, φ(b) = b, φ(c) = c