#6632 ⟨a, b, c | aa=1, aabca=b⟩

Properties

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

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	bc ⇒ ba	[3]

# abc:aa=1,aabca=b abc - -
aa=1
bc=ba

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

4 total

Σ	#	Presentation	Mapping
8	7124	⟨a, b, c \| aa=1, aaba=bc⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7136	⟨a, b, c \| aa=1, aabc=ba⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7174	⟨a, b, c \| aa=1, abca=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7625	⟨a, b, c \| aa=1, abc=aba⟩	φ(a) = a, φ(b) = b, φ(c) = c