#538 ⟨a, b, c | ba=ac, bc=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 b is not injective:
- b ⋅ c² = b²c and b ⋅ bc = b²c, however c² ≠ bc
Not right cancellative, because right multiplication by c is not injective:
- bc ⋅ c = b²c and b² ⋅ c = b²c, however bc ≠ b²

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(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	bc² ⇒ b²c	[4]
2.	a ⇒ bc	[2]

# abc:ba=ac,bc=a bc/a - -
bcc=bbc
a=bc

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

3 total

Σ	#	Presentation	Mapping
8	2965	⟨a, b, c \| aab=c, abb=c⟩	φ(a) = b, φ(b) = c, φ(c) = bbc
8	5715	⟨a, b, c \| aa=b, acc=bc⟩	φ(a) = b, φ(b) = bb, φ(c) = c
8	6003	⟨a, b, c \| ab=c, aab=cb⟩	φ(a) = b, φ(b) = c, φ(c) = bc