#526 ⟨a, b, c | ac=ab, 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 = bcb and b ⋅ cb = bcb, however c² ≠ cb

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 ⇒ bcb	[4]
2.	a ⇒ bc	[2]

# abc:ac=ab,bc=a bc/a - -
bcc=bcb
a=bc

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

2 total

Σ	#	Presentation	Mapping
8	6021	⟨a, b, c \| ab=c, aba=cb⟩	φ(a) = b, φ(b) = c, φ(c) = bc
8	6061	⟨a, b, c \| ab=c, baa=bc⟩	φ(a) = c, φ(b) = b, φ(c) = cb