#405 ⟨a, b, c | abc=a, ccc=1⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = ac² and a ⋅ c² = ac², however b ≠ c²

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

#	Rule	Proof
1.	c³ ⇒ 1	[2]
2.	ab ⇒ ac²	[3]

# abc:abc=a,ccc=1 ac/b - -
ccc=1
ab=acc

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

1 total

Σ	#	Presentation	Mapping
8	1904	⟨a, b, c \| abb=ac, bbb=1⟩	φ(a) = a, φ(b) = c, φ(c) = b