#2949 ⟨a, b, c | aab=b, cac=b⟩

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:
- a²ca ⋅ c = cac and ca ⋅ c = cac, however a²ca ≠ ca

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.	a(ac)² ⇒ cac	[4]
2.	b ⇒ cac	[2]

# abc:aab=b,cac=b ac/b - -
aacac=cac
b=cac

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

1 total

Σ	#	Presentation	Mapping
8	6052	⟨a, b, c \| ab=c, acc=bc⟩	φ(a) = a, φ(b) = c, φ(c) = ac