#3506 ⟨a, b, c | bb=ac, aac=b⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a(ac)² = ac and a ⋅ c = ac, however a(ac)² ≠ c
Not right cancellative, because right multiplication by c is not injective:
- a³ca ⋅ c = ac and a ⋅ c = ac, however a³ca ≠ 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

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.

# abc:bb=ac,aac=b ac/b - -
acaac=aacac
aaacac=ac
b=aac

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

2 total

Σ	#	Presentation	Mapping
8	3512	⟨a, b, c \| bb=ac, abb=b⟩	φ(a) = a, φ(b) = aac, φ(c) = c
8	5539	⟨a, b, c \| ab=c, acac=c⟩	φ(a) = a, φ(b) = c, φ(c) = ac