#3269 ⟨a, b, c | bb=ac, aacb=1⟩

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 ⋅ a²(ca)³ = a and a ⋅ 1 = a, however a²(ca)³ ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- (aca)² ⋅ c = a(ac)³ and a²(ca)² ⋅ c = a(ac)³, however (aca)² ≠ a²(ca)²

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:
- Right-to-left recursive path with deg(c) = deg(a) = 0, c < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:bb=ac,aacb=1 reversed:ca/b - -
acaacac=aacacac
aaacacac=1
b=aacac

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

2 total

Σ	#	Presentation	Mapping
8	3273	⟨a, b, c \| bb=ac, abac=1⟩	φ(a) = a, φ(b) = aacac, φ(c) = c
8	3275	⟨a, b, c \| bb=ac, abbb=1⟩	φ(a) = a, φ(b) = aacac, φ(c) = c