#2912 ⟨a, b, c | aab=b, 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 ⋅ a³c = a²c and a ⋅ ac = a²c, however a³c ≠ ac
Not right cancellative, because right multiplication by c is not injective:
- a⁴ ⋅ c = a²c and a² ⋅ c = a²c, however a⁴ ≠ a²

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.	a⁴c ⇒ a²c	[4]
2.	b ⇒ a²c	[2]

# abc:aab=b,aac=b ac/b - -
aaaac=aac
b=aac

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

1 total

Σ	#	Presentation	Mapping
8	5739	⟨a, b, c \| aa=b, bbc=bc⟩	φ(a) = a, φ(b) = aa, φ(c) = c