#3504 ⟨a, b, c | bb=ac, aab=c⟩

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 b is not injective:
- a³ ⋅ b = b² and b ⋅ b = b², however a³ ≠ b

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

#	Rule	Proof
1.	a³b ⇒ b²	[3]
2.	c ⇒ a²b	[2]

# abc:bb=ac,aab=c ab/c - -
aaab=bb
c=aab

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

3 total

Σ	#	Presentation	Mapping
8	5694	⟨a, b, c \| aa=b, abc=cc⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	5730	⟨a, b, c \| aa=b, bac=cc⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	6009	⟨a, b, c \| ab=c, aac=bb⟩	φ(a) = a, φ(b) = b, φ(c) = ab