#3507 ⟨a, b, c | bb=ac, aac=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:
- a²b ⋅ b = b² and b ⋅ b = b², however a²b ≠ 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.	a²b² ⇒ b²	[3]
2.	c ⇒ ab²	[2]

# abc:bb=ac,aac=c ab/c - -
aabb=bb
c=abb

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

2 total

Σ	#	Presentation	Mapping
8	3513	⟨a, b, c \| bb=ac, abb=c⟩	φ(a) = a, φ(b) = b, φ(c) = abb
8	5757	⟨a, b, c \| aa=b, bcc=cc⟩	φ(a) = a, φ(b) = aa, φ(c) = b