#1047 ⟨a, b, c | ab=c, cac=c⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba²b = ab and a ⋅ b = ab, however ba²b ≠ b
Not right cancellative, because right multiplication by b is not injective:
- aba² ⋅ b = ab and a ⋅ b = ab, however aba² ≠ 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(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	aba²b ⇒ ab	[2]
2.	c ⇒ ab	[1]

# abc:ab=c,cac=c ab/c - -
abaab=ab
c=ab

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

2 total

Σ	#	Presentation	Mapping
8	5518	⟨a, b, c \| ab=c, abac=c⟩	φ(a) = a, φ(b) = b, φ(c) = ab
8	6099	⟨a, b, c \| ab=c, cac=ab⟩	φ(a) = a, φ(b) = b, φ(c) = ab