#1002 ⟨a, b, c | ab=a, ccb=a⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ cb² = c²b and c ⋅ cb = c²b, however cb² ≠ cb
Not right cancellative, because right multiplication by b is not injective:
- c²b ⋅ b = c²b and c² ⋅ b = c²b, however c²b ≠ c²

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

#	Rule	Proof
1.	c²b² ⇒ c²b	[4]
2.	a ⇒ c²b	[2]

# abc:ab=a,ccb=a bc/a - -
ccbb=ccb
a=ccb

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

3 total

Σ	#	Presentation	Mapping
8	5754	⟨a, b, c \| aa=b, bcc=bc⟩	φ(a) = c, φ(b) = cc, φ(c) = b
8	5970	⟨a, b, c \| ab=a, ccb=ab⟩	φ(a) = ccb, φ(b) = b, φ(c) = c
8	6043	⟨a, b, c \| ab=c, acb=ac⟩	φ(a) = c, φ(b) = b, φ(c) = cb