#975 ⟨a, b, c | ab=a, bcb=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 b is not injective:
- b ⋅ cb² = bcb and b ⋅ cb = bcb, however cb² ≠ cb
Not right cancellative, because right multiplication by b is not injective:
- bcb ⋅ b = bcb and bc ⋅ b = bcb, however bcb ≠ bc

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.	bcb² ⇒ bcb	[4]
2.	a ⇒ bcb	[2]

# abc:ab=a,bcb=a bc/a - -
bcbb=bcb
a=bcb

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

1 total

Σ	#	Presentation	Mapping
8	5889	⟨a, b, c \| ab=a, bcb=ab⟩	φ(a) = bcb, φ(b) = b, φ(c) = c

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

2 total

Σ	#	Presentation	Mapping
8	6038	⟨a, b, c \| ab=c, aca=ca⟩	φ(a) = b, φ(b) = c, φ(c) = bc
8	6079	⟨a, b, c \| ab=c, bbc=bc⟩	φ(a) = c, φ(b) = b, φ(c) = cb