#530 ⟨a, b, c | ba=ab, bc=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 ⋅ bc = bcb and b ⋅ cb = bcb, however bc ≠ cb

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

#	Rule	Proof
1.	b²c ⇒ bcb	[4]
2.	a ⇒ bc	[2]

# abc:ba=ab,bc=a cb/a - -
bbc=bcb
a=bc

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

4 total

Σ	#	Presentation	Mapping
8	2964	⟨a, b, c \| aab=c, aba=c⟩	φ(a) = b, φ(b) = c, φ(c) = bcb
8	5699	⟨a, b, c \| aa=b, aca=bc⟩	φ(a) = b, φ(b) = bb, φ(c) = c
8	6002	⟨a, b, c \| ab=c, aab=ca⟩	φ(a) = b, φ(b) = c, φ(c) = bc
8	6016	⟨a, b, c \| ab=c, aba=ac⟩	φ(a) = b, φ(b) = c, φ(c) = bc