#3398 ⟨a, b, c | ac=ab, bbb=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b²c = b⁴ and b ⋅ b³ = b⁴, however b²c ≠ b³

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.	b³c ⇒ b⁴	[4]
2.	a ⇒ b³	[2]

# abc:ac=ab,bbb=a bc/a - -
bbbc=bbbb
a=bbb

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

3 total

Σ	#	Presentation	Mapping
8	3463	⟨a, b, c \| ba=ac, bbb=a⟩	φ(a) = bbb, φ(b) = b, φ(c) = c
8	5690	⟨a, b, c \| aa=b, abc=bb⟩	φ(a) = b, φ(b) = bb, φ(c) = c
8	5726	⟨a, b, c \| aa=b, bac=bb⟩	φ(a) = b, φ(b) = bb, φ(c) = c