#570 ⟨a, b, c | aaa=1, abcc=1⟩

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 ⋅ (c²b)³ = b and b ⋅ 1 = b, however (c²b)³ ≠ 1
Not right cancellative, because right multiplication by c²(bc²)² is not injective:
- (c²b)³ ⋅ c²(bc²)² = c²(bc²)² and 1 ⋅ c²(bc²)² = c²(bc²)², however (c²b)³ ≠ 1

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.	(bc²)³ ⇒ 1	[6]
2.	a ⇒ (bc²)²	[5]

# abc:aaa=1,abcc=1 bc/a - -
bccbccbcc=1
a=bccbcc

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

1 total

Σ	#	Presentation	Mapping
8	3608	⟨a, b, c \| aaa=1, aabcc=1⟩	φ(a) = bcc, φ(b) = b, φ(c) = c