#3618 ⟨a, b, c | aaa=1, abbcc=1⟩

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 ⋅ (bc²b)³ = b and b ⋅ 1 = b, however (bc²b)³ ≠ 1
Not right cancellative, because right multiplication by bc²(b²c²)² is not injective:
- (bc²b)³ ⋅ bc²(b²c²)² = bc²(b²c²)² and 1 ⋅ bc²(b²c²)² = bc²(b²c²)², however (bc²b)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.	(b²c²)³ ⇒ 1	[6]
2.	a ⇒ (b²c²)²	[5]

# abc:aaa=1,abbcc=1 bc/a - -
bbccbbccbbcc=1
a=bbccbbcc

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

1 total

Σ	#	Presentation	Mapping
8	4148	⟨a, b, c \| aaa=1, bbcc=a⟩	φ(a) = bbcc, φ(b) = b, φ(c) = c