#3979 ⟨a, b, c | abc=1, aaaaa=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 ⋅ (cb)⁵ = b and b ⋅ 1 = b, however (cb)⁵ ≠ 1
Not right cancellative, because right multiplication by c(bc)⁴ is not injective:
- (cb)⁵ ⋅ c(bc)⁴ = c(bc)⁴ and 1 ⋅ c(bc)⁴ = c(bc)⁴, however (cb)⁵ ≠ 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.	(bc)⁵ ⇒ 1	[8]
2.	a ⇒ (bc)⁴	[7]

# abc:abc=1,aaaaa=1 bc/a - -
bcbcbcbcbc=1
a=bcbcbcbc

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

1 total

Σ	#	Presentation	Mapping
8	5108	⟨a, b, c \| ab=c, ccccc=1⟩	φ(a) = b, φ(b) = c, φ(c) = bc