#4521 ⟨a, b, c | abc=1, abbb=c⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ bab³a = a and a ⋅ 1 = a, however bab³a ≠ 1
Not right cancellative, because right multiplication by bab³ is not injective:
- bab³a ⋅ bab³ = bab³ and 1 ⋅ bab³ = bab³, however bab³a ≠ 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(a) = deg(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	abab³ ⇒ 1	[3]
2.	c ⇒ ab³	[2]

# abc:abc=1,abbb=c ab/c - -
ababbb=1
c=abbb

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

1 total

Σ	#	Presentation	Mapping
8	7096	⟨a, b, c \| ab=1, caccc=b⟩	φ(a) = a, φ(b) = babbb, φ(c) = b