#7860 ⟨a, b, c | ab=1, ccc=aaa⟩

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 c is not injective:
- c ⋅ c²b³c = c and c ⋅ 1 = c, however c²b³c ≠ 1
Not right cancellative, because right multiplication by c²b³ is not injective:
- c²b³c ⋅ c²b³ = c²b³ and 1 ⋅ c²b³ = c²b³, however c²b³c ≠ 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.

# abc:ab=1,ccc=aaa bc/a - -
cccbbb=1
ccccccb=cccbccc
cccbcccb=cccbbccc
cccbbcccb=ccc
a=cccbb