#1439 ⟨a, b, c | ab=1, aaa=cc⟩

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 c is not injective:
- c ⋅ cb³c = c and c ⋅ 1 = c, however cb³c ≠ 1
Not right cancellative, because right multiplication by cb³ is not injective:
- cb³c ⋅ cb³ = cb³ and 1 ⋅ cb³ = cb³, however cb³c ≠ 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,aaa=cc bc/a - -
ccbbb=1
ccccb=ccbcc
ccbccb=ccbbcc
ccbbccb=cc
a=ccbb