#7281 ⟨a, b, c | ab=1, aaaa=cc⟩

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 ⋅ cb⁴c = c and c ⋅ 1 = c, however cb⁴c ≠ 1
Not right cancellative, because right multiplication by cb⁴ is not injective:
- cb⁴c ⋅ cb⁴ = cb⁴ and 1 ⋅ cb⁴ = cb⁴, however cb⁴c ≠ 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,aaaa=cc bc/a - -
ccccb=ccbcc
ccbbbb=1
ccbccb=ccbbcc
ccbbccb=ccbbbcc
ccbbbccb=cc
a=ccbbb