Input TRS:
    1: double(0()) -> 0()
    2: double(s(x)) -> s(s(double(x)))
    3: +(x,0()) -> x
    4: +(x,s(y)) -> s(+(x,y))
    5: +(s(x),y) -> s(+(x,y))
    6: double(x) -> +(x,x)
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... removes: 1 3 6
     s(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
double(x1)	weight: (/ 41305 2) + 2 * x1
     +(x1,x2)	weight: (/ 82609 4) + x1 + x2
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 4
     s(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
double(x1)	weight: (/ 41305 2) + 2 * x1
     +(x1,x2)	weight: (/ 82609 4) + x1 + 2 * x2
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 5
     s(x1)	weight: (/ 1 8) + x1
     0()	weight: 0
double(x1)	weight: (/ 1 8) + 2 * x1
     +(x1,x2)	weight: (/ 1 8) + 2 * x1 + 2 * x2
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #double(s(x)) -> #double(x)
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
#double(x1)	weight: x1
double(x1)	weight: 0
     +(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES