Input TRS:
    1: double(0()) -> 0()
    2: double(s(x)) -> s(s(double(x)))
    3: half(0()) -> 0()
    4: half(s(0())) -> 0()
    5: half(s(s(x))) -> s(half(x))
    6: -(x,0()) -> x
    7: -(s(x),s(y)) -> -(x,y)
    8: if(0(),y,z) -> y
    9: if(s(x),y,z) -> z
    10: half(double(x)) -> x
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3 5 10 7 9 6
     s(x1)	weight: (/ 1 8) + x1
  half(x1)	weight: (/ 161297 8) + 2 * x1
     0()	weight: 0
    if(x1,x2,x3)	weight: (/ 1 8) + 2 * x1 + x2 + x3
double(x1)	weight: (/ 258281 8) + 2 * x1
     -(x1,x2)	weight: (/ 1 8) + x1 + 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
  half(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	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