Input TRS:
    1: minus(x,0()) -> x
    2: minus(s(x),s(y)) -> minus(x,y)
    3: double(0()) -> 0()
    4: double(s(x)) -> s(s(double(x)))
    5: plus(0(),y) -> y
    6: plus(s(x),y) -> s(plus(x,y))
    7: plus(s(x),y) -> plus(x,s(y))
    8: plus(s(x),y) -> s(plus(minus(x,y),double(y)))
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #minus(s(x),s(y)) -> #minus(x,y)
   #2: #plus(s(x),y) -> #plus(x,y)
   #3: #plus(s(x),y) -> #plus(x,s(y))
   #4: #plus(s(x),y) -> #plus(minus(x,y),double(y))
   #5: #plus(s(x),y) -> #minus(x,y)
   #6: #plus(s(x),y) -> #double(y)
   #7: #double(s(x)) -> #double(x)
Number of SCCs: 3, DPs: 5, edges: 11
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 minus(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
     0()	weight: 0
#double(x1)	weight: x1
double(x1)	weight: 0
#minus(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 2, DPs: 4, edges: 10
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 minus(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
     0()	weight: 0
#double(x1)	weight: 0
double(x1)	weight: 0
#minus(x1,x2)	weight: x2
  plus(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #2..4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 minus(x1,x2)	weight: (/ 1 4) + x1
#plus(x1,x2)	weight: x1
     0()	weight: 0
#double(x1)	weight: 0
double(x1)	weight: (/ 1 4)
#minus(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
    Usable rules: { 1 2 }
    Removed DPs: #2..4
Number of SCCs: 0, DPs: 0, edges: 0
YES