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