Input TRS:
    1: f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
    2: gt(0(),v) -> false()
    3: gt(s(u),0()) -> true()
    4: gt(s(u),s(v)) -> gt(u,v)
    5: and(x,true()) -> x
    6: and(x,false()) -> false()
    7: plus(n,0()) -> n
    8: plus(n,s(m)) -> s(plus(n,m))
    9: double(0()) -> 0()
    10: double(s(x)) -> s(s(double(x)))
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #double(s(x)) -> #double(x)
   #2: #f(true(),x,y) -> #f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
   #3: #f(true(),x,y) -> #and(gt(x,y),gt(y,s(s(0()))))
   #4: #f(true(),x,y) -> #gt(x,y)
   #5: #f(true(),x,y) -> #gt(y,s(s(0())))
   #6: #f(true(),x,y) -> #plus(s(0()),x)
   #7: #f(true(),x,y) -> #double(y)
   #8: #plus(n,s(m)) -> #plus(n,m)
   #9: #gt(s(u),s(v)) -> #gt(u,v)
Number of SCCs: 4, DPs: 4, edges: 4
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
    gt(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
     f(x1,x2,x3)	weight: 0
     0()	weight: 0
#double(x1)	weight: x1
double(x1)	weight: 0
  #gt(x1,x2)	weight: 0
   #f(x1,x2,x3)	weight: 0
  plus(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
    gt(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: x2
 false()	weight: 0
  true()	weight: 0
     f(x1,x2,x3)	weight: 0
     0()	weight: 0
#double(x1)	weight: 0
double(x1)	weight: 0
  #gt(x1,x2)	weight: 0
   #f(x1,x2,x3)	weight: 0
  plus(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
    gt(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
     f(x1,x2,x3)	weight: 0
     0()	weight: 0
#double(x1)	weight: 0
double(x1)	weight: 0
  #gt(x1,x2)	weight: x2
   #f(x1,x2,x3)	weight: 0
  plus(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  failed.
MAYBE