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