Input TRS:
    1: f(true(),true(),x,s(y)) -> f(isNat(x),isNat(y),s(x),double(s(y)))
    2: isNat(0()) -> true()
    3: isNat(s(x)) -> isNat(x)
    4: double(0()) -> 0()
    5: double(s(x)) -> s(s(double(x)))
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Freezing double
1: f(true(),true(),x,s(y)) -> f(isNat(x),isNat(y),s(x),double❆1_s(y))
2: isNat(0()) -> true()
3: isNat(s(x)) -> isNat(x)
4: double❆1_0() -> 0()
5: double❆1_s(x) -> s(s(double(x)))
6: double(0()) ->= double❆1_0()
7: double(s(_1)) ->= double❆1_s(_1)
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #double(0()) ->? #double❆1_0()
   #2: #double(s(_1)) ->? #double❆1_s(_1)
   #3: #double❆1_s(x) -> #double(x)
   #4: #isNat(s(x)) -> #isNat(x)
   #5: #f(true(),true(),x,s(y)) -> #f(isNat(x),isNat(y),s(x),double❆1_s(y))
   #6: #f(true(),true(),x,s(y)) -> #isNat(x)
   #7: #f(true(),true(),x,s(y)) -> #isNat(y)
   #8: #f(true(),true(),x,s(y)) -> #double❆1_s(y)
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#double❆1_0()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#isNat(x1)	weight: x1
#double❆1_s(x1)	weight: 0
  true()	weight: 0
     f(x1,x2,x3,x4)	weight: 0
     0()	weight: 0
#double(x1)	weight: 0
double(x1)	weight: 0
   #f(x1,x2,x3,x4)	weight: 0
double❆1_0()	weight: 0
 isNat(x1)	weight: 0
double❆1_s(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #2 #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#double❆1_0()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#isNat(x1)	weight: 0
#double❆1_s(x1)	weight: (/ 1 4) + x1
  true()	weight: 0
     f(x1,x2,x3,x4)	weight: 0
     0()	weight: 0
#double(x1)	weight: x1
double(x1)	weight: 0
   #f(x1,x2,x3,x4)	weight: 0
double❆1_0()	weight: 0
 isNat(x1)	weight: 0
double❆1_s(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #3
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #5 }
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