Input TRS:
    1: f(0()) -> true()
    2: f(1()) -> false()
    3: f(s(x)) -> f(x)
    4: if(true(),x,y) -> x
    5: if(false(),x,y) -> y
    6: g(s(x),s(y)) -> if(f(x),s(x),s(y))
    7: g(x,c(y)) -> g(x,g(s(c(y)),y))
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #g(s(x),s(y)) -> #if(f(x),s(x),s(y))
   #2: #g(s(x),s(y)) -> #f(x)
   #3: #g(x,c(y)) -> #g(x,g(s(c(y)),y))
   #4: #g(x,c(y)) -> #g(s(c(y)),y)
   #5: #f(s(x)) -> #f(x)
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
 false()	weight: 0
     c(x1)	weight: 0
  true()	weight: 0
     f(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
   #f(x1)	weight: x1
   #g(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
     g(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #3 #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
     s(x1)	weight: (/ 1 4)
 false()	weight: 0
     c(x1)	weight: (/ 3 4) + x1
  true()	weight: 0
     f(x1)	weight: (/ 1 4)
     0()	weight: 0
    if(x1,x2,x3)	weight: x2 + x3
   #f(x1)	weight: 0
   #g(x1,x2)	weight: x2
  #if(x1,x2,x3)	weight: 0
     g(x1,x2)	weight: (/ 1 2)
    Usable rules: { 4..7 }
    Removed DPs: #3 #4
Number of SCCs: 0, DPs: 0, edges: 0
YES