Input TRS:
    1: g(A()) -> A()
    2: g(B()) -> A()
    3: g(B()) -> B()
    4: g(C()) -> A()
    5: g(C()) -> B()
    6: g(C()) -> C()
    7: foldf(x,nil()) -> x
    8: foldf(x,cons(y,z)) -> f(foldf(x,z),y)
    9: f(t,x) -> f'(t,g(x))
    10: f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
    11: f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
    12: f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
    13: f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
Number of strict rules: 13
Direct Order(PosReal,>,Poly) ... removes: 7 12 13
triple(x1,x2,x3)	weight: (/ 1314049 32) + x1 + 2 * x2 + 2 * x3
     C()	weight: 0
     f(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
     B()	weight: 0
     A()	weight: 0
   nil()	weight: 0
    f'(x1,x2)	weight: (/ 1 4) + x1 + x2
  cons(x1,x2)	weight: (/ 1 8) + x1 + x2
 foldf(x1,x2)	weight: (/ 1 32) + x1 + 2 * x2
     g(x1)	weight: x1
   f''(x1)	weight: (/ 1 16) + x1
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... removes: 8 10
triple(x1,x2,x3)	weight: (/ 126965 4) + x1 + x2 + x3
     C()	weight: 0
     f(x1,x2)	weight: (/ 5 4) + x1 + x2
     B()	weight: 0
     A()	weight: 0
   nil()	weight: 0
    f'(x1,x2)	weight: (/ 5 4) + x1 + x2
  cons(x1,x2)	weight: (/ 3 4) + x1 + x2
 foldf(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
     g(x1)	weight: x1
   f''(x1)	weight: (/ 1 4) + x1
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(t,x) -> #f'(t,g(x))
   #2: #f(t,x) -> #g(x)
   #3: #f'(triple(a,b,c),B()) -> #f(triple(a,b,c),A())
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #3 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
  #f'(x1,x2)	weight: max{0, x2}
triple(x1,x2,x3)	weight: 0
     C()	weight: (/ 1 2)
     f(x1,x2)	weight: 0
     B()	weight: (/ 1 2)
     A()	weight: (/ 1 4)
   nil()	weight: 0
   #f(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 4) + x1}
   #g(x1)	weight: 0
    f'(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
 foldf(x1,x2)	weight: 0
     g(x1)	weight: x1
   f''(x1)	weight: 0
    Usable rules: { 1..6 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES