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: foldB(t,0()) -> t
    8: foldB(t,s(n)) -> f(foldB(t,n),B())
    9: foldC(t,0()) -> t
    10: foldC(t,s(n)) -> f(foldC(t,n),C())
    11: f(t,x) -> f'(t,g(x))
    12: f'(triple(a,b,c),C()) -> triple(a,b,s(c))
    13: f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
    14: f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
    15: f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)
Number of strict rules: 15
Direct Order(PosReal,>,Poly) ... removes: 15 7 14 9
     s(x1)	weight: 21387 + x1
triple(x1,x2,x3)	weight: (/ 1 4) + x1 + 2 * x2 + 2 * x3
     C()	weight: 0
     f(x1,x2)	weight: 42774 + x1 + x2
     B()	weight: 0
 foldB(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
     0()	weight: 0
     A()	weight: 0
    f'(x1,x2)	weight: 42774 + x1 + x2
 foldC(x1,x2)	weight: (/ 85545 4) + x1 + 2 * x2
     g(x1)	weight: x1
   f''(x1)	weight: (/ 42773 2) + x1
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... removes: 8 10 12
     s(x1)	weight: (/ 150231 4) + x1
triple(x1,x2,x3)	weight: (/ 1 4) + x1 + 2 * x2 + x3
     C()	weight: 0
     f(x1,x2)	weight: (/ 300461 4) + x1 + x2
     B()	weight: 0
 foldB(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
     0()	weight: 0
     A()	weight: 0
    f'(x1,x2)	weight: (/ 300461 4) + x1 + x2
 foldC(x1,x2)	weight: (/ 150229 4) + x1 + 2 * x2
     g(x1)	weight: x1
   f''(x1)	weight: (/ 150229 4) + x1
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f'(triple(a,b,c),B()) -> #f(triple(a,b,c),A())
   #2: #f(t,x) -> #f'(t,g(x))
   #3: #f(t,x) -> #g(x)
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: 0
  #f'(x1,x2)	weight: max{0, (/ 1 8) + x2}
triple(x1,x2,x3)	weight: 0
     C()	weight: (/ 3 8)
     f(x1,x2)	weight: 0
     B()	weight: (/ 3 8)
 foldB(x1,x2)	weight: 0
     0()	weight: 0
     A()	weight: (/ 1 8)
   #f(x1,x2)	weight: max{0, (/ 1 4) + x2}
   #g(x1)	weight: 0
    f'(x1,x2)	weight: 0
 foldC(x1,x2)	weight: 0
     g(x1)	weight: x1
   f''(x1)	weight: 0
    Usable rules: { 1..6 }
    Removed DPs: #1 #2
Number of SCCs: 0, DPs: 0, edges: 0
YES