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)
    16: fold(t,x,0()) -> t
    17: fold(t,x,s(n)) -> f(fold(t,x,n),x)
Number of strict rules: 17
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)
   #4: #f'(triple(a,b,c),A()) -> #f''(foldB(triple(s(a),0(),c),b))
   #5: #f'(triple(a,b,c),A()) -> #foldB(triple(s(a),0(),c),b)
   #6: #foldC(t,s(n)) -> #f(foldC(t,n),C())
   #7: #foldC(t,s(n)) -> #foldC(t,n)
   #8: #fold(t,x,s(n)) -> #f(fold(t,x,n),x)
   #9: #fold(t,x,s(n)) -> #fold(t,x,n)
   #10: #foldB(t,s(n)) -> #f(foldB(t,n),B())
   #11: #foldB(t,s(n)) -> #foldB(t,n)
   #12: #f''(triple(a,b,c)) -> #foldC(triple(a,b,0()),c)
Number of SCCs: 2, DPs: 10, edges: 16
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
#foldC(x1,x2)	weight: 0
  #f'(x1,x2)	weight: 0
triple(x1,x2,x3)	weight: 0
     C()	weight: 0
     f(x1,x2)	weight: 0
     B()	weight: 0
 foldB(x1,x2)	weight: 0
#fold(x1,x2,x3)	weight: x3
     0()	weight: 0
#foldB(x1,x2)	weight: 0
     A()	weight: 0
   #f(x1,x2)	weight: 0
   #g(x1)	weight: 0
  fold(x1,x2,x3)	weight: 0
    f'(x1,x2)	weight: 0
 foldC(x1,x2)	weight: 0
     g(x1)	weight: 0
   f''(x1)	weight: 0
 #f''(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 1, DPs: 9, edges: 15
	SCC { #1 #2 #4..7 #10..12 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 3 4) + x1
#foldC(x1,x2)	weight: x1 + x2
  #f'(x1,x2)	weight: (/ 1 2) + x1
triple(x1,x2,x3)	weight: (/ 1 4) + x2 + x3
     C()	weight: 0
     f(x1,x2)	weight: (/ 3 4) + x1
     B()	weight: 0
 foldB(x1,x2)	weight: x1 + x2
#fold(x1,x2,x3)	weight: 0
     0()	weight: 0
#foldB(x1,x2)	weight: x1 + x2
     A()	weight: 0
   #f(x1,x2)	weight: (/ 1 2) + x1
   #g(x1)	weight: 0
  fold(x1,x2,x3)	weight: 0
    f'(x1,x2)	weight: (/ 3 4) + x1
 foldC(x1,x2)	weight: x1 + x2
     g(x1)	weight: (/ 1 4)
   f''(x1)	weight: x1
 #f''(x1)	weight: (/ 1 4) + x1
    Usable rules: { 7..15 }
    Removed DPs: #4..7 #10..12
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: 0
#foldC(x1,x2)	weight: 0
  #f'(x1,x2)	weight: max{0, x2}
triple(x1,x2,x3)	weight: max{0, (/ 1 4) + x2}
     C()	weight: (/ 1 2)
     f(x1,x2)	weight: 0
     B()	weight: (/ 3 4)
 foldB(x1,x2)	weight: 0
#fold(x1,x2,x3)	weight: 0
     0()	weight: 0
#foldB(x1,x2)	weight: 0
     A()	weight: (/ 1 4)
   #f(x1,x2)	weight: max{0, (/ 1 4) + x2}
   #g(x1)	weight: 0
  fold(x1,x2,x3)	weight: 0
    f'(x1,x2)	weight: 0
 foldC(x1,x2)	weight: 0
     g(x1)	weight: (/ 1 4) + x1
   f''(x1)	weight: 0
 #f''(x1)	weight: 0
    Usable rules: { 1..6 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES