Input TRS:
    1: f(g(x)) -> g(f(f(x)))
    2: f(h(x)) -> h(g(x))
    3: f'(s(x),y,y) -> f'(y,x,s(x))
    4: rand(x) ->= x
    5: rand(x) ->= rand(s(x))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 4
     h(x1)	weight: (/ 1 4) + x1
     s(x1)	weight: x1
     f(x1)	weight: x1
  rand(x1)	weight: (/ 1 4) + x1
    f'(x1,x2,x3)	weight: x3 + x2 + 2 * x1
     g(x1)	weight: x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f'(s(x),y,y) -> #f'(y,x,s(x))
   #2: #f(g(x)) -> #f(f(x))
   #3: #f(g(x)) -> #f(x)
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h(x1)	weight: (/ 1 2)
     s(x1)	weight: (/ 1 2) + x1
  #f'(x1,x2,x3)	weight: x1 + x2
     f(x1)	weight: (/ 1 2)
  rand(x1)	weight: 0
   #f(x1)	weight: 0
    f'(x1,x2,x3)	weight: 0
     g(x1)	weight: (/ 1 2)
    Removed DPs: #1
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #2 #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h(x1)	weight: (/ 1 2)
     s(x1)	weight: (/ 1 2) + x1
  #f'(x1,x2,x3)	weight: 0
     f(x1)	weight: x1
  rand(x1)	weight: 0
   #f(x1)	weight: x1
    f'(x1,x2,x3)	weight: 0
     g(x1)	weight: (/ 1 2) + x1
    Removed DPs: #2 #3
Number of SCCs: 0, DPs: 0, edges: 0
YES