Input TRS:
    1: f(0()) -> s(0())
    2: f(s(0())) -> s(0())
    3: f(s(s(x))) -> f(f(s(x)))
    4: rand(x) ->= x
    5: rand(x) ->= rand(s(x))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 4
     s(x1)	weight: x1
     f(x1)	weight: x1
  rand(x1)	weight: (/ 1 8) + x1
     0()	weight: (/ 1 8)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆1_0() -> s(0())
2: f❆1_s(0()) -> s(0())
3: f❆1_s(s(x)) -> f(f❆1_s(x))
5: rand(x) ->= rand(s(x))
6: f(0()) ->= f❆1_0()
7: f(s(_1)) ->= f❆1_s(_1)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f(0()) ->? #f❆1_0()
   #2: #f(s(_1)) ->? #f❆1_s(_1)
   #3: #f❆1_s(s(x)) -> #f(f❆1_s(x))
   #4: #f❆1_s(s(x)) -> #f❆1_s(x)
Number of SCCs: 1, DPs: 3, edges: 5
	SCC { #2..4 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#f❆1_s(x1)	weight: (/ 1 4) + x1
     s(x1)	weight: (/ 3 8) + x1
f❆1_s(x1)	weight: (/ 1 2)
     f(x1)	weight: (/ 1 2)
  rand(x1)	weight: 0
     0()	weight: (/ 1 8)
#f❆1_0()	weight: 0
   #f(x1)	weight: x1
f❆1_0()	weight: (/ 1 2)
    Removed DPs: #2..4
Number of SCCs: 0, DPs: 0, edges: 0
YES