Input TRS:
    1: half(0()) -> 0()
    2: half(s(s(x))) -> s(half(x))
    3: log(s(0())) -> 0()
    4: log(s(s(x))) -> s(log(s(half(x))))
    5: rand(x) ->= x
    6: rand(x) ->= rand(s(x))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 3 5
     s(x1)	weight: x1
  rand(x1)	weight: (/ 1 2) + x1
  half(x1)	weight: x1
   log(x1)	weight: (/ 17711 2) + 2 * x1
     0()	weight: (/ 23595 2)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing log
1: half(0()) -> 0()
2: half(s(s(x))) -> s(half(x))
4: log❆1_s(s(x)) -> s(log❆1_s(half(x)))
6: rand(x) ->= rand(s(x))
7: log(s(_1)) ->= log❆1_s(_1)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 7
     s(x1)	weight: x1
  rand(x1)	weight: x1
  half(x1)	weight: x1
   log(x1)	weight: (/ 1 2) + x1
     0()	weight: (/ 1 4)
log❆1_s(x1)	weight: (/ 1 4) + x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #half(s(s(x))) -> #half(x)
   #2: #log❆1_s(s(x)) -> #log❆1_s(half(x))
   #3: #log❆1_s(s(x)) -> #half(x)
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
#half(x1)	weight: x1
#log❆1_s(x1)	weight: 0
  rand(x1)	weight: 0
  half(x1)	weight: x1
   log(x1)	weight: 0
     0()	weight: 0
log❆1_s(x1)	weight: (/ 1 4) + x1
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
#half(x1)	weight: 0
#log❆1_s(x1)	weight: x1
  rand(x1)	weight: 0
  half(x1)	weight: x1
   log(x1)	weight: 0
     0()	weight: 0
log❆1_s(x1)	weight: (/ 1 4) + x1
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES