Input TRS:
    1: g(c(x,s(y))) -> g(c(s(x),y))
    2: f(c(s(x),y)) -> f(c(x,s(y)))
    3: f(f(x)) -> f(d(f(x)))
    4: f(x) -> x
    5: rand(x) ->= x
    6: rand(x) ->= rand(s(x))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 4 5
     d(x1)	weight: x1
     s(x1)	weight: x1
     c(x1,x2)	weight: (/ 1 8) + x2 + x1
     f(x1)	weight: (/ 1 8) + x1
  rand(x1)	weight: (/ 1 8) + x1
     g(x1)	weight: x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing g
1: g❆1_c(x,s(y)) -> g❆1_c(s(x),y)
2: f(c(s(x),y)) -> f(c(x,s(y)))
3: f(f(x)) -> f(d(f(x)))
6: rand(x) ->= rand(s(x))
7: g(c(_1,_2)) ->= g❆1_c(_1,_2)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 7
     d(x1)	weight: x1
     s(x1)	weight: x1
g❆1_c(x1,x2)	weight: x2 + x1
     c(x1,x2)	weight: (/ 1 4) + 2 * x2 + x1
     f(x1)	weight: (/ 35421 4) + x1
  rand(x1)	weight: 2 * x1
     g(x1)	weight: x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f(c(s(x),y)) -> #f(c(x,s(y)))
   #2: #f(f(x)) -> #f(d(f(x)))
   #3: #g❆1_c(x,s(y)) -> #g❆1_c(s(x),y)
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     d(x1)	weight: (/ 1 2)
     s(x1)	weight: (/ 1 2) + x1
g❆1_c(x1,x2)	weight: x2
#g❆1_c(x1,x2)	weight: x2
     c(x1,x2)	weight: (/ 1 2)
     f(x1)	weight: (/ 1 2)
  rand(x1)	weight: 0
   #f(x1)	weight: 0
     g(x1)	weight: 0
    Removed DPs: #3
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     d(x1)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 4) + x1
g❆1_c(x1,x2)	weight: x2
#g❆1_c(x1,x2)	weight: 0
     c(x1,x2)	weight: (/ 1 4) + x1
     f(x1)	weight: (/ 1 4)
  rand(x1)	weight: 0
   #f(x1)	weight: x1
     g(x1)	weight: 0
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES