Input TRS:
    1: f(x,c(y)) -> f(x,s(f(y,y)))
    2: f(s(x),y) -> f(x,s(c(y)))
    3: rand(x) ->= x
    4: rand(x) ->= rand(s(x))
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(s(x),y) -> #f(x,s(c(y)))
   #2: #f(x,c(y)) -> #f(x,s(f(y,y)))
   #3: #f(x,c(y)) -> #f(y,y)
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: 0
     c(x1)	weight: (/ 1 2) + x1
     f(x1,x2)	weight: (/ 1 2)
  rand(x1)	weight: x1
   #f(x1,x2)	weight: x2
    Removed DPs: #3
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
     s(x1)	weight: x1	status: [x1]	precedence above: c f
     c(x1)	weight: 0	status: []	precedence above: f
     f(x1,x2)	weight: max{0, (/ 1 4) + x1}	status: []	precedence above: c
  rand(x1)	weight: (/ 1 4) + x1	status: []	precedence above:
   #f(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above: s c f
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES