Input TRS:
    1: f(|0|(),|1|(),x) -> f(s(x),x,x)
    2: f(x,y,s(z)) -> s(f(|0|(),|1|(),z))
    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(x,y,s(z)) -> #f(|0|(),|1|(),z)
   #2: #f(|0|(),|1|(),x) -> #f(s(x),x,x)
Number of SCCs: 1, DPs: 2, edges: 3
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
   |0|()	weight: 0	status: []	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: |0| f #f |1|
     f(x1,x2,x3)	weight: max{0, x3}	status: x3
  rand(x1)	weight: (/ 1 2) + x1	status: []	precedence above:
   #f(x1,x2,x3)	weight: max{0, x3}	status: [x3]	precedence above: |0| |1|
   |1|()	weight: 0	status: []	precedence above:
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES