Input TRS:
    1: g(x,y) -> x
    2: g(x,y) -> y
    3: f(0(),1(),x) -> f(s(x),x,x)
    4: f(x,y,s(z)) -> s(f(0(),1(),z))
    5: rand(x) ->= x
    6: rand(x) ->= rand(s(x))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(0(),1(),x) -> #f(s(x),x,x)
   #2: #f(x,y,s(z)) -> #f(0(),1(),z)
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.
     1()	weight: (/ 1 4)	status: []	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: f 0 #f
     f(x1,x2,x3)	weight: max{0, x3}	status: x3
  rand(x1)	weight: (/ 1 4) + x1	status: []	precedence above:
     0()	weight: 0	status: []	precedence above: #f
   #f(x1,x2,x3)	weight: max{0, x3}	status: [x3]	precedence above:
   #g(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above:
     g(x1,x2)	weight: (/ 1 4) + x2 + x1	status: [x1,x2]	precedence above:
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES