Input TRS:
    1: f(0()) -> true()
    2: f(1()) -> false()
    3: f(s(x)) -> f(x)
    4: if(true(),s(x),s(y)) -> s(x)
    5: if(false(),s(x),s(y)) -> s(y)
    6: g(x,c(y)) -> c(g(x,y))
    7: g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
    8: rand(x) ->= x
    9: rand(x) ->= rand(s(x))
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #g(x,c(y)) -> #g(x,y)
   #2: #g(x,c(y)) -> #g(x,if(f(x),c(g(s(x),y)),c(y)))
   #3: #g(x,c(y)) -> #if(f(x),c(g(s(x),y)),c(y))
   #4: #g(x,c(y)) -> #f(x)
   #5: #g(x,c(y)) -> #g(s(x),y)
   #6: #f(s(x)) -> #f(x)
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
     1()	weight: 0	status: []	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: false c true f
 false()	weight: 0	status: []	precedence above:
     c(x1)	weight: x1	status: []	precedence above: false true f
  true()	weight: 0	status: []	precedence above:
     f(x1)	weight: 0	status: []	precedence above: false true
  rand(x1)	weight: (/ 1 8) + x1	status: []	precedence above:
     0()	weight: 0	status: []	precedence above:
    if(x1,x2,x3)	weight: max{0, (/ 1 4) + x3, (/ 1 4) + x2}	status: [x3]	precedence above: s false c true f g
   #f(x1)	weight: x1	status: [x1]	precedence above:
   #g(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1,x2]	precedence above:
  #if(x1,x2,x3)	weight: (/ 1 8) + x3 + x2	status: [x2,x3]	precedence above:
     g(x1,x2)	weight: max{0, (/ 1 8) + x1}	status: []	precedence above: s false c true f
    Removed DPs: #6
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #1 #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
     s(x1)	weight: 0
 false()	weight: 0
     c(x1)	weight: (/ 1 4) + x1
  true()	weight: 0
     f(x1)	weight: (/ 1 4)
  rand(x1)	weight: x1
     0()	weight: 0
    if(x1,x2,x3)	weight: (/ 1 4)
   #f(x1)	weight: 0
   #g(x1,x2)	weight: x2
  #if(x1,x2,x3)	weight: 0
     g(x1,x2)	weight: (/ 1 4) + x2
    Removed DPs: #1 #5
Number of SCCs: 0, DPs: 0, edges: 0
YES