Input TRS:
    1: average(s(x),y) -> average(x,s(y))
    2: average(x,s(s(s(y)))) -> s(average(s(x),y))
    3: average(0(),0()) -> 0()
    4: average(0(),s(0())) -> 0()
    5: average(0(),s(s(0()))) -> s(0())
    6: rand(x) ->= x
    7: rand(x) ->= rand(s(x))
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... removes: 4 3 5 6
     s(x1)	weight: x1
average(x1,x2)	weight: (/ 81301 2) + x2 + x1
  rand(x1)	weight: (/ 1 2) + x1
     0()	weight: (/ 20901 2)
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #average(x,s(s(s(y)))) -> #average(s(x),y)
   #2: #average(s(x),y) -> #average(x,s(y))
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
average(x1,x2)	weight: x1 + x2
  rand(x1)	weight: 0
     0()	weight: 0
#average(x1,x2)	weight: x1 + x2
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
average(x1,x2)	weight: x1 + x2
  rand(x1)	weight: 0
     0()	weight: 0
#average(x1,x2)	weight: x1
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES