/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES
Input TRS:
    1: nonZero(0()) -> false()
    2: nonZero(s(x)) -> true()
    3: p(s(0())) -> 0()
    4: p(s(s(x))) -> s(p(s(x)))
    5: id_inc(x) -> x
    6: id_inc(x) -> s(x)
    7: random(x) -> rand(x,0())
    8: rand(x,y) -> if(nonZero(x),x,y)
    9: if(false(),x,y) -> y
    10: if(true(),x,y) -> rand(p(x),id_inc(y))
Number of strict rules: 10
Direct poly ... failed.
Freezing p
1: nonZero(0()) -> false()
2: nonZero(s(x)) -> true()
3: p❆1_s(0()) -> 0()
4: p❆1_s(s(x)) -> s(p❆1_s(x))
5: id_inc(x) -> x
6: id_inc(x) -> s(x)
7: random(x) -> rand(x,0())
8: rand(x,y) -> if(nonZero(x),x,y)
9: if(false(),x,y) -> y
10: if(true(),x,y) -> rand(p(x),id_inc(y))
11: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 10
Direct poly ... failed.
Dependency Pairs:
   #1: #p(s(_1)) ->? #p❆1_s(_1)
   #2: #random(x) -> #rand(x,0())
   #3: #if(true(),x,y) -> #rand(p(x),id_inc(y))
   #4: #if(true(),x,y) -> #p(x)
   #5: #if(true(),x,y) -> #id_inc(y)
   #6: #rand(x,y) -> #if(nonZero(x),x,y)
   #7: #rand(x,y) -> #nonZero(x)
   #8: #p❆1_s(s(x)) -> #p❆1_s(x)
Number of SCCs: 2, DPs: 3
	SCC { #8 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  #rand(x1,x2)		w: (0)
  nonZero(x1)		w: (0)
  p❆1_s(x1)		w: (0)
  false()		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (x1)
  true()		w: (0)
  #nonZero(x1)		w: (0)
  rand(x1,x2)		w: (0)
  #id_inc(x1)		w: (0)
  p(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  random(x1)		w: (0)
  #random(x1)		w: (0)
  id_inc(x1)		w: (0)
  #if(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 2
	SCC { #3 #6 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 5 + x1})
  #rand(x1,x2)		w: (max{0, 2 + x1})
  nonZero(x1)		w: (max{0, -2 + x1})
  p❆1_s(x1)		w: (max{0, 1 + x1})
  false()		w: (1)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  true()		w: (3)
  #nonZero(x1)		w: (0)
  rand(x1,x2)		w: (0)
  #id_inc(x1)		w: (0)
  p(x1)		w: (max{0, -4 + x1})
  0()		w: (3)
  if(x1,x2,x3)		w: (0)
  random(x1)		w: (0)
  #random(x1)		w: (0)
  id_inc(x1)		w: (0)
  #if(x1,x2,x3)		w: (max{0, -1 + x2, 1 + x1})
    USABLE RULES: { 1..4 11 }
    Removed DPs: #3 #6
Number of SCCs: 0, DPs: 0