/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 strict:
  f(0()) -> s(0())
  f(s(0())) -> s(0())
  f(s(s(x))) -> f(f(s(x)))
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [f](x0) = x0,
   
   [rand](x0) = 1x0,
   
   [0] = 13,
   
   [s](x0) = x0
  orientation:
   f(0()) = 13 >= 13 = s(0())
   
   f(s(0())) = 13 >= 13 = s(0())
   
   f(s(s(x))) = x >= x = f(f(s(x)))
   
   rand(x) = 1x >= x = x
   
   rand(x) = 1x >= 1x = rand(s(x))
  problem:
   strict:
    f(0()) -> s(0())
    f(s(0())) -> s(0())
    f(s(s(x))) -> f(f(s(x)))
   weak:
    rand(x) -> rand(s(x))
  Bounds Processor:
   bound: 1
   enrichment: match-rt
   automaton:
    final states: {5}
    transitions:
     s0(5) -> 5*
     s1(33) -> 34*
     s1(8) -> 9*
     s1(56) -> 57*
     rand0(5) -> 5*
     00() -> 5*
     f0(5) -> 5*
     01() -> 8*
     rand1(34) -> 35*
     f1(28) -> 29*
     f1(27) -> 28*
     35 -> 5*
     34 -> 56*
     5 -> 33*
     9 -> 29,28,27,5
     57 -> 34*
     29 -> 5*
   problem:
    strict:
     f(s(0())) -> s(0())
     f(s(s(x))) -> f(f(s(x)))
    weak:
     rand(x) -> rand(s(x))
   Bounds Processor:
    bound: 2
    enrichment: match-rt
    automaton:
     final states: {5}
     transitions:
      s0(5) -> 5*
      s1(41) -> 42*
      s1(8) -> 9*
      s1(48) -> 49*
      rand0(5) -> 5*
      02() -> 28*
      s2(65) -> 66*
      s2(28) -> 29*
      s2(54) -> 55*
      00() -> 5*
      f0(5) -> 5*
      01() -> 8*
      rand1(42) -> 43*
      f1(20) -> 21*
      f1(21) -> 22*
      rand2(55) -> 56*
      56 -> 43*
      43 -> 5*
      42 -> 54*
      66 -> 55*
      28 -> 48*
      22 -> 5*
      49 -> 20*
      55 -> 65*
      5 -> 41*
      9 -> 20,5
      29 -> 22,21
    problem:
     strict:
      f(s(s(x))) -> f(f(s(x)))
     weak:
      rand(x) -> rand(s(x))
    Bounds Processor:
     bound: 1
     enrichment: match-rt
     automaton:
      final states: {4}
      transitions:
       s0(4) -> 4*
       s1(19) -> 20*
       s1(9) -> 10*
       rand0(4) -> 4*
       f0(4) -> 4*
       rand1(17) -> 18*
       f1(10) -> 11*
       f1(11) -> 12*
       17 -> 19*
       12 -> 11,4
       4 -> 9*
       20 -> 17*
       18 -> 4*
       10 -> 17*
     problem:
      strict:
       
      weak:
       rand(x) -> rand(s(x))
     Qed