/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 cond(true(),x) -> cond(odd(x),p(x))
 odd(0()) -> false()
 odd(s(0())) -> true()
 odd(s(s(x))) -> odd(x)
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   cond#(true(),x) -> p#(x)
   cond#(true(),x) -> odd#(x)
   cond#(true(),x) -> cond#(odd(x),p(x))
   odd#(s(s(x))) -> odd#(x)
  TRS:
   cond(true(),x) -> cond(odd(x),p(x))
   odd(0()) -> false()
   odd(s(0())) -> true()
   odd(s(s(x))) -> odd(x)
   p(0()) -> 0()
   p(s(x)) -> x
  TDG Processor:
   DPs:
    cond#(true(),x) -> p#(x)
    cond#(true(),x) -> odd#(x)
    cond#(true(),x) -> cond#(odd(x),p(x))
    odd#(s(s(x))) -> odd#(x)
   TRS:
    cond(true(),x) -> cond(odd(x),p(x))
    odd(0()) -> false()
    odd(s(0())) -> true()
    odd(s(s(x))) -> odd(x)
    p(0()) -> 0()
    p(s(x)) -> x
   graph:
    odd#(s(s(x))) -> odd#(x) -> odd#(s(s(x))) -> odd#(x)
    cond#(true(),x) -> odd#(x) -> odd#(s(s(x))) -> odd#(x)
    cond#(true(),x) -> cond#(odd(x),p(x)) ->
    cond#(true(),x) -> cond#(odd(x),p(x))
    cond#(true(),x) -> cond#(odd(x),p(x)) ->
    cond#(true(),x) -> odd#(x)
    cond#(true(),x) -> cond#(odd(x),p(x)) -> cond#(true(),x) -> p#(x)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 5/16
    DPs:
     cond#(true(),x) -> cond#(odd(x),p(x))
    TRS:
     cond(true(),x) -> cond(odd(x),p(x))
     odd(0()) -> false()
     odd(s(0())) -> true()
     odd(s(s(x))) -> odd(x)
     p(0()) -> 0()
     p(s(x)) -> x
    Usable Rule Processor:
     DPs:
      cond#(true(),x) -> cond#(odd(x),p(x))
     TRS:
      p(0()) -> 0()
      p(s(x)) -> x
      odd(0()) -> false()
      odd(s(0())) -> true()
      odd(s(s(x))) -> odd(x)
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       p(0()) -> 0()
       p(s(x)) -> x
       odd(0()) -> false()
       odd(s(0())) -> true()
       odd(s(s(x))) -> odd(x)
      interpretation:
       [cond#](x0, x1) = x0 + 1x1 + 2,
       
       [s](x0) = 1x0 + 4,
       
       [false] = 0,
       
       [0] = 0,
       
       [p](x0) = -1x0 + 0,
       
       [odd](x0) = x0,
       
       [true] = 4
      orientation:
       cond#(true(),x) = 1x + 4 >= x + 2 = cond#(odd(x),p(x))
       
       p(0()) = 0 >= 0 = 0()
       
       p(s(x)) = x + 3 >= x = x
       
       odd(0()) = 0 >= 0 = false()
       
       odd(s(0())) = 4 >= 4 = true()
       
       odd(s(s(x))) = 2x + 5 >= x = odd(x)
      problem:
       DPs:
        
       TRS:
        p(0()) -> 0()
        p(s(x)) -> x
        odd(0()) -> false()
        odd(s(0())) -> true()
        odd(s(s(x))) -> odd(x)
      Qed
    
    DPs:
     odd#(s(s(x))) -> odd#(x)
    TRS:
     cond(true(),x) -> cond(odd(x),p(x))
     odd(0()) -> false()
     odd(s(0())) -> true()
     odd(s(s(x))) -> odd(x)
     p(0()) -> 0()
     p(s(x)) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(odd#) = 0
     problem:
      DPs:
       
      TRS:
       cond(true(),x) -> cond(odd(x),p(x))
       odd(0()) -> false()
       odd(s(0())) -> true()
       odd(s(s(x))) -> odd(x)
       p(0()) -> 0()
       p(s(x)) -> x
     Qed