/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(and(even(x),gr(x,0())),p(x))
 and(x,false()) -> false()
 and(false(),x) -> false()
 and(true(),true()) -> true()
 even(0()) -> true()
 even(s(0())) -> false()
 even(s(s(x))) -> even(x)
 gr(0(),x) -> false()
 gr(s(x),0()) -> true()
 gr(s(x),s(y())) -> gr(x,y())
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   cond#(true(),x) -> p#(x)
   cond#(true(),x) -> gr#(x,0())
   cond#(true(),x) -> even#(x)
   cond#(true(),x) -> and#(even(x),gr(x,0()))
   cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
   even#(s(s(x))) -> even#(x)
   gr#(s(x),s(y())) -> gr#(x,y())
  TRS:
   cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
   and(x,false()) -> false()
   and(false(),x) -> false()
   and(true(),true()) -> true()
   even(0()) -> true()
   even(s(0())) -> false()
   even(s(s(x))) -> even(x)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y())) -> gr(x,y())
   p(0()) -> 0()
   p(s(x)) -> x
  TDG Processor:
   DPs:
    cond#(true(),x) -> p#(x)
    cond#(true(),x) -> gr#(x,0())
    cond#(true(),x) -> even#(x)
    cond#(true(),x) -> and#(even(x),gr(x,0()))
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
    even#(s(s(x))) -> even#(x)
    gr#(s(x),s(y())) -> gr#(x,y())
   TRS:
    cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
    and(x,false()) -> false()
    and(false(),x) -> false()
    and(true(),true()) -> true()
    even(0()) -> true()
    even(s(0())) -> false()
    even(s(s(x))) -> even(x)
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y())) -> gr(x,y())
    p(0()) -> 0()
    p(s(x)) -> x
   graph:
    even#(s(s(x))) -> even#(x) -> even#(s(s(x))) -> even#(x)
    gr#(s(x),s(y())) -> gr#(x,y()) -> gr#(s(x),s(y())) -> gr#(x,y())
    cond#(true(),x) -> even#(x) -> even#(s(s(x))) -> even#(x)
    cond#(true(),x) -> gr#(x,0()) ->
    gr#(s(x),s(y())) -> gr#(x,y())
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
    cond#(true(),x) -> and#(even(x),gr(x,0()))
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
    cond#(true(),x) -> even#(x)
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
    cond#(true(),x) -> gr#(x,0())
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) -> cond#(true(),x) -> p#(x)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 9/49
    DPs:
     cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
    TRS:
     cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
     and(x,false()) -> false()
     and(false(),x) -> false()
     and(true(),true()) -> true()
     even(0()) -> true()
     even(s(0())) -> false()
     even(s(s(x))) -> even(x)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y())) -> gr(x,y())
     p(0()) -> 0()
     p(s(x)) -> x
    Usable Rule Processor:
     DPs:
      cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
     TRS:
      p(0()) -> 0()
      p(s(x)) -> x
      gr(0(),x) -> false()
      gr(s(x),0()) -> true()
      even(0()) -> true()
      even(s(0())) -> false()
      even(s(s(x))) -> even(x)
      and(x,false()) -> false()
      and(false(),x) -> false()
      and(true(),true()) -> true()
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       p(0()) -> 0()
       p(s(x)) -> x
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       even(0()) -> true()
       even(s(0())) -> false()
       even(s(s(x))) -> even(x)
       and(x,false()) -> false()
       and(false(),x) -> false()
       and(true(),true()) -> true()
      interpretation:
       [cond#](x0, x1) = -3x0 + -1x1 + 0,
       
       [s](x0) = 1x0 + 4,
       
       [false] = 0,
       
       [p](x0) = -1x0 + 0,
       
       [and](x0, x1) = -8x0 + 1x1 + 0,
       
       [gr](x0, x1) = x0 + 2x1 + 0,
       
       [0] = 0,
       
       [even](x0) = 9,
       
       [true] = 4
      orientation:
       cond#(true(),x) = -1x + 1 >= -2x + 0 = cond#(and(even(x),gr(x,0())),p(x))
       
       p(0()) = 0 >= 0 = 0()
       
       p(s(x)) = x + 3 >= x = x
       
       gr(0(),x) = 2x + 0 >= 0 = false()
       
       gr(s(x),0()) = 1x + 4 >= 4 = true()
       
       even(0()) = 9 >= 4 = true()
       
       even(s(0())) = 9 >= 0 = false()
       
       even(s(s(x))) = 9 >= 9 = even(x)
       
       and(x,false()) = -8x + 1 >= 0 = false()
       
       and(false(),x) = 1x + 0 >= 0 = false()
       
       and(true(),true()) = 5 >= 4 = true()
      problem:
       DPs:
        
       TRS:
        p(0()) -> 0()
        p(s(x)) -> x
        gr(0(),x) -> false()
        gr(s(x),0()) -> true()
        even(0()) -> true()
        even(s(0())) -> false()
        even(s(s(x))) -> even(x)
        and(x,false()) -> false()
        and(false(),x) -> false()
        and(true(),true()) -> true()
      Qed
    
    DPs:
     gr#(s(x),s(y())) -> gr#(x,y())
    TRS:
     cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
     and(x,false()) -> false()
     and(false(),x) -> false()
     and(true(),true()) -> true()
     even(0()) -> true()
     even(s(0())) -> false()
     even(s(s(x))) -> even(x)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y())) -> gr(x,y())
     p(0()) -> 0()
     p(s(x)) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(gr#) = 0
     problem:
      DPs:
       
      TRS:
       cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
       and(x,false()) -> false()
       and(false(),x) -> false()
       and(true(),true()) -> true()
       even(0()) -> true()
       even(s(0())) -> false()
       even(s(s(x))) -> even(x)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y())) -> gr(x,y())
       p(0()) -> 0()
       p(s(x)) -> x
     Qed
    
    DPs:
     even#(s(s(x))) -> even#(x)
    TRS:
     cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
     and(x,false()) -> false()
     and(false(),x) -> false()
     and(true(),true()) -> true()
     even(0()) -> true()
     even(s(0())) -> false()
     even(s(s(x))) -> even(x)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y())) -> gr(x,y())
     p(0()) -> 0()
     p(s(x)) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(even#) = 0
     problem:
      DPs:
       
      TRS:
       cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
       and(x,false()) -> false()
       and(false(),x) -> false()
       and(true(),true()) -> true()
       even(0()) -> true()
       even(s(0())) -> false()
       even(s(s(x))) -> even(x)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y())) -> gr(x,y())
       p(0()) -> 0()
       p(s(x)) -> x
     Qed