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


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YES

Problem:
 cond(true(),x,y) -> cond(gr(x,y),p(x),y)
 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,y) -> p#(x)
   cond#(true(),x,y) -> gr#(x,y)
   cond#(true(),x,y) -> cond#(gr(x,y),p(x),y)
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond(true(),x,y) -> cond(gr(x,y),p(x),y)
   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,y) -> p#(x)
    cond#(true(),x,y) -> gr#(x,y)
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y)
    gr#(s(x),s(y)) -> gr#(x,y)
   TRS:
    cond(true(),x,y) -> cond(gr(x,y),p(x),y)
    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:
    gr#(s(x),s(y)) -> gr#(x,y) -> gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y) -> gr#(x,y) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y) ->
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y)
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y) ->
    cond#(true(),x,y) -> gr#(x,y)
    cond#(true(),x,y) -> cond#(gr(x,y),p(x),y) -> cond#(true(),x,y) -> p#(x)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 5/16
    DPs:
     cond#(true(),x,y) -> cond#(gr(x,y),p(x),y)
    TRS:
     cond(true(),x,y) -> cond(gr(x,y),p(x),y)
     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,y) -> cond#(gr(x,y),p(x),y)
     TRS:
      p(0()) -> 0()
      p(s(x)) -> x
      gr(0(),x) -> false()
      gr(s(x),0()) -> true()
      gr(s(x),s(y)) -> gr(x,y)
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       p(0()) -> 0()
       p(s(x)) -> x
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
      interpretation:
       [cond#](x0, x1, x2) = 2x0 + 2x1 + 0,
       
       [s](x0) = 6x0 + 13,
       
       [false] = 1,
       
       [0] = 1,
       
       [p](x0) = -6x0 + 1,
       
       [gr](x0, x1) = -9x0 + 1,
       
       [true] = 4
      orientation:
       cond#(true(),x,y) = 2x + 6 >= -4x + 3 = cond#(gr(x,y),p(x),y)
       
       p(0()) = 1 >= 1 = 0()
       
       p(s(x)) = x + 7 >= x = x
       
       gr(0(),x) = 1 >= 1 = false()
       
       gr(s(x),0()) = -3x + 4 >= 4 = true()
       
       gr(s(x),s(y)) = -3x + 4 >= -9x + 1 = gr(x,y)
      problem:
       DPs:
        
       TRS:
        p(0()) -> 0()
        p(s(x)) -> x
        gr(0(),x) -> false()
        gr(s(x),0()) -> true()
        gr(s(x),s(y)) -> gr(x,y)
      Qed
    
    DPs:
     gr#(s(x),s(y)) -> gr#(x,y)
    TRS:
     cond(true(),x,y) -> cond(gr(x,y),p(x),y)
     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,y) -> cond(gr(x,y),p(x),y)
       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