/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:
 cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
 cond2(true(),x,y,z) -> cond2(gr(y,z),x,p(y),z)
 cond2(false(),x,y,z) -> cond1(gr(x,z),p(x),y,z)
 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:
   cond1#(true(),x,y,z) -> gr#(y,z)
   cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z)
   cond2#(true(),x,y,z) -> p#(y)
   cond2#(true(),x,y,z) -> gr#(y,z)
   cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
   cond2#(false(),x,y,z) -> p#(x)
   cond2#(false(),x,y,z) -> gr#(x,z)
   cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z)
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
   cond2(true(),x,y,z) -> cond2(gr(y,z),x,p(y),z)
   cond2(false(),x,y,z) -> cond1(gr(x,z),p(x),y,z)
   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:
    cond1#(true(),x,y,z) -> gr#(y,z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z)
    cond2#(true(),x,y,z) -> p#(y)
    cond2#(true(),x,y,z) -> gr#(y,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
    cond2#(false(),x,y,z) -> p#(x)
    cond2#(false(),x,y,z) -> gr#(x,z)
    cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z)
    gr#(s(x),s(y)) -> gr#(x,y)
   TRS:
    cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
    cond2(true(),x,y,z) -> cond2(gr(y,z),x,p(y),z)
    cond2(false(),x,y,z) -> cond1(gr(x,z),p(x),y,z)
    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:
    cond2#(false(),x,y,z) -> gr#(x,z) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z) ->
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z)
    cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z) ->
    cond1#(true(),x,y,z) -> gr#(y,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z) ->
    cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z) ->
    cond2#(false(),x,y,z) -> gr#(x,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z) ->
    cond2#(false(),x,y,z) -> p#(x)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z) ->
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z) ->
    cond2#(true(),x,y,z) -> gr#(y,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z) ->
    cond2#(true(),x,y,z) -> p#(y)
    cond2#(true(),x,y,z) -> gr#(y,z) -> gr#(s(x),s(y)) -> gr#(x,y)
    gr#(s(x),s(y)) -> gr#(x,y) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(false(),x,y,z) -> gr#(x,z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(false(),x,y,z) -> p#(x)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(true(),x,y,z) -> gr#(y,z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(true(),x,y,z) -> p#(y)
    cond1#(true(),x,y,z) -> gr#(y,z) -> gr#(s(x),s(y)) -> gr#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 18/81
    DPs:
     cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z)
     cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z)
     cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
    TRS:
     cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
     cond2(true(),x,y,z) -> cond2(gr(y,z),x,p(y),z)
     cond2(false(),x,y,z) -> cond1(gr(x,z),p(x),y,z)
     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:
      cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z)
      cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z)
      cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
     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:
       [cond2#](x0, x1, x2, x3) = -6x1 + 0,
       
       [cond1#](x0, x1, x2, x3) = x0 + x1 + 0,
       
       [s](x0) = 7x0 + 9,
       
       [0] = 0,
       
       [false] = 0,
       
       [p](x0) = -7x0 + 0,
       
       [gr](x0, x1) = -7x0 + 0,
       
       [true] = 2
      orientation:
       cond2#(false(),x,y,z) = -6x + 0 >= -7x + 0 = cond1#(gr(x,z),p(x),y,z)
       
       cond1#(true(),x,y,z) = x + 2 >= -6x + 0 = cond2#(gr(y,z),x,y,z)
       
       cond2#(true(),x,y,z) = -6x + 0 >= -6x + 0 = cond2#(gr(y,z),x,p(y),z)
       
       p(0()) = 0 >= 0 = 0()
       
       p(s(x)) = x + 2 >= x = x
       
       gr(0(),x) = 0 >= 0 = false()
       
       gr(s(x),0()) = x + 2 >= 2 = true()
       
       gr(s(x),s(y)) = x + 2 >= -7x + 0 = gr(x,y)
      problem:
       DPs:
        cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z)
        cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
       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)
      Restore Modifier:
       DPs:
        cond2#(false(),x,y,z) -> cond1#(gr(x,z),p(x),y,z)
        cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
       TRS:
        cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
        cond2(true(),x,y,z) -> cond2(gr(y,z),x,p(y),z)
        cond2(false(),x,y,z) -> cond1(gr(x,z),p(x),y,z)
        gr(0(),x) -> false()
        gr(s(x),0()) -> true()
        gr(s(x),s(y)) -> gr(x,y)
        p(0()) -> 0()
        p(s(x)) -> x
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 5/4
        DPs:
         cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
        TRS:
         cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
         cond2(true(),x,y,z) -> cond2(gr(y,z),x,p(y),z)
         cond2(false(),x,y,z) -> cond1(gr(x,z),p(x),y,z)
         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:
          cond2#(true(),x,y,z) -> cond2#(gr(y,z),x,p(y),z)
         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)
         Matrix Interpretation Processor: dim=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:
           [cond2#](x0, x1, x2, x3) = 1/4x0 + x2 + 1/2,
           
           [s](x0) = 2x0 + 2,
           
           [0] = 0,
           
           [false] = 0,
           
           [p](x0) = 1/2x0,
           
           [gr](x0, x1) = 2x0,
           
           [true] = 2
          orientation:
           cond2#(true(),x,y,z) = y + 1 >= y + 1/2 = cond2#(gr(y,z),x,p(y),z)
           
           p(0()) = 0 >= 0 = 0()
           
           p(s(x)) = x + 1 >= x = x
           
           gr(0(),x) = 0 >= 0 = false()
           
           gr(s(x),0()) = 4x + 4 >= 2 = true()
           
           gr(s(x),s(y)) = 4x + 4 >= 2x = 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:
     cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
     cond2(true(),x,y,z) -> cond2(gr(y,z),x,p(y),z)
     cond2(false(),x,y,z) -> cond1(gr(x,z),p(x),y,z)
     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:
       cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
       cond2(true(),x,y,z) -> cond2(gr(y,z),x,p(y),z)
       cond2(false(),x,y,z) -> cond1(gr(x,z),p(x),y,z)
       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