/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,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
 and(true(),true()) -> true()
 and(x,false()) -> false()
 and(false(),x) -> false()
 gr(0(),0()) -> false()
 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,z) -> p#(y)
   cond#(true(),x,y,z) -> p#(x)
   cond#(true(),x,y,z) -> gr#(y,z)
   cond#(true(),x,y,z) -> gr#(x,z)
   cond#(true(),x,y,z) -> and#(gr(x,z),gr(y,z))
   cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
   and(true(),true()) -> true()
   and(x,false()) -> false()
   and(false(),x) -> false()
   gr(0(),0()) -> false()
   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,z) -> p#(y)
    cond#(true(),x,y,z) -> p#(x)
    cond#(true(),x,y,z) -> gr#(y,z)
    cond#(true(),x,y,z) -> gr#(x,z)
    cond#(true(),x,y,z) -> and#(gr(x,z),gr(y,z))
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
    gr#(s(x),s(y)) -> gr#(x,y)
   TRS:
    cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
    and(true(),true()) -> true()
    and(x,false()) -> false()
    and(false(),x) -> false()
    gr(0(),0()) -> false()
    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,z) -> gr#(y,z) -> gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y,z) -> gr#(x,z) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> and#(gr(x,z),gr(y,z))
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> gr#(x,z)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> gr#(y,z)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> p#(x)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) -> 
    cond#(true(),x,y,z) -> p#(y)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 9/49
    DPs:
     cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
    TRS:
     cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
     and(true(),true()) -> true()
     and(x,false()) -> false()
     and(false(),x) -> false()
     gr(0(),0()) -> false()
     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,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
     TRS:
      p(0()) -> 0()
      p(s(x)) -> x
      gr(0(),0()) -> false()
      gr(0(),x) -> false()
      gr(s(x),0()) -> true()
      gr(s(x),s(y)) -> gr(x,y)
      and(true(),true()) -> true()
      and(x,false()) -> false()
      and(false(),x) -> false()
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       p(0()) -> 0()
       p(s(x)) -> x
       gr(0(),0()) -> false()
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       and(true(),true()) -> true()
       and(x,false()) -> false()
       and(false(),x) -> false()
      interpretation:
       [cond#](x0, x1, x2, x3) = 1x0 + x1 + x2 + 0,
       
       [s](x0) = 7x0 + 6,
       
       [0] = 1,
       
       [false] = 0,
       
       [p](x0) = -7x0 + 1,
       
       [and](x0, x1) = x1 + 1,
       
       [gr](x0, x1) = -3x0 + 2,
       
       [true] = 3
      orientation:
       cond#(true(),x,y,z) = x + y + 4 >= -7x + -2y + 3 = cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
       
       p(0()) = 1 >= 1 = 0()
       
       p(s(x)) = x + 1 >= x = x
       
       gr(0(),0()) = 2 >= 0 = false()
       
       gr(0(),x) = 2 >= 0 = false()
       
       gr(s(x),0()) = 4x + 3 >= 3 = true()
       
       gr(s(x),s(y)) = 4x + 3 >= -3x + 2 = gr(x,y)
       
       and(true(),true()) = 3 >= 3 = true()
       
       and(x,false()) = 1 >= 0 = false()
       
       and(false(),x) = x + 1 >= 0 = false()
      problem:
       DPs:
        
       TRS:
        p(0()) -> 0()
        p(s(x)) -> x
        gr(0(),0()) -> false()
        gr(0(),x) -> false()
        gr(s(x),0()) -> true()
        gr(s(x),s(y)) -> gr(x,y)
        and(true(),true()) -> true()
        and(x,false()) -> false()
        and(false(),x) -> false()
      Qed
    
    DPs:
     gr#(s(x),s(y)) -> gr#(x,y)
    TRS:
     cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
     and(true(),true()) -> true()
     and(x,false()) -> false()
     and(false(),x) -> false()
     gr(0(),0()) -> false()
     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,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
       and(true(),true()) -> true()
       and(x,false()) -> false()
       and(false(),x) -> false()
       gr(0(),0()) -> false()
       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