/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:
 b(a(),f(b(b(z,y),a()))) -> z
 c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
 f(f(c(a(),y,z))) -> b(y,b(z,z))

Proof:
 DP Processor:
  DPs:
   c#(c(z,x,a()),a(),y) -> c#(z,y,x)
   c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
   c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
   c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
   c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
   f#(f(c(a(),y,z))) -> b#(z,z)
   f#(f(c(a(),y,z))) -> b#(y,b(z,z))
  TRS:
   b(a(),f(b(b(z,y),a()))) -> z
   c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
   f(f(c(a(),y,z))) -> b(y,b(z,z))
  TDG Processor:
   DPs:
    c#(c(z,x,a()),a(),y) -> c#(z,y,x)
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
    f#(f(c(a(),y,z))) -> b#(z,z)
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
   TRS:
    b(a(),f(b(b(z,y),a()))) -> z
    c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
    f(f(c(a(),y,z))) -> b(y,b(z,z))
   graph:
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x)))) ->
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x)))) ->
    f#(f(c(a(),y,z))) -> b#(z,z)
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x)) ->
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x)) ->
    f#(f(c(a(),y,z))) -> b#(z,z)
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x))))) ->
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x))))) ->
    f#(f(c(a(),y,z))) -> b#(z,z)
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> c#(z,y,x)
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) -> c#(c(z,x,a()),a(),y) -> c#(z,y,x)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 16/49
    DPs:
     c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
     c#(c(z,x,a()),a(),y) -> c#(z,y,x)
    TRS:
     b(a(),f(b(b(z,y),a()))) -> z
     c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
     f(f(c(a(),y,z))) -> b(y,b(z,z))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      b(a(),f(b(b(z,y),a()))) -> z
      c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
      f(f(c(a(),y,z))) -> b(y,b(z,z))
     interpretation:
      [c#](x0, x1, x2) = [1 0]x0 + [1 0]x2,
      
                        [1 0]     [1  0 ]     [1 0]     [0]
      [c](x0, x1, x2) = [1 0]x0 + [0  -&]x1 + [1 0]x2 + [0],
      
                [-& 0 ]     [1]
      [f](x0) = [0  0 ]x0 + [3],
      
                    [0 0]     [0 0]     [-&]
      [b](x0, x1) = [0 0]x0 + [0 0]x1 + [3 ],
      
            [1]
      [a] = [0]
     orientation:
      c#(c(z,x,a()),a(),y) = [2 1]x + [1 0]y + [2 1]z + [3] >= [2 1]x + [1 0]y + [2 1]z + [3] = c#(y,a(),f(c(z,y,x)))
      
      c#(c(z,x,a()),a(),y) = [2 1]x + [1 0]y + [2 1]z + [3] >= [1 0]x + [1 0]z = c#(z,y,x)
      
                                [0 0]    [0 0]    [3]         
      b(a(),f(b(b(z,y),a()))) = [0 0]y + [0 0]z + [3] >= z = z
      
                            [2 1]    [1 0]    [2 1]    [3]    [2 1]    [1 0]    [2 1]    [3]                             
      c(c(z,x,a()),a(),y) = [2 1]x + [1 0]y + [2 1]z + [3] >= [2 1]x + [1 0]y + [2 1]z + [3] = f(f(c(y,a(),f(c(z,y,x)))))
      
                         [1 0]    [1 0]    [3]    [0 0]    [0 0]    [3]              
      f(f(c(a(),y,z))) = [1 0]y + [1 0]z + [3] >= [0 0]y + [0 0]z + [3] = b(y,b(z,z))
     problem:
      DPs:
       c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
      TRS:
       b(a(),f(b(b(z,y),a()))) -> z
       c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
       f(f(c(a(),y,z))) -> b(y,b(z,z))
     Restore Modifier:
      DPs:
       c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
      TRS:
       b(a(),f(b(b(z,y),a()))) -> z
       c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
       f(f(c(a(),y,z))) -> b(y,b(z,z))
      Bounds Processor:
       bound: 2
       enrichment: top-dp
       automaton:
        final states: {7}
        transitions:
         b1(12,12) -> 21*
         b1(13,21) -> 11*
         f0(6) -> 6*
         b0(6,6) -> 6*
         c{#,1}(6,13,12) -> 7*
         a1() -> 13*
         f1(20) -> 17*
         f1(17) -> 18*
         f1(19) -> 20*
         f1(11) -> 12*
         f1(18) -> 11*
         c1(6,6,6) -> 11*
         c1(12,13,15) -> 19*
         c1(6,13,12) -> 17*
         c{#,2}(12,16,15) -> 7*
         a2() -> 16*
         c{#,0}(6,6,6) -> 7*
         f2(14) -> 15*
         c0(6,6,6) -> 6*
         c2(6,12,6) -> 14*
         a0() -> 6*
       problem:
        DPs:
         
        TRS:
         b(a(),f(b(b(z,y),a()))) -> z
         c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
         f(f(c(a(),y,z))) -> b(y,b(z,z))
       Qed