/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:
 a(b(x1)) -> b(r(x1))
 r(a(x1)) -> d(r(x1))
 r(x1) -> d(x1)
 d(a(x1)) -> a(a(d(x1)))
 d(x1) -> a(x1)

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> r#(x1)
   r#(a(x1)) -> r#(x1)
   r#(a(x1)) -> d#(r(x1))
   r#(x1) -> d#(x1)
   d#(a(x1)) -> d#(x1)
   d#(a(x1)) -> a#(d(x1))
   d#(a(x1)) -> a#(a(d(x1)))
   d#(x1) -> a#(x1)
  TRS:
   a(b(x1)) -> b(r(x1))
   r(a(x1)) -> d(r(x1))
   r(x1) -> d(x1)
   d(a(x1)) -> a(a(d(x1)))
   d(x1) -> a(x1)
  TDG Processor:
   DPs:
    a#(b(x1)) -> r#(x1)
    r#(a(x1)) -> r#(x1)
    r#(a(x1)) -> d#(r(x1))
    r#(x1) -> d#(x1)
    d#(a(x1)) -> d#(x1)
    d#(a(x1)) -> a#(d(x1))
    d#(a(x1)) -> a#(a(d(x1)))
    d#(x1) -> a#(x1)
   TRS:
    a(b(x1)) -> b(r(x1))
    r(a(x1)) -> d(r(x1))
    r(x1) -> d(x1)
    d(a(x1)) -> a(a(d(x1)))
    d(x1) -> a(x1)
   graph:
    d#(a(x1)) -> d#(x1) -> d#(x1) -> a#(x1)
    d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> a#(a(d(x1)))
    d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> a#(d(x1))
    d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(x1)
    d#(a(x1)) -> a#(d(x1)) -> a#(b(x1)) -> r#(x1)
    d#(a(x1)) -> a#(a(d(x1))) -> a#(b(x1)) -> r#(x1)
    d#(x1) -> a#(x1) -> a#(b(x1)) -> r#(x1)
    r#(a(x1)) -> d#(r(x1)) -> d#(x1) -> a#(x1)
    r#(a(x1)) -> d#(r(x1)) -> d#(a(x1)) -> a#(a(d(x1)))
    r#(a(x1)) -> d#(r(x1)) -> d#(a(x1)) -> a#(d(x1))
    r#(a(x1)) -> d#(r(x1)) -> d#(a(x1)) -> d#(x1)
    r#(a(x1)) -> r#(x1) -> r#(x1) -> d#(x1)
    r#(a(x1)) -> r#(x1) -> r#(a(x1)) -> d#(r(x1))
    r#(a(x1)) -> r#(x1) -> r#(a(x1)) -> r#(x1)
    r#(x1) -> d#(x1) -> d#(x1) -> a#(x1)
    r#(x1) -> d#(x1) -> d#(a(x1)) -> a#(a(d(x1)))
    r#(x1) -> d#(x1) -> d#(a(x1)) -> a#(d(x1))
    r#(x1) -> d#(x1) -> d#(a(x1)) -> d#(x1)
    a#(b(x1)) -> r#(x1) -> r#(x1) -> d#(x1)
    a#(b(x1)) -> r#(x1) -> r#(a(x1)) -> d#(r(x1))
    a#(b(x1)) -> r#(x1) -> r#(a(x1)) -> r#(x1)
   Polynomial Interpretation Processor:
    dimension: 1
    interpretation:
     [d#](x0) = x0,
     
     [r#](x0) = x0,
     
     [a#](x0) = x0,
     
     [d](x0) = x0,
     
     [r](x0) = x0,
     
     [a](x0) = x0,
     
     [b](x0) = x0 + 1
    orientation:
     a#(b(x1)) = x1 + 1 >= x1 = r#(x1)
     
     r#(a(x1)) = x1 >= x1 = r#(x1)
     
     r#(a(x1)) = x1 >= x1 = d#(r(x1))
     
     r#(x1) = x1 >= x1 = d#(x1)
     
     d#(a(x1)) = x1 >= x1 = d#(x1)
     
     d#(a(x1)) = x1 >= x1 = a#(d(x1))
     
     d#(a(x1)) = x1 >= x1 = a#(a(d(x1)))
     
     d#(x1) = x1 >= x1 = a#(x1)
     
     a(b(x1)) = x1 + 1 >= x1 + 1 = b(r(x1))
     
     r(a(x1)) = x1 >= x1 = d(r(x1))
     
     r(x1) = x1 >= x1 = d(x1)
     
     d(a(x1)) = x1 >= x1 = a(a(d(x1)))
     
     d(x1) = x1 >= x1 = a(x1)
    problem:
     DPs:
      r#(a(x1)) -> r#(x1)
      r#(a(x1)) -> d#(r(x1))
      r#(x1) -> d#(x1)
      d#(a(x1)) -> d#(x1)
      d#(a(x1)) -> a#(d(x1))
      d#(a(x1)) -> a#(a(d(x1)))
      d#(x1) -> a#(x1)
     TRS:
      a(b(x1)) -> b(r(x1))
      r(a(x1)) -> d(r(x1))
      r(x1) -> d(x1)
      d(a(x1)) -> a(a(d(x1)))
      d(x1) -> a(x1)
    SCC Processor:
     #sccs: 2
     #rules: 2
     #arcs: 21/49
     DPs:
      r#(a(x1)) -> r#(x1)
     TRS:
      a(b(x1)) -> b(r(x1))
      r(a(x1)) -> d(r(x1))
      r(x1) -> d(x1)
      d(a(x1)) -> a(a(d(x1)))
      d(x1) -> a(x1)
     Usable Rule Processor:
      DPs:
       r#(a(x1)) -> r#(x1)
      TRS:
       
      Polynomial Interpretation Processor:
       dimension: 1
       interpretation:
        [r#](x0) = x0,
        
        [a](x0) = x0 + 1
       orientation:
        r#(a(x1)) = x1 + 1 >= x1 = r#(x1)
       problem:
        DPs:
         
        TRS:
         
       Qed
     
     DPs:
      d#(a(x1)) -> d#(x1)
     TRS:
      a(b(x1)) -> b(r(x1))
      r(a(x1)) -> d(r(x1))
      r(x1) -> d(x1)
      d(a(x1)) -> a(a(d(x1)))
      d(x1) -> a(x1)
     Usable Rule Processor:
      DPs:
       d#(a(x1)) -> d#(x1)
      TRS:
       
      Polynomial Interpretation Processor:
       dimension: 1
       interpretation:
        [d#](x0) = x0,
        
        [a](x0) = x0 + 1
       orientation:
        d#(a(x1)) = x1 + 1 >= x1 = d#(x1)
       problem:
        DPs:
         
        TRS:
         
       Qed