/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(x1) -> b(x1)
 a(b(x1)) -> b(a(c(x1)))
 b(b(x1)) -> x1
 c(c(x1)) -> a(x1)

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  b(a(x1)) -> c(a(b(x1)))
  b(b(x1)) -> x1
  c(c(x1)) -> a(x1)
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(b(x1))
    b#(a(x1)) -> c#(a(b(x1)))
    c#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> b(x1)
    b(a(x1)) -> c(a(b(x1)))
    b(b(x1)) -> x1
    c(c(x1)) -> a(x1)
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> a#(b(x1))
     b#(a(x1)) -> c#(a(b(x1)))
     c#(c(x1)) -> a#(x1)
    TRS:
     a(x1) -> b(x1)
     b(a(x1)) -> c(a(b(x1)))
     b(b(x1)) -> x1
     c(c(x1)) -> a(x1)
    graph:
     c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
     b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> a#(b(x1)) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
     a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
     a#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> b(x1)
      b(a(x1)) -> c(a(b(x1)))
      b(b(x1)) -> x1
      c(c(x1)) -> a(x1)
     interpretation:
      [c#](x0) = [0 1]x0,
      
      [b#](x0) = [2 0]x0,
      
      [a#](x0) = [2 0]x0,
      
                [0  0 ]  
      [c](x0) = [1  -&]x0,
      
                [0  -&]  
      [b](x0) = [1  0 ]x0,
      
                [1 0]  
      [a](x0) = [1 0]x0
     orientation:
      a#(x1) = [2 0]x1 >= [2 0]x1 = b#(x1)
      
      b#(a(x1)) = [3 2]x1 >= [2 0]x1 = b#(x1)
      
      b#(a(x1)) = [3 2]x1 >= [2 0]x1 = a#(b(x1))
      
      b#(a(x1)) = [3 2]x1 >= [2 1]x1 = c#(a(b(x1)))
      
      c#(c(x1)) = [2 0]x1 >= [2 0]x1 = a#(x1)
      
              [1 0]      [0  -&]          
      a(x1) = [1 0]x1 >= [1  0 ]x1 = b(x1)
      
                 [1 0]      [1 0]                
      b(a(x1)) = [2 1]x1 >= [2 1]x1 = c(a(b(x1)))
      
                 [0  -&]             
      b(b(x1)) = [1  0 ]x1 >= x1 = x1
      
                 [1 0]      [1 0]          
      c(c(x1)) = [1 1]x1 >= [1 0]x1 = a(x1)
     problem:
      DPs:
       a#(x1) -> b#(x1)
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> b(x1)
       b(a(x1)) -> c(a(b(x1)))
       b(b(x1)) -> x1
       c(c(x1)) -> a(x1)
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> b(x1)
       b(a(x1)) -> c(a(b(x1)))
       b(b(x1)) -> x1
       c(c(x1)) -> a(x1)
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        c#(c(x1)) -> a#(x1)
       TRS:
        a(x1) -> b(x1)
        b(a(x1)) -> c(a(b(x1)))
        b(b(x1)) -> x1
        c(c(x1)) -> a(x1)
       graph:
        c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 1/4