/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 a(a(x1)) -> b(b(c(x1)))
 b(a(x1)) -> c(x1)
 c(b(x1)) -> a(a(x1))

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