/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES

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

Proof:
 String Reversal Processor:
  b(a(x1)) -> x1
  c(a(x1)) -> a(a(c(b(x1))))
  b(c(x1)) -> c(a(x1))
  DP Processor:
   DPs:
    c#(a(x1)) -> b#(x1)
    c#(a(x1)) -> c#(b(x1))
    b#(c(x1)) -> c#(a(x1))
   TRS:
    b(a(x1)) -> x1
    c(a(x1)) -> a(a(c(b(x1))))
    b(c(x1)) -> c(a(x1))
   TDG Processor:
    DPs:
     c#(a(x1)) -> b#(x1)
     c#(a(x1)) -> c#(b(x1))
     b#(c(x1)) -> c#(a(x1))
    TRS:
     b(a(x1)) -> x1
     c(a(x1)) -> a(a(c(b(x1))))
     b(c(x1)) -> c(a(x1))
    graph:
     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(x1)
     c#(a(x1)) -> b#(x1) -> b#(c(x1)) -> c#(a(x1))
     b#(c(x1)) -> c#(a(x1)) -> c#(a(x1)) -> c#(b(x1))
     b#(c(x1)) -> c#(a(x1)) -> c#(a(x1)) -> b#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      b(a(x1)) -> x1
      c(a(x1)) -> a(a(c(b(x1))))
      b(c(x1)) -> c(a(x1))
     interpretation:
      [c#](x0) = 1x0 + 1,
      
      [a](x0) = x0,
      
      [b#](x0) = x0 + 0,
      
      [b](x0) = x0 + 0,
      
      [c](x0) = 1x0 + 1
     orientation:
      c#(a(x1)) = 1x1 + 1 >= x1 + 0 = b#(x1)
      
      c#(a(x1)) = 1x1 + 1 >= 1x1 + 1 = c#(b(x1))
      
      b#(c(x1)) = 1x1 + 1 >= 1x1 + 1 = c#(a(x1))
      
      b(a(x1)) = x1 + 0 >= x1 = x1
      
      c(a(x1)) = 1x1 + 1 >= 1x1 + 1 = a(a(c(b(x1))))
      
      b(c(x1)) = 1x1 + 1 >= 1x1 + 1 = c(a(x1))
     problem:
      DPs:
       c#(a(x1)) -> c#(b(x1))
       b#(c(x1)) -> c#(a(x1))
      TRS:
       b(a(x1)) -> x1
       c(a(x1)) -> a(a(c(b(x1))))
       b(c(x1)) -> c(a(x1))
     Restore Modifier:
      DPs:
       c#(a(x1)) -> c#(b(x1))
       b#(c(x1)) -> c#(a(x1))
      TRS:
       b(a(x1)) -> x1
       c(a(x1)) -> a(a(c(b(x1))))
       b(c(x1)) -> c(a(x1))
      EDG Processor:
       DPs:
        c#(a(x1)) -> c#(b(x1))
        b#(c(x1)) -> c#(a(x1))
       TRS:
        b(a(x1)) -> x1
        c(a(x1)) -> a(a(c(b(x1))))
        b(c(x1)) -> c(a(x1))
       graph:
        c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
        b#(c(x1)) -> c#(a(x1)) -> c#(a(x1)) -> c#(b(x1))
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 2/4
        DPs:
         c#(a(x1)) -> c#(b(x1))
        TRS:
         b(a(x1)) -> x1
         c(a(x1)) -> a(a(c(b(x1))))
         b(c(x1)) -> c(a(x1))
        Bounds Processor:
         bound: 1
         enrichment: match-dp
         automaton:
          final states: {1}
          transitions:
           f50() -> 2*
           b1(34) -> 35*
           b1(20) -> 21*
           b0(15) -> 16*
           b0(2) -> 3*
           c{#,1}(21) -> 22*
           a0(17) -> 18*
           a0(4) -> 5*
           a0(18) -> 19*
           a0(32) -> 33*
           a0(31) -> 32*
           c0(16) -> 17*
           c0(5) -> 6*
           c0(30) -> 31*
           c{#,0}(3) -> 1*
           19 -> 17,21,30,6,3
           17 -> 21*
           35 -> 21*
           4 -> 15*
           2 -> 16,4,3
           22 -> 1*
           6 -> 16,3
           21 -> 30*
           31 -> 35,21
           18 -> 20*
           32 -> 34*
           33 -> 31,17,21
         problem:
          DPs:
           
          TRS:
           b(a(x1)) -> x1
           c(a(x1)) -> a(a(c(b(x1))))
           b(c(x1)) -> c(a(x1))
         Qed