/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__f(f(X)) -> a__c(f(g(f(X))))
 a__c(X) -> d(X)
 a__h(X) -> a__c(d(X))
 mark(f(X)) -> a__f(mark(X))
 mark(c(X)) -> a__c(X)
 mark(h(X)) -> a__h(mark(X))
 mark(g(X)) -> g(X)
 mark(d(X)) -> d(X)
 a__f(X) -> f(X)
 a__c(X) -> c(X)
 a__h(X) -> h(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [h](x0) = 2x0 + 2,
   
   [c](x0) = x0,
   
   [mark](x0) = 4x0,
   
   [a__h](x0) = 2x0 + 2,
   
   [d](x0) = x0,
   
   [a__c](x0) = x0,
   
   [g](x0) = x0,
   
   [a__f](x0) = 4x0,
   
   [f](x0) = 4x0
  orientation:
   a__f(f(X)) = 16X >= 16X = a__c(f(g(f(X))))
   
   a__c(X) = X >= X = d(X)
   
   a__h(X) = 2X + 2 >= X = a__c(d(X))
   
   mark(f(X)) = 16X >= 16X = a__f(mark(X))
   
   mark(c(X)) = 4X >= X = a__c(X)
   
   mark(h(X)) = 8X + 8 >= 8X + 2 = a__h(mark(X))
   
   mark(g(X)) = 4X >= X = g(X)
   
   mark(d(X)) = 4X >= X = d(X)
   
   a__f(X) = 4X >= 4X = f(X)
   
   a__c(X) = X >= X = c(X)
   
   a__h(X) = 2X + 2 >= 2X + 2 = h(X)
  problem:
   a__f(f(X)) -> a__c(f(g(f(X))))
   a__c(X) -> d(X)
   mark(f(X)) -> a__f(mark(X))
   mark(c(X)) -> a__c(X)
   mark(g(X)) -> g(X)
   mark(d(X)) -> d(X)
   a__f(X) -> f(X)
   a__c(X) -> c(X)
   a__h(X) -> h(X)
  String Reversal Processor:
   f(a__f(X)) -> f(g(f(a__c(X))))
   a__c(X) -> d(X)
   f(mark(X)) -> mark(a__f(X))
   c(mark(X)) -> a__c(X)
   g(mark(X)) -> g(X)
   d(mark(X)) -> d(X)
   a__f(X) -> f(X)
   a__c(X) -> c(X)
   a__h(X) -> h(X)
   Bounds Processor:
    bound: 1
    enrichment: match
    automaton:
     final states: {12,11,10,9,3,7,6,1}
     transitions:
      h0(2) -> 12*
      c1(21) -> 22*
      f1(19) -> 20*
      d1(13) -> 14*
      f90() -> 2*
      f0(5) -> 1*
      f0(2) -> 10*
      f0(3) -> 4*
      g0(2) -> 9*
      g0(4) -> 5*
      a__c0(2) -> 3*
      d0(2) -> 6*
      mark0(8) -> 7*
      a__f0(2) -> 8*
      c0(2) -> 11*
      1 -> 20,10,8
      2 -> 21,19,13
      3 -> 22,11
      7 -> 20,10,8
      14 -> 3*
      20 -> 8*
      22 -> 3*
    problem:
     
    Qed