/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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NO

Problem:
 a__f(b(),X,c()) -> a__f(X,a__c(),X)
 a__c() -> b()
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
 mark(c()) -> a__c()
 mark(b()) -> b()
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 a__c() -> c()

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [mark](x0) = 2x0,
   
   [f](x0, x1, x2) = x0 + 6x1 + 2x2,
   
   [a__c] = 2,
   
   [a__f](x0, x1, x2) = 2x0 + 6x1 + 4x2,
   
   [c] = 2,
   
   [b] = 2
  orientation:
   a__f(b(),X,c()) = 6X + 12 >= 6X + 12 = a__f(X,a__c(),X)
   
   a__c() = 2 >= 2 = b()
   
   mark(f(X1,X2,X3)) = 2X1 + 12X2 + 4X3 >= 2X1 + 12X2 + 4X3 = a__f(X1,mark(X2),X3)
   
   mark(c()) = 4 >= 2 = a__c()
   
   mark(b()) = 4 >= 2 = b()
   
   a__f(X1,X2,X3) = 2X1 + 6X2 + 4X3 >= X1 + 6X2 + 2X3 = f(X1,X2,X3)
   
   a__c() = 2 >= 2 = c()
  problem:
   a__f(b(),X,c()) -> a__f(X,a__c(),X)
   a__c() -> b()
   mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
   a__f(X1,X2,X3) -> f(X1,X2,X3)
   a__c() -> c()
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [mark](x0) = 2x0,
    
    [f](x0, x1, x2) = x0 + 4x1 + 2x2 + 1,
    
    [a__c] = 0,
    
    [a__f](x0, x1, x2) = 2x0 + 4x1 + 2x2 + 2,
    
    [c] = 0,
    
    [b] = 0
   orientation:
    a__f(b(),X,c()) = 4X + 2 >= 4X + 2 = a__f(X,a__c(),X)
    
    a__c() = 0 >= 0 = b()
    
    mark(f(X1,X2,X3)) = 2X1 + 8X2 + 4X3 + 2 >= 2X1 + 8X2 + 2X3 + 2 = a__f(X1,mark(X2),X3)
    
    a__f(X1,X2,X3) = 2X1 + 4X2 + 2X3 + 2 >= X1 + 4X2 + 2X3 + 1 = f(X1,X2,X3)
    
    a__c() = 0 >= 0 = c()
   problem:
    a__f(b(),X,c()) -> a__f(X,a__c(),X)
    a__c() -> b()
    mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
    a__c() -> c()
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [mark](x0) = 4x0 + 6,
     
     [f](x0, x1, x2) = 2x0 + 4x1 + x2 + 5,
     
     [a__c] = 0,
     
     [a__f](x0, x1, x2) = x0 + 4x1 + 3x2,
     
     [c] = 0,
     
     [b] = 0
    orientation:
     a__f(b(),X,c()) = 4X >= 4X = a__f(X,a__c(),X)
     
     a__c() = 0 >= 0 = b()
     
     mark(f(X1,X2,X3)) = 8X1 + 16X2 + 4X3 + 26 >= X1 + 16X2 + 3X3 + 24 = a__f(X1,mark(X2),X3)
     
     a__c() = 0 >= 0 = c()
    problem:
     a__f(b(),X,c()) -> a__f(X,a__c(),X)
     a__c() -> b()
     a__c() -> c()
    Unfolding Processor:
     loop length: 3
     terms:
      a__f(a__c(),a__c(),a__c())
      a__f(a__c(),a__c(),c())
      a__f(b(),a__c(),c())
     context: []
     substitution:
      
     Qed