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


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YES

Problem:
 active(and(tt(),X)) -> mark(X)
 active(plus(N,0())) -> mark(N)
 active(plus(N,s(M))) -> mark(s(plus(N,M)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(tt()) -> active(tt())
 mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
 mark(0()) -> active(0())
 mark(s(X)) -> active(s(mark(X)))
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 and(active(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 plus(mark(X1),X2) -> plus(X1,X2)
 plus(X1,mark(X2)) -> plus(X1,X2)
 plus(active(X1),X2) -> plus(X1,X2)
 plus(X1,active(X2)) -> plus(X1,X2)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [0] = 0,
   
   [and](x0, x1) = 4x0 + 4x1,
   
   [mark](x0) = x0,
   
   [plus](x0, x1) = x0 + x1,
   
   [tt] = 6,
   
   [s](x0) = x0,
   
   [active](x0) = x0
  orientation:
   active(and(tt(),X)) = 4X + 24 >= X = mark(X)
   
   active(plus(N,0())) = N >= N = mark(N)
   
   active(plus(N,s(M))) = M + N >= M + N = mark(s(plus(N,M)))
   
   mark(and(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = active(and(mark(X1),X2))
   
   mark(tt()) = 6 >= 6 = active(tt())
   
   mark(plus(X1,X2)) = X1 + X2 >= X1 + X2 = active(plus(mark(X1),mark(X2)))
   
   mark(0()) = 0 >= 0 = active(0())
   
   mark(s(X)) = X >= X = active(s(mark(X)))
   
   and(mark(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = and(X1,X2)
   
   and(X1,mark(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = and(X1,X2)
   
   and(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = and(X1,X2)
   
   and(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = and(X1,X2)
   
   plus(mark(X1),X2) = X1 + X2 >= X1 + X2 = plus(X1,X2)
   
   plus(X1,mark(X2)) = X1 + X2 >= X1 + X2 = plus(X1,X2)
   
   plus(active(X1),X2) = X1 + X2 >= X1 + X2 = plus(X1,X2)
   
   plus(X1,active(X2)) = X1 + X2 >= X1 + X2 = plus(X1,X2)
   
   s(mark(X)) = X >= X = s(X)
   
   s(active(X)) = X >= X = s(X)
  problem:
   active(plus(N,0())) -> mark(N)
   active(plus(N,s(M))) -> mark(s(plus(N,M)))
   mark(and(X1,X2)) -> active(and(mark(X1),X2))
   mark(tt()) -> active(tt())
   mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
   mark(0()) -> active(0())
   mark(s(X)) -> active(s(mark(X)))
   and(mark(X1),X2) -> and(X1,X2)
   and(X1,mark(X2)) -> and(X1,X2)
   and(active(X1),X2) -> and(X1,X2)
   and(X1,active(X2)) -> and(X1,X2)
   plus(mark(X1),X2) -> plus(X1,X2)
   plus(X1,mark(X2)) -> plus(X1,X2)
   plus(active(X1),X2) -> plus(X1,X2)
   plus(X1,active(X2)) -> plus(X1,X2)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [0] = 0,
    
    [and](x0, x1) = x0 + 2x1,
    
    [mark](x0) = x0,
    
    [plus](x0, x1) = x0 + 4x1 + 5,
    
    [tt] = 0,
    
    [s](x0) = x0 + 3,
    
    [active](x0) = x0
   orientation:
    active(plus(N,0())) = N + 5 >= N = mark(N)
    
    active(plus(N,s(M))) = 4M + N + 17 >= 4M + N + 8 = mark(s(plus(N,M)))
    
    mark(and(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = active(and(mark(X1),X2))
    
    mark(tt()) = 0 >= 0 = active(tt())
    
    mark(plus(X1,X2)) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = active(plus(mark(X1),mark(X2)))
    
    mark(0()) = 0 >= 0 = active(0())
    
    mark(s(X)) = X + 3 >= X + 3 = active(s(mark(X)))
    
    and(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = and(X1,X2)
    
    and(X1,mark(X2)) = X1 + 2X2 >= X1 + 2X2 = and(X1,X2)
    
    and(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = and(X1,X2)
    
    and(X1,active(X2)) = X1 + 2X2 >= X1 + 2X2 = and(X1,X2)
    
    plus(mark(X1),X2) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = plus(X1,X2)
    
    plus(X1,mark(X2)) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = plus(X1,X2)
    
    plus(active(X1),X2) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = plus(X1,X2)
    
    plus(X1,active(X2)) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = plus(X1,X2)
    
    s(mark(X)) = X + 3 >= X + 3 = s(X)
    
    s(active(X)) = X + 3 >= X + 3 = s(X)
   problem:
    mark(and(X1,X2)) -> active(and(mark(X1),X2))
    mark(tt()) -> active(tt())
    mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
    mark(0()) -> active(0())
    mark(s(X)) -> active(s(mark(X)))
    and(mark(X1),X2) -> and(X1,X2)
    and(X1,mark(X2)) -> and(X1,X2)
    and(active(X1),X2) -> and(X1,X2)
    and(X1,active(X2)) -> and(X1,X2)
    plus(mark(X1),X2) -> plus(X1,X2)
    plus(X1,mark(X2)) -> plus(X1,X2)
    plus(active(X1),X2) -> plus(X1,X2)
    plus(X1,active(X2)) -> plus(X1,X2)
    s(mark(X)) -> s(X)
    s(active(X)) -> s(X)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [0] = 0,
     
     [and](x0, x1) = 3x0 + 4x1 + 1,
     
     [mark](x0) = 7x0 + 1,
     
     [plus](x0, x1) = 4x0 + 4x1 + 4,
     
     [tt] = 2,
     
     [s](x0) = 4x0 + 1,
     
     [active](x0) = x0
    orientation:
     mark(and(X1,X2)) = 21X1 + 28X2 + 8 >= 21X1 + 4X2 + 4 = active(and(mark(X1),X2))
     
     mark(tt()) = 15 >= 2 = active(tt())
     
     mark(plus(X1,X2)) = 28X1 + 28X2 + 29 >= 28X1 + 28X2 + 12 = active(plus(mark(X1),mark(X2)))
     
     mark(0()) = 1 >= 0 = active(0())
     
     mark(s(X)) = 28X + 8 >= 28X + 5 = active(s(mark(X)))
     
     and(mark(X1),X2) = 21X1 + 4X2 + 4 >= 3X1 + 4X2 + 1 = and(X1,X2)
     
     and(X1,mark(X2)) = 3X1 + 28X2 + 5 >= 3X1 + 4X2 + 1 = and(X1,X2)
     
     and(active(X1),X2) = 3X1 + 4X2 + 1 >= 3X1 + 4X2 + 1 = and(X1,X2)
     
     and(X1,active(X2)) = 3X1 + 4X2 + 1 >= 3X1 + 4X2 + 1 = and(X1,X2)
     
     plus(mark(X1),X2) = 28X1 + 4X2 + 8 >= 4X1 + 4X2 + 4 = plus(X1,X2)
     
     plus(X1,mark(X2)) = 4X1 + 28X2 + 8 >= 4X1 + 4X2 + 4 = plus(X1,X2)
     
     plus(active(X1),X2) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = plus(X1,X2)
     
     plus(X1,active(X2)) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = plus(X1,X2)
     
     s(mark(X)) = 28X + 5 >= 4X + 1 = s(X)
     
     s(active(X)) = 4X + 1 >= 4X + 1 = s(X)
    problem:
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     plus(active(X1),X2) -> plus(X1,X2)
     plus(X1,active(X2)) -> plus(X1,X2)
     s(active(X)) -> s(X)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [and](x0, x1) = x0 + 4x1,
      
      [plus](x0, x1) = x0 + x1,
      
      [s](x0) = x0 + 7,
      
      [active](x0) = 4x0 + 1
     orientation:
      and(active(X1),X2) = 4X1 + 4X2 + 1 >= X1 + 4X2 = and(X1,X2)
      
      and(X1,active(X2)) = X1 + 16X2 + 4 >= X1 + 4X2 = and(X1,X2)
      
      plus(active(X1),X2) = 4X1 + X2 + 1 >= X1 + X2 = plus(X1,X2)
      
      plus(X1,active(X2)) = X1 + 4X2 + 1 >= X1 + X2 = plus(X1,X2)
      
      s(active(X)) = 4X + 8 >= X + 7 = s(X)
     problem:
      
     Qed