/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:
 f(x,0(),0()) -> s(x)
 f(0(),y,0()) -> s(y)
 f(0(),0(),z) -> s(z)
 f(s(0()),y,z) -> f(0(),s(y),s(z))
 f(s(x),s(y),0()) -> f(x,y,s(0()))
 f(s(x),0(),s(z)) -> f(x,s(0()),z)
 f(0(),s(0()),s(0())) -> s(s(0()))
 f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
 f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
 f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
 f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))

Proof:
 DP Processor:
  DPs:
   f#(s(0()),y,z) -> f#(0(),s(y),s(z))
   f#(s(x),s(y),0()) -> f#(x,y,s(0()))
   f#(s(x),0(),s(z)) -> f#(x,s(0()),z)
   f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
   f#(s(x),s(y),s(z)) -> f#(x,y,f(s(x),s(y),z))
   f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
   f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
   f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
   f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z)))
  TRS:
   f(x,0(),0()) -> s(x)
   f(0(),y,0()) -> s(y)
   f(0(),0(),z) -> s(z)
   f(s(0()),y,z) -> f(0(),s(y),s(z))
   f(s(x),s(y),0()) -> f(x,y,s(0()))
   f(s(x),0(),s(z)) -> f(x,s(0()),z)
   f(0(),s(0()),s(0())) -> s(s(0()))
   f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
   f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
   f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
   f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
  Subterm Criterion Processor:
   simple projection:
    pi(f#) = 0
   problem:
    DPs:
     f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
     f#(0(),s(s(y)),s(0())) -> f#(0(),y,s(0()))
     f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
     f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
     f#(0(),s(s(y)),s(s(z))) -> f#(0(),y,f(0(),s(s(y)),s(z)))
    TRS:
     f(x,0(),0()) -> s(x)
     f(0(),y,0()) -> s(y)
     f(0(),0(),z) -> s(z)
     f(s(0()),y,z) -> f(0(),s(y),s(z))
     f(s(x),s(y),0()) -> f(x,y,s(0()))
     f(s(x),0(),s(z)) -> f(x,s(0()),z)
     f(0(),s(0()),s(0())) -> s(s(0()))
     f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
     f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
     f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
     f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
   Subterm Criterion Processor:
    simple projection:
     pi(f#) = 1
    problem:
     DPs:
      f#(s(x),s(y),s(z)) -> f#(s(x),s(y),z)
      f#(0(),s(0()),s(s(z))) -> f#(0(),s(0()),z)
      f#(0(),s(s(y)),s(s(z))) -> f#(0(),s(s(y)),s(z))
     TRS:
      f(x,0(),0()) -> s(x)
      f(0(),y,0()) -> s(y)
      f(0(),0(),z) -> s(z)
      f(s(0()),y,z) -> f(0(),s(y),s(z))
      f(s(x),s(y),0()) -> f(x,y,s(0()))
      f(s(x),0(),s(z)) -> f(x,s(0()),z)
      f(0(),s(0()),s(0())) -> s(s(0()))
      f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
      f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
      f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
      f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 2
     problem:
      DPs:
       
      TRS:
       f(x,0(),0()) -> s(x)
       f(0(),y,0()) -> s(y)
       f(0(),0(),z) -> s(z)
       f(s(0()),y,z) -> f(0(),s(y),s(z))
       f(s(x),s(y),0()) -> f(x,y,s(0()))
       f(s(x),0(),s(z)) -> f(x,s(0()),z)
       f(0(),s(0()),s(0())) -> s(s(0()))
       f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
       f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
       f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
       f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
     Qed