/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 f_0(x) -> a()
 f_1(x) -> g_1(x,x)
 g_1(s(x),y) -> b(f_0(y),g_1(x,y))
 f_2(x) -> g_2(x,x)
 g_2(s(x),y) -> b(f_1(y),g_2(x,y))
 f_3(x) -> g_3(x,x)
 g_3(s(x),y) -> b(f_2(y),g_3(x,y))
 f_4(x) -> g_4(x,x)
 g_4(s(x),y) -> b(f_3(y),g_4(x,y))
 f_5(x) -> g_5(x,x)
 g_5(s(x),y) -> b(f_4(y),g_5(x,y))

Proof:
 DP Processor:
  DPs:
   f_1#(x) -> g_1#(x,x)
   g_1#(s(x),y) -> g_1#(x,y)
   g_1#(s(x),y) -> f_0#(y)
   f_2#(x) -> g_2#(x,x)
   g_2#(s(x),y) -> g_2#(x,y)
   g_2#(s(x),y) -> f_1#(y)
   f_3#(x) -> g_3#(x,x)
   g_3#(s(x),y) -> g_3#(x,y)
   g_3#(s(x),y) -> f_2#(y)
   f_4#(x) -> g_4#(x,x)
   g_4#(s(x),y) -> g_4#(x,y)
   g_4#(s(x),y) -> f_3#(y)
   f_5#(x) -> g_5#(x,x)
   g_5#(s(x),y) -> g_5#(x,y)
   g_5#(s(x),y) -> f_4#(y)
  TRS:
   f_0(x) -> a()
   f_1(x) -> g_1(x,x)
   g_1(s(x),y) -> b(f_0(y),g_1(x,y))
   f_2(x) -> g_2(x,x)
   g_2(s(x),y) -> b(f_1(y),g_2(x,y))
   f_3(x) -> g_3(x,x)
   g_3(s(x),y) -> b(f_2(y),g_3(x,y))
   f_4(x) -> g_4(x,x)
   g_4(s(x),y) -> b(f_3(y),g_4(x,y))
   f_5(x) -> g_5(x,x)
   g_5(s(x),y) -> b(f_4(y),g_5(x,y))
  TDG Processor:
   DPs:
    f_1#(x) -> g_1#(x,x)
    g_1#(s(x),y) -> g_1#(x,y)
    g_1#(s(x),y) -> f_0#(y)
    f_2#(x) -> g_2#(x,x)
    g_2#(s(x),y) -> g_2#(x,y)
    g_2#(s(x),y) -> f_1#(y)
    f_3#(x) -> g_3#(x,x)
    g_3#(s(x),y) -> g_3#(x,y)
    g_3#(s(x),y) -> f_2#(y)
    f_4#(x) -> g_4#(x,x)
    g_4#(s(x),y) -> g_4#(x,y)
    g_4#(s(x),y) -> f_3#(y)
    f_5#(x) -> g_5#(x,x)
    g_5#(s(x),y) -> g_5#(x,y)
    g_5#(s(x),y) -> f_4#(y)
   TRS:
    f_0(x) -> a()
    f_1(x) -> g_1(x,x)
    g_1(s(x),y) -> b(f_0(y),g_1(x,y))
    f_2(x) -> g_2(x,x)
    g_2(s(x),y) -> b(f_1(y),g_2(x,y))
    f_3(x) -> g_3(x,x)
    g_3(s(x),y) -> b(f_2(y),g_3(x,y))
    f_4(x) -> g_4(x,x)
    g_4(s(x),y) -> b(f_3(y),g_4(x,y))
    f_5(x) -> g_5(x,x)
    g_5(s(x),y) -> b(f_4(y),g_5(x,y))
   graph:
    g_5#(s(x),y) -> g_5#(x,y) -> g_5#(s(x),y) -> f_4#(y)
    g_5#(s(x),y) -> g_5#(x,y) -> g_5#(s(x),y) -> g_5#(x,y)
    g_5#(s(x),y) -> f_4#(y) -> f_4#(x) -> g_4#(x,x)
    f_5#(x) -> g_5#(x,x) -> g_5#(s(x),y) -> f_4#(y)
    f_5#(x) -> g_5#(x,x) -> g_5#(s(x),y) -> g_5#(x,y)
    g_4#(s(x),y) -> g_4#(x,y) -> g_4#(s(x),y) -> f_3#(y)
    g_4#(s(x),y) -> g_4#(x,y) -> g_4#(s(x),y) -> g_4#(x,y)
    g_4#(s(x),y) -> f_3#(y) -> f_3#(x) -> g_3#(x,x)
    f_4#(x) -> g_4#(x,x) -> g_4#(s(x),y) -> f_3#(y)
    f_4#(x) -> g_4#(x,x) -> g_4#(s(x),y) -> g_4#(x,y)
    g_3#(s(x),y) -> g_3#(x,y) -> g_3#(s(x),y) -> f_2#(y)
    g_3#(s(x),y) -> g_3#(x,y) -> g_3#(s(x),y) -> g_3#(x,y)
    g_3#(s(x),y) -> f_2#(y) -> f_2#(x) -> g_2#(x,x)
    f_3#(x) -> g_3#(x,x) -> g_3#(s(x),y) -> f_2#(y)
    f_3#(x) -> g_3#(x,x) -> g_3#(s(x),y) -> g_3#(x,y)
    g_2#(s(x),y) -> g_2#(x,y) -> g_2#(s(x),y) -> f_1#(y)
    g_2#(s(x),y) -> g_2#(x,y) -> g_2#(s(x),y) -> g_2#(x,y)
    g_2#(s(x),y) -> f_1#(y) -> f_1#(x) -> g_1#(x,x)
    f_2#(x) -> g_2#(x,x) -> g_2#(s(x),y) -> f_1#(y)
    f_2#(x) -> g_2#(x,x) -> g_2#(s(x),y) -> g_2#(x,y)
    g_1#(s(x),y) -> g_1#(x,y) -> g_1#(s(x),y) -> f_0#(y)
    g_1#(s(x),y) -> g_1#(x,y) -> g_1#(s(x),y) -> g_1#(x,y)
    f_1#(x) -> g_1#(x,x) -> g_1#(s(x),y) -> f_0#(y)
    f_1#(x) -> g_1#(x,x) -> g_1#(s(x),y) -> g_1#(x,y)
   SCC Processor:
    #sccs: 5
    #rules: 5
    #arcs: 24/225
    DPs:
     g_5#(s(x),y) -> g_5#(x,y)
    TRS:
     f_0(x) -> a()
     f_1(x) -> g_1(x,x)
     g_1(s(x),y) -> b(f_0(y),g_1(x,y))
     f_2(x) -> g_2(x,x)
     g_2(s(x),y) -> b(f_1(y),g_2(x,y))
     f_3(x) -> g_3(x,x)
     g_3(s(x),y) -> b(f_2(y),g_3(x,y))
     f_4(x) -> g_4(x,x)
     g_4(s(x),y) -> b(f_3(y),g_4(x,y))
     f_5(x) -> g_5(x,x)
     g_5(s(x),y) -> b(f_4(y),g_5(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(g_5#) = 0
     problem:
      DPs:
       
      TRS:
       f_0(x) -> a()
       f_1(x) -> g_1(x,x)
       g_1(s(x),y) -> b(f_0(y),g_1(x,y))
       f_2(x) -> g_2(x,x)
       g_2(s(x),y) -> b(f_1(y),g_2(x,y))
       f_3(x) -> g_3(x,x)
       g_3(s(x),y) -> b(f_2(y),g_3(x,y))
       f_4(x) -> g_4(x,x)
       g_4(s(x),y) -> b(f_3(y),g_4(x,y))
       f_5(x) -> g_5(x,x)
       g_5(s(x),y) -> b(f_4(y),g_5(x,y))
     Qed
    
    DPs:
     g_4#(s(x),y) -> g_4#(x,y)
    TRS:
     f_0(x) -> a()
     f_1(x) -> g_1(x,x)
     g_1(s(x),y) -> b(f_0(y),g_1(x,y))
     f_2(x) -> g_2(x,x)
     g_2(s(x),y) -> b(f_1(y),g_2(x,y))
     f_3(x) -> g_3(x,x)
     g_3(s(x),y) -> b(f_2(y),g_3(x,y))
     f_4(x) -> g_4(x,x)
     g_4(s(x),y) -> b(f_3(y),g_4(x,y))
     f_5(x) -> g_5(x,x)
     g_5(s(x),y) -> b(f_4(y),g_5(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(g_4#) = 0
     problem:
      DPs:
       
      TRS:
       f_0(x) -> a()
       f_1(x) -> g_1(x,x)
       g_1(s(x),y) -> b(f_0(y),g_1(x,y))
       f_2(x) -> g_2(x,x)
       g_2(s(x),y) -> b(f_1(y),g_2(x,y))
       f_3(x) -> g_3(x,x)
       g_3(s(x),y) -> b(f_2(y),g_3(x,y))
       f_4(x) -> g_4(x,x)
       g_4(s(x),y) -> b(f_3(y),g_4(x,y))
       f_5(x) -> g_5(x,x)
       g_5(s(x),y) -> b(f_4(y),g_5(x,y))
     Qed
    
    DPs:
     g_3#(s(x),y) -> g_3#(x,y)
    TRS:
     f_0(x) -> a()
     f_1(x) -> g_1(x,x)
     g_1(s(x),y) -> b(f_0(y),g_1(x,y))
     f_2(x) -> g_2(x,x)
     g_2(s(x),y) -> b(f_1(y),g_2(x,y))
     f_3(x) -> g_3(x,x)
     g_3(s(x),y) -> b(f_2(y),g_3(x,y))
     f_4(x) -> g_4(x,x)
     g_4(s(x),y) -> b(f_3(y),g_4(x,y))
     f_5(x) -> g_5(x,x)
     g_5(s(x),y) -> b(f_4(y),g_5(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(g_3#) = 0
     problem:
      DPs:
       
      TRS:
       f_0(x) -> a()
       f_1(x) -> g_1(x,x)
       g_1(s(x),y) -> b(f_0(y),g_1(x,y))
       f_2(x) -> g_2(x,x)
       g_2(s(x),y) -> b(f_1(y),g_2(x,y))
       f_3(x) -> g_3(x,x)
       g_3(s(x),y) -> b(f_2(y),g_3(x,y))
       f_4(x) -> g_4(x,x)
       g_4(s(x),y) -> b(f_3(y),g_4(x,y))
       f_5(x) -> g_5(x,x)
       g_5(s(x),y) -> b(f_4(y),g_5(x,y))
     Qed
    
    DPs:
     g_2#(s(x),y) -> g_2#(x,y)
    TRS:
     f_0(x) -> a()
     f_1(x) -> g_1(x,x)
     g_1(s(x),y) -> b(f_0(y),g_1(x,y))
     f_2(x) -> g_2(x,x)
     g_2(s(x),y) -> b(f_1(y),g_2(x,y))
     f_3(x) -> g_3(x,x)
     g_3(s(x),y) -> b(f_2(y),g_3(x,y))
     f_4(x) -> g_4(x,x)
     g_4(s(x),y) -> b(f_3(y),g_4(x,y))
     f_5(x) -> g_5(x,x)
     g_5(s(x),y) -> b(f_4(y),g_5(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(g_2#) = 0
     problem:
      DPs:
       
      TRS:
       f_0(x) -> a()
       f_1(x) -> g_1(x,x)
       g_1(s(x),y) -> b(f_0(y),g_1(x,y))
       f_2(x) -> g_2(x,x)
       g_2(s(x),y) -> b(f_1(y),g_2(x,y))
       f_3(x) -> g_3(x,x)
       g_3(s(x),y) -> b(f_2(y),g_3(x,y))
       f_4(x) -> g_4(x,x)
       g_4(s(x),y) -> b(f_3(y),g_4(x,y))
       f_5(x) -> g_5(x,x)
       g_5(s(x),y) -> b(f_4(y),g_5(x,y))
     Qed
    
    DPs:
     g_1#(s(x),y) -> g_1#(x,y)
    TRS:
     f_0(x) -> a()
     f_1(x) -> g_1(x,x)
     g_1(s(x),y) -> b(f_0(y),g_1(x,y))
     f_2(x) -> g_2(x,x)
     g_2(s(x),y) -> b(f_1(y),g_2(x,y))
     f_3(x) -> g_3(x,x)
     g_3(s(x),y) -> b(f_2(y),g_3(x,y))
     f_4(x) -> g_4(x,x)
     g_4(s(x),y) -> b(f_3(y),g_4(x,y))
     f_5(x) -> g_5(x,x)
     g_5(s(x),y) -> b(f_4(y),g_5(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(g_1#) = 0
     problem:
      DPs:
       
      TRS:
       f_0(x) -> a()
       f_1(x) -> g_1(x,x)
       g_1(s(x),y) -> b(f_0(y),g_1(x,y))
       f_2(x) -> g_2(x,x)
       g_2(s(x),y) -> b(f_1(y),g_2(x,y))
       f_3(x) -> g_3(x,x)
       g_3(s(x),y) -> b(f_2(y),g_3(x,y))
       f_4(x) -> g_4(x,x)
       g_4(s(x),y) -> b(f_3(y),g_4(x,y))
       f_5(x) -> g_5(x,x)
       g_5(s(x),y) -> b(f_4(y),g_5(x,y))
     Qed