/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(0()) -> 1()
 f(s(x)) -> g(x,s(x))
 g(0(),y) -> y
 g(s(x),y) -> g(x,+(y,s(x)))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 g(s(x),y) -> g(x,s(+(y,x)))

Proof:
 DP Processor:
  DPs:
   f#(s(x)) -> g#(x,s(x))
   g#(s(x),y) -> +#(y,s(x))
   g#(s(x),y) -> g#(x,+(y,s(x)))
   +#(x,s(y)) -> +#(x,y)
   g#(s(x),y) -> +#(y,x)
   g#(s(x),y) -> g#(x,s(+(y,x)))
  TRS:
   f(0()) -> 1()
   f(s(x)) -> g(x,s(x))
   g(0(),y) -> y
   g(s(x),y) -> g(x,+(y,s(x)))
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   g(s(x),y) -> g(x,s(+(y,x)))
  TDG Processor:
   DPs:
    f#(s(x)) -> g#(x,s(x))
    g#(s(x),y) -> +#(y,s(x))
    g#(s(x),y) -> g#(x,+(y,s(x)))
    +#(x,s(y)) -> +#(x,y)
    g#(s(x),y) -> +#(y,x)
    g#(s(x),y) -> g#(x,s(+(y,x)))
   TRS:
    f(0()) -> 1()
    f(s(x)) -> g(x,s(x))
    g(0(),y) -> y
    g(s(x),y) -> g(x,+(y,s(x)))
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    g(s(x),y) -> g(x,s(+(y,x)))
   graph:
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    g#(s(x),y) -> +#(y,s(x)) -> +#(x,s(y)) -> +#(x,y)
    g#(s(x),y) -> +#(y,x) -> +#(x,s(y)) -> +#(x,y)
    g#(s(x),y) -> g#(x,+(y,s(x))) -> g#(s(x),y) -> g#(x,s(+(y,x)))
    g#(s(x),y) -> g#(x,+(y,s(x))) -> g#(s(x),y) -> +#(y,x)
    g#(s(x),y) -> g#(x,+(y,s(x))) -> g#(s(x),y) -> g#(x,+(y,s(x)))
    g#(s(x),y) -> g#(x,+(y,s(x))) -> g#(s(x),y) -> +#(y,s(x))
    g#(s(x),y) -> g#(x,s(+(y,x))) -> g#(s(x),y) -> g#(x,s(+(y,x)))
    g#(s(x),y) -> g#(x,s(+(y,x))) -> g#(s(x),y) -> +#(y,x)
    g#(s(x),y) -> g#(x,s(+(y,x))) -> g#(s(x),y) -> g#(x,+(y,s(x)))
    g#(s(x),y) -> g#(x,s(+(y,x))) -> g#(s(x),y) -> +#(y,s(x))
    f#(s(x)) -> g#(x,s(x)) -> g#(s(x),y) -> g#(x,s(+(y,x)))
    f#(s(x)) -> g#(x,s(x)) -> g#(s(x),y) -> +#(y,x)
    f#(s(x)) -> g#(x,s(x)) -> g#(s(x),y) -> g#(x,+(y,s(x)))
    f#(s(x)) -> g#(x,s(x)) -> g#(s(x),y) -> +#(y,s(x))
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 15/36
    DPs:
     g#(s(x),y) -> g#(x,+(y,s(x)))
     g#(s(x),y) -> g#(x,s(+(y,x)))
    TRS:
     f(0()) -> 1()
     f(s(x)) -> g(x,s(x))
     g(0(),y) -> y
     g(s(x),y) -> g(x,+(y,s(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     g(s(x),y) -> g(x,s(+(y,x)))
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       f(0()) -> 1()
       f(s(x)) -> g(x,s(x))
       g(0(),y) -> y
       g(s(x),y) -> g(x,+(y,s(x)))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       g(s(x),y) -> g(x,s(+(y,x)))
     Qed
    
    DPs:
     +#(x,s(y)) -> +#(x,y)
    TRS:
     f(0()) -> 1()
     f(s(x)) -> g(x,s(x))
     g(0(),y) -> y
     g(s(x),y) -> g(x,+(y,s(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     g(s(x),y) -> g(x,s(+(y,x)))
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     problem:
      DPs:
       
      TRS:
       f(0()) -> 1()
       f(s(x)) -> g(x,s(x))
       g(0(),y) -> y
       g(s(x),y) -> g(x,+(y,s(x)))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       g(s(x),y) -> g(x,s(+(y,x)))
     Qed