/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:
 fac(0()) -> 1()
 fac(s(x)) -> *(s(x),fac(x))
 floop(0(),y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
 *(x,0()) -> 0()
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 1() -> s(0())
 fac(0()) -> s(0())

Proof:
 DP Processor:
  DPs:
   fac#(0()) -> 1#()
   fac#(s(x)) -> fac#(x)
   fac#(s(x)) -> *#(s(x),fac(x))
   floop#(s(x),y) -> *#(s(x),y)
   floop#(s(x),y) -> floop#(x,*(s(x),y))
   *#(x,s(y)) -> *#(x,y)
   *#(x,s(y)) -> +#(*(x,y),x)
   +#(x,s(y)) -> +#(x,y)
  TRS:
   fac(0()) -> 1()
   fac(s(x)) -> *(s(x),fac(x))
   floop(0(),y) -> y
   floop(s(x),y) -> floop(x,*(s(x),y))
   *(x,0()) -> 0()
   *(x,s(y)) -> +(*(x,y),x)
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   1() -> s(0())
   fac(0()) -> s(0())
  TDG Processor:
   DPs:
    fac#(0()) -> 1#()
    fac#(s(x)) -> fac#(x)
    fac#(s(x)) -> *#(s(x),fac(x))
    floop#(s(x),y) -> *#(s(x),y)
    floop#(s(x),y) -> floop#(x,*(s(x),y))
    *#(x,s(y)) -> *#(x,y)
    *#(x,s(y)) -> +#(*(x,y),x)
    +#(x,s(y)) -> +#(x,y)
   TRS:
    fac(0()) -> 1()
    fac(s(x)) -> *(s(x),fac(x))
    floop(0(),y) -> y
    floop(s(x),y) -> floop(x,*(s(x),y))
    *(x,0()) -> 0()
    *(x,s(y)) -> +(*(x,y),x)
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    1() -> s(0())
    fac(0()) -> s(0())
   graph:
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    floop#(s(x),y) -> floop#(x,*(s(x),y)) ->
    floop#(s(x),y) -> floop#(x,*(s(x),y))
    floop#(s(x),y) -> floop#(x,*(s(x),y)) ->
    floop#(s(x),y) -> *#(s(x),y)
    floop#(s(x),y) -> *#(s(x),y) -> *#(x,s(y)) -> +#(*(x,y),x)
    floop#(s(x),y) -> *#(s(x),y) -> *#(x,s(y)) -> *#(x,y)
    *#(x,s(y)) -> +#(*(x,y),x) -> +#(x,s(y)) -> +#(x,y)
    *#(x,s(y)) -> *#(x,y) -> *#(x,s(y)) -> +#(*(x,y),x)
    *#(x,s(y)) -> *#(x,y) -> *#(x,s(y)) -> *#(x,y)
    fac#(s(x)) -> *#(s(x),fac(x)) -> *#(x,s(y)) -> +#(*(x,y),x)
    fac#(s(x)) -> *#(s(x),fac(x)) -> *#(x,s(y)) -> *#(x,y)
    fac#(s(x)) -> fac#(x) -> fac#(s(x)) -> *#(s(x),fac(x))
    fac#(s(x)) -> fac#(x) -> fac#(s(x)) -> fac#(x)
    fac#(s(x)) -> fac#(x) -> fac#(0()) -> 1#()
   SCC Processor:
    #sccs: 4
    #rules: 4
    #arcs: 13/64
    DPs:
     fac#(s(x)) -> fac#(x)
    TRS:
     fac(0()) -> 1()
     fac(s(x)) -> *(s(x),fac(x))
     floop(0(),y) -> y
     floop(s(x),y) -> floop(x,*(s(x),y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(*(x,y),x)
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     1() -> s(0())
     fac(0()) -> s(0())
    Subterm Criterion Processor:
     simple projection:
      pi(fac#) = 0
     problem:
      DPs:
       
      TRS:
       fac(0()) -> 1()
       fac(s(x)) -> *(s(x),fac(x))
       floop(0(),y) -> y
       floop(s(x),y) -> floop(x,*(s(x),y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(*(x,y),x)
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       1() -> s(0())
       fac(0()) -> s(0())
     Qed
    
    DPs:
     floop#(s(x),y) -> floop#(x,*(s(x),y))
    TRS:
     fac(0()) -> 1()
     fac(s(x)) -> *(s(x),fac(x))
     floop(0(),y) -> y
     floop(s(x),y) -> floop(x,*(s(x),y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(*(x,y),x)
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     1() -> s(0())
     fac(0()) -> s(0())
    Subterm Criterion Processor:
     simple projection:
      pi(floop#) = 0
     problem:
      DPs:
       
      TRS:
       fac(0()) -> 1()
       fac(s(x)) -> *(s(x),fac(x))
       floop(0(),y) -> y
       floop(s(x),y) -> floop(x,*(s(x),y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(*(x,y),x)
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       1() -> s(0())
       fac(0()) -> s(0())
     Qed
    
    DPs:
     *#(x,s(y)) -> *#(x,y)
    TRS:
     fac(0()) -> 1()
     fac(s(x)) -> *(s(x),fac(x))
     floop(0(),y) -> y
     floop(s(x),y) -> floop(x,*(s(x),y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(*(x,y),x)
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     1() -> s(0())
     fac(0()) -> s(0())
    Subterm Criterion Processor:
     simple projection:
      pi(*#) = 1
     problem:
      DPs:
       
      TRS:
       fac(0()) -> 1()
       fac(s(x)) -> *(s(x),fac(x))
       floop(0(),y) -> y
       floop(s(x),y) -> floop(x,*(s(x),y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(*(x,y),x)
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       1() -> s(0())
       fac(0()) -> s(0())
     Qed
    
    DPs:
     +#(x,s(y)) -> +#(x,y)
    TRS:
     fac(0()) -> 1()
     fac(s(x)) -> *(s(x),fac(x))
     floop(0(),y) -> y
     floop(s(x),y) -> floop(x,*(s(x),y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(*(x,y),x)
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     1() -> s(0())
     fac(0()) -> s(0())
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     problem:
      DPs:
       
      TRS:
       fac(0()) -> 1()
       fac(s(x)) -> *(s(x),fac(x))
       floop(0(),y) -> y
       floop(s(x),y) -> floop(x,*(s(x),y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(*(x,y),x)
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       1() -> s(0())
       fac(0()) -> s(0())
     Qed