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


--------------------------------------------------------------------------------


YES

Problem:
 sum(0()) -> 0()
 sum(s(x)) -> +(sum(x),s(x))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))

Proof:
 DP Processor:
  DPs:
   sum#(s(x)) -> sum#(x)
   sum#(s(x)) -> +#(sum(x),s(x))
   +#(x,s(y)) -> +#(x,y)
  TRS:
   sum(0()) -> 0()
   sum(s(x)) -> +(sum(x),s(x))
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
  TDG Processor:
   DPs:
    sum#(s(x)) -> sum#(x)
    sum#(s(x)) -> +#(sum(x),s(x))
    +#(x,s(y)) -> +#(x,y)
   TRS:
    sum(0()) -> 0()
    sum(s(x)) -> +(sum(x),s(x))
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
   graph:
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    sum#(s(x)) -> +#(sum(x),s(x)) -> +#(x,s(y)) -> +#(x,y)
    sum#(s(x)) -> sum#(x) -> sum#(s(x)) -> +#(sum(x),s(x))
    sum#(s(x)) -> sum#(x) -> sum#(s(x)) -> sum#(x)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 4/9
    DPs:
     sum#(s(x)) -> sum#(x)
    TRS:
     sum(0()) -> 0()
     sum(s(x)) -> +(sum(x),s(x))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(sum#) = 0
     problem:
      DPs:
       
      TRS:
       sum(0()) -> 0()
       sum(s(x)) -> +(sum(x),s(x))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
     Qed
    
    DPs:
     +#(x,s(y)) -> +#(x,y)
    TRS:
     sum(0()) -> 0()
     sum(s(x)) -> +(sum(x),s(x))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     problem:
      DPs:
       
      TRS:
       sum(0()) -> 0()
       sum(s(x)) -> +(sum(x),s(x))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
     Qed