/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:
 prime(0()) -> false()
 prime(s(0())) -> false()
 prime(s(s(x))) -> prime1(s(s(x)),s(x))
 prime1(x,0()) -> false()
 prime1(x,s(0())) -> true()
 prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
 divp(x,y) -> =(rem(x,y),0())

Proof:
 DP Processor:
  DPs:
   prime#(s(s(x))) -> prime1#(s(s(x)),s(x))
   prime1#(x,s(s(y))) -> prime1#(x,s(y))
   prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
  TRS:
   prime(0()) -> false()
   prime(s(0())) -> false()
   prime(s(s(x))) -> prime1(s(s(x)),s(x))
   prime1(x,0()) -> false()
   prime1(x,s(0())) -> true()
   prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
   divp(x,y) -> =(rem(x,y),0())
  TDG Processor:
   DPs:
    prime#(s(s(x))) -> prime1#(s(s(x)),s(x))
    prime1#(x,s(s(y))) -> prime1#(x,s(y))
    prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
   TRS:
    prime(0()) -> false()
    prime(s(0())) -> false()
    prime(s(s(x))) -> prime1(s(s(x)),s(x))
    prime1(x,0()) -> false()
    prime1(x,s(0())) -> true()
    prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
    divp(x,y) -> =(rem(x,y),0())
   graph:
    prime1#(x,s(s(y))) -> prime1#(x,s(y)) ->
    prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
    prime1#(x,s(s(y))) -> prime1#(x,s(y)) ->
    prime1#(x,s(s(y))) -> prime1#(x,s(y))
    prime#(s(s(x))) -> prime1#(s(s(x)),s(x)) ->
    prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
    prime#(s(s(x))) -> prime1#(s(s(x)),s(x)) -> prime1#(x,s(s(y))) -> prime1#(x,s(y))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/9
    DPs:
     prime1#(x,s(s(y))) -> prime1#(x,s(y))
    TRS:
     prime(0()) -> false()
     prime(s(0())) -> false()
     prime(s(s(x))) -> prime1(s(s(x)),s(x))
     prime1(x,0()) -> false()
     prime1(x,s(0())) -> true()
     prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
     divp(x,y) -> =(rem(x,y),0())
    Subterm Criterion Processor:
     simple projection:
      pi(prime1#) = 1
     problem:
      DPs:
       
      TRS:
       prime(0()) -> false()
       prime(s(0())) -> false()
       prime(s(s(x))) -> prime1(s(s(x)),s(x))
       prime1(x,0()) -> false()
       prime1(x,s(0())) -> true()
       prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
       divp(x,y) -> =(rem(x,y),0())
     Qed