/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:
 ack_in(0(),n) -> ack_out(s(n))
 ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
 u11(ack_out(n)) -> ack_out(n)
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)

Proof:
 DP Processor:
  DPs:
   ack_in#(s(m),0()) -> ack_in#(m,s(0()))
   ack_in#(s(m),0()) -> u11#(ack_in(m,s(0())))
   ack_in#(s(m),s(n)) -> ack_in#(s(m),n)
   ack_in#(s(m),s(n)) -> u21#(ack_in(s(m),n),m)
   u21#(ack_out(n),m) -> ack_in#(m,n)
   u21#(ack_out(n),m) -> u22#(ack_in(m,n))
  TRS:
   ack_in(0(),n) -> ack_out(s(n))
   ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
   u11(ack_out(n)) -> ack_out(n)
   ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
   u21(ack_out(n),m) -> u22(ack_in(m,n))
   u22(ack_out(n)) -> ack_out(n)
  TDG Processor:
   DPs:
    ack_in#(s(m),0()) -> ack_in#(m,s(0()))
    ack_in#(s(m),0()) -> u11#(ack_in(m,s(0())))
    ack_in#(s(m),s(n)) -> ack_in#(s(m),n)
    ack_in#(s(m),s(n)) -> u21#(ack_in(s(m),n),m)
    u21#(ack_out(n),m) -> ack_in#(m,n)
    u21#(ack_out(n),m) -> u22#(ack_in(m,n))
   TRS:
    ack_in(0(),n) -> ack_out(s(n))
    ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
    u11(ack_out(n)) -> ack_out(n)
    ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
    u21(ack_out(n),m) -> u22(ack_in(m,n))
    u22(ack_out(n)) -> ack_out(n)
   graph:
    u21#(ack_out(n),m) -> ack_in#(m,n) ->
    ack_in#(s(m),s(n)) -> u21#(ack_in(s(m),n),m)
    u21#(ack_out(n),m) -> ack_in#(m,n) ->
    ack_in#(s(m),s(n)) -> ack_in#(s(m),n)
    u21#(ack_out(n),m) -> ack_in#(m,n) ->
    ack_in#(s(m),0()) -> u11#(ack_in(m,s(0())))
    u21#(ack_out(n),m) -> ack_in#(m,n) ->
    ack_in#(s(m),0()) -> ack_in#(m,s(0()))
    ack_in#(s(m),s(n)) -> u21#(ack_in(s(m),n),m) ->
    u21#(ack_out(n),m) -> u22#(ack_in(m,n))
    ack_in#(s(m),s(n)) -> u21#(ack_in(s(m),n),m) ->
    u21#(ack_out(n),m) -> ack_in#(m,n)
    ack_in#(s(m),s(n)) -> ack_in#(s(m),n) ->
    ack_in#(s(m),s(n)) -> u21#(ack_in(s(m),n),m)
    ack_in#(s(m),s(n)) -> ack_in#(s(m),n) ->
    ack_in#(s(m),s(n)) -> ack_in#(s(m),n)
    ack_in#(s(m),s(n)) -> ack_in#(s(m),n) ->
    ack_in#(s(m),0()) -> u11#(ack_in(m,s(0())))
    ack_in#(s(m),s(n)) -> ack_in#(s(m),n) ->
    ack_in#(s(m),0()) -> ack_in#(m,s(0()))
    ack_in#(s(m),0()) -> ack_in#(m,s(0())) ->
    ack_in#(s(m),s(n)) -> u21#(ack_in(s(m),n),m)
    ack_in#(s(m),0()) -> ack_in#(m,s(0())) ->
    ack_in#(s(m),s(n)) -> ack_in#(s(m),n)
    ack_in#(s(m),0()) -> ack_in#(m,s(0())) ->
    ack_in#(s(m),0()) -> u11#(ack_in(m,s(0())))
    ack_in#(s(m),0()) -> ack_in#(m,s(0())) -> ack_in#(s(m),0()) -> ack_in#(m,s(0()))
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 14/36
    DPs:
     u21#(ack_out(n),m) -> ack_in#(m,n)
     ack_in#(s(m),0()) -> ack_in#(m,s(0()))
     ack_in#(s(m),s(n)) -> ack_in#(s(m),n)
     ack_in#(s(m),s(n)) -> u21#(ack_in(s(m),n),m)
    TRS:
     ack_in(0(),n) -> ack_out(s(n))
     ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
     u11(ack_out(n)) -> ack_out(n)
     ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
     u21(ack_out(n),m) -> u22(ack_in(m,n))
     u22(ack_out(n)) -> ack_out(n)
    Subterm Criterion Processor:
     simple projection:
      pi(ack_in#) = 0
      pi(u21#) = 1
     problem:
      DPs:
       u21#(ack_out(n),m) -> ack_in#(m,n)
       ack_in#(s(m),s(n)) -> ack_in#(s(m),n)
      TRS:
       ack_in(0(),n) -> ack_out(s(n))
       ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
       u11(ack_out(n)) -> ack_out(n)
       ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
       u21(ack_out(n),m) -> u22(ack_in(m,n))
       u22(ack_out(n)) -> ack_out(n)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 10/4
      DPs:
       ack_in#(s(m),s(n)) -> ack_in#(s(m),n)
      TRS:
       ack_in(0(),n) -> ack_out(s(n))
       ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
       u11(ack_out(n)) -> ack_out(n)
       ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
       u21(ack_out(n),m) -> u22(ack_in(m,n))
       u22(ack_out(n)) -> ack_out(n)
      Subterm Criterion Processor:
       simple projection:
        pi(ack_in#) = 1
       problem:
        DPs:
         
        TRS:
         ack_in(0(),n) -> ack_out(s(n))
         ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
         u11(ack_out(n)) -> ack_out(n)
         ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
         u21(ack_out(n),m) -> u22(ack_in(m,n))
         u22(ack_out(n)) -> ack_out(n)
       Qed