/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:
 app(nil(),k) -> k
 app(l,nil()) -> l
 app(cons(x,l),k) -> cons(x,app(l,k))
 sum(cons(x,nil())) -> cons(x,nil())
 sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
 a(h(),h(),x) -> s(x)
 a(x,s(y),h()) -> a(x,y,s(h()))
 a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
 a(s(x),h(),z) -> a(x,z,z)

Proof:
 DP Processor:
  DPs:
   app#(cons(x,l),k) -> app#(l,k)
   sum#(cons(x,cons(y,l))) -> a#(x,y,h())
   sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l))
   a#(x,s(y),h()) -> a#(x,y,s(h()))
   a#(x,s(y),s(z)) -> a#(x,s(y),z)
   a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
   a#(s(x),h(),z) -> a#(x,z,z)
  TRS:
   app(nil(),k) -> k
   app(l,nil()) -> l
   app(cons(x,l),k) -> cons(x,app(l,k))
   sum(cons(x,nil())) -> cons(x,nil())
   sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
   a(h(),h(),x) -> s(x)
   a(x,s(y),h()) -> a(x,y,s(h()))
   a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
   a(s(x),h(),z) -> a(x,z,z)
  TDG Processor:
   DPs:
    app#(cons(x,l),k) -> app#(l,k)
    sum#(cons(x,cons(y,l))) -> a#(x,y,h())
    sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l))
    a#(x,s(y),h()) -> a#(x,y,s(h()))
    a#(x,s(y),s(z)) -> a#(x,s(y),z)
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
    a#(s(x),h(),z) -> a#(x,z,z)
   TRS:
    app(nil(),k) -> k
    app(l,nil()) -> l
    app(cons(x,l),k) -> cons(x,app(l,k))
    sum(cons(x,nil())) -> cons(x,nil())
    sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
    a(h(),h(),x) -> s(x)
    a(x,s(y),h()) -> a(x,y,s(h()))
    a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
    a(s(x),h(),z) -> a(x,z,z)
   graph:
    a#(s(x),h(),z) -> a#(x,z,z) -> a#(s(x),h(),z) -> a#(x,z,z)
    a#(s(x),h(),z) -> a#(x,z,z) ->
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
    a#(s(x),h(),z) -> a#(x,z,z) -> a#(x,s(y),s(z)) -> a#(x,s(y),z)
    a#(s(x),h(),z) -> a#(x,z,z) -> a#(x,s(y),h()) -> a#(x,y,s(h()))
    a#(x,s(y),s(z)) -> a#(x,s(y),z) -> a#(s(x),h(),z) -> a#(x,z,z)
    a#(x,s(y),s(z)) -> a#(x,s(y),z) ->
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
    a#(x,s(y),s(z)) -> a#(x,s(y),z) ->
    a#(x,s(y),s(z)) -> a#(x,s(y),z)
    a#(x,s(y),s(z)) -> a#(x,s(y),z) ->
    a#(x,s(y),h()) -> a#(x,y,s(h()))
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z)) ->
    a#(s(x),h(),z) -> a#(x,z,z)
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z)) ->
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z)) ->
    a#(x,s(y),s(z)) -> a#(x,s(y),z)
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z)) ->
    a#(x,s(y),h()) -> a#(x,y,s(h()))
    a#(x,s(y),h()) -> a#(x,y,s(h())) -> a#(s(x),h(),z) -> a#(x,z,z)
    a#(x,s(y),h()) -> a#(x,y,s(h())) ->
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
    a#(x,s(y),h()) -> a#(x,y,s(h())) ->
    a#(x,s(y),s(z)) -> a#(x,s(y),z)
    a#(x,s(y),h()) -> a#(x,y,s(h())) ->
    a#(x,s(y),h()) -> a#(x,y,s(h()))
    sum#(cons(x,cons(y,l))) -> a#(x,y,h()) ->
    a#(s(x),h(),z) -> a#(x,z,z)
    sum#(cons(x,cons(y,l))) -> a#(x,y,h()) ->
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
    sum#(cons(x,cons(y,l))) -> a#(x,y,h()) ->
    a#(x,s(y),s(z)) -> a#(x,s(y),z)
    sum#(cons(x,cons(y,l))) -> a#(x,y,h()) ->
    a#(x,s(y),h()) -> a#(x,y,s(h()))
    sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l)) ->
    sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l))
    sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l)) ->
    sum#(cons(x,cons(y,l))) -> a#(x,y,h())
    app#(cons(x,l),k) -> app#(l,k) -> app#(cons(x,l),k) -> app#(l,k)
   SCC Processor:
    #sccs: 3
    #rules: 6
    #arcs: 23/49
    DPs:
     app#(cons(x,l),k) -> app#(l,k)
    TRS:
     app(nil(),k) -> k
     app(l,nil()) -> l
     app(cons(x,l),k) -> cons(x,app(l,k))
     sum(cons(x,nil())) -> cons(x,nil())
     sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
     a(h(),h(),x) -> s(x)
     a(x,s(y),h()) -> a(x,y,s(h()))
     a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
     a(s(x),h(),z) -> a(x,z,z)
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 0
     problem:
      DPs:
       
      TRS:
       app(nil(),k) -> k
       app(l,nil()) -> l
       app(cons(x,l),k) -> cons(x,app(l,k))
       sum(cons(x,nil())) -> cons(x,nil())
       sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
       a(h(),h(),x) -> s(x)
       a(x,s(y),h()) -> a(x,y,s(h()))
       a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
       a(s(x),h(),z) -> a(x,z,z)
     Qed
    
    DPs:
     sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l))
    TRS:
     app(nil(),k) -> k
     app(l,nil()) -> l
     app(cons(x,l),k) -> cons(x,app(l,k))
     sum(cons(x,nil())) -> cons(x,nil())
     sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
     a(h(),h(),x) -> s(x)
     a(x,s(y),h()) -> a(x,y,s(h()))
     a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
     a(s(x),h(),z) -> a(x,z,z)
    Subterm Criterion Processor:
     simple projection:
      pi(cons) = [1,1]
      pi(sum#) = 0
     problem:
      DPs:
       
      TRS:
       app(nil(),k) -> k
       app(l,nil()) -> l
       app(cons(x,l),k) -> cons(x,app(l,k))
       sum(cons(x,nil())) -> cons(x,nil())
       sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
       a(h(),h(),x) -> s(x)
       a(x,s(y),h()) -> a(x,y,s(h()))
       a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
       a(s(x),h(),z) -> a(x,z,z)
     Qed
    
    DPs:
     a#(s(x),h(),z) -> a#(x,z,z)
     a#(x,s(y),h()) -> a#(x,y,s(h()))
     a#(x,s(y),s(z)) -> a#(x,s(y),z)
     a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
    TRS:
     app(nil(),k) -> k
     app(l,nil()) -> l
     app(cons(x,l),k) -> cons(x,app(l,k))
     sum(cons(x,nil())) -> cons(x,nil())
     sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
     a(h(),h(),x) -> s(x)
     a(x,s(y),h()) -> a(x,y,s(h()))
     a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
     a(s(x),h(),z) -> a(x,z,z)
    Subterm Criterion Processor:
     simple projection:
      pi(a#) = 0
     problem:
      DPs:
       a#(x,s(y),h()) -> a#(x,y,s(h()))
       a#(x,s(y),s(z)) -> a#(x,s(y),z)
       a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
      TRS:
       app(nil(),k) -> k
       app(l,nil()) -> l
       app(cons(x,l),k) -> cons(x,app(l,k))
       sum(cons(x,nil())) -> cons(x,nil())
       sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
       a(h(),h(),x) -> s(x)
       a(x,s(y),h()) -> a(x,y,s(h()))
       a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
       a(s(x),h(),z) -> a(x,z,z)
     Subterm Criterion Processor:
      simple projection:
       pi(a#) = 1
      problem:
       DPs:
        a#(x,s(y),s(z)) -> a#(x,s(y),z)
       TRS:
        app(nil(),k) -> k
        app(l,nil()) -> l
        app(cons(x,l),k) -> cons(x,app(l,k))
        sum(cons(x,nil())) -> cons(x,nil())
        sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
        a(h(),h(),x) -> s(x)
        a(x,s(y),h()) -> a(x,y,s(h()))
        a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
        a(s(x),h(),z) -> a(x,z,z)
      Subterm Criterion Processor:
       simple projection:
        pi(a#) = 2
       problem:
        DPs:
         
        TRS:
         app(nil(),k) -> k
         app(l,nil()) -> l
         app(cons(x,l),k) -> cons(x,app(l,k))
         sum(cons(x,nil())) -> cons(x,nil())
         sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
         a(h(),h(),x) -> s(x)
         a(x,s(y),h()) -> a(x,y,s(h()))
         a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
         a(s(x),h(),z) -> a(x,z,z)
       Qed