/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 a__eq(0(),0()) -> true()
 a__eq(s(X),s(Y)) -> a__eq(X,Y)
 a__eq(X,Y) -> false()
 a__inf(X) -> cons(X,inf(s(X)))
 a__take(0(),X) -> nil()
 a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
 a__length(nil()) -> 0()
 a__length(cons(X,L)) -> s(length(L))
 mark(eq(X1,X2)) -> a__eq(X1,X2)
 mark(inf(X)) -> a__inf(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(length(X)) -> a__length(mark(X))
 mark(0()) -> 0()
 mark(true()) -> true()
 mark(s(X)) -> s(X)
 mark(false()) -> false()
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(nil()) -> nil()
 a__eq(X1,X2) -> eq(X1,X2)
 a__inf(X) -> inf(X)
 a__take(X1,X2) -> take(X1,X2)
 a__length(X) -> length(X)

Proof:
 DP Processor:
  DPs:
   a__eq#(s(X),s(Y)) -> a__eq#(X,Y)
   mark#(eq(X1,X2)) -> a__eq#(X1,X2)
   mark#(inf(X)) -> mark#(X)
   mark#(inf(X)) -> a__inf#(mark(X))
   mark#(take(X1,X2)) -> mark#(X2)
   mark#(take(X1,X2)) -> mark#(X1)
   mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
   mark#(length(X)) -> mark#(X)
   mark#(length(X)) -> a__length#(mark(X))
  TRS:
   a__eq(0(),0()) -> true()
   a__eq(s(X),s(Y)) -> a__eq(X,Y)
   a__eq(X,Y) -> false()
   a__inf(X) -> cons(X,inf(s(X)))
   a__take(0(),X) -> nil()
   a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
   a__length(nil()) -> 0()
   a__length(cons(X,L)) -> s(length(L))
   mark(eq(X1,X2)) -> a__eq(X1,X2)
   mark(inf(X)) -> a__inf(mark(X))
   mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
   mark(length(X)) -> a__length(mark(X))
   mark(0()) -> 0()
   mark(true()) -> true()
   mark(s(X)) -> s(X)
   mark(false()) -> false()
   mark(cons(X1,X2)) -> cons(X1,X2)
   mark(nil()) -> nil()
   a__eq(X1,X2) -> eq(X1,X2)
   a__inf(X) -> inf(X)
   a__take(X1,X2) -> take(X1,X2)
   a__length(X) -> length(X)
  TDG Processor:
   DPs:
    a__eq#(s(X),s(Y)) -> a__eq#(X,Y)
    mark#(eq(X1,X2)) -> a__eq#(X1,X2)
    mark#(inf(X)) -> mark#(X)
    mark#(inf(X)) -> a__inf#(mark(X))
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(length(X)) -> mark#(X)
    mark#(length(X)) -> a__length#(mark(X))
   TRS:
    a__eq(0(),0()) -> true()
    a__eq(s(X),s(Y)) -> a__eq(X,Y)
    a__eq(X,Y) -> false()
    a__inf(X) -> cons(X,inf(s(X)))
    a__take(0(),X) -> nil()
    a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
    a__length(nil()) -> 0()
    a__length(cons(X,L)) -> s(length(L))
    mark(eq(X1,X2)) -> a__eq(X1,X2)
    mark(inf(X)) -> a__inf(mark(X))
    mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    mark(length(X)) -> a__length(mark(X))
    mark(0()) -> 0()
    mark(true()) -> true()
    mark(s(X)) -> s(X)
    mark(false()) -> false()
    mark(cons(X1,X2)) -> cons(X1,X2)
    mark(nil()) -> nil()
    a__eq(X1,X2) -> eq(X1,X2)
    a__inf(X) -> inf(X)
    a__take(X1,X2) -> take(X1,X2)
    a__length(X) -> length(X)
   graph:
    mark#(eq(X1,X2)) -> a__eq#(X1,X2) ->
    a__eq#(s(X),s(Y)) -> a__eq#(X,Y)
    mark#(length(X)) -> mark#(X) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    mark#(length(X)) -> mark#(X) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1)
    mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(length(X)) -> mark#(X) -> mark#(inf(X)) -> a__inf#(mark(X))
    mark#(length(X)) -> mark#(X) -> mark#(inf(X)) -> mark#(X)
    mark#(length(X)) -> mark#(X) ->
    mark#(eq(X1,X2)) -> a__eq#(X1,X2)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(inf(X)) -> a__inf#(mark(X))
    mark#(take(X1,X2)) -> mark#(X2) -> mark#(inf(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X2) ->
    mark#(eq(X1,X2)) -> a__eq#(X1,X2)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(mark(X))
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X1) ->
    mark#(inf(X)) -> a__inf#(mark(X))
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(inf(X)) -> mark#(X)
    mark#(take(X1,X2)) -> mark#(X1) -> mark#(eq(X1,X2)) -> a__eq#(X1,X2)
    mark#(inf(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X))
    mark#(inf(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
    mark#(inf(X)) -> mark#(X) ->
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1)
    mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2)
    mark#(inf(X)) -> mark#(X) -> mark#(inf(X)) -> a__inf#(mark(X))
    mark#(inf(X)) -> mark#(X) -> mark#(inf(X)) -> mark#(X)
    mark#(inf(X)) -> mark#(X) -> mark#(eq(X1,X2)) -> a__eq#(X1,X2)
    a__eq#(s(X),s(Y)) -> a__eq#(X,Y) -> a__eq#(s(X),s(Y)) -> a__eq#(X,Y)
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 34/81
    DPs:
     mark#(length(X)) -> mark#(X)
     mark#(inf(X)) -> mark#(X)
     mark#(take(X1,X2)) -> mark#(X2)
     mark#(take(X1,X2)) -> mark#(X1)
    TRS:
     a__eq(0(),0()) -> true()
     a__eq(s(X),s(Y)) -> a__eq(X,Y)
     a__eq(X,Y) -> false()
     a__inf(X) -> cons(X,inf(s(X)))
     a__take(0(),X) -> nil()
     a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
     a__length(nil()) -> 0()
     a__length(cons(X,L)) -> s(length(L))
     mark(eq(X1,X2)) -> a__eq(X1,X2)
     mark(inf(X)) -> a__inf(mark(X))
     mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
     mark(length(X)) -> a__length(mark(X))
     mark(0()) -> 0()
     mark(true()) -> true()
     mark(s(X)) -> s(X)
     mark(false()) -> false()
     mark(cons(X1,X2)) -> cons(X1,X2)
     mark(nil()) -> nil()
     a__eq(X1,X2) -> eq(X1,X2)
     a__inf(X) -> inf(X)
     a__take(X1,X2) -> take(X1,X2)
     a__length(X) -> length(X)
    Subterm Criterion Processor:
     simple projection:
      pi(mark#) = 0
     problem:
      DPs:
       
      TRS:
       a__eq(0(),0()) -> true()
       a__eq(s(X),s(Y)) -> a__eq(X,Y)
       a__eq(X,Y) -> false()
       a__inf(X) -> cons(X,inf(s(X)))
       a__take(0(),X) -> nil()
       a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
       a__length(nil()) -> 0()
       a__length(cons(X,L)) -> s(length(L))
       mark(eq(X1,X2)) -> a__eq(X1,X2)
       mark(inf(X)) -> a__inf(mark(X))
       mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
       mark(length(X)) -> a__length(mark(X))
       mark(0()) -> 0()
       mark(true()) -> true()
       mark(s(X)) -> s(X)
       mark(false()) -> false()
       mark(cons(X1,X2)) -> cons(X1,X2)
       mark(nil()) -> nil()
       a__eq(X1,X2) -> eq(X1,X2)
       a__inf(X) -> inf(X)
       a__take(X1,X2) -> take(X1,X2)
       a__length(X) -> length(X)
     Qed
    
    DPs:
     a__eq#(s(X),s(Y)) -> a__eq#(X,Y)
    TRS:
     a__eq(0(),0()) -> true()
     a__eq(s(X),s(Y)) -> a__eq(X,Y)
     a__eq(X,Y) -> false()
     a__inf(X) -> cons(X,inf(s(X)))
     a__take(0(),X) -> nil()
     a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
     a__length(nil()) -> 0()
     a__length(cons(X,L)) -> s(length(L))
     mark(eq(X1,X2)) -> a__eq(X1,X2)
     mark(inf(X)) -> a__inf(mark(X))
     mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
     mark(length(X)) -> a__length(mark(X))
     mark(0()) -> 0()
     mark(true()) -> true()
     mark(s(X)) -> s(X)
     mark(false()) -> false()
     mark(cons(X1,X2)) -> cons(X1,X2)
     mark(nil()) -> nil()
     a__eq(X1,X2) -> eq(X1,X2)
     a__inf(X) -> inf(X)
     a__take(X1,X2) -> take(X1,X2)
     a__length(X) -> length(X)
    Subterm Criterion Processor:
     simple projection:
      pi(a__eq#) = 0
     problem:
      DPs:
       
      TRS:
       a__eq(0(),0()) -> true()
       a__eq(s(X),s(Y)) -> a__eq(X,Y)
       a__eq(X,Y) -> false()
       a__inf(X) -> cons(X,inf(s(X)))
       a__take(0(),X) -> nil()
       a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
       a__length(nil()) -> 0()
       a__length(cons(X,L)) -> s(length(L))
       mark(eq(X1,X2)) -> a__eq(X1,X2)
       mark(inf(X)) -> a__inf(mark(X))
       mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
       mark(length(X)) -> a__length(mark(X))
       mark(0()) -> 0()
       mark(true()) -> true()
       mark(s(X)) -> s(X)
       mark(false()) -> false()
       mark(cons(X1,X2)) -> cons(X1,X2)
       mark(nil()) -> nil()
       a__eq(X1,X2) -> eq(X1,X2)
       a__inf(X) -> inf(X)
       a__take(X1,X2) -> take(X1,X2)
       a__length(X) -> length(X)
     Qed