/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:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
 a__f(X1,X2) -> f(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__f#(g(X),Y) -> mark#(X)
   a__f#(g(X),Y) -> a__f#(mark(X),f(g(X),Y))
   mark#(f(X1,X2)) -> mark#(X1)
   mark#(f(X1,X2)) -> a__f#(mark(X1),X2)
   mark#(g(X)) -> mark#(X)
  TRS:
   a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
   mark(f(X1,X2)) -> a__f(mark(X1),X2)
   mark(g(X)) -> g(mark(X))
   a__f(X1,X2) -> f(X1,X2)
  TDG Processor:
   DPs:
    a__f#(g(X),Y) -> mark#(X)
    a__f#(g(X),Y) -> a__f#(mark(X),f(g(X),Y))
    mark#(f(X1,X2)) -> mark#(X1)
    mark#(f(X1,X2)) -> a__f#(mark(X1),X2)
    mark#(g(X)) -> mark#(X)
   TRS:
    a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
    mark(f(X1,X2)) -> a__f(mark(X1),X2)
    mark(g(X)) -> g(mark(X))
    a__f(X1,X2) -> f(X1,X2)
   graph:
    mark#(f(X1,X2)) -> mark#(X1) -> mark#(g(X)) -> mark#(X)
    mark#(f(X1,X2)) -> mark#(X1) ->
    mark#(f(X1,X2)) -> a__f#(mark(X1),X2)
    mark#(f(X1,X2)) -> mark#(X1) ->
    mark#(f(X1,X2)) -> mark#(X1)
    mark#(f(X1,X2)) -> a__f#(mark(X1),X2) ->
    a__f#(g(X),Y) -> a__f#(mark(X),f(g(X),Y))
    mark#(f(X1,X2)) -> a__f#(mark(X1),X2) -> a__f#(g(X),Y) -> mark#(X)
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2)) -> a__f#(mark(X1),X2)
    mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2)) -> mark#(X1)
    a__f#(g(X),Y) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    a__f#(g(X),Y) -> mark#(X) -> mark#(f(X1,X2)) -> a__f#(mark(X1),X2)
    a__f#(g(X),Y) -> mark#(X) ->
    mark#(f(X1,X2)) -> mark#(X1)
    a__f#(g(X),Y) -> a__f#(mark(X),f(g(X),Y)) ->
    a__f#(g(X),Y) -> a__f#(mark(X),f(g(X),Y))
    a__f#(g(X),Y) -> a__f#(mark(X),f(g(X),Y)) -> a__f#(g(X),Y) -> mark#(X)
   Subterm Criterion Processor:
    simple projection:
     pi(g) = [0,0,0]
     pi(a__f) = [0,0,0]
     pi(mark) = [0,0]
     pi(f) = [0,0,0]
     pi(a__f#) = 0
     pi(mark#) = [0,0]
    problem:
     DPs:
      
     TRS:
      a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
      mark(f(X1,X2)) -> a__f(mark(X1),X2)
      mark(g(X)) -> g(mark(X))
      a__f(X1,X2) -> f(X1,X2)
    Qed