/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
 u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
 u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
 din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
 u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
 u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
 din(der(der(X))) -> u41(din(der(X)),X)
 u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
 u42(dout(DDX),X,DX) -> dout(DDX)

Proof:
 DP Processor:
  DPs:
   din#(der(plus(X,Y))) -> din#(der(X))
   din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y)
   u21#(dout(DX),X,Y) -> din#(der(Y))
   u21#(dout(DX),X,Y) -> u22#(din(der(Y)),X,Y,DX)
   din#(der(times(X,Y))) -> din#(der(X))
   din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y)
   u31#(dout(DX),X,Y) -> din#(der(Y))
   u31#(dout(DX),X,Y) -> u32#(din(der(Y)),X,Y,DX)
   din#(der(der(X))) -> din#(der(X))
   din#(der(der(X))) -> u41#(din(der(X)),X)
   u41#(dout(DX),X) -> din#(der(DX))
   u41#(dout(DX),X) -> u42#(din(der(DX)),X,DX)
  TRS:
   din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
   u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
   u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
   din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
   u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
   u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
   din(der(der(X))) -> u41(din(der(X)),X)
   u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
   u42(dout(DDX),X,DX) -> dout(DDX)
  TDG Processor:
   DPs:
    din#(der(plus(X,Y))) -> din#(der(X))
    din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y)
    u21#(dout(DX),X,Y) -> din#(der(Y))
    u21#(dout(DX),X,Y) -> u22#(din(der(Y)),X,Y,DX)
    din#(der(times(X,Y))) -> din#(der(X))
    din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y)
    u31#(dout(DX),X,Y) -> din#(der(Y))
    u31#(dout(DX),X,Y) -> u32#(din(der(Y)),X,Y,DX)
    din#(der(der(X))) -> din#(der(X))
    din#(der(der(X))) -> u41#(din(der(X)),X)
    u41#(dout(DX),X) -> din#(der(DX))
    u41#(dout(DX),X) -> u42#(din(der(DX)),X,DX)
   TRS:
    din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
    u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
    u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
    din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
    u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
    u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
    din(der(der(X))) -> u41(din(der(X)),X)
    u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
    u42(dout(DDX),X,DX) -> dout(DDX)
   graph:
    u41#(dout(DX),X) -> din#(der(DX)) ->
    din#(der(der(X))) -> u41#(din(der(X)),X)
    u41#(dout(DX),X) -> din#(der(DX)) ->
    din#(der(der(X))) -> din#(der(X))
    u41#(dout(DX),X) -> din#(der(DX)) ->
    din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y)
    u41#(dout(DX),X) -> din#(der(DX)) ->
    din#(der(times(X,Y))) -> din#(der(X))
    u41#(dout(DX),X) -> din#(der(DX)) ->
    din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y)
    u41#(dout(DX),X) -> din#(der(DX)) ->
    din#(der(plus(X,Y))) -> din#(der(X))
    u31#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(der(X))) -> u41#(din(der(X)),X)
    u31#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(der(X))) -> din#(der(X))
    u31#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y)
    u31#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(times(X,Y))) -> din#(der(X))
    u31#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y)
    u31#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(plus(X,Y))) -> din#(der(X))
    u21#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(der(X))) -> u41#(din(der(X)),X)
    u21#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(der(X))) -> din#(der(X))
    u21#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y)
    u21#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(times(X,Y))) -> din#(der(X))
    u21#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y)
    u21#(dout(DX),X,Y) -> din#(der(Y)) ->
    din#(der(plus(X,Y))) -> din#(der(X))
    din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) ->
    u31#(dout(DX),X,Y) -> u32#(din(der(Y)),X,Y,DX)
    din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y) ->
    u31#(dout(DX),X,Y) -> din#(der(Y))
    din#(der(times(X,Y))) -> din#(der(X)) ->
    din#(der(der(X))) -> u41#(din(der(X)),X)
    din#(der(times(X,Y))) -> din#(der(X)) ->
    din#(der(der(X))) -> din#(der(X))
    din#(der(times(X,Y))) -> din#(der(X)) ->
    din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y)
    din#(der(times(X,Y))) -> din#(der(X)) ->
    din#(der(times(X,Y))) -> din#(der(X))
    din#(der(times(X,Y))) -> din#(der(X)) ->
    din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y)
    din#(der(times(X,Y))) -> din#(der(X)) ->
    din#(der(plus(X,Y))) -> din#(der(X))
    din#(der(der(X))) -> u41#(din(der(X)),X) ->
    u41#(dout(DX),X) -> u42#(din(der(DX)),X,DX)
    din#(der(der(X))) -> u41#(din(der(X)),X) ->
    u41#(dout(DX),X) -> din#(der(DX))
    din#(der(der(X))) -> din#(der(X)) ->
    din#(der(der(X))) -> u41#(din(der(X)),X)
    din#(der(der(X))) -> din#(der(X)) ->
    din#(der(der(X))) -> din#(der(X))
    din#(der(der(X))) -> din#(der(X)) ->
    din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y)
    din#(der(der(X))) -> din#(der(X)) ->
    din#(der(times(X,Y))) -> din#(der(X))
    din#(der(der(X))) -> din#(der(X)) ->
    din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y)
    din#(der(der(X))) -> din#(der(X)) ->
    din#(der(plus(X,Y))) -> din#(der(X))
    din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) ->
    u21#(dout(DX),X,Y) -> u22#(din(der(Y)),X,Y,DX)
    din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y) ->
    u21#(dout(DX),X,Y) -> din#(der(Y))
    din#(der(plus(X,Y))) -> din#(der(X)) ->
    din#(der(der(X))) -> u41#(din(der(X)),X)
    din#(der(plus(X,Y))) -> din#(der(X)) ->
    din#(der(der(X))) -> din#(der(X))
    din#(der(plus(X,Y))) -> din#(der(X)) ->
    din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y)
    din#(der(plus(X,Y))) -> din#(der(X)) ->
    din#(der(times(X,Y))) -> din#(der(X))
    din#(der(plus(X,Y))) -> din#(der(X)) ->
    din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y)
    din#(der(plus(X,Y))) -> din#(der(X)) -> din#(der(plus(X,Y))) -> din#(der(X))
   SCC Processor:
    #sccs: 1
    #rules: 9
    #arcs: 42/144
    DPs:
     u41#(dout(DX),X) -> din#(der(DX))
     din#(der(plus(X,Y))) -> din#(der(X))
     din#(der(plus(X,Y))) -> u21#(din(der(X)),X,Y)
     u21#(dout(DX),X,Y) -> din#(der(Y))
     din#(der(times(X,Y))) -> din#(der(X))
     din#(der(times(X,Y))) -> u31#(din(der(X)),X,Y)
     u31#(dout(DX),X,Y) -> din#(der(Y))
     din#(der(der(X))) -> din#(der(X))
     din#(der(der(X))) -> u41#(din(der(X)),X)
    TRS:
     din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
     u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
     u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
     din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
     u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
     u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
     din(der(der(X))) -> u41(din(der(X)),X)
     u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
     u42(dout(DDX),X,DX) -> dout(DDX)
    Bounds Processor:
     bound: 2
     enrichment: roof
     automaton:
      final states: {10,9,8,7}
      transitions:
       u320(6,6,6,6) -> 6*
       u410(6,6) -> 6*
       u420(6,6,6) -> 6*
       dout1(15) -> 6*
       dout1(6) -> 6*
       u421(14,6,6) -> 6*
       u421(14,6,15) -> 6*
       din1(12) -> 14*
       der1(15) -> 12*
       der1(6) -> 12*
       u411(14,6) -> 20,14,6
       plus1(6,6) -> 15*
       plus1(6,15) -> 6*
       times1(6,6) -> 6*
       times1(6,15) -> 6*
       u321(14,6,6,15) -> 6*
       u321(14,6,6,6) -> 6*
       u311(14,6,6) -> 6*
       u311(14,6,15) -> 6*
       u221(14,6,6,15) -> 6*
       u221(14,6,6,6) -> 6*
       u211(14,6,6) -> 20,14,6
       u211(14,6,15) -> 6*
       u41{#,1}(14,6) -> 7,9,10,8
       din{#,1}(12) -> 10,9,8,7
       u31{#,1}(14,6,6) -> 8*
       u31{#,1}(14,6,15) -> 8*
       u21{#,1}(14,6,6) -> 7,9,10,8
       u21{#,1}(14,6,15) -> 8*
       u312(20,6,6) -> 20,14
       u312(20,6,15) -> 20,14
       u41{#,0}(6,6) -> 7*
       din2(19) -> 20*
       dout0(6) -> 6*
       der2(6) -> 19*
       din{#,0}(6) -> 8*
       u31{#,2}(20,6,6) -> 7,10,8,9
       u31{#,2}(20,6,15) -> 7,10,8,9
       der0(6) -> 6*
       din{#,2}(19) -> 7,10,8,9
       plus0(6,6) -> 6*
       u212(20,6,6) -> 14*
       u212(20,6,15) -> 20,14
       u21{#,0}(6,6,6) -> 9*
       u21{#,2}(20,6,6) -> 7,10,8,9
       u21{#,2}(20,6,15) -> 7,10,8,9
       din0(6) -> 6*
       times0(6,6) -> 6*
       u31{#,0}(6,6,6) -> 10*
       u210(6,6,6) -> 6*
       u220(6,6,6,6) -> 6*
       u310(6,6,6) -> 6*
     problem:
      DPs:
       
      TRS:
       din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
       u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
       u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
       din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
       u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
       u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
       din(der(der(X))) -> u41(din(der(X)),X)
       u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
       u42(dout(DDX),X,DX) -> dout(DDX)
     Qed