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


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YES
Input TRS:
    1: din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
    2: u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
    3: u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
    4: din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
    5: u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
    6: u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
    7: din(der(der(X))) -> u41(din(der(X)),X)
    8: u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
    9: u42(dout(DDX),X,DX) -> dout(DDX)
Number of strict rules: 9
Direct POLO(bPol) ... failed.
Uncurrying din
1: din^1_der(plus(X,Y)) -> u21(din^1_der(X),X,Y)
2: u21(dout(DX),X,Y) -> u22(din^1_der(Y),X,Y,DX)
3: u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
4: din^1_der(times(X,Y)) -> u31(din^1_der(X),X,Y)
5: u31(dout(DX),X,Y) -> u32(din^1_der(Y),X,Y,DX)
6: u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
7: din^1_der(der(X)) -> u41(din^1_der(X),X)
8: u41(dout(DX),X) -> u42(din^1_der(DX),X,DX)
9: u42(dout(DDX),X,DX) -> dout(DDX)
10: din(der(_1)) ->= din^1_der(_1)
Number of strict rules: 9
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #u21(dout(DX),X,Y) -> #u22(din^1_der(Y),X,Y,DX)
   #2: #u21(dout(DX),X,Y) -> #din^1_der(Y)
   #3: #din^1_der(der(X)) -> #u41(din^1_der(X),X)
   #4: #din^1_der(der(X)) -> #din^1_der(X)
   #5: #din(der(_1)) ->? #din^1_der(_1)
   #6: #u31(dout(DX),X,Y) -> #u32(din^1_der(Y),X,Y,DX)
   #7: #u31(dout(DX),X,Y) -> #din^1_der(Y)
   #8: #din^1_der(plus(X,Y)) -> #u21(din^1_der(X),X,Y)
   #9: #din^1_der(plus(X,Y)) -> #din^1_der(X)
   #10: #u41(dout(DX),X) -> #u42(din^1_der(DX),X,DX)
   #11: #u41(dout(DX),X) -> #din^1_der(DX)
   #12: #din^1_der(times(X,Y)) -> #u31(din^1_der(X),X,Y)
   #13: #din^1_der(times(X,Y)) -> #din^1_der(X)
Number of SCCs: 1, DPs: 9
  SCC { #2..4 #7..9 #11..13 }
POLO(Sum)... succeeded.
      din	w: 0
      #u22	w: 0
      der	w: 3
      #u21	w: x1
      #din	w: 0
      u41	w: 1
      times	w: 2
      u32	w: x1
      din^1_der	w: 1
      u21	w: 1
      #u41	w: 2
      plus	w: 1
      #u42	w: 0
      #u31	w: 2
      u22	w: x1
      u42	w: x1
      #u32	w: 0
      dout	w: 3
      #din^1_der	w: 2
      u31	w: 1
    USABLE RULES: { 1..9 }
    Removed DPs: #2 #8
Number of SCCs: 1, DPs: 7
  SCC { #3 #4 #7 #9 #11..13 }
POLO(Sum)... succeeded.
      din	w: 0
      #u22	w: 0
      der	w: 3
      #u21	w: x1
      #din	w: 0
      u41	w: 1
      times	w: 2
      u32	w: x1
      din^1_der	w: 1
      u21	w: 1
      #u41	w: x1
      plus	w: 0
      #u42	w: 0
      #u31	w: 2
      u22	w: x1
      u42	w: x1
      #u32	w: 0
      dout	w: x1 + 3
      #din^1_der	w: 2
      u31	w: 1
    USABLE RULES: { 1..9 }
    Removed DPs: #3 #11
Number of SCCs: 1, DPs: 5
  SCC { #4 #7 #9 #12 #13 }
POLO(Sum)... succeeded.
      din	w: 0
      #u22	w: 0
      der	w: 3
      #u21	w: x1
      #din	w: 0
      u41	w: 1
      times	w: 2
      u32	w: x1
      din^1_der	w: 1
      u21	w: 1
      #u41	w: x1
      plus	w: 0
      #u42	w: 0
      #u31	w: x1
      u22	w: x1
      u42	w: x1
      #u32	w: 0
      dout	w: x1 + 3
      #din^1_der	w: 2
      u31	w: 1
    USABLE RULES: { 1..9 }
    Removed DPs: #7 #12
Number of SCCs: 1, DPs: 3
  SCC { #4 #9 #13 }
POLO(Sum)... succeeded.
      din	w: 0
      #u22	w: 0
      der	w: x1 + 1
      #u21	w: x1
      #din	w: 0
      u41	w: 1
      times	w: x1 + 2
      u32	w: x1
      din^1_der	w: 1
      u21	w: 1
      #u41	w: x1
      plus	w: x1 + 1
      #u42	w: 0
      #u31	w: x1
      u22	w: x1
      u42	w: x1
      #u32	w: 0
      dout	w: 3
      #din^1_der	w: x1 + 2
      u31	w: 1
    USABLE RULES: { 1..9 }
    Removed DPs: #4 #9 #13
Number of SCCs: 0, DPs: 0