/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: a__f(X) -> cons(mark(X),f(g(X)))
    2: a__g(0()) -> s(0())
    3: a__g(s(X)) -> s(s(a__g(mark(X))))
    4: a__sel(0(),cons(X,Y)) -> mark(X)
    5: a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
    6: mark(f(X)) -> a__f(mark(X))
    7: mark(g(X)) -> a__g(mark(X))
    8: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    9: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    10: mark(0()) -> 0()
    11: mark(s(X)) -> s(mark(X))
    12: a__f(X) -> f(X)
    13: a__g(X) -> g(X)
    14: a__sel(X1,X2) -> sel(X1,X2)
Number of strict rules: 14
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #mark(f(X)) -> #a__f(mark(X))
   #2: #mark(f(X)) -> #mark(X)
   #3: #mark(cons(X1,X2)) -> #mark(X1)
   #4: #mark(s(X)) -> #mark(X)
   #5: #mark(g(X)) -> #a__g(mark(X))
   #6: #mark(g(X)) -> #mark(X)
   #7: #a__sel(s(X),cons(Y,Z)) -> #a__sel(mark(X),mark(Z))
   #8: #a__sel(s(X),cons(Y,Z)) -> #mark(X)
   #9: #a__sel(s(X),cons(Y,Z)) -> #mark(Z)
   #10: #a__g(s(X)) -> #a__g(mark(X))
   #11: #a__g(s(X)) -> #mark(X)
   #12: #a__f(X) -> #mark(X)
   #13: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #14: #mark(sel(X1,X2)) -> #mark(X1)
   #15: #mark(sel(X1,X2)) -> #mark(X2)
   #16: #a__sel(0(),cons(X,Y)) -> #mark(X)
Number of SCCs: 1, DPs: 16
  SCC { #1..16 }
POLO(Sum)... POLO(max)... succeeded.
      a__g	w: x1
      s 	w: x1
      #a__g	w: x1 + 1
      a__f	w: x1 + 1
      f 	w: x1 + 1
      #mark	w: x1 + 1
      0 	w: 1
      sel	w: max(x1, x2)
      #a__sel	w: max(x1 + 1, x2 + 1)
      mark	w: x1
      a__sel	w: max(x1, x2)
      cons	w: max(x1, x2)
      #a__f	w: x1 + 2
      g 	w: x1
    USABLE RULES: { 1..14 }
    Removed DPs: #2 #12
Number of SCCs: 1, DPs: 13
  SCC { #3..11 #13..16 }
POLO(Sum)... POLO(max)... succeeded.
      a__g	w: x1
      s 	w: x1
      #a__g	w: x1 + 1
      a__f	w: x1 + 1
      f 	w: x1 + 1
      #mark	w: x1 + 1
      0 	w: 1
      sel	w: max(x1, x2)
      #a__sel	w: max(x1 + 1, x2 + 1)
      mark	w: x1
      a__sel	w: max(x1, x2)
      cons	w: max(x1 + 1, x2)
      #a__f	w: x1 + 2
      g 	w: x1
    USABLE RULES: { 1..14 }
    Removed DPs: #3 #16
Number of SCCs: 1, DPs: 11
  SCC { #4..11 #13..15 }
POLO(Sum)... POLO(max)... succeeded.
      a__g	w: x1
      s 	w: x1
      #a__g	w: x1
      a__f	w: x1 + 1
      f 	w: x1 + 1
      #mark	w: x1
      0 	w: 1
      sel	w: max(x1 + 3, x2 + 3)
      #a__sel	w: max(x1 + 1, x2 + 2)
      mark	w: x1
      a__sel	w: max(x1 + 3, x2 + 3)
      cons	w: max(x1 + 1, x2)
      #a__f	w: 2
      g 	w: x1
    USABLE RULES: { 1..14 }
    Removed DPs: #8 #9 #13..15
Number of SCCs: 2, DPs: 6
  SCC { #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      a__g	s: [1]	p: 6	w: x1
      s 	s: [1]	p: 5	w: x1
      #a__g	s: []	p: 0	w: 0
      a__f	s: []	p: 2	w: x1 + 2
      f 	s: []	p: 2	w: x1 + 2
      #mark	s: []	p: 0	w: 0
      0 	s: []	p: 4	w: 1
      sel	s: [1]	p: 2	w: x1 + x2
      #a__sel	s: [1,2]	p: 0	w: x1 + x2 + 2
      mark	s: 1
      a__sel	s: [1]	p: 2	w: x1 + x2
      cons	s: [1]	p: 1	w: max(x1 + 1, x2)
      #a__f	s: []	p: 0	w: 0
      g 	s: [1]	p: 6	w: x1
    USABLE RULES: { 1..14 }
    Removed DPs: #7
Number of SCCs: 1, DPs: 5
  SCC { #4..6 #10 #11 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      a__g	s: [1]	p: 6	w: x1
      s 	s: [1]	p: 5	w: x1
      #a__g	s: [1]	p: 0	w: x1
      a__f	s: []	p: 2	w: x1 + 2
      f 	s: []	p: 2	w: x1 + 2
      #mark	s: [1]	p: 1	w: x1
      0 	s: []	p: 4	w: 1
      sel	s: [1]	p: 2	w: x1 + x2
      #a__sel	s: [1,2]	p: 0	w: x1 + x2 + 2
      mark	s: 1
      a__sel	s: [1]	p: 2	w: x1 + x2
      cons	s: [1]	p: 1	w: max(x1 + 1, x2)
      #a__f	s: []	p: 0	w: 0
      g 	s: [1]	p: 6	w: x1
    USABLE RULES: { 1..14 }
    Removed DPs: #4..6 #10 #11
Number of SCCs: 0, DPs: 0