/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: active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
    2: active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
    3: active(from(X)) -> mark(cons(X,from(s(X))))
    4: active(2nd(X)) -> 2nd(active(X))
    5: active(cons(X1,X2)) -> cons(active(X1),X2)
    6: active(from(X)) -> from(active(X))
    7: active(s(X)) -> s(active(X))
    8: active(cons1(X1,X2)) -> cons1(active(X1),X2)
    9: active(cons1(X1,X2)) -> cons1(X1,active(X2))
    10: 2nd(mark(X)) -> mark(2nd(X))
    11: cons(mark(X1),X2) -> mark(cons(X1,X2))
    12: from(mark(X)) -> mark(from(X))
    13: s(mark(X)) -> mark(s(X))
    14: cons1(mark(X1),X2) -> mark(cons1(X1,X2))
    15: cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
    16: proper(2nd(X)) -> 2nd(proper(X))
    17: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    18: proper(from(X)) -> from(proper(X))
    19: proper(s(X)) -> s(proper(X))
    20: proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
    21: 2nd(ok(X)) -> ok(2nd(X))
    22: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    23: from(ok(X)) -> ok(from(X))
    24: s(ok(X)) -> ok(s(X))
    25: cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
    26: top(mark(X)) -> top(proper(X))
    27: top(ok(X)) -> top(active(X))
Number of strict rules: 27
Direct POLO(bPol) ... removes: 15 8 1 26 27 22 5 25 14 9 2
      s 	w: x1
      top	w: x1
      2nd	w: x1
      cons1	w: 2 * x1 + 2 * x2 + 4
      proper	w: x1
      ok	w: 2 * x1 + 4
      from	w: x1
      mark	w: x1 + 1
      active	w: 2 * x1 + 3
      cons	w: x1 + x2 + 2
Number of strict rules: 16
Direct POLO(bPol) ... removes: 3
      s 	w: x1
      top	w: x1
      2nd	w: x1
      cons1	w: 2 * x1 + 2 * x2 + 4
      proper	w: x1
      ok	w: 2 * x1 + 4
      from	w: x1
      mark	w: x1 + 1
      active	w: 2 * x1 + 3
      cons	w: x1 + x2 + 1
Number of strict rules: 15
Direct POLO(bPol) ... removes: 20
      s 	w: x1
      top	w: x1
      2nd	w: x1
      cons1	w: x1 + x2 + 1
      proper	w: 2 * x1
      ok	w: 2 * x1 + 4
      from	w: x1
      mark	w: x1 + 1
      active	w: 2 * x1 + 4
      cons	w: x1 + x2
Number of strict rules: 14
Direct POLO(bPol) ... removes: 18 16 19 17
      s 	w: x1 + 1
      top	w: x1
      2nd	w: x1 + 1
      cons1	w: 2 * x1 + 2 * x2 + 6
      proper	w: 2 * x1 + 2
      ok	w: x1 + 1
      from	w: x1 + 1
      mark	w: x1 + 1
      active	w: x1 + 2
      cons	w: x1 + x2 + 3
Number of strict rules: 10
Direct POLO(bPol) ... removes: 11
      s 	w: x1 + 1
      top	w: x1
      2nd	w: x1 + 1
      cons1	w: 2 * x1 + x2 + 1
      proper	w: x1 + 30
      ok	w: x1 + 1
      from	w: x1 + 2
      mark	w: x1 + 29
      active	w: x1 + 2
      cons	w: 2 * x1 + x2 + 1
Number of strict rules: 9
Direct POLO(bPol) ... removes: 10 13
      s 	w: 2 * x1 + 2
      top	w: x1
      2nd	w: 2 * x1 + 2
      cons1	w: 2 * x1 + x2 + 1
      proper	w: x1 + 30
      ok	w: x1
      from	w: x1
      mark	w: x1 + 29
      active	w: 2 * x1 + 2
      cons	w: 2 * x1 + x2 + 1
Number of strict rules: 7
Direct POLO(bPol) ... removes: 4 7
      s 	w: 2 * x1 + 3
      top	w: x1
      2nd	w: 2 * x1 + 3
      cons1	w: 2 * x1 + x2 + 1
      proper	w: x1 + 30
      ok	w: x1
      from	w: x1
      mark	w: x1 + 29
      active	w: 2 * x1 + 2
      cons	w: 2 * x1 + x2 + 1
Number of strict rules: 5
Direct POLO(bPol) ... removes: 6
      s 	w: x1
      top	w: x1
      2nd	w: 2 * x1 + 1
      cons1	w: 2 * x1 + x2
      proper	w: x1 + 1
      ok	w: x1
      from	w: x1 + 1
      mark	w: x1 + 29
      active	w: 2 * x1 + 2
      cons	w: 2 * x1 + x2 + 1
Number of strict rules: 4
Direct POLO(bPol) ... removes: 12 23 24
      s 	w: 2 * x1 + 7
      top	w: x1
      2nd	w: x1 + 1
      cons1	w: 2 * x1 + x2 + 1
      proper	w: 2 * x1 + 8
      ok	w: x1 + 1
      from	w: 2 * x1 + 1
      mark	w: 2 * x1 + 6
      active	w: x1 + 2
      cons	w: x1 + x2 + 1
Number of strict rules: 1
Direct POLO(bPol) ... removes: 21
      s 	w: x1 + 2
      top	w: x1
      2nd	w: 2 * x1 + 1
      cons1	w: x1 + x2 + 2
      proper	w: 2 * x1 + 28
      ok	w: x1 + 1
      from	w: 2 * x1 + 1
      mark	w: x1 + 26
      active	w: 2 * x1 + 2
      cons	w: x1 + x2 + 1
Number of strict rules: 0