/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 poly ... removes: 4 8 1 3 21 26 27 22 5 10 25 12 23 11 9 6 2
  s(x1)		w: (x1)
  top(x1)		w: (12104 + x1)
  2nd(x1)		w: (2 + 2 * x1)
  cons1(x1,x2)		w: (1 + x2 + x1)
  proper(x1)		w: (x1)
  ok(x1)		w: (4 + 2 * x1)
  from(x1)		w: (3 + 2 * x1)
  mark(x1)		w: (1 + x1)
  active(x1)		w: (1 + 2 * x1)
  cons(x1,x2)		w: (2 + x2 + 2 * x1)
Number of strict rules: 10
Direct poly ... removes: 15
  s(x1)		w: (x1)
  top(x1)		w: (25928 + x1)
  2nd(x1)		w: (1 + 2 * x1)
  cons1(x1,x2)		w: (2 + 2 * x2 + x1)
  proper(x1)		w: (x1)
  ok(x1)		w: (1 + 2 * x1)
  from(x1)		w: (1 + 2 * x1)
  mark(x1)		w: (1 + x1)
  active(x1)		w: (2 + 2 * x1)
  cons(x1,x2)		w: (2 + x2 + 2 * x1)
Number of strict rules: 9
Direct poly ... removes: 16 20
  s(x1)		w: (x1)
  top(x1)		w: (28254 + 2 * x1)
  2nd(x1)		w: (1 + x1)
  cons1(x1,x2)		w: (2 + 2 * x2 + x1)
  proper(x1)		w: (2 * x1)
  ok(x1)		w: (1 + 2 * x1)
  from(x1)		w: (2 * x1)
  mark(x1)		w: (1 + x1)
  active(x1)		w: (2 + 2 * x1)
  cons(x1,x2)		w: (x2 + x1)
Number of strict rules: 7
Direct poly ... removes: 14
  s(x1)		w: (x1)
  top(x1)		w: (28254 + 2 * x1)
  2nd(x1)		w: (1 + x1)
  cons1(x1,x2)		w: (3 + 2 * x2 + 2 * x1)
  proper(x1)		w: (x1)
  ok(x1)		w: (1 + 2 * x1)
  from(x1)		w: (2 * x1)
  mark(x1)		w: (1 + x1)
  active(x1)		w: (3 + 2 * x1)
  cons(x1,x2)		w: (x2 + x1)
Number of strict rules: 6
Direct poly ... removes: 17
  s(x1)		w: (x1)
  top(x1)		w: (57416 + 2 * x1)
  2nd(x1)		w: (8483 + 2 * x1)
  cons1(x1,x2)		w: (20952 + x2 + 2 * x1)
  proper(x1)		w: (1 + 2 * x1)
  ok(x1)		w: (1 + x1)
  from(x1)		w: (x1)
  mark(x1)		w: (1 + x1)
  active(x1)		w: (20950 + 2 * x1)
  cons(x1,x2)		w: (20949 + x2 + x1)
Number of strict rules: 5
Direct poly ... removes: 18
  s(x1)		w: (x1)
  top(x1)		w: (57416 + 2 * x1)
  2nd(x1)		w: (1 + 2 * x1)
  cons1(x1,x2)		w: (2 + x2 + 2 * x1)
  proper(x1)		w: (1 + 2 * x1)
  ok(x1)		w: (1 + 2 * x1)
  from(x1)		w: (1 + x1)
  mark(x1)		w: (1 + x1)
  active(x1)		w: (2 + 2 * x1)
  cons(x1,x2)		w: (1 + x2 + x1)
Number of strict rules: 4
Direct poly ... removes: 7
  s(x1)		w: (8702 + x1)
  top(x1)		w: (57416 + 2 * x1)
  2nd(x1)		w: (1 + 2 * x1)
  cons1(x1,x2)		w: (27072 + x2 + 2 * x1)
  proper(x1)		w: (167909 + x1)
  ok(x1)		w: (24636 + x1)
  from(x1)		w: (1 + x1)
  mark(x1)		w: (167908 + x1)
  active(x1)		w: (27073 + 2 * x1)
  cons(x1,x2)		w: (8136 + x2 + x1)
Number of strict rules: 3
Direct poly ... removes: 24 13
  s(x1)		w: (21195 + 2 * x1)
  top(x1)		w: (57416 + x1)
  2nd(x1)		w: (13068 + x1)
  cons1(x1,x2)		w: (63589 + 2 * x2 + 2 * x1)
  proper(x1)		w: (x1)
  ok(x1)		w: (21196 + 2 * x1)
  from(x1)		w: (1 + x1)
  mark(x1)		w: (182641 + 2 * x1)
  active(x1)		w: (21197 + x1)
  cons(x1,x2)		w: (42393 + 2 * x2 + x1)
Number of strict rules: 1
Direct poly ... removes: 19
  s(x1)		w: (1 + x1)
  top(x1)		w: (57416 + 2 * x1)
  2nd(x1)		w: (8924 + 2 * x1)
  cons1(x1,x2)		w: (3 + 2 * x2 + x1)
  proper(x1)		w: (124930 + 2 * x1)
  ok(x1)		w: (1 + 2 * x1)
  from(x1)		w: (2806 + 2 * x1)
  mark(x1)		w: (124929 + 2 * x1)
  active(x1)		w: (8924 + 2 * x1)
  cons(x1,x2)		w: (12268 + x2 + x1)
Number of strict rules: 0