/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: app(nil(),k) -> k
    2: app(l,nil()) -> l
    3: app(cons(x,l),k) -> cons(x,app(l,k))
    4: sum(cons(x,nil())) -> cons(x,nil())
    5: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
    6: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
    7: plus(0(),y) -> y
    8: plus(s(x),y) -> s(plus(x,y))
    9: sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l))))
    10: pred(cons(s(x),nil())) -> cons(x,nil())
Number of strict rules: 10
Direct poly ... removes: 1 5 10 7 9 2
  s(x1)		w: (1 + x1)
  pred(x1)		w: (x1)
  sum(x1)		w: (x1)
  0()		w: (591)
  nil()		w: (1)
  plus(x1,x2)		w: (1 + x2 + x1)
  cons(x1,x2)		w: (2448 + x2 + x1)
  app(x1,x2)		w: (1 + 2 * x2 + x1)
Number of strict rules: 4
Direct poly ... removes: 8
  s(x1)		w: (1 + x1)
  pred(x1)		w: (x1)
  sum(x1)		w: (x1)
  0()		w: (1)
  nil()		w: (1)
  plus(x1,x2)		w: (1 + x2 + 2 * x1)
  cons(x1,x2)		w: (1 + x2 + x1)
  app(x1,x2)		w: (1 + 2 * x2 + x1)
Number of strict rules: 3
Direct poly ... removes: 3
  s(x1)		w: (4 + x1)
  pred(x1)		w: (x1)
  sum(x1)		w: (x1)
  0()		w: (1)
  nil()		w: (31112)
  plus(x1,x2)		w: (1 + x2 + 2 * x1)
  cons(x1,x2)		w: (2 + x2 + x1)
  app(x1,x2)		w: (17067 + 2 * x2 + 2 * x1)
Number of strict rules: 2
Direct poly ... failed.
Freezing sum
4: sum❆1_cons(x,nil()) -> cons(x,nil())
6: sum❆1_app(l,cons(x,cons(y,k))) -> sum❆1_app(l,sum❆1_cons(x,cons(y,k)))
11: sum(cons(_1,_2)) ->= sum❆1_cons(_1,_2)
12: sum(app(_1,_2)) ->= sum❆1_app(_1,_2)
Number of strict rules: 2
Direct poly ... removes: 4 12 11 6
  sum❆1_app(x1,x2)		w: (2 * x2 + x1)
  s(x1)		w: (x1)
  sum❆1_cons(x1,x2)		w: (16735 + x2 + 2 * x1)
  pred(x1)		w: (x1)
  sum(x1)		w: (2 * x1)
  0()		w: (0)
  nil()		w: (1)
  plus(x1,x2)		w: (x2 + x1)
  cons(x1,x2)		w: (8368 + 2 * x2 + 2 * x1)
  app(x1,x2)		w: (1 + x2 + x1)
Number of strict rules: 0