/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
Input TRS:
    1: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
    2: sum(cons(0(),x),y) -> sum(x,y)
    3: sum(nil(),y) -> y
    4: weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
    5: weight(cons(n,nil())) -> n
Number of strict rules: 5
Direct poly ... failed.
Freezing sum
1: sum❆1_cons(s(n),x,cons(m,y)) -> sum❆1_cons(n,x,cons(s(m),y))
2: sum❆1_cons(0(),x,y) -> sum(x,y)
3: sum❆1_nil(y) -> y
4: weight(cons(n,cons(m,x))) -> weight(sum❆1_cons(n,cons(m,x),cons(0(),x)))
5: weight(cons(n,nil())) -> n
6: sum(cons(_1,_2),_3) ->= sum❆1_cons(_1,_2,_3)
7: sum(nil(),_1) ->= sum❆1_nil(_1)
Number of strict rules: 5
Direct poly ... removes: 4 3 5 7 6 2
  s(x1)		w: (1 + x1)
  sum❆1_cons(x1,x2,x3)		w: (x3 + x2 + 2 * x1)
  sum(x1,x2)		w: (1 + x2 + x1)
  0()		w: (1)
  nil()		w: (18458)
  weight(x1)		w: (25906 + x1)
  cons(x1,x2)		w: (3 + 2 * x2 + 2 * x1)
  sum❆1_nil(x1)		w: (1 + x1)
Number of strict rules: 1
Direct poly ... removes: 1
  s(x1)		w: (12457 + x1)
  sum❆1_cons(x1,x2,x3)		w: (x3 + x2 + 2 * x1)
  sum(x1,x2)		w: (1 + x2 + x1)
  0()		w: (1)
  nil()		w: (868)
  weight(x1)		w: (99740 + x1)
  cons(x1,x2)		w: (1 + 2 * x2 + x1)
  sum❆1_nil(x1)		w: (x1)
Number of strict rules: 0