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


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MAYBE
Input TRS:
    1: f(s(x)) -> f(id_inc(c(x,x)))
    2: f(c(s(x),y)) -> g(c(x,y))
    3: g(c(s(x),y)) -> g(c(y,x))
    4: g(c(x,s(y))) -> g(c(y,x))
    5: g(c(x,x)) -> f(x)
    6: id_inc(c(x,y)) -> c(id_inc(x),id_inc(y))
    7: id_inc(s(x)) -> s(id_inc(x))
    8: id_inc(0()) -> 0()
    9: id_inc(0()) -> s(0())
Number of strict rules: 9
Direct poly ... failed.
Freezing g id_inc
1: f(s(x)) -> f(id_inc❆1_c(x,x))
2: f(c(s(x),y)) -> g❆1_c(x,y)
3: g❆1_c(s(x),y) -> g❆1_c(y,x)
4: g❆1_c(x,s(y)) -> g❆1_c(y,x)
5: g❆1_c(x,x) -> f(x)
6: id_inc❆1_c(x,y) -> c(id_inc(x),id_inc(y))
7: id_inc❆1_s(x) -> s(id_inc(x))
8: id_inc❆1_0() -> 0()
9: id_inc❆1_0() -> s(0())
10: id_inc(0()) ->= id_inc❆1_0()
11: id_inc(s(_1)) ->= id_inc❆1_s(_1)
12: id_inc(c(_1,_2)) ->= id_inc❆1_c(_1,_2)
13: g(c(_1,_2)) ->= g❆1_c(_1,_2)
Number of strict rules: 9
Direct poly ... removes: 13
  s(x1)		w: (2 * x1)
  g❆1_c(x1,x2)		w: (20976 + x2 + x1)
  id_inc❆1_0()		w: (0)
  c(x1,x2)		w: (x2 + x1)
  f(x1)		w: (20976 + x1)
  0()		w: (0)
  id_inc❆1_c(x1,x2)		w: (x2 + x1)
  id_inc❆1_s(x1)		w: (2 * x1)
  id_inc(x1)		w: (x1)
  g(x1)		w: (20978 + x1)
Number of strict rules: 9
Direct poly ... failed.
Dependency Pairs:
   #1: #f(c(s(x),y)) -> #g❆1_c(x,y)
   #2: #id_inc❆1_c(x,y) -> #id_inc(x)
   #3: #id_inc❆1_c(x,y) -> #id_inc(y)
   #4: #id_inc(s(_1)) ->? #id_inc❆1_s(_1)
   #5: #id_inc(c(_1,_2)) ->? #id_inc❆1_c(_1,_2)
   #6: #id_inc❆1_s(x) -> #id_inc(x)
   #7: #id_inc(0()) ->? #id_inc❆1_0()
   #8: #g❆1_c(x,x) -> #f(x)
   #9: #g❆1_c(s(x),y) -> #g❆1_c(y,x)
   #10: #f(s(x)) -> #f(id_inc❆1_c(x,x))
   #11: #f(s(x)) -> #id_inc❆1_c(x,x)
   #12: #g❆1_c(x,s(y)) -> #g❆1_c(y,x)
Number of SCCs: 2, DPs: 10
	SCC { #2..6 }
Sum... succeeded.
  s(x1)		w: (2 + x1)
  g❆1_c(x1,x2)		w: (0)
  id_inc❆1_0()		w: (0)
  #g❆1_c(x1,x2)		w: (0)
  c(x1,x2)		w: (2 + x2 + x1)
  f(x1)		w: (0)
  #id_inc(x1)		w: (38 + x1)
  #id_inc❆1_0()		w: (0)
  0()		w: (0)
  #f(x1)		w: (0)
  id_inc❆1_c(x1,x2)		w: (0)
  id_inc❆1_s(x1)		w: (0)
  #id_inc❆1_s(x1)		w: (39 + x1)
  id_inc(x1)		w: (0)
  #id_inc❆1_c(x1,x2)		w: (39 + x2 + x1)
  g(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2..6
Number of SCCs: 1, DPs: 5
	SCC { #1 #8..10 #12 }
Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... sum_sum_int,sum_neg... heuristic_int,sum_neg... failed.
Finding a loop...  failed.