/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: app(app(max(),0()),x) -> x
    2: app(app(max(),x),0()) -> x
    3: app(app(max(),app(s(),x)),app(s(),y)) -> app(app(max(),x),y)
    4: app(app(min(),0()),x) -> 0()
    5: app(app(min(),x),0()) -> 0()
    6: app(app(min(),app(s(),x)),app(s(),y)) -> app(app(min(),x),y)
    7: app(app(app(app(insert(),f),g),nil()),x) -> app(app(cons(),x),nil())
    8: app(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app(app(cons(),app(app(f,x),h)),app(app(app(app(insert(),f),g),t),app(app(g,x),h)))
    9: app(app(app(sort(),f),g),nil()) -> nil()
    10: app(app(app(sort(),f),g),app(app(cons(),h),t)) -> app(app(app(app(insert(),f),g),app(app(app(sort(),f),g),t)),h)
    11: app(ascending_sort(),l) -> app(app(app(sort(),min()),max()),l)
    12: app(descending_sort(),l) -> app(app(app(sort(),max()),min()),l)
Number of strict rules: 12
Direct poly ... failed.
Freezing app
1: app❆2_max(0(),x) -> x
2: app❆2_max(x,0()) -> x
3: app❆2_max(app❆1_s(x),app❆1_s(y)) -> app❆2_max(x,y)
4: app❆2_min(0(),x) -> 0()
5: app❆2_min(x,0()) -> 0()
6: app❆2_min(app❆1_s(x),app❆1_s(y)) -> app❆2_min(x,y)
7: app❆4_insert(f,g,nil(),x) -> app❆2_cons(x,nil())
8: app❆4_insert(f,g,app❆2_cons(h,t),x) -> app❆2_cons(app(app(f,x),h),app❆4_insert(f,g,t,app(app(g,x),h)))
9: app❆3_sort(f,g,nil()) -> nil()
10: app❆3_sort(f,g,app❆2_cons(h,t)) -> app❆4_insert(f,g,app❆3_sort(f,g,t),h)
11: app❆1_ascending_sort(l) -> app❆3_sort(min(),max(),l)
12: app❆1_descending_sort(l) -> app❆3_sort(max(),min(),l)
13: app(min(),_1) ->= app❆1_min(_1)
14: app(app❆1_min(_1),_2) ->= app❆2_min(_1,_2)
15: app(cons(),_1) ->= app❆1_cons(_1)
16: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
17: app(max(),_1) ->= app❆1_max(_1)
18: app(app❆1_max(_1),_2) ->= app❆2_max(_1,_2)
19: app(s(),_1) ->= app❆1_s(_1)
20: app(descending_sort(),_1) ->= app❆1_descending_sort(_1)
21: app(sort(),_1) ->= app❆1_sort(_1)
22: app(app❆1_sort(_1),_2) ->= app❆2_sort(_1,_2)
23: app(app❆2_sort(_1,_2),_3) ->= app❆3_sort(_1,_2,_3)
24: app(ascending_sort(),_1) ->= app❆1_ascending_sort(_1)
25: app(insert(),_1) ->= app❆1_insert(_1)
26: app(app❆1_insert(_1),_2) ->= app❆2_insert(_1,_2)
27: app(app❆2_insert(_1,_2),_3) ->= app❆3_insert(_1,_2,_3)
28: app(app❆3_insert(_1,_2,_3),_4) ->= app❆4_insert(_1,_2,_3,_4)
Number of strict rules: 12
Direct poly ... failed.
Dependency Pairs:
   #1: #app❆2_min(app❆1_s(x),app❆1_s(y)) -> #app❆2_min(x,y)
   #2: #app❆1_ascending_sort(l) -> #app❆3_sort(min(),max(),l)
   #3: #app(ascending_sort(),_1) ->? #app❆1_ascending_sort(_1)
   #4: #app(app❆2_sort(_1,_2),_3) ->? #app❆3_sort(_1,_2,_3)
   #5: #app❆1_descending_sort(l) -> #app❆3_sort(max(),min(),l)
   #6: #app(app❆1_min(_1),_2) ->? #app❆2_min(_1,_2)
   #7: #app(descending_sort(),_1) ->? #app❆1_descending_sort(_1)
   #8: #app❆3_sort(f,g,app❆2_cons(h,t)) -> #app❆4_insert(f,g,app❆3_sort(f,g,t),h)
   #9: #app❆3_sort(f,g,app❆2_cons(h,t)) -> #app❆3_sort(f,g,t)
   #10: #app(app❆3_insert(_1,_2,_3),_4) ->? #app❆4_insert(_1,_2,_3,_4)
   #11: #app❆2_max(app❆1_s(x),app❆1_s(y)) -> #app❆2_max(x,y)
   #12: #app❆4_insert(f,g,app❆2_cons(h,t),x) -> #app(app(f,x),h)
   #13: #app❆4_insert(f,g,app❆2_cons(h,t),x) -> #app(f,x)
   #14: #app❆4_insert(f,g,app❆2_cons(h,t),x) -> #app❆4_insert(f,g,t,app(app(g,x),h))
   #15: #app❆4_insert(f,g,app❆2_cons(h,t),x) -> #app(app(g,x),h)
   #16: #app❆4_insert(f,g,app❆2_cons(h,t),x) -> #app(g,x)
   #17: #app(app❆1_max(_1),_2) ->? #app❆2_max(_1,_2)
Number of SCCs: 3, DPs: 15
	SCC { #1 }
Sum... succeeded.
  s()		w: (0)
  app❆2_insert(x1,x2)		w: (0)
  insert()		w: (0)
  app❆2_sort(x1,x2)		w: (0)
  #app❆2_max(x1,x2)		w: (0)
  #app❆1_descending_sort(x1)		w: (0)
  app❆1_sort(x1)		w: (0)
  app❆2_max(x1,x2)		w: (0)
  app❆1_min(x1)		w: (0)
  app❆3_sort(x1,x2,x3)		w: (0)
  app❆4_insert(x1,x2,x3,x4)		w: (0)
  descending_sort()		w: (0)
  app❆1_descending_sort(x1)		w: (0)
  app❆3_insert(x1,x2,x3)		w: (0)
  #app❆4_insert(x1,x2,x3,x4)		w: (0)
  app❆1_insert(x1)		w: (0)
  0()		w: (0)
  max()		w: (0)
  #app❆1_ascending_sort(x1)		w: (0)
  nil()		w: (0)
  app❆1_ascending_sort(x1)		w: (0)
  app❆2_min(x1,x2)		w: (0)
  #app(x1,x2)		w: (0)
  sort()		w: (0)
  ascending_sort()		w: (0)
  min()		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  #app❆3_sort(x1,x2,x3)		w: (0)
  app❆1_s(x1)		w: (1 + x1)
  app❆1_cons(x1)		w: (0)
  #app❆2_min(x1,x2)		w: (x2 + x1)
  app❆1_max(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 14
	SCC { #11 }
Sum... succeeded.
  s()		w: (0)
  app❆2_insert(x1,x2)		w: (0)
  insert()		w: (0)
  app❆2_sort(x1,x2)		w: (0)
  #app❆2_max(x1,x2)		w: (x2)
  #app❆1_descending_sort(x1)		w: (0)
  app❆1_sort(x1)		w: (0)
  app❆2_max(x1,x2)		w: (0)
  app❆1_min(x1)		w: (0)
  app❆3_sort(x1,x2,x3)		w: (0)
  app❆4_insert(x1,x2,x3,x4)		w: (0)
  descending_sort()		w: (0)
  app❆1_descending_sort(x1)		w: (0)
  app❆3_insert(x1,x2,x3)		w: (0)
  #app❆4_insert(x1,x2,x3,x4)		w: (0)
  app❆1_insert(x1)		w: (0)
  0()		w: (0)
  max()		w: (0)
  #app❆1_ascending_sort(x1)		w: (0)
  nil()		w: (0)
  app❆1_ascending_sort(x1)		w: (0)
  app❆2_min(x1,x2)		w: (0)
  #app(x1,x2)		w: (0)
  sort()		w: (0)
  ascending_sort()		w: (0)
  min()		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  #app❆3_sort(x1,x2,x3)		w: (0)
  app❆1_s(x1)		w: (1 + x1)
  app❆1_cons(x1)		w: (0)
  #app❆2_min(x1,x2)		w: (0)
  app❆1_max(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 1, DPs: 13
	SCC { #2..5 #7..10 #12..16 }
Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... sum_sum_int,sum_neg... heuristic_int,sum_neg... failed.
Finding a loop...  failed.