/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(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) -> app(app(:(),app(app(:(),x),z)),app(app(:(),app(app(:(),app(app(:(),x),y)),z)),u))
    2: app(app(map(),f),nil()) -> nil()
    3: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    4: app(app(filter(),f),nil()) -> nil()
    5: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
    6: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
    7: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 7
Direct poly ... failed.
Freezing app
1: app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> app❆2_:(app❆2_:(x,z),app❆2_:(app❆2_:(app❆2_:(x,y),z),u))
2: app❆2_map(f,nil()) -> nil()
3: app❆2_map(f,app❆2_cons(x,xs)) -> app❆2_cons(app(f,x),app❆2_map(f,xs))
4: app❆2_filter(f,nil()) -> nil()
5: app❆2_filter(f,app❆2_cons(x,xs)) -> app❆4_filter2(app(f,x),f,x,xs)
6: app❆4_filter2(true(),f,x,xs) -> app❆2_cons(x,app❆2_filter(f,xs))
7: app❆4_filter2(false(),f,x,xs) -> app❆2_filter(f,xs)
8: app(cons(),_1) ->= app❆1_cons(_1)
9: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
10: app(:(),_1) ->= app❆1_:(_1)
11: app(app❆1_:(_1),_2) ->= app❆2_:(_1,_2)
12: app(filter(),_1) ->= app❆1_filter(_1)
13: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
14: app(map(),_1) ->= app❆1_map(_1)
15: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
16: app(filter2(),_1) ->= app❆1_filter2(_1)
17: app(app❆1_filter2(_1),_2) ->= app❆2_filter2(_1,_2)
18: app(app❆2_filter2(_1,_2),_3) ->= app❆3_filter2(_1,_2,_3)
19: app(app❆3_filter2(_1,_2,_3),_4) ->= app❆4_filter2(_1,_2,_3,_4)
Number of strict rules: 7
Direct poly ... failed.
Dependency Pairs:
   #1: #app❆4_filter2(true(),f,x,xs) -> #app❆2_filter(f,xs)
   #2: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #3: #app(app❆1_:(_1),_2) ->? #app❆2_:(_1,_2)
   #4: #app❆4_filter2(false(),f,x,xs) -> #app❆2_filter(f,xs)
   #5: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app❆4_filter2(app(f,x),f,x,xs)
   #6: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app(f,x)
   #7: #app(app❆3_filter2(_1,_2,_3),_4) ->? #app❆4_filter2(_1,_2,_3,_4)
   #8: #app❆2_map(f,app❆2_cons(x,xs)) -> #app(f,x)
   #9: #app❆2_map(f,app❆2_cons(x,xs)) -> #app❆2_map(f,xs)
   #10: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(app❆2_:(x,z),app❆2_:(app❆2_:(app❆2_:(x,y),z),u))
   #11: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(x,z)
   #12: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(app❆2_:(app❆2_:(x,y),z),u)
   #13: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(app❆2_:(x,y),z)
   #14: #app❆2_:(app❆2_:(app❆2_:(app❆2_:(C(),x),y),z),u) -> #app❆2_:(x,y)
   #15: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
Number of SCCs: 2, DPs: 13
	SCC { #1 #2 #4 #6..9 #15 }
Sum... succeeded.
  #app❆2_map(x1,x2)		w: (21238 + x2 + x1)
  app❆1_map(x1)		w: (21239 + x1)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  false()		w: (1)
  app❆2_:(x1,x2)		w: (0)
  C()		w: (0)
  app❆1_:(x1)		w: (0)
  true()		w: (1)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  :()		w: (0)
  nil()		w: (0)
  app❆1_filter(x1)		w: (7720 + x1)
  #app(x1,x2)		w: (x2 + x1)
  map()		w: (0)
  #app❆4_filter2(x1,x2,x3,x4)		w: (7719 + x4 + x2 + x1)
  app❆2_filter2(x1,x2)		w: (0)
  #app❆2_filter(x1,x2)		w: (7719 + x2 + x1)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (1 + x2 + x1)
  filter()		w: (0)
  app❆1_filter2(x1)		w: (0)
  #app❆2_:(x1,x2)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (7758 + x2 + x1)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1 #2 #4 #6..9 #15
Number of SCCs: 1, DPs: 5
	SCC { #10..14 }
Sum... Max... succeeded.
  #app❆2_map(x1,x2)		w: (0)
  app❆1_map(x1)		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  false()		w: (0)
  app❆2_:(x1,x2)		w: (max{x2, 21239 + x1})
  C()		w: (0)
  app❆1_:(x1)		w: (0)
  true()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  :()		w: (0)
  nil()		w: (0)
  app❆1_filter(x1)		w: (0)
  #app(x1,x2)		w: (0)
  map()		w: (0)
  #app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_filter2(x1,x2)		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  filter()		w: (0)
  app❆1_filter2(x1)		w: (0)
  #app❆2_:(x1,x2)		w: (max{0, 39 + x1})
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { 1 }
    Removed DPs: #11 #13 #14
Number of SCCs: 1, DPs: 2
	SCC { #10 #12 }
Sum... Max... QLPOpS... succeeded.
  #app❆2_map(x1,x2)	0[x2,x1]
  app❆1_map(x1)	0[]
  app❆4_filter2(x1,x2,x3,x4)	0[x3,x4,x1]
  app❆2_map(x1,x2)	0[x1,x2]
  false()	0
  app❆2_:(x1,x2)	1[x1,x2]
  C()	0
  app❆1_:(x1)	0[]
  true()	0
  filter2()	0
  app❆2_filter(x1,x2)	0[x2]
  :()	0
  nil()	0
  app❆1_filter(x1)	0[]
  #app(x1,x2)	0[x1,x2]
  map()	0
  #app❆4_filter2(x1,x2,x3,x4)	0[x2,x4,x1,x3]
  app❆2_filter2(x1,x2)	0[x2]
  #app❆2_filter(x1,x2)	0[x2]
  cons()	0
  app❆2_cons(x1,x2)	0[x1,x2]
  filter()	0
  app❆1_filter2(x1)	0[]
  #app❆2_:(x1,x2)	1[x1]
  app❆1_cons(x1)	0[]
  app❆3_filter2(x1,x2,x3)	0[x1]
  app(x1,x2)	0[x2]
    USABLE RULES: { 1 }
    Removed DPs: #12
Number of SCCs: 1, DPs: 1
	SCC { #10 }
Sum... Max... QLPOpS... succeeded.
  #app❆2_map(x1,x2)	0[x2,x1]
  app❆1_map(x1)	0[]
  app❆4_filter2(x1,x2,x3,x4)	0[x3,x4,x1]
  app❆2_map(x1,x2)	0[x1,x2]
  false()	0
  app❆2_:(x1,x2)	2[x1,x2]
  C()	0
  app❆1_:(x1)	0[]
  true()	0
  filter2()	0
  app❆2_filter(x1,x2)	0[x2]
  :()	0
  nil()	0
  app❆1_filter(x1)	0[]
  #app(x1,x2)	0[x1,x2]
  map()	0
  #app❆4_filter2(x1,x2,x3,x4)	0[x2,x4,x1,x3]
  app❆2_filter2(x1,x2)	0[x2]
  #app❆2_filter(x1,x2)	0[x2]
  cons()	0
  app❆2_cons(x1,x2)	0[x1,x2]
  filter()	0
  app❆1_filter2(x1)	0[]
  #app❆2_:(x1,x2)	1[x1]
  app❆1_cons(x1)	0[]
  app❆3_filter2(x1,x2,x3)	0[x1]
  app(x1,x2)	0[x2]
    USABLE RULES: { 1 }
    Removed DPs: #10
Number of SCCs: 0, DPs: 0