/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 POLO(bPol) ... failed.
Uncurrying 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 POLO(bPol) ... 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 }
POLO(Sum)... succeeded.
      app^1_cons	w: 0
      #app^2_map	w: x1 + x2
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      app^2_:	w: 0
      #app^2_:	w: 0
      false	w: 1
      app^1_filter2	w: 0
      C 	w: 0
      true	w: 1
      filter2	w: 0
      app^1_:	w: 0
      : 	w: 0
      #app^4_filter2	w: x1 + x2 + x4
      nil	w: 0
      #app	w: x1 + x2
      map	w: 0
      app^1_filter	w: x1 + 1
      cons	w: 0
      filter	w: 0
      app^3_filter2	w: x1 + x2 + x3 + 1
      app^2_filter	w: 0
      app^1_map	w: x1 + 1
      app^2_cons	w: x1 + x2 + 1
      app^2_map	w: 0
      #app^2_filter	w: x1 + x2
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #2 #4 #6..9 #15
Number of SCCs: 1, DPs: 5
  SCC { #10..14 }
POLO(Sum)... POLO(max)... succeeded.
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      app^2_:	w: max(x1 + 1, x2)
      #app^2_:	w: max(x1 + 1)
      false	w: 0
      app^1_filter2	w: 0
      C 	w: 0
      true	w: 0
      filter2	w: 0
      app^1_:	w: 0
      : 	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      #app	w: 0
      map	w: 0
      app^1_filter	w: 0
      cons	w: 0
      filter	w: 0
      app^3_filter2	w: 0
      app^2_filter	w: 0
      app^1_map	w: 0
      app^2_cons	w: 0
      app^2_map	w: 0
      #app^2_filter	w: 0
      app	w: 0
    USABLE RULES: { 1 }
    Removed DPs: #11 #13 #14
Number of SCCs: 1, DPs: 2
  SCC { #10 #12 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      app^1_cons	s: []	p: 0
      #app^2_map	s: []	p: 0
      app^2_filter2	s: [1]	p: 0
      app^4_filter2	s: [3,2,4]	p: 0
      app^2_:	s: [1,2]	p: 1
      #app^2_:	s: [1]	p: 1
      false	s: []	p: 0
      app^1_filter2	s: []	p: 0
      C 	s: []	p: 0
      true	s: []	p: 0
      filter2	s: []	p: 0
      app^1_:	s: []	p: 0
      : 	s: []	p: 0
      #app^4_filter2	s: [1,2,4]	p: 0
      nil	s: []	p: 0
      #app	s: []	p: 0
      map	s: []	p: 0
      app^1_filter	s: []	p: 0
      cons	s: []	p: 0
      filter	s: []	p: 0
      app^3_filter2	s: [1,3]	p: 0
      app^2_filter	s: []	p: 0
      app^1_map	s: []	p: 0
      app^2_cons	s: [2,1]	p: 0
      app^2_map	s: []	p: 0
      #app^2_filter	s: [1]	p: 0
      app	s: [1,2]	p: 0
    USABLE RULES: { 1 }
    Removed DPs: #10 #12
Number of SCCs: 0, DPs: 0