/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: app(app(.(),1()),x) -> x
    2: app(app(.(),x),1()) -> x
    3: app(app(.(),app(i(),x)),x) -> 1()
    4: app(app(.(),x),app(i(),x)) -> 1()
    5: app(app(.(),app(i(),y)),app(app(.(),y),z)) -> z
    6: app(app(.(),y),app(app(.(),app(i(),y)),z)) -> z
    7: app(i(),1()) -> 1()
    8: app(i(),app(i(),x)) -> x
    9: app(app(map(),f),nil()) -> nil()
    10: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    11: app(app(filter(),f),nil()) -> nil()
    12: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
    13: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
    14: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 14
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^2_.(1(),x) -> x
2: app^2_.(x,1()) -> x
3: app^2_.(app^1_i(x),x) -> 1()
4: app^2_.(x,app^1_i(x)) -> 1()
5: app^2_.(app^1_i(y),app^2_.(y,z)) -> z
6: app^2_.(y,app^2_.(app^1_i(y),z)) -> z
7: app^1_i(1()) -> 1()
8: app^1_i(app^1_i(x)) -> x
9: app^2_map(f,nil()) -> nil()
10: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
11: app^2_filter(f,nil()) -> nil()
12: app^2_filter(f,app^2_cons(x,xs)) -> app^4_filter2(app(f,x),f,x,xs)
13: app^4_filter2(true(),f,x,xs) -> app^2_cons(x,app^2_filter(f,xs))
14: app^4_filter2(false(),f,x,xs) -> app^2_filter(f,xs)
15: app(cons(),_1) ->= app^1_cons(_1)
16: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
17: app(filter(),_1) ->= app^1_filter(_1)
18: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2)
19: app(map(),_1) ->= app^1_map(_1)
20: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
21: app(filter2(),_1) ->= app^1_filter2(_1)
22: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2)
23: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3)
24: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4)
25: app(.(),_1) ->= app^1_.(_1)
26: app(app^1_.(_1),_2) ->= app^2_.(_1,_2)
27: app(i(),_1) ->= app^1_i(_1)
Number of strict rules: 14
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^4_filter2(true(),f,x,xs) -> #app^2_filter(f,xs)
   #2: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4)
   #3: #app^2_filter(f,app^2_cons(x,xs)) -> #app^4_filter2(app(f,x),f,x,xs)
   #4: #app^2_filter(f,app^2_cons(x,xs)) -> #app(f,x)
   #5: #app^4_filter2(false(),f,x,xs) -> #app^2_filter(f,xs)
   #6: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
   #7: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
   #8: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
   #9: #app(i(),_1) ->? #app^1_i(_1)
   #10: #app(app^1_.(_1),_2) ->? #app^2_.(_1,_2)
   #11: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2)
Number of SCCs: 1, DPs: 9
  SCC { #1..8 #11 }
POLO(Sum)... succeeded.
      1 	w: 2
      #app^2_.	w: 0
      app^1_cons	w: x1 + 1
      #app^2_map	w: x1 + x2
      app^2_filter2	w: x1 + x2 + 3
      app^4_filter2	w: x1
      #app^1_i	w: 0
      false	w: 1
      app^2_.	w: x1 + x2 + 1
      app^1_i	w: 1
      app^1_filter2	w: 1
      true	w: 1
      filter2	w: 1
      #app^4_filter2	w: x2 + x3 + x4 + 1
      nil	w: 2
      #app	w: x1 + x2
      map	w: 1
      app^1_filter	w: x1 + 1
      . 	w: 1
      i 	w: 1
      app^1_.	w: x1 + 1
      cons	w: 1
      filter	w: 1
      app^3_filter2	w: x1 + x2 + x3 + 2
      app^2_filter	w: x1 + x2 + 2
      app^1_map	w: x1 + 2
      app^2_cons	w: x1 + x2 + 2
      app^2_map	w: 1
      #app^2_filter	w: x1 + x2
      app	w: x1 + x2 + 1
    USABLE RULES: { 1..6 }
    Removed DPs: #1..8 #11
Number of SCCs: 0, DPs: 0