/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(not(),app(not(),x)) -> x
    2: app(not(),app(app(or(),x),y)) -> app(app(and(),app(not(),x)),app(not(),y))
    3: app(not(),app(app(and(),x),y)) -> app(app(or(),app(not(),x)),app(not(),y))
    4: app(app(and(),x),app(app(or(),y),z)) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
    5: app(app(and(),app(app(or(),y),z)),x) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
    6: app(app(map(),f),nil()) -> nil()
    7: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    8: app(app(filter(),f),nil()) -> nil()
    9: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
    10: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
    11: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^1_not(app^1_not(x)) -> x
2: app^1_not(app^2_or(x,y)) -> app^2_and(app^1_not(x),app^1_not(y))
3: app^1_not(app^2_and(x,y)) -> app^2_or(app^1_not(x),app^1_not(y))
4: app^2_and(x,app^2_or(y,z)) -> app^2_or(app^2_and(x,y),app^2_and(x,z))
5: app^2_and(app^2_or(y,z),x) -> app^2_or(app^2_and(x,y),app^2_and(x,z))
6: app^2_map(f,nil()) -> nil()
7: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
8: app^2_filter(f,nil()) -> nil()
9: app^2_filter(f,app^2_cons(x,xs)) -> app^4_filter2(app(f,x),f,x,xs)
10: app^4_filter2(true(),f,x,xs) -> app^2_cons(x,app^2_filter(f,xs))
11: app^4_filter2(false(),f,x,xs) -> app^2_filter(f,xs)
12: app(cons(),_1) ->= app^1_cons(_1)
13: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
14: app(filter(),_1) ->= app^1_filter(_1)
15: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2)
16: app(or(),_1) ->= app^1_or(_1)
17: app(app^1_or(_1),_2) ->= app^2_or(_1,_2)
18: app(map(),_1) ->= app^1_map(_1)
19: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
20: app(not(),_1) ->= app^1_not(_1)
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(and(),_1) ->= app^1_and(_1)
26: app(app^1_and(_1),_2) ->= app^2_and(_1,_2)
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^1_not(app^2_or(x,y)) -> #app^2_and(app^1_not(x),app^1_not(y))
   #2: #app^1_not(app^2_or(x,y)) -> #app^1_not(x)
   #3: #app^1_not(app^2_or(x,y)) -> #app^1_not(y)
   #4: #app^2_filter(f,app^2_cons(x,xs)) -> #app^4_filter2(app(f,x),f,x,xs)
   #5: #app^2_filter(f,app^2_cons(x,xs)) -> #app(f,x)
   #6: #app^4_filter2(false(),f,x,xs) -> #app^2_filter(f,xs)
   #7: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4)
   #8: #app(not(),_1) ->? #app^1_not(_1)
   #9: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
   #10: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
   #11: #app^4_filter2(true(),f,x,xs) -> #app^2_filter(f,xs)
   #12: #app^2_and(app^2_or(y,z),x) -> #app^2_and(x,y)
   #13: #app^2_and(app^2_or(y,z),x) -> #app^2_and(x,z)
   #14: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
   #15: #app(app^1_and(_1),_2) ->? #app^2_and(_1,_2)
   #16: #app^1_not(app^2_and(x,y)) -> #app^1_not(x)
   #17: #app^1_not(app^2_and(x,y)) -> #app^1_not(y)
   #18: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2)
   #19: #app^2_and(x,app^2_or(y,z)) -> #app^2_and(x,y)
   #20: #app^2_and(x,app^2_or(y,z)) -> #app^2_and(x,z)
Number of SCCs: 3, DPs: 17
  SCC { #2 #3 #16 #17 }
POLO(Sum)... succeeded.
      app^1_cons	w: 0
      #app^2_map	w: 0
      and	w: 0
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      false	w: 0
      #app^2_and	w: 0
      app^2_or	w: x1 + x2 + 1
      app^1_filter2	w: 0
      true	w: 0
      filter2	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      or	w: 0
      #app	w: 0
      app^1_and	w: 0
      map	w: 0
      app^1_filter	w: 0
      app^2_and	w: x1 + x2 + 1
      app^1_not	w: 0
      cons	w: 0
      app^1_or	w: 0
      filter	w: 0
      app^3_filter2	w: 0
      app^2_filter	w: 0
      app^1_map	w: 0
      #app^1_not	w: x1
      app^2_cons	w: 0
      not	w: 0
      app^2_map	w: 0
      #app^2_filter	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #2 #3 #16 #17
Number of SCCs: 2, DPs: 13
  SCC { #12 #13 #19 #20 }
POLO(Sum)... succeeded.
      app^1_cons	w: 0
      #app^2_map	w: 0
      and	w: 0
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      false	w: 0
      #app^2_and	w: x1 + x2
      app^2_or	w: x1 + x2 + 1
      app^1_filter2	w: 0
      true	w: 0
      filter2	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      or	w: 0
      #app	w: 0
      app^1_and	w: 0
      map	w: 0
      app^1_filter	w: 0
      app^2_and	w: 1
      app^1_not	w: 0
      cons	w: 0
      app^1_or	w: 0
      filter	w: 0
      app^3_filter2	w: 0
      app^2_filter	w: 0
      app^1_map	w: 0
      #app^1_not	w: 0
      app^2_cons	w: 0
      not	w: 0
      app^2_map	w: 0
      #app^2_filter	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #12 #13 #19 #20
Number of SCCs: 1, DPs: 9
  SCC { #4..7 #9..11 #14 #18 }
POLO(Sum)... succeeded.
      app^1_cons	w: 1
      #app^2_map	w: x1 + x2
      and	w: 1
      app^2_filter2	w: 1
      app^4_filter2	w: 4
      false	w: 1
      #app^2_and	w: 0
      app^2_or	w: x1 + x2 + 6
      app^1_filter2	w: 3
      true	w: 1
      filter2	w: 1
      #app^4_filter2	w: x2 + x3 + x4 + 1
      nil	w: 2
      or	w: 1
      #app	w: x1 + x2
      app^1_and	w: 1
      map	w: 1
      app^1_filter	w: x1 + 3
      app^2_and	w: x1 + x2 + 3
      app^1_not	w: x1 + 3
      cons	w: 1
      app^1_or	w: 3
      filter	w: 1
      app^3_filter2	w: x1 + x2 + x3 + 3
      app^2_filter	w: x2 + 5
      app^1_map	w: x1 + 3
      #app^1_not	w: 0
      app^2_cons	w: x1 + x2 + 3
      not	w: 1
      app^2_map	w: 1
      #app^2_filter	w: x1 + x2
      app	w: x1 + 1
    USABLE RULES: { }
    Removed DPs: #4..7 #9..11 #14 #18
Number of SCCs: 0, DPs: 0