/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(map(),f),nil()) -> nil()
    2: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    3: app(app(app(comp(),f),g),x) -> app(f,app(g,x))
    4: app(twice(),f) -> app(app(comp(),f),f)
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^2_map(f,nil()) -> nil()
2: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
3: app^3_comp(f,g,x) -> app(f,app(g,x))
4: app^1_twice(f) -> app^2_comp(f,f)
5: app(cons(),_1) ->= app^1_cons(_1)
6: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
7: app(twice(),_1) ->= app^1_twice(_1)
8: app(map(),_1) ->= app^1_map(_1)
9: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
10: app(comp(),_1) ->= app^1_comp(_1)
11: app(app^1_comp(_1),_2) ->= app^2_comp(_1,_2)
12: app(app^2_comp(_1,_2),_3) ->= app^3_comp(_1,_2,_3)
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
   #2: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
   #3: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
   #4: #app(app^2_comp(_1,_2),_3) ->? #app^3_comp(_1,_2,_3)
   #5: #app(twice(),_1) ->? #app^1_twice(_1)
   #6: #app^3_comp(f,g,x) -> #app(f,app(g,x))
   #7: #app^3_comp(f,g,x) -> #app(g,x)
Number of SCCs: 1, DPs: 6
  SCC { #1..4 #6 #7 }
POLO(Sum)... succeeded.
      app^1_twice	w: 0
      app^1_cons	w: 1
      #app^2_map	w: x1 + 1
      app^2_comp	w: x1 + x2 + 2
      twice	w: 1
      app^1_comp	w: 1
      nil	w: 4
      #app	w: x1
      app^3_comp	w: 1
      map	w: 1
      #app^3_comp	w: x1 + x2 + 1
      cons	w: 1
      app^1_map	w: x1 + 2
      #app^1_twice	w: 0
      app^2_cons	w: x1 + 2
      app^2_map	w: x1 + 3
      comp	w: 1
      app	w: 1
    USABLE RULES: { }
    Removed DPs: #1 #3 #4 #6 #7
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... succeeded.
      app^1_twice	w: 0
      app^1_cons	w: 1
      #app^2_map	w: x2 + 1
      app^2_comp	w: x1 + x2 + 2
      twice	w: 1
      app^1_comp	w: 1
      nil	w: 2
      #app	w: 0
      app^3_comp	w: x3 + 2
      map	w: 1
      #app^3_comp	w: 1
      cons	w: 1
      app^1_map	w: x1 + 2
      #app^1_twice	w: 0
      app^2_cons	w: x2 + 1
      app^2_map	w: 2
      comp	w: 1
      app	w: x2 + 1
    USABLE RULES: { 1 }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0