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