/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(neq(),0()),0()) -> false()
    2: app(app(neq(),0()),app(s(),y)) -> true()
    3: app(app(neq(),app(s(),x)),0()) -> true()
    4: app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
    5: app(app(filter(),f),nil()) -> nil()
    6: app(app(filter(),f),app(app(cons(),y),ys)) -> app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    7: app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app(app(cons(),y),app(app(filter(),f),ys))
    8: app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
    9: nonzero() -> app(filter(),app(neq(),0()))
Number of strict rules: 9
Direct poly ... failed.
Freezing app
1: app❆2_neq(0(),0()) -> false()
2: app❆2_neq(0(),app❆1_s(y)) -> true()
3: app❆2_neq(app❆1_s(x),0()) -> true()
4: app❆2_neq(app❆1_s(x),app❆1_s(y)) -> app❆2_neq(x,y)
5: app❆2_filter(f,nil()) -> nil()
6: app❆2_filter(f,app❆2_cons(y,ys)) -> app❆3_filtersub(app(f,y),f,app❆2_cons(y,ys))
7: app❆3_filtersub(true(),f,app❆2_cons(y,ys)) -> app❆2_cons(y,app❆2_filter(f,ys))
8: app❆3_filtersub(false(),f,app❆2_cons(y,ys)) -> app❆2_filter(f,ys)
9: nonzero() -> app❆1_filter(app❆1_neq(0()))
10: app(cons(),_1) ->= app❆1_cons(_1)
11: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
12: app(neq(),_1) ->= app❆1_neq(_1)
13: app(app❆1_neq(_1),_2) ->= app❆2_neq(_1,_2)
14: app(s(),_1) ->= app❆1_s(_1)
15: app(filter(),_1) ->= app❆1_filter(_1)
16: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
17: app(filtersub(),_1) ->= app❆1_filtersub(_1)
18: app(app❆1_filtersub(_1),_2) ->= app❆2_filtersub(_1,_2)
19: app(app❆2_filtersub(_1,_2),_3) ->= app❆3_filtersub(_1,_2,_3)
Number of strict rules: 9
Direct poly ... failed.
Dependency Pairs:
   #1: #app❆2_filter(f,app❆2_cons(y,ys)) -> #app❆3_filtersub(app(f,y),f,app❆2_cons(y,ys))
   #2: #app❆2_filter(f,app❆2_cons(y,ys)) -> #app(f,y)
   #3: #app(app❆1_neq(_1),_2) ->? #app❆2_neq(_1,_2)
   #4: #app❆3_filtersub(true(),f,app❆2_cons(y,ys)) -> #app❆2_filter(f,ys)
   #5: #app(app❆2_filtersub(_1,_2),_3) ->? #app❆3_filtersub(_1,_2,_3)
   #6: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #7: #app❆3_filtersub(false(),f,app❆2_cons(y,ys)) -> #app❆2_filter(f,ys)
   #8: #app❆2_neq(app❆1_s(x),app❆1_s(y)) -> #app❆2_neq(x,y)
Number of SCCs: 2, DPs: 7
	SCC { #8 }
Sum... succeeded.
  neq()		w: (0)
  s()		w: (0)
  app❆1_filtersub(x1)		w: (0)
  app❆2_filtersub(x1,x2)		w: (0)
  false()		w: (0)
  nonzero()		w: (0)
  true()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  filtersub()		w: (0)
  app❆2_neq(x1,x2)		w: (0)
  0()		w: (0)
  nil()		w: (0)
  #app❆2_neq(x1,x2)		w: (x2 + x1)
  app❆1_filter(x1)		w: (0)
  #app(x1,x2)		w: (0)
  app❆1_neq(x1)		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  #nonzero()		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  filter()		w: (0)
  app❆1_s(x1)		w: (1 + x1)
  app❆3_filtersub(x1,x2,x3)		w: (0)
  #app❆3_filtersub(x1,x2,x3)		w: (0)
  app❆1_cons(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 6
	SCC { #1 #2 #4..7 }
Sum... succeeded.
  neq()		w: (1)
  s()		w: (1)
  app❆1_filtersub(x1)		w: (32287 + x1)
  app❆2_filtersub(x1,x2)		w: (32287 + x2 + x1)
  false()		w: (49020)
  nonzero()		w: (0)
  true()		w: (72941)
  app❆2_filter(x1,x2)		w: (105229 + x1)
  filtersub()		w: (1)
  app❆2_neq(x1,x2)		w: (32287 + x2 + x1)
  0()		w: (8366)
  nil()		w: (105230)
  #app❆2_neq(x1,x2)		w: (0)
  app❆1_filter(x1)		w: (32287 + x1)
  #app(x1,x2)		w: (40657 + x2 + x1)
  app❆1_neq(x1)		w: (32287 + x1)
  #app❆2_filter(x1,x2)		w: (1 + x2 + x1)
  #nonzero()		w: (0)
  cons()		w: (1)
  app❆2_cons(x1,x2)		w: (40657 + x2 + x1)
  filter()		w: (1)
  app❆1_s(x1)		w: (32287 + x1)
  app❆3_filtersub(x1,x2,x3)		w: (32287 + x3 + x2 + x1)
  #app❆3_filtersub(x1,x2,x3)		w: (x3 + x2)
  app❆1_cons(x1)		w: (32287 + x1)
  app(x1,x2)		w: (32286)
    USABLE RULES: { }
    Removed DPs: #1 #2 #4..7
Number of SCCs: 0, DPs: 0