/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(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 POLO(bPol) ... failed.
Uncurrying 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 POLO(bPol) ... 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 }
POLO(Sum)... succeeded.
      neq	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_neq	w: x1 + x2
      app^2_filtersub	w: 0
      false	w: 0
      nonzero	w: 0
      true	w: 0
      app^2_neq	w: 0
      app^1_neq	w: 0
      filtersub	w: 0
      0 	w: 0
      app^3_filtersub	w: 0
      nil	w: 0
      app^1_filtersub	w: 0
      #app	w: 0
      app^1_filter	w: 0
      #app^3_filtersub	w: 0
      #nonzero	w: 0
      cons	w: 0
      filter	w: 0
      app^2_filter	w: 0
      app^2_cons	w: 0
      app^1_s	w: x1 + 1
      #app^2_filter	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 6
  SCC { #1 #2 #4..7 }
POLO(Sum)... succeeded.
      neq	w: 1
      s 	w: 1
      app^1_cons	w: 1
      #app^2_neq	w: 0
      app^2_filtersub	w: x1 + x2 + 2
      false	w: 1
      nonzero	w: 0
      true	w: 1
      app^2_neq	w: 0
      app^1_neq	w: 1
      filtersub	w: 1
      0 	w: 1
      app^3_filtersub	w: x1 + x2 + 2
      nil	w: 4
      app^1_filtersub	w: 1
      #app	w: x1 + x2
      app^1_filter	w: x1 + 2
      #app^3_filtersub	w: x2 + x3
      #nonzero	w: 0
      cons	w: 1
      filter	w: 1
      app^2_filter	w: x1 + 3
      app^2_cons	w: x1 + x2 + 2
      app^1_s	w: 1
      #app^2_filter	w: x1 + x2 + 1
      app	w: 1
    USABLE RULES: { }
    Removed DPs: #1 #2 #4..7
Number of SCCs: 0, DPs: 0