/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: ap(ap(ff(),x),x) -> ap(ap(x,ap(ff(),x)),ap(ap(cons(),x),nil()))
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Uncurrying ap
1: ap^2_ff(x,x) -> ap(ap(x,ap^1_ff(x)),ap^2_cons(x,nil()))
2: ap(cons(),_1) ->= ap^1_cons(_1)
3: ap(ap^1_cons(_1),_2) ->= ap^2_cons(_1,_2)
4: ap(ff(),_1) ->= ap^1_ff(_1)
5: ap(ap^1_ff(_1),_2) ->= ap^2_ff(_1,_2)
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #ap(ap^1_ff(_1),_2) ->? #ap^2_ff(_1,_2)
   #2: #ap^2_ff(x,x) -> #ap(ap(x,ap^1_ff(x)),ap^2_cons(x,nil()))
   #3: #ap^2_ff(x,x) -> #ap(x,ap^1_ff(x))
Number of SCCs: 1, DPs: 3
  SCC { #1..3 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      ap^2_cons	w: 0
      ap	w: max(x1 - 2, x2 - 2, 0)
      ff	w: 4
      #ap^2_ff	w: max(x2 + 1, 0)
      nil	w: 0
      ap^1_ff	w: 2
      #ap	w: max(x1 + x2 - 1, 0)
      cons	w: 5
      ap^2_ff	w: max(x2 - 2, 0)
      ap^1_cons	w: 3
    USABLE RULES: { 1..5 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2
  SCC { #1 #3 }
POLO(Sum)... succeeded.
      ap^2_cons	w: 0
      ap	w: x2 + 2
      ff	w: 1
      #ap^2_ff	w: x1 + 1
      nil	w: 1
      ap^1_ff	w: x1 + 2
      #ap	w: x1
      cons	w: 1
      ap^2_ff	w: 2
      ap^1_cons	w: 1
    USABLE RULES: { 1..5 }
    Removed DPs: #1 #3
Number of SCCs: 0, DPs: 0