/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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NO
Input TRS:
    1: incr(nil()) -> nil()
    2: incr(cons(X,L)) -> cons(s(X),n__incr(activate(L)))
    3: adx(nil()) -> nil()
    4: adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L))))
    5: nats() -> adx(zeros())
    6: zeros() -> cons(0(),n__zeros())
    7: head(cons(X,L)) -> X
    8: tail(cons(X,L)) -> activate(L)
    9: incr(X) -> n__incr(X)
    10: adx(X) -> n__adx(X)
    11: zeros() -> n__zeros()
    12: activate(n__incr(X)) -> incr(activate(X))
    13: activate(n__adx(X)) -> adx(activate(X))
    14: activate(n__zeros()) -> zeros()
    15: activate(X) -> X
Number of strict rules: 15
Direct POLO(bPol) ... removes: 8 3 5 7
      incr	w: x1
      s 	w: x1
      n__adx	w: x1 + 1
      activate	w: x1
      n__zeros	w: 1
      adx	w: x1 + 1
      zeros	w: 1
      tail	w: x1 + 1
      0 	w: 0
      nil	w: 1
      nats	w: 6
      head	w: 2 * x1 + 1
      cons	w: x1 + x2
      n__incr	w: x1
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #incr(cons(X,L)) -> #activate(L)
   #2: #activate(n__adx(X)) -> #adx(activate(X))
   #3: #activate(n__adx(X)) -> #activate(X)
   #4: #activate(n__incr(X)) -> #incr(activate(X))
   #5: #activate(n__incr(X)) -> #activate(X)
   #6: #activate(n__zeros()) -> #zeros()
   #7: #adx(cons(X,L)) -> #incr(cons(X,n__adx(activate(L))))
   #8: #adx(cons(X,L)) -> #activate(L)
Number of SCCs: 1, DPs: 7
  SCC { #1..5 #7 #8 }
POLO(Sum)... succeeded.
      #adx	w: x1 + 1
      incr	w: x1
      s 	w: 1
      n__adx	w: x1 + 1
      activate	w: x1
      n__zeros	w: 1
      #activate	w: x1
      adx	w: x1 + 1
      zeros	w: 1
      tail	w: 0
      0 	w: 1
      #zeros	w: 0
      nil	w: 1
      #incr	w: x1
      nats	w: 0
      head	w: 0
      cons	w: x2
      n__incr	w: x1
    USABLE RULES: { 1 2 4 6 9..15 }
    Removed DPs: #3 #8
Number of SCCs: 1, DPs: 5
  SCC { #1 #2 #4 #5 #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      #adx	w: 2
      incr	w: max(x1 + 2, 0)
      s 	w: 1
      n__adx	w: 3
      activate	w: max(x1, 0)
      n__zeros	w: 1
      #activate	w: max(x1 - 1, 0)
      adx	w: 3
      zeros	w: 1
      tail	w: max(x1 - 1, 0)
      0 	w: 1
      #zeros	w: 0
      nil	w: 1
      #incr	w: max(x1 + 1, 0)
      nats	w: 0
      head	w: max(x1 - 1, 0)
      cons	w: max(x2 - 2, 0)
      n__incr	w: max(x1 + 2, 0)
    USABLE RULES: { 1 2 4 6 9..15 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 4
  SCC { #1 #2 #4 #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  found.
  #adx(cons(X_{1},n__zeros()))	-#7->
  #incr(cons(X_{1},n__adx(activate(n__zeros()))))	--->*
  #incr(cons(X_{1},n__adx(activate(n__zeros()))))	-#1->
  #activate(n__adx(activate(n__zeros())))	--->*
  #activate(n__adx(activate(n__zeros())))	-#2->
  #adx(activate(activate(n__zeros())))	--->*
  #adx(cons(0(),n__zeros()))
  Looping with: [ X_{1} := 0(); ]