/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: a__fib(N) -> a__sel(mark(N),a__fib1(s(0()),s(0())))
    2: a__fib1(X,Y) -> cons(mark(X),fib1(Y,add(X,Y)))
    3: a__add(0(),X) -> mark(X)
    4: a__add(s(X),Y) -> s(a__add(mark(X),mark(Y)))
    5: a__sel(0(),cons(X,XS)) -> mark(X)
    6: a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS))
    7: mark(fib(X)) -> a__fib(mark(X))
    8: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    9: mark(fib1(X1,X2)) -> a__fib1(mark(X1),mark(X2))
    10: mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
    11: mark(s(X)) -> s(mark(X))
    12: mark(0()) -> 0()
    13: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    14: a__fib(X) -> fib(X)
    15: a__sel(X1,X2) -> sel(X1,X2)
    16: a__fib1(X1,X2) -> fib1(X1,X2)
    17: a__add(X1,X2) -> add(X1,X2)
Number of strict rules: 17
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__fib1(X,Y) -> #mark(X)
   #2: #a__sel(s(N),cons(X,XS)) -> #a__sel(mark(N),mark(XS))
   #3: #a__sel(s(N),cons(X,XS)) -> #mark(N)
   #4: #a__sel(s(N),cons(X,XS)) -> #mark(XS)
   #5: #mark(cons(X1,X2)) -> #mark(X1)
   #6: #mark(fib1(X1,X2)) -> #a__fib1(mark(X1),mark(X2))
   #7: #mark(fib1(X1,X2)) -> #mark(X1)
   #8: #mark(fib1(X1,X2)) -> #mark(X2)
   #9: #mark(s(X)) -> #mark(X)
   #10: #mark(fib(X)) -> #a__fib(mark(X))
   #11: #mark(fib(X)) -> #mark(X)
   #12: #mark(add(X1,X2)) -> #a__add(mark(X1),mark(X2))
   #13: #mark(add(X1,X2)) -> #mark(X1)
   #14: #mark(add(X1,X2)) -> #mark(X2)
   #15: #a__sel(0(),cons(X,XS)) -> #mark(X)
   #16: #a__add(0(),X) -> #mark(X)
   #17: #a__fib(N) -> #a__sel(mark(N),a__fib1(s(0()),s(0())))
   #18: #a__fib(N) -> #mark(N)
   #19: #a__fib(N) -> #a__fib1(s(0()),s(0()))
   #20: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #21: #mark(sel(X1,X2)) -> #mark(X1)
   #22: #mark(sel(X1,X2)) -> #mark(X2)
   #23: #a__add(s(X),Y) -> #a__add(mark(X),mark(Y))
   #24: #a__add(s(X),Y) -> #mark(X)
   #25: #a__add(s(X),Y) -> #mark(Y)
Number of SCCs: 1, DPs: 25
	SCC { #1..25 }
Sum... Max... succeeded.
  s(x1)		w: (x1)
  #a__add(x1,x2)		w: (max{17498 + x2, 17498 + x1})
  a__add(x1,x2)		w: (max{x2, x1})
  #a__fib1(x1,x2)		w: (max{19945 + x2, 17499 + x1})
  fib1(x1,x2)		w: (max{2448 + x2, 2448 + x1})
  fib(x1)		w: (21880 + x1)
  #mark(x1)		w: (17498 + x1)
  0()		w: (18588)
  sel(x1,x2)		w: (max{843 + x2, 844 + x1})
  #a__sel(x1,x2)		w: (max{18340 + x2, 18339 + x1})
  mark(x1)		w: (x1)
  a__sel(x1,x2)		w: (max{843 + x2, 844 + x1})
  #a__fib(x1)		w: (39377 + x1)
  cons(x1,x2)		w: (max{x2, 2448 + x1})
  a__fib(x1)		w: (21880 + x1)
  add(x1,x2)		w: (max{x2, x1})
  a__fib1(x1,x2)		w: (max{2448 + x2, 2448 + x1})
    USABLE RULES: { 1..17 }
    Removed DPs: #1 #3..8 #10 #11 #15 #17..22
Number of SCCs: 2, DPs: 9
	SCC { #2 }
Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... succeeded.
  s(x1)	3[x1]	w: (x1)
  #a__add(x1,x2)	0[x2,x1]	w: (max{1 + x2, x1})
  a__add(x1,x2)	4[x2,x1]	w: (max{x2, x1})
  #a__fib1(x1,x2)	0[]	w: (x2)
  fib1(x1,x2)	5[]	w: (max{18589 + x2, 18589 + x1})
  fib(x1)	5[x1]	w: (37179 + x1)
  #mark(x1)	0[]	w: (1)
  0()	5	w: (1)
  sel(x1,x2)	4[]	w: (18588 + x2)
  #a__sel(x1,x2)	0[x1]	w: (x1)
  mark(x1)	x1	w: (x1)
  a__sel(x1,x2)	4[]	w: (18588 + x2)
  #a__fib(x1)	0[]	w: (x1)
  cons(x1,x2)	1[]	w: (max{x2, 18589 + x1})
  a__fib(x1)	5[x1]	w: (37179 + x1)
  add(x1,x2)	4[x2,x1]	w: (max{x2, x1})
  a__fib1(x1,x2)	5[]	w: (max{18589 + x2, 18589 + x1})
    USABLE RULES: { 1..17 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 8
	SCC { #9 #12..14 #16 #23..25 }
Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... succeeded.
  s(x1)	3[x1]	w: (x1)
  #a__add(x1,x2)	3[x2,x1]	w: (max{x2, x1})
  a__add(x1,x2)	4[x2,x1]	w: (max{x2, x1})
  #a__fib1(x1,x2)	0[]	w: (x2)
  fib1(x1,x2)	5[]	w: (max{21239 + x2, 21239 + x1})
  fib(x1)	5[x1]	w: (42479 + x1)
  #mark(x1)	3[x1]	w: (x1)
  0()	5	w: (1)
  sel(x1,x2)	4[]	w: (21238 + x2)
  #a__sel(x1,x2)	0[x1]	w: (x1)
  mark(x1)	x1	w: (x1)
  a__sel(x1,x2)	4[]	w: (21238 + x2)
  #a__fib(x1)	0[]	w: (x1)
  cons(x1,x2)	1[]	w: (max{x2, 21239 + x1})
  a__fib(x1)	5[x1]	w: (42479 + x1)
  add(x1,x2)	4[x2,x1]	w: (max{x2, x1})
  a__fib1(x1,x2)	5[]	w: (max{21239 + x2, 21239 + x1})
    USABLE RULES: { 1..17 }
    Removed DPs: #9 #12..14 #16 #23..25
Number of SCCs: 0, DPs: 0