/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__from(X) -> cons(mark(X),from(s(X)))
    2: a__2ndspos(0(),Z) -> rnil()
    3: a__2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z)))
    4: a__2ndsneg(0(),Z) -> rnil()
    5: a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z)))
    6: a__pi(X) -> a__2ndspos(mark(X),a__from(0()))
    7: a__plus(0(),Y) -> mark(Y)
    8: a__plus(s(X),Y) -> s(a__plus(mark(X),mark(Y)))
    9: a__times(0(),Y) -> 0()
    10: a__times(s(X),Y) -> a__plus(mark(Y),a__times(mark(X),mark(Y)))
    11: a__square(X) -> a__times(mark(X),mark(X))
    12: mark(from(X)) -> a__from(mark(X))
    13: mark(2ndspos(X1,X2)) -> a__2ndspos(mark(X1),mark(X2))
    14: mark(2ndsneg(X1,X2)) -> a__2ndsneg(mark(X1),mark(X2))
    15: mark(pi(X)) -> a__pi(mark(X))
    16: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    17: mark(times(X1,X2)) -> a__times(mark(X1),mark(X2))
    18: mark(square(X)) -> a__square(mark(X))
    19: mark(0()) -> 0()
    20: mark(s(X)) -> s(mark(X))
    21: mark(posrecip(X)) -> posrecip(mark(X))
    22: mark(negrecip(X)) -> negrecip(mark(X))
    23: mark(nil()) -> nil()
    24: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    25: mark(rnil()) -> rnil()
    26: mark(rcons(X1,X2)) -> rcons(mark(X1),mark(X2))
    27: a__from(X) -> from(X)
    28: a__2ndspos(X1,X2) -> 2ndspos(X1,X2)
    29: a__2ndsneg(X1,X2) -> 2ndsneg(X1,X2)
    30: a__pi(X) -> pi(X)
    31: a__plus(X1,X2) -> plus(X1,X2)
    32: a__times(X1,X2) -> times(X1,X2)
    33: a__square(X) -> square(X)
Number of strict rules: 33
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__pi(X) -> #a__2ndspos(mark(X),a__from(0()))
   #2: #a__pi(X) -> #mark(X)
   #3: #a__pi(X) -> #a__from(0())
   #4: #mark(2ndspos(X1,X2)) -> #a__2ndspos(mark(X1),mark(X2))
   #5: #mark(2ndspos(X1,X2)) -> #mark(X1)
   #6: #mark(2ndspos(X1,X2)) -> #mark(X2)
   #7: #a__square(X) -> #a__times(mark(X),mark(X))
   #8: #a__square(X) -> #mark(X)
   #9: #a__square(X) -> #mark(X)
   #10: #mark(cons(X1,X2)) -> #mark(X1)
   #11: #mark(from(X)) -> #a__from(mark(X))
   #12: #mark(from(X)) -> #mark(X)
   #13: #mark(2ndsneg(X1,X2)) -> #a__2ndsneg(mark(X1),mark(X2))
   #14: #mark(2ndsneg(X1,X2)) -> #mark(X1)
   #15: #mark(2ndsneg(X1,X2)) -> #mark(X2)
   #16: #mark(s(X)) -> #mark(X)
   #17: #a__plus(0(),Y) -> #mark(Y)
   #18: #a__times(s(X),Y) -> #a__plus(mark(Y),a__times(mark(X),mark(Y)))
   #19: #a__times(s(X),Y) -> #mark(Y)
   #20: #a__times(s(X),Y) -> #a__times(mark(X),mark(Y))
   #21: #a__times(s(X),Y) -> #mark(X)
   #22: #a__times(s(X),Y) -> #mark(Y)
   #23: #a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> #mark(Y)
   #24: #a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> #a__2ndspos(mark(N),mark(Z))
   #25: #a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> #mark(N)
   #26: #a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> #mark(Z)
   #27: #mark(negrecip(X)) -> #mark(X)
   #28: #mark(times(X1,X2)) -> #a__times(mark(X1),mark(X2))
   #29: #mark(times(X1,X2)) -> #mark(X1)
   #30: #mark(times(X1,X2)) -> #mark(X2)
   #31: #mark(rcons(X1,X2)) -> #mark(X1)
   #32: #mark(rcons(X1,X2)) -> #mark(X2)
   #33: #mark(posrecip(X)) -> #mark(X)
   #34: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
   #35: #mark(plus(X1,X2)) -> #mark(X1)
   #36: #mark(plus(X1,X2)) -> #mark(X2)
   #37: #a__2ndspos(s(N),cons(X,cons(Y,Z))) -> #mark(Y)
   #38: #a__2ndspos(s(N),cons(X,cons(Y,Z))) -> #a__2ndsneg(mark(N),mark(Z))
   #39: #a__2ndspos(s(N),cons(X,cons(Y,Z))) -> #mark(N)
   #40: #a__2ndspos(s(N),cons(X,cons(Y,Z))) -> #mark(Z)
   #41: #a__from(X) -> #mark(X)
   #42: #a__plus(s(X),Y) -> #a__plus(mark(X),mark(Y))
   #43: #a__plus(s(X),Y) -> #mark(X)
   #44: #a__plus(s(X),Y) -> #mark(Y)
   #45: #mark(pi(X)) -> #a__pi(mark(X))
   #46: #mark(pi(X)) -> #mark(X)
   #47: #mark(square(X)) -> #a__square(mark(X))
   #48: #mark(square(X)) -> #mark(X)
Number of SCCs: 1, DPs: 47
	SCC { #2..48 }
Sum... Max... succeeded.
  a__plus(x1,x2)		w: (max{x2, 36719 + x1})
  a__2ndsneg(x1,x2)		w: (max{1 + x2, 11652 + x1})
  negrecip(x1)		w: (4476 + x1)
  s(x1)		w: (x1)
  #a__pi(x1)		w: (81142 + x1)
  #a__from(x1)		w: (32771 + x1)
  2ndspos(x1,x2)		w: (max{1 + x2, 11652 + x1})
  a__from(x1)		w: (11652 + x1)
  rnil()		w: (48372)
  square(x1)		w: (36720 + x1)
  #a__times(x1,x2)		w: (max{69489 + x2, 69488 + x1})
  pi(x1)		w: (48373 + x1)
  rcons(x1,x2)		w: (max{x2, 7177 + x1})
  a__2ndspos(x1,x2)		w: (max{1 + x2, 11652 + x1})
  #a__2ndsneg(x1,x2)		w: (max{32770 + x2, 44421 + x1})
  #a__plus(x1,x2)		w: (max{32770 + x2, 69489 + x1})
  #mark(x1)		w: (32770 + x1)
  0()		w: (36720)
  from(x1)		w: (11652 + x1)
  times(x1,x2)		w: (max{36719 + x2, 36718 + x1})
  a__pi(x1)		w: (48373 + x1)
  nil()		w: (2332)
  mark(x1)		w: (x1)
  2ndsneg(x1,x2)		w: (max{1 + x2, 11652 + x1})
  plus(x1,x2)		w: (max{x2, 36719 + x1})
  a__square(x1)		w: (36720 + x1)
  cons(x1,x2)		w: (max{x2, 11652 + x1})
  a__times(x1,x2)		w: (max{36719 + x2, 36718 + x1})
  #a__square(x1)		w: (69489 + x1)
  #a__2ndspos(x1,x2)		w: (max{32770 + x2, 44421 + x1})
  posrecip(x1)		w: (4476 + x1)
    USABLE RULES: { 1..33 }
    Removed DPs: #2..6 #8..15 #19 #21..23 #25 #27 #29..31 #33 #35 #37 #39 #41 #43 #45..48
Number of SCCs: 2, DPs: 12
	SCC { #24 #38 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	3[x1,x2]
  a__2ndsneg(x1,x2)	4[x1,x2]
  negrecip(x1)	4[]
  s(x1)	2[x1]
  #a__pi(x1)	0[]
  #a__from(x1)	0[]
  2ndspos(x1,x2)	0[x2,x1]
  a__from(x1)	5[x1]
  rnil()	0
  square(x1)	7[x1]
  #a__times(x1,x2)	0[x1]
  pi(x1)	6[x1]
  rcons(x1,x2)	x1
  a__2ndspos(x1,x2)	0[x2,x1]
  #a__2ndsneg(x1,x2)	2[x1]
  #a__plus(x1,x2)	0[x2,x1]
  #mark(x1)	0[]
  0()	6
  from(x1)	5[x1]
  times(x1,x2)	6[x2,x1]
  a__pi(x1)	6[x1]
  nil()	2
  mark(x1)	x1
  2ndsneg(x1,x2)	4[x1,x2]
  plus(x1,x2)	3[x1,x2]
  a__square(x1)	7[x1]
  cons(x1,x2)	4[x1]
  a__times(x1,x2)	6[x2,x1]
  #a__square(x1)	0[]
  #a__2ndspos(x1,x2)	x1
  posrecip(x1)	4[]
    USABLE RULES: { 1..33 }
    Removed DPs: #24
Number of SCCs: 1, DPs: 10
	SCC { #16..18 #20 #28 #32 #34 #36 #42 #44 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	3[x1,x2]
  a__2ndsneg(x1,x2)	1[x1]
  negrecip(x1)	0[]
  s(x1)	2[x1]
  #a__pi(x1)	0[]
  #a__from(x1)	0[]
  2ndspos(x1,x2)	x1
  a__from(x1)	2[x1]
  rnil()	0
  square(x1)	6[x1]
  #a__times(x1,x2)	5[x2,x1]
  pi(x1)	x1
  rcons(x1,x2)	1[x1,x2]
  a__2ndspos(x1,x2)	x1
  #a__2ndsneg(x1,x2)	2[x1]
  #a__plus(x1,x2)	3[x1,x2]
  #mark(x1)	x1
  0()	6
  from(x1)	2[x1]
  times(x1,x2)	5[x2,x1]
  a__pi(x1)	x1
  nil()	2
  mark(x1)	x1
  2ndsneg(x1,x2)	1[x1]
  plus(x1,x2)	3[x1,x2]
  a__square(x1)	6[x1]
  cons(x1,x2)	2[x1]
  a__times(x1,x2)	5[x2,x1]
  #a__square(x1)	0[]
  #a__2ndspos(x1,x2)	x1
  posrecip(x1)	2[]
    USABLE RULES: { 1..33 }
    Removed DPs: #16..18 #32 #36 #44
Number of SCCs: 2, DPs: 2
	SCC { #42 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	3[x1,x2]
  a__2ndsneg(x1,x2)	1[x1]
  negrecip(x1)	0[]
  s(x1)	2[x1]
  #a__pi(x1)	0[]
  #a__from(x1)	0[]
  2ndspos(x1,x2)	x1
  a__from(x1)	2[x1]
  rnil()	0
  square(x1)	6[x1]
  #a__times(x1,x2)	5[x2,x1]
  pi(x1)	x1
  rcons(x1,x2)	1[x1,x2]
  a__2ndspos(x1,x2)	x1
  #a__2ndsneg(x1,x2)	2[x1]
  #a__plus(x1,x2)	1[x1,x2]
  #mark(x1)	x1
  0()	6
  from(x1)	2[x1]
  times(x1,x2)	5[x2,x1]
  a__pi(x1)	x1
  nil()	2
  mark(x1)	x1
  2ndsneg(x1,x2)	1[x1]
  plus(x1,x2)	3[x1,x2]
  a__square(x1)	6[x1]
  cons(x1,x2)	2[x1]
  a__times(x1,x2)	5[x2,x1]
  #a__square(x1)	0[]
  #a__2ndspos(x1,x2)	x1
  posrecip(x1)	2[]
    USABLE RULES: { 1..33 }
    Removed DPs: #42
Number of SCCs: 1, DPs: 1
	SCC { #20 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	3[x1,x2]
  a__2ndsneg(x1,x2)	1[x1]
  negrecip(x1)	0[]
  s(x1)	2[x1]
  #a__pi(x1)	0[]
  #a__from(x1)	0[]
  2ndspos(x1,x2)	x1
  a__from(x1)	2[x1]
  rnil()	0
  square(x1)	6[x1]
  #a__times(x1,x2)	3[x2,x1]
  pi(x1)	x1
  rcons(x1,x2)	1[x1,x2]
  a__2ndspos(x1,x2)	x1
  #a__2ndsneg(x1,x2)	2[x1]
  #a__plus(x1,x2)	1[x1,x2]
  #mark(x1)	x1
  0()	6
  from(x1)	2[x1]
  times(x1,x2)	5[x2,x1]
  a__pi(x1)	x1
  nil()	2
  mark(x1)	x1
  2ndsneg(x1,x2)	1[x1]
  plus(x1,x2)	3[x1,x2]
  a__square(x1)	6[x1]
  cons(x1,x2)	2[x1]
  a__times(x1,x2)	5[x2,x1]
  #a__square(x1)	0[]
  #a__2ndspos(x1,x2)	x1
  posrecip(x1)	2[]
    USABLE RULES: { 1..33 }
    Removed DPs: #20
Number of SCCs: 0, DPs: 0