/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,Z)) -> a__2ndspos(s(mark(N)),cons2(X,mark(Z)))
    4: a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z)))
    5: a__2ndsneg(0(),Z) -> rnil()
    6: a__2ndsneg(s(N),cons(X,Z)) -> a__2ndsneg(s(mark(N)),cons2(X,mark(Z)))
    7: a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z)))
    8: a__pi(X) -> a__2ndspos(mark(X),a__from(0()))
    9: a__plus(0(),Y) -> mark(Y)
    10: a__plus(s(X),Y) -> s(a__plus(mark(X),mark(Y)))
    11: a__times(0(),Y) -> 0()
    12: a__times(s(X),Y) -> a__plus(mark(Y),a__times(mark(X),mark(Y)))
    13: a__square(X) -> a__times(mark(X),mark(X))
    14: mark(from(X)) -> a__from(mark(X))
    15: mark(2ndspos(X1,X2)) -> a__2ndspos(mark(X1),mark(X2))
    16: mark(2ndsneg(X1,X2)) -> a__2ndsneg(mark(X1),mark(X2))
    17: mark(pi(X)) -> a__pi(mark(X))
    18: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    19: mark(times(X1,X2)) -> a__times(mark(X1),mark(X2))
    20: mark(square(X)) -> a__square(mark(X))
    21: mark(0()) -> 0()
    22: mark(s(X)) -> s(mark(X))
    23: mark(posrecip(X)) -> posrecip(mark(X))
    24: mark(negrecip(X)) -> negrecip(mark(X))
    25: mark(nil()) -> nil()
    26: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    27: mark(cons2(X1,X2)) -> cons2(X1,mark(X2))
    28: mark(rnil()) -> rnil()
    29: mark(rcons(X1,X2)) -> rcons(mark(X1),mark(X2))
    30: a__from(X) -> from(X)
    31: a__2ndspos(X1,X2) -> 2ndspos(X1,X2)
    32: a__2ndsneg(X1,X2) -> 2ndsneg(X1,X2)
    33: a__pi(X) -> pi(X)
    34: a__plus(X1,X2) -> plus(X1,X2)
    35: a__times(X1,X2) -> times(X1,X2)
    36: a__square(X) -> square(X)
Number of strict rules: 36
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #mark(rcons(X1,X2)) -> #mark(X1)
   #2: #mark(rcons(X1,X2)) -> #mark(X2)
   #3: #a__2ndsneg(s(N),cons(X,Z)) -> #a__2ndsneg(s(mark(N)),cons2(X,mark(Z)))
   #4: #a__2ndsneg(s(N),cons(X,Z)) -> #mark(N)
   #5: #a__2ndsneg(s(N),cons(X,Z)) -> #mark(Z)
   #6: #a__square(X) -> #a__times(mark(X),mark(X))
   #7: #a__square(X) -> #mark(X)
   #8: #a__square(X) -> #mark(X)
   #9: #a__plus(0(),Y) -> #mark(Y)
   #10: #mark(negrecip(X)) -> #mark(X)
   #11: #mark(posrecip(X)) -> #mark(X)
   #12: #a__times(s(X),Y) -> #a__plus(mark(Y),a__times(mark(X),mark(Y)))
   #13: #a__times(s(X),Y) -> #mark(Y)
   #14: #a__times(s(X),Y) -> #a__times(mark(X),mark(Y))
   #15: #a__times(s(X),Y) -> #mark(X)
   #16: #a__times(s(X),Y) -> #mark(Y)
   #17: #mark(from(X)) -> #a__from(mark(X))
   #18: #mark(from(X)) -> #mark(X)
   #19: #mark(square(X)) -> #a__square(mark(X))
   #20: #mark(square(X)) -> #mark(X)
   #21: #a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #mark(Y)
   #22: #a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #a__2ndspos(mark(N),mark(Z))
   #23: #a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #mark(N)
   #24: #a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #mark(Z)
   #25: #a__plus(s(X),Y) -> #a__plus(mark(X),mark(Y))
   #26: #a__plus(s(X),Y) -> #mark(X)
   #27: #a__plus(s(X),Y) -> #mark(Y)
   #28: #mark(s(X)) -> #mark(X)
   #29: #mark(cons2(X1,X2)) -> #mark(X2)
   #30: #mark(pi(X)) -> #a__pi(mark(X))
   #31: #mark(pi(X)) -> #mark(X)
   #32: #mark(times(X1,X2)) -> #a__times(mark(X1),mark(X2))
   #33: #mark(times(X1,X2)) -> #mark(X1)
   #34: #mark(times(X1,X2)) -> #mark(X2)
   #35: #mark(cons(X1,X2)) -> #mark(X1)
   #36: #mark(2ndsneg(X1,X2)) -> #a__2ndsneg(mark(X1),mark(X2))
   #37: #mark(2ndsneg(X1,X2)) -> #mark(X1)
   #38: #mark(2ndsneg(X1,X2)) -> #mark(X2)
   #39: #a__2ndspos(s(N),cons(X,Z)) -> #a__2ndspos(s(mark(N)),cons2(X,mark(Z)))
   #40: #a__2ndspos(s(N),cons(X,Z)) -> #mark(N)
   #41: #a__2ndspos(s(N),cons(X,Z)) -> #mark(Z)
   #42: #a__from(X) -> #mark(X)
   #43: #a__pi(X) -> #a__2ndspos(mark(X),a__from(0()))
   #44: #a__pi(X) -> #mark(X)
   #45: #a__pi(X) -> #a__from(0())
   #46: #mark(2ndspos(X1,X2)) -> #a__2ndspos(mark(X1),mark(X2))
   #47: #mark(2ndspos(X1,X2)) -> #mark(X1)
   #48: #mark(2ndspos(X1,X2)) -> #mark(X2)
   #49: #a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> #mark(Y)
   #50: #a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> #a__2ndsneg(mark(N),mark(Z))
   #51: #a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> #mark(N)
   #52: #a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> #mark(Z)
   #53: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
   #54: #mark(plus(X1,X2)) -> #mark(X1)
   #55: #mark(plus(X1,X2)) -> #mark(X2)
Number of SCCs: 1, DPs: 55
	SCC { #1..55 }
Sum... Max... succeeded.
  a__plus(x1,x2)		w: (max{x2, 23507 + x1})
  a__2ndsneg(x1,x2)		w: (max{4189 + x2, 4190 + x1})
  negrecip(x1)		w: (2 + x1)
  s(x1)		w: (x1)
  #a__pi(x1)		w: (68236 + x1)
  #a__from(x1)		w: (11821 + x1)
  2ndspos(x1,x2)		w: (max{4189 + x2, 4190 + x1})
  a__from(x1)		w: (31743 + x1)
  rnil()		w: (4190)
  square(x1)		w: (23509 + x1)
  #a__times(x1,x2)		w: (max{35327 + x2, 35326 + x1})
  pi(x1)		w: (56417 + x1)
  rcons(x1,x2)		w: (max{x2, 3786 + x1})
  a__2ndspos(x1,x2)		w: (max{4189 + x2, 4190 + x1})
  #a__2ndsneg(x1,x2)		w: (max{16008 + x2, 16007 + x1})
  #a__plus(x1,x2)		w: (max{11820 + x2, 35325 + x1})
  #mark(x1)		w: (11820 + x1)
  0()		w: (20484)
  from(x1)		w: (31743 + x1)
  times(x1,x2)		w: (max{23507 + x2, 23506 + x1})
  a__pi(x1)		w: (56417 + x1)
  nil()		w: (10336)
  mark(x1)		w: (x1)
  2ndsneg(x1,x2)		w: (max{4189 + x2, 4190 + x1})
  plus(x1,x2)		w: (max{x2, 23507 + x1})
  cons2(x1,x2)		w: (max{x2, 1 + x1})
  a__square(x1)		w: (23509 + x1)
  cons(x1,x2)		w: (max{x2, 28939 + x1})
  a__times(x1,x2)		w: (max{23507 + x2, 23506 + x1})
  #a__square(x1)		w: (35328 + x1)
  #a__2ndspos(x1,x2)		w: (max{16008 + x2, 16007 + x1})
  posrecip(x1)		w: (1 + x1)
    USABLE RULES: { 1..36 }
    Removed DPs: #1 #4..8 #10 #11 #13 #15..21 #23 #24 #26 #30 #31 #33..38 #40..49 #51 #52 #54
Number of SCCs: 2, DPs: 15
	SCC { #3 #22 #39 #50 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	6[x2,x1]
  a__2ndsneg(x1,x2)	7[]
  negrecip(x1)	3[]
  s(x1)	5[x1]
  #a__pi(x1)	0[]
  #a__from(x1)	0[]
  2ndspos(x1,x2)	8[x2]
  a__from(x1)	4[x1]
  rnil()	1
  square(x1)	8[x1]
  #a__times(x1,x2)	0[x2]
  pi(x1)	9[x1]
  rcons(x1,x2)	6[]
  a__2ndspos(x1,x2)	8[x2]
  #a__2ndsneg(x1,x2)	5[x1]
  #a__plus(x1,x2)	0[]
  #mark(x1)	0[]
  0()	0
  from(x1)	4[x1]
  times(x1,x2)	7[x1,x2]
  a__pi(x1)	9[x1]
  nil()	3
  mark(x1)	x1
  2ndsneg(x1,x2)	7[]
  plus(x1,x2)	6[x2,x1]
  cons2(x1,x2)	1[]
  a__square(x1)	8[x1]
  cons(x1,x2)	4[]
  a__times(x1,x2)	7[x1,x2]
  #a__square(x1)	0[]
  #a__2ndspos(x1,x2)	5[x1]
  posrecip(x1)	x1
    USABLE RULES: { 1..36 }
    Removed DPs: #22 #50
Number of SCCs: 1, DPs: 11
	SCC { #2 #9 #12 #14 #25 #27..29 #32 #53 #55 }
Sum... succeeded.
  a__plus(x1,x2)		w: (x2)
  a__2ndsneg(x1,x2)		w: (10282)
  negrecip(x1)		w: (22142)
  s(x1)		w: (x1)
  #a__pi(x1)		w: (1)
  #a__from(x1)		w: (1)
  2ndspos(x1,x2)		w: (10282)
  a__from(x1)		w: (29178)
  rnil()		w: (10282)
  square(x1)		w: (28776)
  #a__times(x1,x2)		w: (28778)
  pi(x1)		w: (19222)
  rcons(x1,x2)		w: (x2)
  a__2ndspos(x1,x2)		w: (10282)
  #a__2ndsneg(x1,x2)		w: (0)
  #a__plus(x1,x2)		w: (2 + x2)
  #mark(x1)		w: (2 + x1)
  0()		w: (9123)
  from(x1)		w: (29178)
  times(x1,x2)		w: (28776)
  a__pi(x1)		w: (19222)
  nil()		w: (12148)
  mark(x1)		w: (x1)
  2ndsneg(x1,x2)		w: (10282)
  plus(x1,x2)		w: (x2)
  cons2(x1,x2)		w: (1 + x2)
  a__square(x1)		w: (28776)
  cons(x1,x2)		w: (6617)
  a__times(x1,x2)		w: (28776)
  #a__square(x1)		w: (1)
  #a__2ndspos(x1,x2)		w: (0)
  posrecip(x1)		w: (5744)
    USABLE RULES: { 1..36 }
    Removed DPs: #29
Number of SCCs: 1, DPs: 10
	SCC { #2 #9 #12 #14 #25 #27 #28 #32 #53 #55 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	8[x1,x2]
  a__2ndsneg(x1,x2)	5[x1]
  negrecip(x1)	3[]
  s(x1)	6[x1]
  #a__pi(x1)	0[]
  #a__from(x1)	0[]
  2ndspos(x1,x2)	5[x1]
  a__from(x1)	4[x1]
  rnil()	1
  square(x1)	10[x1]
  #a__times(x1,x2)	9[x1,x2]
  pi(x1)	6[x1]
  rcons(x1,x2)	3[x1,x2]
  a__2ndspos(x1,x2)	5[x1]
  #a__2ndsneg(x1,x2)	5[x1]
  #a__plus(x1,x2)	7[x2]
  #mark(x1)	x1
  0()	0
  from(x1)	4[x1]
  times(x1,x2)	9[x1,x2]
  a__pi(x1)	6[x1]
  nil()	3
  mark(x1)	x1
  2ndsneg(x1,x2)	5[x1]
  plus(x1,x2)	8[x1,x2]
  cons2(x1,x2)	1[]
  a__square(x1)	10[x1]
  cons(x1,x2)	4[]
  a__times(x1,x2)	9[x1,x2]
  #a__square(x1)	0[]
  #a__2ndspos(x1,x2)	5[x1]
  posrecip(x1)	6[]
    USABLE RULES: { 1..36 }
    Removed DPs: #2 #9 #12 #14 #27 #28 #53 #55
Number of SCCs: 1, DPs: 1
	SCC { #25 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	8[x1,x2]
  a__2ndsneg(x1,x2)	5[x1]
  negrecip(x1)	3[]
  s(x1)	6[x1]
  #a__pi(x1)	0[]
  #a__from(x1)	0[]
  2ndspos(x1,x2)	5[x1]
  a__from(x1)	4[x1]
  rnil()	1
  square(x1)	10[x1]
  #a__times(x1,x2)	9[x1,x2]
  pi(x1)	6[x1]
  rcons(x1,x2)	3[x1,x2]
  a__2ndspos(x1,x2)	5[x1]
  #a__2ndsneg(x1,x2)	5[x1]
  #a__plus(x1,x2)	1[x2,x1]
  #mark(x1)	x1
  0()	0
  from(x1)	4[x1]
  times(x1,x2)	9[x1,x2]
  a__pi(x1)	6[x1]
  nil()	3
  mark(x1)	x1
  2ndsneg(x1,x2)	5[x1]
  plus(x1,x2)	8[x1,x2]
  cons2(x1,x2)	1[]
  a__square(x1)	10[x1]
  cons(x1,x2)	4[]
  a__times(x1,x2)	9[x1,x2]
  #a__square(x1)	0[]
  #a__2ndspos(x1,x2)	5[x1]
  posrecip(x1)	6[]
    USABLE RULES: { 1..36 }
    Removed DPs: #25
Number of SCCs: 0, DPs: 0