/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: active(and(tt(),X)) -> mark(X)
    2: active(plus(N,0())) -> mark(N)
    3: active(plus(N,s(M))) -> mark(s(plus(N,M)))
    4: active(x(N,0())) -> mark(0())
    5: active(x(N,s(M))) -> mark(plus(x(N,M),N))
    6: active(and(X1,X2)) -> and(active(X1),X2)
    7: active(plus(X1,X2)) -> plus(active(X1),X2)
    8: active(plus(X1,X2)) -> plus(X1,active(X2))
    9: active(s(X)) -> s(active(X))
    10: active(x(X1,X2)) -> x(active(X1),X2)
    11: active(x(X1,X2)) -> x(X1,active(X2))
    12: and(mark(X1),X2) -> mark(and(X1,X2))
    13: plus(mark(X1),X2) -> mark(plus(X1,X2))
    14: plus(X1,mark(X2)) -> mark(plus(X1,X2))
    15: s(mark(X)) -> mark(s(X))
    16: x(mark(X1),X2) -> mark(x(X1,X2))
    17: x(X1,mark(X2)) -> mark(x(X1,X2))
    18: proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    19: proper(tt()) -> ok(tt())
    20: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
    21: proper(0()) -> ok(0())
    22: proper(s(X)) -> s(proper(X))
    23: proper(x(X1,X2)) -> x(proper(X1),proper(X2))
    24: and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    25: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
    26: s(ok(X)) -> ok(s(X))
    27: x(ok(X1),ok(X2)) -> ok(x(X1,X2))
    28: top(mark(X)) -> top(proper(X))
    29: top(ok(X)) -> top(active(X))
Number of strict rules: 29
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #top(ok(X)) -> #top(active(X))
   #2: #top(ok(X)) -> #active(X)
   #3: #active(and(X1,X2)) -> #and(active(X1),X2)
   #4: #active(and(X1,X2)) -> #active(X1)
   #5: #plus(mark(X1),X2) -> #plus(X1,X2)
   #6: #active(s(X)) -> #s(active(X))
   #7: #active(s(X)) -> #active(X)
   #8: #active(x(X1,X2)) -> #x(X1,active(X2))
   #9: #active(x(X1,X2)) -> #active(X2)
   #10: #and(ok(X1),ok(X2)) -> #and(X1,X2)
   #11: #proper(x(X1,X2)) -> #x(proper(X1),proper(X2))
   #12: #proper(x(X1,X2)) -> #proper(X1)
   #13: #proper(x(X1,X2)) -> #proper(X2)
   #14: #and(mark(X1),X2) -> #and(X1,X2)
   #15: #plus(X1,mark(X2)) -> #plus(X1,X2)
   #16: #plus(ok(X1),ok(X2)) -> #plus(X1,X2)
   #17: #proper(plus(X1,X2)) -> #plus(proper(X1),proper(X2))
   #18: #proper(plus(X1,X2)) -> #proper(X1)
   #19: #proper(plus(X1,X2)) -> #proper(X2)
   #20: #active(plus(X1,X2)) -> #plus(active(X1),X2)
   #21: #active(plus(X1,X2)) -> #active(X1)
   #22: #active(x(X1,X2)) -> #x(active(X1),X2)
   #23: #active(x(X1,X2)) -> #active(X1)
   #24: #active(x(N,s(M))) -> #plus(x(N,M),N)
   #25: #active(x(N,s(M))) -> #x(N,M)
   #26: #top(mark(X)) -> #top(proper(X))
   #27: #top(mark(X)) -> #proper(X)
   #28: #proper(s(X)) -> #s(proper(X))
   #29: #proper(s(X)) -> #proper(X)
   #30: #x(ok(X1),ok(X2)) -> #x(X1,X2)
   #31: #x(X1,mark(X2)) -> #x(X1,X2)
   #32: #s(ok(X)) -> #s(X)
   #33: #x(mark(X1),X2) -> #x(X1,X2)
   #34: #active(plus(N,s(M))) -> #s(plus(N,M))
   #35: #active(plus(N,s(M))) -> #plus(N,M)
   #36: #active(plus(X1,X2)) -> #plus(X1,active(X2))
   #37: #active(plus(X1,X2)) -> #active(X2)
   #38: #s(mark(X)) -> #s(X)
   #39: #proper(and(X1,X2)) -> #and(proper(X1),proper(X2))
   #40: #proper(and(X1,X2)) -> #proper(X1)
   #41: #proper(and(X1,X2)) -> #proper(X2)
Number of SCCs: 7, DPs: 25
	SCC { #32 #38 }
Sum... succeeded.
  s(x1)		w: (0)
  top(x1)		w: (0)
  and(x1,x2)		w: (0)
  #plus(x1,x2)		w: (0)
  #top(x1)		w: (0)
  x(x1,x2)		w: (0)
  proper(x1)		w: (0)
  ok(x1)		w: (1 + x1)
  0()		w: (0)
  #x(x1,x2)		w: (0)
  #s(x1)		w: (x1)
  mark(x1)		w: (1 + x1)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (0)
  active(x1)		w: (0)
  #active(x1)		w: (0)
  tt()		w: (0)
  #and(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #32 #38
Number of SCCs: 6, DPs: 23
	SCC { #1 #26 }
Sum... Max... QLPOpS... succeeded.
  s(x1)	4[x1]
  top(x1)	0[]
  and(x1,x2)	5[x2,x1]
  #plus(x1,x2)	0[]
  #top(x1)	0[x1]
  x(x1,x2)	6[x1,x2]
  proper(x1)	x1
  ok(x1)	x1
  0()	7
  #x(x1,x2)	0[x1,x2]
  #s(x1)	0[]
  mark(x1)	4[x1]
  #proper(x1)	0[]
  plus(x1,x2)	5[x1,x2]
  active(x1)	x1
  #active(x1)	0[]
  tt()	3
  #and(x1,x2)	0[x1]
    USABLE RULES: { 1..27 }
    Removed DPs: #26
Number of SCCs: 6, DPs: 22
	SCC { #1 }
Sum... succeeded.
  s(x1)		w: (x1)
  top(x1)		w: (0)
  and(x1,x2)		w: (x1)
  #plus(x1,x2)		w: (0)
  #top(x1)		w: (x1)
  x(x1,x2)		w: (x2)
  proper(x1)		w: (21239 + x1)
  ok(x1)		w: (21239 + x1)
  0()		w: (1)
  #x(x1,x2)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (0)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (1 + x1)
  active(x1)		w: (1 + x1)
  #active(x1)		w: (0)
  tt()		w: (23612)
  #and(x1,x2)		w: (0)
    USABLE RULES: { 1..27 }
    Removed DPs: #1
Number of SCCs: 5, DPs: 21
	SCC { #10 #14 }
Sum... succeeded.
  s(x1)		w: (x1)
  top(x1)		w: (0)
  and(x1,x2)		w: (x1)
  #plus(x1,x2)		w: (0)
  #top(x1)		w: (x1)
  x(x1,x2)		w: (x2)
  proper(x1)		w: (1 + x1)
  ok(x1)		w: (1 + x1)
  0()		w: (28224)
  #x(x1,x2)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (0)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (1 + x1)
  active(x1)		w: (29534 + x1)
  #active(x1)		w: (0)
  tt()		w: (17888)
  #and(x1,x2)		w: (6878 + x2)
    USABLE RULES: { 1..27 }
    Removed DPs: #10
Number of SCCs: 5, DPs: 20
	SCC { #14 }
Sum... succeeded.
  s(x1)		w: (0)
  top(x1)		w: (0)
  and(x1,x2)		w: (x1)
  #plus(x1,x2)		w: (0)
  #top(x1)		w: (0)
  x(x1,x2)		w: (0)
  proper(x1)		w: (1 + x1)
  ok(x1)		w: (x1)
  0()		w: (0)
  #x(x1,x2)		w: (0)
  #s(x1)		w: (0)
  mark(x1)		w: (5 + x1)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (3 + x2)
  active(x1)		w: (1 + x1)
  #active(x1)		w: (0)
  tt()		w: (22118)
  #and(x1,x2)		w: (6878 + x1)
    USABLE RULES: { 19 21 }
    Removed DPs: #14
Number of SCCs: 4, DPs: 19
	SCC { #30 #31 #33 }
Sum... succeeded.
  s(x1)		w: (0)
  top(x1)		w: (0)
  and(x1,x2)		w: (x1)
  #plus(x1,x2)		w: (0)
  #top(x1)		w: (0)
  x(x1,x2)		w: (0)
  proper(x1)		w: (1 + x1)
  ok(x1)		w: (x1)
  0()		w: (0)
  #x(x1,x2)		w: (24337 + x2)
  #s(x1)		w: (0)
  mark(x1)		w: (3 + x1)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (1 + x2)
  active(x1)		w: (1 + x1)
  #active(x1)		w: (0)
  tt()		w: (33456)
  #and(x1,x2)		w: (6878)
    USABLE RULES: { 19 21 }
    Removed DPs: #31
Number of SCCs: 4, DPs: 18
	SCC { #30 #33 }
Sum... succeeded.
  s(x1)		w: (0)
  top(x1)		w: (0)
  and(x1,x2)		w: (x1)
  #plus(x1,x2)		w: (0)
  #top(x1)		w: (0)
  x(x1,x2)		w: (0)
  proper(x1)		w: (19826 + x1)
  ok(x1)		w: (x1)
  0()		w: (0)
  #x(x1,x2)		w: (18004 + x1)
  #s(x1)		w: (0)
  mark(x1)		w: (3 + x1)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (1 + x2)
  active(x1)		w: (1 + x1)
  #active(x1)		w: (0)
  tt()		w: (12200)
  #and(x1,x2)		w: (6878)
    USABLE RULES: { 19 21 }
    Removed DPs: #33
Number of SCCs: 4, DPs: 17
	SCC { #30 }
Sum... succeeded.
  s(x1)		w: (1)
  top(x1)		w: (0)
  and(x1,x2)		w: (1 + x1)
  #plus(x1,x2)		w: (0)
  #top(x1)		w: (0)
  x(x1,x2)		w: (x2)
  proper(x1)		w: (27570)
  ok(x1)		w: (27571 + x1)
  0()		w: (0)
  #x(x1,x2)		w: (18004 + x1)
  #s(x1)		w: (0)
  mark(x1)		w: (4 + x1)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (x2)
  active(x1)		w: (1 + x1)
  #active(x1)		w: (0)
  tt()		w: (1)
  #and(x1,x2)		w: (6878)
    USABLE RULES: { }
    Removed DPs: #30
Number of SCCs: 3, DPs: 16
	SCC { #5 #15 #16 }
Sum... succeeded.
  s(x1)		w: (1)
  top(x1)		w: (0)
  and(x1,x2)		w: (1 + x1)
  #plus(x1,x2)		w: (24323 + x2)
  #top(x1)		w: (0)
  x(x1,x2)		w: (x2)
  proper(x1)		w: (1)
  ok(x1)		w: (2 + x1)
  0()		w: (0)
  #x(x1,x2)		w: (18004)
  #s(x1)		w: (0)
  mark(x1)		w: (12704 + x1)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (x2)
  active(x1)		w: (12701 + x1)
  #active(x1)		w: (0)
  tt()		w: (1)
  #and(x1,x2)		w: (6878)
    USABLE RULES: { }
    Removed DPs: #15 #16
Number of SCCs: 3, DPs: 14
	SCC { #5 }
Sum... succeeded.
  s(x1)		w: (1)
  top(x1)		w: (0)
  and(x1,x2)		w: (1 + x1)
  #plus(x1,x2)		w: (24323 + x1)
  #top(x1)		w: (0)
  x(x1,x2)		w: (x2)
  proper(x1)		w: (1)
  ok(x1)		w: (2 + x1)
  0()		w: (0)
  #x(x1,x2)		w: (18004)
  #s(x1)		w: (0)
  mark(x1)		w: (3569 + x1)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (x2)
  active(x1)		w: (3566 + x1)
  #active(x1)		w: (0)
  tt()		w: (1)
  #and(x1,x2)		w: (6878)
    USABLE RULES: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 13
	SCC { #4 #7 #9 #21 #23 #37 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  top(x1)		w: (0)
  and(x1,x2)		w: (1 + x1)
  #plus(x1,x2)		w: (24323)
  #top(x1)		w: (0)
  x(x1,x2)		w: (1 + x2 + x1)
  proper(x1)		w: (1)
  ok(x1)		w: (2)
  0()		w: (15047)
  #x(x1,x2)		w: (18004)
  #s(x1)		w: (0)
  mark(x1)		w: (40581 + x1)
  #proper(x1)		w: (0)
  plus(x1,x2)		w: (1 + x2 + x1)
  active(x1)		w: (25532 + x1)
  #active(x1)		w: (x1)
  tt()		w: (14459)
  #and(x1,x2)		w: (6878)
    USABLE RULES: { 13..15 25 26 }
    Removed DPs: #4 #7 #9 #21 #23 #37
Number of SCCs: 1, DPs: 7
	SCC { #12 #13 #18 #19 #29 #40 #41 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  top(x1)		w: (0)
  and(x1,x2)		w: (400 + x2 + x1)
  #plus(x1,x2)		w: (24323)
  #top(x1)		w: (0)
  x(x1,x2)		w: (1 + x2 + x1)
  proper(x1)		w: (1)
  ok(x1)		w: (2)
  0()		w: (13825)
  #x(x1,x2)		w: (18004)
  #s(x1)		w: (0)
  mark(x1)		w: (57448 + x1)
  #proper(x1)		w: (x1)
  plus(x1,x2)		w: (1 + x2 + x1)
  active(x1)		w: (23150 + x1)
  #active(x1)		w: (0)
  tt()		w: (1370)
  #and(x1,x2)		w: (6878)
    USABLE RULES: { 13..15 25 26 }
    Removed DPs: #12 #13 #18 #19 #29 #40 #41
Number of SCCs: 0, DPs: 0