/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
Input TRS:
    1: a__U11(tt(),N) -> mark(N)
    2: a__U21(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
    3: a__U31(tt()) -> 0()
    4: a__U41(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
    5: a__and(tt(),X) -> mark(X)
    6: a__isNat(0()) -> tt()
    7: a__isNat(plus(V1,V2)) -> a__and(a__isNat(V1),isNat(V2))
    8: a__isNat(s(V1)) -> a__isNat(V1)
    9: a__isNat(x(V1,V2)) -> a__and(a__isNat(V1),isNat(V2))
    10: a__plus(N,0()) -> a__U11(a__isNat(N),N)
    11: a__plus(N,s(M)) -> a__U21(a__and(a__isNat(M),isNat(N)),M,N)
    12: a__x(N,0()) -> a__U31(a__isNat(N))
    13: a__x(N,s(M)) -> a__U41(a__and(a__isNat(M),isNat(N)),M,N)
    14: mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
    15: mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
    16: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    17: mark(U31(X)) -> a__U31(mark(X))
    18: mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
    19: mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
    20: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    21: mark(isNat(X)) -> a__isNat(X)
    22: mark(tt()) -> tt()
    23: mark(s(X)) -> s(mark(X))
    24: mark(0()) -> 0()
    25: a__U11(X1,X2) -> U11(X1,X2)
    26: a__U21(X1,X2,X3) -> U21(X1,X2,X3)
    27: a__plus(X1,X2) -> plus(X1,X2)
    28: a__U31(X) -> U31(X)
    29: a__U41(X1,X2,X3) -> U41(X1,X2,X3)
    30: a__x(X1,X2) -> x(X1,X2)
    31: a__and(X1,X2) -> and(X1,X2)
    32: a__isNat(X) -> isNat(X)
Number of strict rules: 32
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__U21(tt(),M,N) -> #a__plus(mark(N),mark(M))
   #2: #a__U21(tt(),M,N) -> #mark(N)
   #3: #a__U21(tt(),M,N) -> #mark(M)
   #4: #a__x(N,s(M)) -> #a__U41(a__and(a__isNat(M),isNat(N)),M,N)
   #5: #a__x(N,s(M)) -> #a__and(a__isNat(M),isNat(N))
   #6: #a__x(N,s(M)) -> #a__isNat(M)
   #7: #a__isNat(x(V1,V2)) -> #a__and(a__isNat(V1),isNat(V2))
   #8: #a__isNat(x(V1,V2)) -> #a__isNat(V1)
   #9: #a__plus(N,s(M)) -> #a__U21(a__and(a__isNat(M),isNat(N)),M,N)
   #10: #a__plus(N,s(M)) -> #a__and(a__isNat(M),isNat(N))
   #11: #a__plus(N,s(M)) -> #a__isNat(M)
   #12: #mark(s(X)) -> #mark(X)
   #13: #a__x(N,0()) -> #a__U31(a__isNat(N))
   #14: #a__x(N,0()) -> #a__isNat(N)
   #15: #mark(U11(X1,X2)) -> #a__U11(mark(X1),X2)
   #16: #mark(U11(X1,X2)) -> #mark(X1)
   #17: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
   #18: #mark(and(X1,X2)) -> #mark(X1)
   #19: #a__isNat(plus(V1,V2)) -> #a__and(a__isNat(V1),isNat(V2))
   #20: #a__isNat(plus(V1,V2)) -> #a__isNat(V1)
   #21: #a__plus(N,0()) -> #a__U11(a__isNat(N),N)
   #22: #a__plus(N,0()) -> #a__isNat(N)
   #23: #a__and(tt(),X) -> #mark(X)
   #24: #mark(U31(X)) -> #a__U31(mark(X))
   #25: #mark(U31(X)) -> #mark(X)
   #26: #mark(x(X1,X2)) -> #a__x(mark(X1),mark(X2))
   #27: #mark(x(X1,X2)) -> #mark(X1)
   #28: #mark(x(X1,X2)) -> #mark(X2)
   #29: #mark(isNat(X)) -> #a__isNat(X)
   #30: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
   #31: #mark(plus(X1,X2)) -> #mark(X1)
   #32: #mark(plus(X1,X2)) -> #mark(X2)
   #33: #a__U11(tt(),N) -> #mark(N)
   #34: #a__isNat(s(V1)) -> #a__isNat(V1)
   #35: #mark(U21(X1,X2,X3)) -> #a__U21(mark(X1),X2,X3)
   #36: #mark(U21(X1,X2,X3)) -> #mark(X1)
   #37: #a__U41(tt(),M,N) -> #a__plus(a__x(mark(N),mark(M)),mark(N))
   #38: #a__U41(tt(),M,N) -> #a__x(mark(N),mark(M))
   #39: #a__U41(tt(),M,N) -> #mark(N)
   #40: #a__U41(tt(),M,N) -> #mark(M)
   #41: #a__U41(tt(),M,N) -> #mark(N)
   #42: #mark(U41(X1,X2,X3)) -> #a__U41(mark(X1),X2,X3)
   #43: #mark(U41(X1,X2,X3)) -> #mark(X1)
Number of SCCs: 1, DPs: 41
	SCC { #1..12 #14..23 #25..43 }
Sum... Max... succeeded.
  a__plus(x1,x2)		w: (max{14010 + x2, x1})
  U21(x1,x2,x3)		w: (max{x3, 14010 + x2, 1 + x1})
  U11(x1,x2)		w: (max{x2, 1 + x1})
  s(x1)		w: (x1)
  #a__U31(x1)		w: (0)
  #a__isNat(x1)		w: (3)
  and(x1,x2)		w: (max{x2, x1})
  #a__x(x1,x2)		w: (max{9 + x2, 35667 + x1})
  #a__U11(x1,x2)		w: (max{2 + x2, 0})
  a__U31(x1)		w: (35664 + x1)
  a__x(x1,x2)		w: (max{7 + x2, 35665 + x1})
  a__U41(x1,x2,x3)		w: (max{35665 + x3, 7 + x2, 5 + x1})
  x(x1,x2)		w: (max{7 + x2, 35665 + x1})
  #a__U21(x1,x2,x3)		w: (max{2 + x3, 6 + x2, 3 + x1})
  #a__plus(x1,x2)		w: (max{6 + x2, 2 + x1})
  #mark(x1)		w: (2 + x1)
  0()		w: (20977)
  #a__and(x1,x2)		w: (max{2 + x2, 0})
  a__U21(x1,x2,x3)		w: (max{x3, 14010 + x2, 1 + x1})
  mark(x1)		w: (x1)
  a__U11(x1,x2)		w: (max{x2, 1 + x1})
  isNat(x1)		w: (1)
  plus(x1,x2)		w: (max{14010 + x2, x1})
  U31(x1)		w: (35664 + x1)
  #a__U41(x1,x2,x3)		w: (max{35667 + x3, 9 + x2, 7 + x1})
  tt()		w: (1)
  a__isNat(x1)		w: (1)
  a__and(x1,x2)		w: (max{x2, x1})
  U41(x1,x2,x3)		w: (max{35665 + x3, 7 + x2, 5 + x1})
    USABLE RULES: { 1..32 }
    Removed DPs: #3 #5 #6 #10 #11 #14 #16 #22 #25 #27 #28 #32 #36 #39..41 #43
Number of SCCs: 1, DPs: 24
	SCC { #1 #2 #4 #7..9 #12 #15 #17..21 #23 #26 #29..31 #33..35 #37 #38 #42 }
Sum... Max... succeeded.
  a__plus(x1,x2)		w: (max{123 + x2, x1})
  U21(x1,x2,x3)		w: (max{x3, 123 + x2, 0})
  U11(x1,x2)		w: (max{x2, 0})
  s(x1)		w: (x1)
  #a__U31(x1)		w: (0)
  #a__isNat(x1)		w: (23613 + x1)
  and(x1,x2)		w: (max{9 + x2, x1})
  #a__x(x1,x2)		w: (max{23738 + x2, 23747 + x1})
  #a__U11(x1,x2)		w: (max{23616 + x2, 0})
  a__U31(x1)		w: (4 + x1)
  a__x(x1,x2)		w: (max{122 + x2, 131 + x1})
  a__U41(x1,x2,x3)		w: (max{131 + x3, 122 + x2, 5 + x1})
  x(x1,x2)		w: (max{122 + x2, 131 + x1})
  #a__U21(x1,x2,x3)		w: (max{23616 + x3, 0})
  #a__plus(x1,x2)		w: (max{0, 23616 + x1})
  #mark(x1)		w: (23616 + x1)
  0()		w: (10)
  #a__and(x1,x2)		w: (max{23617 + x2, 23493 + x1})
  a__U21(x1,x2,x3)		w: (max{x3, 123 + x2, 0})
  mark(x1)		w: (x1)
  a__U11(x1,x2)		w: (max{x2, 0})
  isNat(x1)		w: (117 + x1)
  plus(x1,x2)		w: (max{123 + x2, x1})
  U31(x1)		w: (4 + x1)
  #a__U41(x1,x2,x3)		w: (max{23747 + x3, 23738 + x2, 23621 + x1})
  tt()		w: (127)
  a__isNat(x1)		w: (117 + x1)
  a__and(x1,x2)		w: (max{9 + x2, x1})
  U41(x1,x2,x3)		w: (max{131 + x3, 122 + x2, 5 + x1})
    USABLE RULES: { 1..32 }
    Removed DPs: #7 #8 #17 #19 #23 #29
Number of SCCs: 2, DPs: 18
	SCC { #20 #34 }
Sum... succeeded.
  a__plus(x1,x2)		w: (14027)
  U21(x1,x2,x3)		w: (14029 + x1)
  U11(x1,x2)		w: (27853)
  s(x1)		w: (4 + x1)
  #a__U31(x1)		w: (0)
  #a__isNat(x1)		w: (6 + x1)
  and(x1,x2)		w: (14024)
  #a__x(x1,x2)		w: (7)
  #a__U11(x1,x2)		w: (6)
  a__U31(x1)		w: (4 + x1)
  a__x(x1,x2)		w: (14025)
  a__U41(x1,x2,x3)		w: (14026 + x3 + x2)
  x(x1,x2)		w: (14026 + x2 + x1)
  #a__U21(x1,x2,x3)		w: (6)
  #a__plus(x1,x2)		w: (6)
  #mark(x1)		w: (6)
  0()		w: (14030)
  #a__and(x1,x2)		w: (6)
  a__U21(x1,x2,x3)		w: (14028)
  mark(x1)		w: (14024)
  a__U11(x1,x2)		w: (27852)
  isNat(x1)		w: (14023)
  plus(x1,x2)		w: (14028 + x2 + x1)
  U31(x1)		w: (5)
  #a__U41(x1,x2,x3)		w: (7)
  tt()		w: (14025)
  a__isNat(x1)		w: (14022)
  a__and(x1,x2)		w: (14023)
  U41(x1,x2,x3)		w: (14027 + x1)
    USABLE RULES: { }
    Removed DPs: #20 #34
Number of SCCs: 1, DPs: 16
	SCC { #1 #2 #4 #9 #12 #15 #18 #21 #26 #30 #31 #33 #35 #37 #38 #42 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	6[x2,x1]
  U21(x1,x2,x3)	6[x2,x3,x1]
  U11(x1,x2)	1[x2]
  s(x1)	2[x1]
  #a__U31(x1)	0[]
  #a__isNat(x1)	0[]
  and(x1,x2)	5[x2,x1]
  #a__x(x1,x2)	7[x1,x2]
  #a__U11(x1,x2)	x2
  a__U31(x1)	7[x1]
  a__x(x1,x2)	7[x1,x2]
  a__U41(x1,x2,x3)	7[x3,x2,x1]
  x(x1,x2)	7[x1,x2]
  #a__U21(x1,x2,x3)	x3
  #a__plus(x1,x2)	x1
  #mark(x1)	x1
  0()	7
  #a__and(x1,x2)	0[x1]
  a__U21(x1,x2,x3)	6[x2,x3,x1]
  mark(x1)	x1
  a__U11(x1,x2)	1[x2]
  isNat(x1)	x1
  plus(x1,x2)	6[x2,x1]
  U31(x1)	7[x1]
  #a__U41(x1,x2,x3)	7[x3,x2]
  tt()	0
  a__isNat(x1)	x1
  a__and(x1,x2)	5[x2,x1]
  U41(x1,x2,x3)	7[x3,x2,x1]
    USABLE RULES: { 1..32 }
    Removed DPs: #4 #12 #15 #18 #30 #31 #35 #42
Number of SCCs: 1, DPs: 2
	SCC { #1 #9 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	3[x1,x2]
  U21(x1,x2,x3)	3[x3,x2,x1]
  U11(x1,x2)	x2
  s(x1)	2[x1]
  #a__U31(x1)	0[]
  #a__isNat(x1)	0[]
  and(x1,x2)	0[x1,x2]
  #a__x(x1,x2)	7[]
  #a__U11(x1,x2)	5[]
  a__U31(x1)	6[]
  a__x(x1,x2)	4[x1,x2]
  a__U41(x1,x2,x3)	4[x3,x2,x1]
  x(x1,x2)	4[x1,x2]
  #a__U21(x1,x2,x3)	1[x2,x3,x1]
  #a__plus(x1,x2)	1[x2,x1]
  #mark(x1)	6[]
  0()	6
  #a__and(x1,x2)	0[x1,x2]
  a__U21(x1,x2,x3)	3[x3,x2,x1]
  mark(x1)	x1
  a__U11(x1,x2)	x2
  isNat(x1)	0[x1]
  plus(x1,x2)	3[x1,x2]
  U31(x1)	6[]
  #a__U41(x1,x2,x3)	7[x1]
  tt()	6
  a__isNat(x1)	0[x1]
  a__and(x1,x2)	0[x1,x2]
  U41(x1,x2,x3)	4[x3,x2,x1]
    USABLE RULES: { 1..32 }
    Removed DPs: #1 #9
Number of SCCs: 0, DPs: 0