/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__and(tt(),X) -> mark(X)
    4: a__isNat(0()) -> tt()
    5: a__isNat(plus(V1,V2)) -> a__and(a__isNat(V1),isNat(V2))
    6: a__isNat(s(V1)) -> a__isNat(V1)
    7: a__plus(N,0()) -> a__U11(a__isNat(N),N)
    8: a__plus(N,s(M)) -> a__U21(a__and(a__isNat(M),isNat(N)),M,N)
    9: mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
    10: mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
    11: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    12: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    13: mark(isNat(X)) -> a__isNat(X)
    14: mark(tt()) -> tt()
    15: mark(s(X)) -> s(mark(X))
    16: mark(0()) -> 0()
    17: a__U11(X1,X2) -> U11(X1,X2)
    18: a__U21(X1,X2,X3) -> U21(X1,X2,X3)
    19: a__plus(X1,X2) -> plus(X1,X2)
    20: a__and(X1,X2) -> and(X1,X2)
    21: a__isNat(X) -> isNat(X)
Number of strict rules: 21
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__isNat(s(V1)) -> #a__isNat(V1)
   #5: #mark(isNat(X)) -> #a__isNat(X)
   #6: #mark(U11(X1,X2)) -> #a__U11(mark(X1),X2)
   #7: #mark(U11(X1,X2)) -> #mark(X1)
   #8: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
   #9: #mark(plus(X1,X2)) -> #mark(X1)
   #10: #mark(plus(X1,X2)) -> #mark(X2)
   #11: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
   #12: #mark(and(X1,X2)) -> #mark(X1)
   #13: #a__plus(N,0()) -> #a__U11(a__isNat(N),N)
   #14: #a__plus(N,0()) -> #a__isNat(N)
   #15: #mark(U21(X1,X2,X3)) -> #a__U21(mark(X1),X2,X3)
   #16: #mark(U21(X1,X2,X3)) -> #mark(X1)
   #17: #a__isNat(plus(V1,V2)) -> #a__and(a__isNat(V1),isNat(V2))
   #18: #a__isNat(plus(V1,V2)) -> #a__isNat(V1)
   #19: #a__and(tt(),X) -> #mark(X)
   #20: #a__U11(tt(),N) -> #mark(N)
   #21: #a__plus(N,s(M)) -> #a__U21(a__and(a__isNat(M),isNat(N)),M,N)
   #22: #a__plus(N,s(M)) -> #a__and(a__isNat(M),isNat(N))
   #23: #a__plus(N,s(M)) -> #a__isNat(M)
   #24: #mark(s(X)) -> #mark(X)
Number of SCCs: 1, DPs: 24
	SCC { #1..24 }
Sum... succeeded.
  a__plus(x1,x2)		w: (2998 + x2 + x1)
  U21(x1,x2,x3)		w: (23976 + x3 + x2 + x1)
  U11(x1,x2)		w: (2682 + x2 + x1)
  s(x1)		w: (20978 + x1)
  #a__isNat(x1)		w: (47262)
  and(x1,x2)		w: (x2 + x1)
  #a__U11(x1,x2)		w: (47263 + x2)
  #a__U21(x1,x2,x3)		w: (47262 + x3 + x2)
  #a__plus(x1,x2)		w: (26285 + x2 + x1)
  #mark(x1)		w: (47262 + x1)
  0()		w: (20979)
  #a__and(x1,x2)		w: (47262 + x2)
  a__U21(x1,x2,x3)		w: (23976 + x3 + x2 + x1)
  mark(x1)		w: (x1)
  a__U11(x1,x2)		w: (2682 + x2 + x1)
  isNat(x1)		w: (0)
  plus(x1,x2)		w: (2998 + x2 + x1)
  tt()		w: (0)
  a__isNat(x1)		w: (0)
  a__and(x1,x2)		w: (x2 + x1)
    USABLE RULES: { 1..21 }
    Removed DPs: #1 #6..10 #13..16 #20..24
Number of SCCs: 1, DPs: 7
	SCC { #4 #5 #11 #12 #17..19 }
Sum... succeeded.
  a__plus(x1,x2)		w: (2998)
  U21(x1,x2,x3)		w: (35868 + x2)
  U11(x1,x2)		w: (10277)
  s(x1)		w: (592 + x1)
  #a__isNat(x1)		w: (47261 + x1)
  and(x1,x2)		w: (2 + x2 + x1)
  #a__U11(x1,x2)		w: (47263)
  #a__U21(x1,x2,x3)		w: (47262)
  #a__plus(x1,x2)		w: (26285)
  #mark(x1)		w: (47262 + x1)
  0()		w: (1)
  #a__and(x1,x2)		w: (47263 + x2)
  a__U21(x1,x2,x3)		w: (3589 + x3)
  mark(x1)		w: (x1)
  a__U11(x1,x2)		w: (12724)
  isNat(x1)		w: (x1)
  plus(x1,x2)		w: (2998 + x2 + x1)
  tt()		w: (0)
  a__isNat(x1)		w: (x1)
  a__and(x1,x2)		w: (2 + x2 + x1)
    USABLE RULES: { }
    Removed DPs: #4 #5 #11 #12 #17..19
Number of SCCs: 0, DPs: 0