/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__and(tt(),X) -> mark(X)
    2: a__plus(N,0()) -> mark(N)
    3: a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
    4: a__x(N,0()) -> 0()
    5: a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
    6: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    7: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    8: mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
    9: mark(tt()) -> tt()
    10: mark(0()) -> 0()
    11: mark(s(X)) -> s(mark(X))
    12: a__and(X1,X2) -> and(X1,X2)
    13: a__plus(X1,X2) -> plus(X1,X2)
    14: a__x(X1,X2) -> x(X1,X2)
Number of strict rules: 14
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__plus(N,0()) -> #mark(N)
   #2: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
   #3: #mark(and(X1,X2)) -> #mark(X1)
   #4: #mark(s(X)) -> #mark(X)
   #5: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
   #6: #mark(plus(X1,X2)) -> #mark(X1)
   #7: #mark(plus(X1,X2)) -> #mark(X2)
   #8: #a__x(N,s(M)) -> #a__plus(a__x(mark(N),mark(M)),mark(N))
   #9: #a__x(N,s(M)) -> #a__x(mark(N),mark(M))
   #10: #a__x(N,s(M)) -> #mark(N)
   #11: #a__x(N,s(M)) -> #mark(M)
   #12: #a__x(N,s(M)) -> #mark(N)
   #13: #a__plus(N,s(M)) -> #a__plus(mark(N),mark(M))
   #14: #a__plus(N,s(M)) -> #mark(N)
   #15: #a__plus(N,s(M)) -> #mark(M)
   #16: #a__and(tt(),X) -> #mark(X)
   #17: #mark(x(X1,X2)) -> #a__x(mark(X1),mark(X2))
   #18: #mark(x(X1,X2)) -> #mark(X1)
   #19: #mark(x(X1,X2)) -> #mark(X2)
Number of SCCs: 1, DPs: 19
	SCC { #1..19 }
Sum... Max... succeeded.
  a__plus(x1,x2)		w: (max{x2, x1})
  s(x1)		w: (x1)
  and(x1,x2)		w: (max{21238 + x2, 21239 + x1})
  #a__x(x1,x2)		w: (max{84182 + x2, 84183 + x1})
  a__x(x1,x2)		w: (max{16908 + x2, 16909 + x1})
  x(x1,x2)		w: (max{16908 + x2, 16909 + x1})
  #a__plus(x1,x2)		w: (max{67274 + x2, 67274 + x1})
  #mark(x1)		w: (67274 + x1)
  0()		w: (16910)
  #a__and(x1,x2)		w: (max{88512 + x2, 25074 + x1})
  mark(x1)		w: (x1)
  plus(x1,x2)		w: (max{x2, x1})
  tt()		w: (23612)
  a__and(x1,x2)		w: (max{21238 + x2, 21239 + x1})
    USABLE RULES: { 1..14 }
    Removed DPs: #3 #10..12 #16 #18 #19
Number of SCCs: 1, DPs: 11
	SCC { #1 #4..9 #13..15 #17 }
Sum... Max... succeeded.
  a__plus(x1,x2)		w: (max{31599 + x2, x1})
  s(x1)		w: (x1)
  and(x1,x2)		w: (max{1 + x2, 2 + x1})
  #a__x(x1,x2)		w: (max{70071 + x2, 70072 + x1})
  a__x(x1,x2)		w: (max{31599 + x2, 31600 + x1})
  x(x1,x2)		w: (max{31599 + x2, 31600 + x1})
  #a__plus(x1,x2)		w: (max{70070 + x2, 38472 + x1})
  #mark(x1)		w: (38472 + x1)
  0()		w: (31601)
  #a__and(x1,x2)		w: (max{0, 25074 + x1})
  mark(x1)		w: (x1)
  plus(x1,x2)		w: (max{31599 + x2, x1})
  tt()		w: (23612)
  a__and(x1,x2)		w: (max{1 + x2, 2 + x1})
    USABLE RULES: { 1..14 }
    Removed DPs: #7 #15
Number of SCCs: 1, DPs: 9
	SCC { #1 #4..6 #8 #9 #13 #14 #17 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	2[x2,x1]
  s(x1)	1[x1]
  and(x1,x2)	x2
  #a__x(x1,x2)	3[x1,x2]
  a__x(x1,x2)	3[x1,x2]
  x(x1,x2)	3[x1,x2]
  #a__plus(x1,x2)	2[x2,x1]
  #mark(x1)	x1
  0()	2
  #a__and(x1,x2)	0[x2,x1]
  mark(x1)	x1
  plus(x1,x2)	2[x2,x1]
  tt()	0
  a__and(x1,x2)	x2
    USABLE RULES: { 1..14 }
    Removed DPs: #1 #4 #6 #8 #9 #13 #14
Number of SCCs: 0, DPs: 0