/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__U11(tt(),M,N) -> a__U12(tt(),M,N)
    2: a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
    3: a__U21(tt(),M,N) -> a__U22(tt(),M,N)
    4: a__U22(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
    5: a__plus(N,0()) -> mark(N)
    6: a__plus(N,s(M)) -> a__U11(tt(),M,N)
    7: a__x(N,0()) -> 0()
    8: a__x(N,s(M)) -> a__U21(tt(),M,N)
    9: mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
    10: mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
    11: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    12: mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
    13: mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3)
    14: mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
    15: mark(tt()) -> tt()
    16: mark(s(X)) -> s(mark(X))
    17: mark(0()) -> 0()
    18: a__U11(X1,X2,X3) -> U11(X1,X2,X3)
    19: a__U12(X1,X2,X3) -> U12(X1,X2,X3)
    20: a__plus(X1,X2) -> plus(X1,X2)
    21: a__U21(X1,X2,X3) -> U21(X1,X2,X3)
    22: a__U22(X1,X2,X3) -> U22(X1,X2,X3)
    23: a__x(X1,X2) -> x(X1,X2)
Number of strict rules: 23
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__U12(tt(),M,N) -> #a__plus(mark(N),mark(M))
   #2: #a__U12(tt(),M,N) -> #mark(N)
   #3: #a__U12(tt(),M,N) -> #mark(M)
   #4: #a__plus(N,s(M)) -> #a__U11(tt(),M,N)
   #5: #mark(U22(X1,X2,X3)) -> #a__U22(mark(X1),X2,X3)
   #6: #mark(U22(X1,X2,X3)) -> #mark(X1)
   #7: #mark(U11(X1,X2,X3)) -> #a__U11(mark(X1),X2,X3)
   #8: #mark(U11(X1,X2,X3)) -> #mark(X1)
   #9: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
   #10: #mark(plus(X1,X2)) -> #mark(X1)
   #11: #mark(plus(X1,X2)) -> #mark(X2)
   #12: #mark(U21(X1,X2,X3)) -> #a__U21(mark(X1),X2,X3)
   #13: #mark(U21(X1,X2,X3)) -> #mark(X1)
   #14: #mark(x(X1,X2)) -> #a__x(mark(X1),mark(X2))
   #15: #mark(x(X1,X2)) -> #mark(X1)
   #16: #mark(x(X1,X2)) -> #mark(X2)
   #17: #mark(U12(X1,X2,X3)) -> #a__U12(mark(X1),X2,X3)
   #18: #mark(U12(X1,X2,X3)) -> #mark(X1)
   #19: #a__plus(N,0()) -> #mark(N)
   #20: #mark(s(X)) -> #mark(X)
   #21: #a__U21(tt(),M,N) -> #a__U22(tt(),M,N)
   #22: #a__U11(tt(),M,N) -> #a__U12(tt(),M,N)
   #23: #a__x(N,s(M)) -> #a__U21(tt(),M,N)
   #24: #a__U22(tt(),M,N) -> #a__plus(a__x(mark(N),mark(M)),mark(N))
   #25: #a__U22(tt(),M,N) -> #a__x(mark(N),mark(M))
   #26: #a__U22(tt(),M,N) -> #mark(N)
   #27: #a__U22(tt(),M,N) -> #mark(M)
   #28: #a__U22(tt(),M,N) -> #mark(N)
Number of SCCs: 1, DPs: 28
	SCC { #1..28 }
Sum... Max... succeeded.
  a__plus(x1,x2)		w: (max{12 + x2, x1})
  U21(x1,x2,x3)		w: (max{12 + x3, 16 + x2, 10 + x1})
  U11(x1,x2,x3)		w: (max{x3, 12 + x2, 7 + x1})
  s(x1)		w: (x1)
  #a__x(x1,x2)		w: (max{21696 + x2, 21692 + x1})
  a__U22(x1,x2,x3)		w: (max{12 + x3, 16 + x2, 13 + x1})
  #a__U11(x1,x2,x3)		w: (max{21680 + x3, 21686 + x2, 21681 + x1})
  a__x(x1,x2)		w: (max{16 + x2, 12 + x1})
  U12(x1,x2,x3)		w: (max{x3, 12 + x2, 8 + x1})
  x(x1,x2)		w: (max{16 + x2, 12 + x1})
  #a__U12(x1,x2,x3)		w: (max{21680 + x3, 21686 + x2, 21682 + x1})
  #a__U21(x1,x2,x3)		w: (max{21692 + x3, 21696 + x2, 21690 + x1})
  #a__plus(x1,x2)		w: (max{21686 + x2, 21680 + x1})
  #mark(x1)		w: (21680 + x1)
  0()		w: (294)
  a__U21(x1,x2,x3)		w: (max{12 + x3, 16 + x2, 10 + x1})
  mark(x1)		w: (x1)
  a__U11(x1,x2,x3)		w: (max{x3, 12 + x2, 7 + x1})
  a__U12(x1,x2,x3)		w: (max{x3, 12 + x2, 8 + x1})
  plus(x1,x2)		w: (max{12 + x2, x1})
  #a__U22(x1,x2,x3)		w: (max{21692 + x3, 21696 + x2, 21691 + x1})
  tt()		w: (3)
  U22(x1,x2,x3)		w: (max{12 + x3, 16 + x2, 13 + x1})
    USABLE RULES: { 1..23 }
    Removed DPs: #3 #6 #8 #11 #13 #15 #16 #18 #26..28
Number of SCCs: 1, DPs: 17
	SCC { #1 #2 #4 #5 #7 #9 #10 #12 #14 #17 #19..25 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	4[x1,x2]
  U21(x1,x2,x3)	5[x3,x2,x1]
  U11(x1,x2,x3)	4[x3,x2,x1]
  s(x1)	3[x1]
  #a__x(x1,x2)	5[x1,x2]
  a__U22(x1,x2,x3)	5[x3,x2,x1]
  #a__U11(x1,x2,x3)	4[x3,x2]
  a__x(x1,x2)	5[x1,x2]
  U12(x1,x2,x3)	4[x3,x2,x1]
  x(x1,x2)	5[x1,x2]
  #a__U12(x1,x2,x3)	4[x3,x2]
  #a__U21(x1,x2,x3)	5[x3,x2,x1]
  #a__plus(x1,x2)	4[x1,x2]
  #mark(x1)	1[x1]
  0()	5
  a__U21(x1,x2,x3)	5[x3,x2,x1]
  mark(x1)	x1
  a__U11(x1,x2,x3)	4[x3,x2,x1]
  a__U12(x1,x2,x3)	4[x3,x2,x1]
  plus(x1,x2)	4[x1,x2]
  #a__U22(x1,x2,x3)	5[x3,x2,x1]
  tt()	2
  U22(x1,x2,x3)	5[x3,x2,x1]
    USABLE RULES: { 1..23 }
    Removed DPs: #2 #5 #7 #9 #10 #12 #14 #17 #19 #20 #23..25
Number of SCCs: 1, DPs: 3
	SCC { #1 #4 #22 }
Sum... Max... QLPOpS... succeeded.
  a__plus(x1,x2)	3[x1,x2]
  U21(x1,x2,x3)	5[x3,x2,x1]
  U11(x1,x2,x3)	3[x3,x2,x1]
  s(x1)	2[x1]
  #a__x(x1,x2)	5[x1,x2]
  a__U22(x1,x2,x3)	5[x3,x2,x1]
  #a__U11(x1,x2,x3)	0[x3,x2]
  a__x(x1,x2)	5[x1,x2]
  U12(x1,x2,x3)	3[x3,x2,x1]
  x(x1,x2)	5[x1,x2]
  #a__U12(x1,x2,x3)	0[x3,x2]
  #a__U21(x1,x2,x3)	5[x3,x2,x1]
  #a__plus(x1,x2)	0[x1,x2]
  #mark(x1)	1[x1]
  0()	5
  a__U21(x1,x2,x3)	5[x3,x2,x1]
  mark(x1)	x1
  a__U11(x1,x2,x3)	3[x3,x2,x1]
  a__U12(x1,x2,x3)	3[x3,x2,x1]
  plus(x1,x2)	3[x1,x2]
  #a__U22(x1,x2,x3)	5[x3,x2,x1]
  tt()	1
  U22(x1,x2,x3)	5[x3,x2,x1]
    USABLE RULES: { 1..23 }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0