/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: min(x,0()) -> 0()
    2: min(0(),y) -> 0()
    3: min(s(x),s(y)) -> s(min(x,y))
    4: max(x,0()) -> x
    5: max(0(),y) -> y
    6: max(s(x),s(y)) -> s(max(x,y))
    7: minus(x,0()) -> x
    8: minus(s(x),s(y)) -> s(minus(x,y))
    9: gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
    10: transform(x) -> s(s(x))
    11: transform(cons(x,y)) -> cons(cons(x,x),x)
    12: transform(cons(x,y)) -> y
    13: transform(s(x)) -> s(s(transform(x)))
    14: cons(x,y) -> y
    15: cons(x,cons(y,s(z))) -> cons(y,x)
    16: cons(cons(x,z),s(y)) -> transform(x)
Number of strict rules: 16
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #max(s(x),s(y)) -> #max(x,y)
   #2: #transform(s(x)) -> #transform(x)
   #3: #gcd(s(x),s(y)) -> #gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
   #4: #gcd(s(x),s(y)) -> #minus(max(x,y),min(x,transform(y)))
   #5: #gcd(s(x),s(y)) -> #max(x,y)
   #6: #gcd(s(x),s(y)) -> #min(x,transform(y))
   #7: #gcd(s(x),s(y)) -> #transform(y)
   #8: #gcd(s(x),s(y)) -> #min(x,y)
   #9: #transform(cons(x,y)) -> #cons(cons(x,x),x)
   #10: #transform(cons(x,y)) -> #cons(x,x)
   #11: #cons(cons(x,z),s(y)) -> #transform(x)
   #12: #min(s(x),s(y)) -> #min(x,y)
   #13: #minus(s(x),s(y)) -> #minus(x,y)
   #14: #cons(x,cons(y,s(z))) -> #cons(y,x)
Number of SCCs: 5, DPs: 9
	SCC { #13 }
Sum... succeeded.
  #cons(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (0)
  gcd(x1,x2)		w: (0)
  #min(x1,x2)		w: (0)
  #transform(x1)		w: (0)
  0()		w: (0)
  transform(x1)		w: (0)
  max(x1,x2)		w: (0)
  #max(x1,x2)		w: (0)
  #minus(x1,x2)		w: (x2 + x1)
  min(x1,x2)		w: (0)
  cons(x1,x2)		w: (0)
  #gcd(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #13
Number of SCCs: 4, DPs: 8
	SCC { #12 }
Sum... succeeded.
  #cons(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (0)
  gcd(x1,x2)		w: (0)
  #min(x1,x2)		w: (x2)
  #transform(x1)		w: (0)
  0()		w: (0)
  transform(x1)		w: (0)
  max(x1,x2)		w: (0)
  #max(x1,x2)		w: (0)
  #minus(x1,x2)		w: (0)
  min(x1,x2)		w: (0)
  cons(x1,x2)		w: (0)
  #gcd(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #12
Number of SCCs: 3, DPs: 7
	SCC { #1 }
Sum... succeeded.
  #cons(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (0)
  gcd(x1,x2)		w: (0)
  #min(x1,x2)		w: (0)
  #transform(x1)		w: (0)
  0()		w: (0)
  transform(x1)		w: (0)
  max(x1,x2)		w: (0)
  #max(x1,x2)		w: (x2)
  #minus(x1,x2)		w: (0)
  min(x1,x2)		w: (0)
  cons(x1,x2)		w: (0)
  #gcd(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 6
	SCC { #3 }
Sum... Max... succeeded.
  #cons(x1,x2)		w: (0)
  s(x1)		w: (5862 + x1)
  minus(x1,x2)		w: (max{1 + x2, 2 + x1})
  gcd(x1,x2)		w: (0)
  #min(x1,x2)		w: (0)
  #transform(x1)		w: (0)
  0()		w: (1)
  transform(x1)		w: (0)
  max(x1,x2)		w: (max{x2, 1 + x1})
  #max(x1,x2)		w: (0)
  #minus(x1,x2)		w: (0)
  min(x1,x2)		w: (max{0, 4 + x1})
  cons(x1,x2)		w: (max{1 + x2, 0})
  #gcd(x1,x2)		w: (max{x2, 5858 + x1})
    USABLE RULES: { 1..8 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 5
	SCC { #2 #9..11 #14 }
Sum... Max... succeeded.
  #cons(x1,x2)		w: (max{14681 + x2, 14682 + x1})
  s(x1)		w: (x1)
  minus(x1,x2)		w: (max{1 + x2, 2 + x1})
  gcd(x1,x2)		w: (0)
  #min(x1,x2)		w: (0)
  #transform(x1)		w: (17680 + x1)
  0()		w: (1)
  transform(x1)		w: (2999 + x1)
  max(x1,x2)		w: (max{x2, 1 + x1})
  #max(x1,x2)		w: (0)
  #minus(x1,x2)		w: (0)
  min(x1,x2)		w: (max{0, 4 + x1})
  cons(x1,x2)		w: (max{2999 + x2, 2999 + x1})
  #gcd(x1,x2)		w: (max{x2, 5858 + x1})
    USABLE RULES: { 1..8 10..16 }
    Removed DPs: #9..11 #14
Number of SCCs: 1, DPs: 1
	SCC { #2 }
Sum... succeeded.
  #cons(x1,x2)		w: (1)
  s(x1)		w: (1 + x1)
  minus(x1,x2)		w: (2998 + x1)
  gcd(x1,x2)		w: (0)
  #min(x1,x2)		w: (0)
  #transform(x1)		w: (1 + x1)
  0()		w: (2)
  transform(x1)		w: (0)
  max(x1,x2)		w: (20977 + x2 + x1)
  #max(x1,x2)		w: (0)
  #minus(x1,x2)		w: (0)
  min(x1,x2)		w: (1)
  cons(x1,x2)		w: (1 + x1)
  #gcd(x1,x2)		w: (0)
    USABLE RULES: { 4 5 }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0