/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: eq(0(),0()) -> true()
    2: eq(0(),s(Y)) -> false()
    3: eq(s(X),0()) -> false()
    4: eq(s(X),s(Y)) -> eq(X,Y)
    5: le(0(),Y) -> true()
    6: le(s(X),0()) -> false()
    7: le(s(X),s(Y)) -> le(X,Y)
    8: min(cons(0(),nil())) -> 0()
    9: min(cons(s(N),nil())) -> s(N)
    10: min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L)))
    11: ifmin(true(),cons(N,cons(M,L))) -> min(cons(N,L))
    12: ifmin(false(),cons(N,cons(M,L))) -> min(cons(M,L))
    13: replace(N,M,nil()) -> nil()
    14: replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
    15: ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
    16: ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
    17: selsort(nil()) -> nil()
    18: selsort(cons(N,L)) -> ifselsort(eq(N,min(cons(N,L))),cons(N,L))
    19: ifselsort(true(),cons(N,L)) -> cons(N,selsort(L))
    20: ifselsort(false(),cons(N,L)) -> cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))
Number of strict rules: 20
Direct POLO(bPol) ... failed.
Uncurrying min
1: eq(0(),0()) -> true()
2: eq(0(),s(Y)) -> false()
3: eq(s(X),0()) -> false()
4: eq(s(X),s(Y)) -> eq(X,Y)
5: le(0(),Y) -> true()
6: le(s(X),0()) -> false()
7: le(s(X),s(Y)) -> le(X,Y)
8: min^1_cons(0(),nil()) -> 0()
9: min^1_cons(s(N),nil()) -> s(N)
10: min^1_cons(N,cons(M,L)) -> ifmin(le(N,M),cons(N,cons(M,L)))
11: ifmin(true(),cons(N,cons(M,L))) -> min^1_cons(N,L)
12: ifmin(false(),cons(N,cons(M,L))) -> min^1_cons(M,L)
13: replace(N,M,nil()) -> nil()
14: replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
15: ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
16: ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
17: selsort(nil()) -> nil()
18: selsort(cons(N,L)) -> ifselsort(eq(N,min^1_cons(N,L)),cons(N,L))
19: ifselsort(true(),cons(N,L)) -> cons(N,selsort(L))
20: ifselsort(false(),cons(N,L)) -> cons(min^1_cons(N,L),selsort(replace(min^1_cons(N,L),N,L)))
21: min(cons(_1,_2)) ->= min^1_cons(_1,_2)
Number of strict rules: 20
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #ifmin(true(),cons(N,cons(M,L))) -> #min^1_cons(N,L)
   #2: #ifmin(false(),cons(N,cons(M,L))) -> #min^1_cons(M,L)
   #3: #replace(N,M,cons(K,L)) -> #ifrepl(eq(N,K),N,M,cons(K,L))
   #4: #replace(N,M,cons(K,L)) -> #eq(N,K)
   #5: #ifselsort(false(),cons(N,L)) -> #min^1_cons(N,L)
   #6: #ifselsort(false(),cons(N,L)) -> #selsort(replace(min^1_cons(N,L),N,L))
   #7: #ifselsort(false(),cons(N,L)) -> #replace(min^1_cons(N,L),N,L)
   #8: #ifselsort(false(),cons(N,L)) -> #min^1_cons(N,L)
   #9: #le(s(X),s(Y)) -> #le(X,Y)
   #10: #min^1_cons(N,cons(M,L)) -> #ifmin(le(N,M),cons(N,cons(M,L)))
   #11: #min^1_cons(N,cons(M,L)) -> #le(N,M)
   #12: #ifselsort(true(),cons(N,L)) -> #selsort(L)
   #13: #min(cons(_1,_2)) ->? #min^1_cons(_1,_2)
   #14: #ifrepl(false(),N,M,cons(K,L)) -> #replace(N,M,L)
   #15: #eq(s(X),s(Y)) -> #eq(X,Y)
   #16: #selsort(cons(N,L)) -> #ifselsort(eq(N,min^1_cons(N,L)),cons(N,L))
   #17: #selsort(cons(N,L)) -> #eq(N,min^1_cons(N,L))
   #18: #selsort(cons(N,L)) -> #min^1_cons(N,L)
Number of SCCs: 5, DPs: 10
  SCC { #15 }
POLO(Sum)... succeeded.
      ifselsort	w: 0
      le	w: 0
      s 	w: x1 + 1
      #le	w: 0
      ifmin	w: 0
      min^1_cons	w: 0
      eq	w: 0
      false	w: 0
      #min	w: 0
      true	w: 0
      #eq	w: x1 + x2
      0 	w: 0
      nil	w: 0
      ifrepl	w: 0
      selsort	w: 0
      #ifrepl	w: 0
      #selsort	w: 0
      #replace	w: 0
      #ifselsort	w: 0
      min	w: 0
      #min^1_cons	w: 0
      cons	w: 0
      #ifmin	w: 0
      replace	w: 0
    USABLE RULES: { }
    Removed DPs: #15
Number of SCCs: 4, DPs: 9
  SCC { #9 }
POLO(Sum)... succeeded.
      ifselsort	w: 0
      le	w: 0
      s 	w: x1 + 1
      #le	w: x1
      ifmin	w: 0
      min^1_cons	w: 0
      eq	w: 0
      false	w: 0
      #min	w: 0
      true	w: 0
      #eq	w: 0
      0 	w: 0
      nil	w: 0
      ifrepl	w: 0
      selsort	w: 0
      #ifrepl	w: 0
      #selsort	w: 0
      #replace	w: 0
      #ifselsort	w: 0
      min	w: 0
      #min^1_cons	w: 0
      cons	w: 0
      #ifmin	w: 0
      replace	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 3, DPs: 8
  SCC { #3 #14 }
POLO(Sum)... succeeded.
      ifselsort	w: 0
      le	w: 0
      s 	w: x1 + 1
      #le	w: 0
      ifmin	w: 0
      min^1_cons	w: 0
      eq	w: x1 + x2 + 1
      false	w: 4
      #min	w: 0
      true	w: 4
      #eq	w: 0
      0 	w: 1
      nil	w: 0
      ifrepl	w: 0
      selsort	w: 0
      #ifrepl	w: x2 + x4
      #selsort	w: 0
      #replace	w: x1 + x3 + 1
      #ifselsort	w: 0
      min	w: 0
      #min^1_cons	w: 0
      cons	w: x2 + 2
      #ifmin	w: 0
      replace	w: 0
    USABLE RULES: { }
    Removed DPs: #3 #14
Number of SCCs: 2, DPs: 6
  SCC { #6 #12 #16 }
POLO(Sum)... succeeded.
      ifselsort	w: 0
      le	w: 3
      s 	w: 1
      #le	w: 0
      ifmin	w: x1 + x2
      min^1_cons	w: 5
      eq	w: 4
      false	w: 5
      #min	w: 0
      true	w: 5
      #eq	w: 0
      0 	w: 6
      nil	w: 1
      ifrepl	w: x4 + 1
      selsort	w: 0
      #ifrepl	w: 0
      #selsort	w: x1 + 1
      #replace	w: 1
      #ifselsort	w: x2
      min	w: 0
      #min^1_cons	w: 0
      cons	w: x2 + 3
      #ifmin	w: 0
      replace	w: x3 + 1
    USABLE RULES: { 13..16 }
    Removed DPs: #6 #12 #16
Number of SCCs: 1, DPs: 3
  SCC { #1 #2 #10 }
POLO(Sum)... succeeded.
      ifselsort	w: 0
      le	w: x1 + x2 + 1
      s 	w: 1
      #le	w: 0
      ifmin	w: x2
      min^1_cons	w: 1
      eq	w: 4
      false	w: 5
      #min	w: 0
      true	w: 5
      #eq	w: 0
      0 	w: 2
      nil	w: 1
      ifrepl	w: x4 + 1
      selsort	w: 0
      #ifrepl	w: 0
      #selsort	w: x1 + 1
      #replace	w: 1
      #ifselsort	w: 0
      min	w: 0
      #min^1_cons	w: x2 + 5
      cons	w: x2 + 3
      #ifmin	w: x2
      replace	w: x3 + 1
    USABLE RULES: { 13..16 }
    Removed DPs: #1 #2 #10
Number of SCCs: 0, DPs: 0