/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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MAYBE
Input TRS:
    1: max(nil()) -> 0()
    2: max(cons(x,nil())) -> x
    3: max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
    4: if1(true(),x,y,xs) -> max(cons(x,xs))
    5: if1(false(),x,y,xs) -> max(cons(y,xs))
    6: del(x,nil()) -> nil()
    7: del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
    8: if2(true(),x,y,xs) -> xs
    9: if2(false(),x,y,xs) -> cons(y,del(x,xs))
    10: eq(0(),0()) -> true()
    11: eq(0(),s(y)) -> false()
    12: eq(s(x),0()) -> false()
    13: eq(s(x),s(y)) -> eq(x,y)
    14: sort(xs) -> if3(empty(xs),xs)
    15: if3(true(),xs) -> nil()
    16: if3(false(),xs) -> sort(del(max(xs),xs))
    17: empty(nil()) -> true()
    18: empty(cons(x,xs)) -> false()
    19: ge(x,0()) -> true()
    20: ge(0(),s(x)) -> false()
    21: ge(s(x),s(y)) -> ge(x,y)
Number of strict rules: 21
Direct POLO(bPol) ... failed.
Uncurrying max
1: max^1_nil() -> 0()
2: max^1_cons(x,nil()) -> x
3: max^1_cons(x,cons(y,xs)) -> if1(ge(x,y),x,y,xs)
4: if1(true(),x,y,xs) -> max^1_cons(x,xs)
5: if1(false(),x,y,xs) -> max^1_cons(y,xs)
6: del(x,nil()) -> nil()
7: del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
8: if2(true(),x,y,xs) -> xs
9: if2(false(),x,y,xs) -> cons(y,del(x,xs))
10: eq(0(),0()) -> true()
11: eq(0(),s(y)) -> false()
12: eq(s(x),0()) -> false()
13: eq(s(x),s(y)) -> eq(x,y)
14: sort(xs) -> if3(empty(xs),xs)
15: if3(true(),xs) -> nil()
16: if3(false(),xs) -> sort(del(max(xs),xs))
17: empty(nil()) -> true()
18: empty(cons(x,xs)) -> false()
19: ge(x,0()) -> true()
20: ge(0(),s(x)) -> false()
21: ge(s(x),s(y)) -> ge(x,y)
22: max(cons(_1,_2)) ->= max^1_cons(_1,_2)
23: max(nil()) ->= max^1_nil()
Number of strict rules: 21
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #eq(s(x),s(y)) -> #eq(x,y)
   #2: #if2(false(),x,y,xs) -> #del(x,xs)
   #3: #max(nil()) ->? #max^1_nil()
   #4: #sort(xs) -> #if3(empty(xs),xs)
   #5: #sort(xs) -> #empty(xs)
   #6: #del(x,cons(y,xs)) -> #if2(eq(x,y),x,y,xs)
   #7: #del(x,cons(y,xs)) -> #eq(x,y)
   #8: #if1(false(),x,y,xs) -> #max^1_cons(y,xs)
   #9: #max(cons(_1,_2)) ->? #max^1_cons(_1,_2)
   #10: #ge(s(x),s(y)) -> #ge(x,y)
   #11: #if3(false(),xs) -> #sort(del(max(xs),xs))
   #12: #if3(false(),xs) -> #del(max(xs),xs)
   #13: #if3(false(),xs) -> #max(xs)
   #14: #max^1_cons(x,cons(y,xs)) -> #if1(ge(x,y),x,y,xs)
   #15: #max^1_cons(x,cons(y,xs)) -> #ge(x,y)
   #16: #if1(true(),x,y,xs) -> #max^1_cons(x,xs)
Number of SCCs: 5, DPs: 9
  SCC { #10 }
POLO(Sum)... succeeded.
      #del	w: 0
      #empty	w: 0
      s 	w: x1 + 1
      max^1_cons	w: 0
      #max^1_cons	w: 0
      eq	w: 0
      if1	w: 0
      false	w: 0
      max^1_nil	w: 0
      #ge	w: x1 + x2
      true	w: 0
      #eq	w: 0
      #if1	w: 0
      #sort	w: 0
      if2	w: 0
      #if3	w: 0
      0 	w: 0
      ge	w: 0
      del	w: 0
      max	w: 0
      nil	w: 0
      #max	w: 0
      sort	w: 0
      #max^1_nil	w: 0
      if3	w: 0
      cons	w: 0
      empty	w: 0
      #if2	w: 0
    USABLE RULES: { }
    Removed DPs: #10
Number of SCCs: 4, DPs: 8
  SCC { #1 }
POLO(Sum)... succeeded.
      #del	w: 0
      #empty	w: 0
      s 	w: x1 + 1
      max^1_cons	w: 0
      #max^1_cons	w: 0
      eq	w: 0
      if1	w: 0
      false	w: 0
      max^1_nil	w: 0
      #ge	w: 0
      true	w: 0
      #eq	w: x2
      #if1	w: 0
      #sort	w: 0
      if2	w: 0
      #if3	w: 0
      0 	w: 0
      ge	w: 0
      del	w: 0
      max	w: 0
      nil	w: 0
      #max	w: 0
      sort	w: 0
      #max^1_nil	w: 0
      if3	w: 0
      cons	w: 0
      empty	w: 0
      #if2	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 3, DPs: 7
  SCC { #4 #11 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.