/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: app(app(max(),0()),x) -> x
    2: app(app(max(),x),0()) -> x
    3: app(app(max(),app(s(),x)),app(s(),y)) -> app(app(max(),x),y)
    4: app(app(min(),0()),x) -> 0()
    5: app(app(min(),x),0()) -> 0()
    6: app(app(min(),app(s(),x)),app(s(),y)) -> app(app(min(),x),y)
    7: app(app(app(app(insert(),f),g),nil()),x) -> app(app(cons(),x),nil())
    8: app(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app(app(cons(),app(app(f,x),h)),app(app(app(app(insert(),f),g),t),app(app(g,x),h)))
    9: app(app(app(sort(),f),g),nil()) -> nil()
    10: app(app(app(sort(),f),g),app(app(cons(),h),t)) -> app(app(app(app(insert(),f),g),app(app(app(sort(),f),g),t)),h)
    11: app(ascending_sort(),l) -> app(app(app(sort(),min()),max()),l)
    12: app(descending_sort(),l) -> app(app(app(sort(),max()),min()),l)
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^2_max(0(),x) -> x
2: app^2_max(x,0()) -> x
3: app^2_max(app^1_s(x),app^1_s(y)) -> app^2_max(x,y)
4: app^2_min(0(),x) -> 0()
5: app^2_min(x,0()) -> 0()
6: app^2_min(app^1_s(x),app^1_s(y)) -> app^2_min(x,y)
7: app^4_insert(f,g,nil(),x) -> app^2_cons(x,nil())
8: app^4_insert(f,g,app^2_cons(h,t),x) -> app^2_cons(app(app(f,x),h),app^4_insert(f,g,t,app(app(g,x),h)))
9: app^3_sort(f,g,nil()) -> nil()
10: app^3_sort(f,g,app^2_cons(h,t)) -> app^4_insert(f,g,app^3_sort(f,g,t),h)
11: app^1_ascending_sort(l) -> app^3_sort(min(),max(),l)
12: app^1_descending_sort(l) -> app^3_sort(max(),min(),l)
13: app(min(),_1) ->= app^1_min(_1)
14: app(app^1_min(_1),_2) ->= app^2_min(_1,_2)
15: app(cons(),_1) ->= app^1_cons(_1)
16: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
17: app(max(),_1) ->= app^1_max(_1)
18: app(app^1_max(_1),_2) ->= app^2_max(_1,_2)
19: app(s(),_1) ->= app^1_s(_1)
20: app(descending_sort(),_1) ->= app^1_descending_sort(_1)
21: app(sort(),_1) ->= app^1_sort(_1)
22: app(app^1_sort(_1),_2) ->= app^2_sort(_1,_2)
23: app(app^2_sort(_1,_2),_3) ->= app^3_sort(_1,_2,_3)
24: app(ascending_sort(),_1) ->= app^1_ascending_sort(_1)
25: app(insert(),_1) ->= app^1_insert(_1)
26: app(app^1_insert(_1),_2) ->= app^2_insert(_1,_2)
27: app(app^2_insert(_1,_2),_3) ->= app^3_insert(_1,_2,_3)
28: app(app^3_insert(_1,_2,_3),_4) ->= app^4_insert(_1,_2,_3,_4)
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^2_min(app^1_s(x),app^1_s(y)) -> #app^2_min(x,y)
   #2: #app^1_ascending_sort(l) -> #app^3_sort(min(),max(),l)
   #3: #app(ascending_sort(),_1) ->? #app^1_ascending_sort(_1)
   #4: #app(app^2_sort(_1,_2),_3) ->? #app^3_sort(_1,_2,_3)
   #5: #app^1_descending_sort(l) -> #app^3_sort(max(),min(),l)
   #6: #app(app^1_min(_1),_2) ->? #app^2_min(_1,_2)
   #7: #app(descending_sort(),_1) ->? #app^1_descending_sort(_1)
   #8: #app^3_sort(f,g,app^2_cons(h,t)) -> #app^4_insert(f,g,app^3_sort(f,g,t),h)
   #9: #app^3_sort(f,g,app^2_cons(h,t)) -> #app^3_sort(f,g,t)
   #10: #app(app^3_insert(_1,_2,_3),_4) ->? #app^4_insert(_1,_2,_3,_4)
   #11: #app^2_max(app^1_s(x),app^1_s(y)) -> #app^2_max(x,y)
   #12: #app^4_insert(f,g,app^2_cons(h,t),x) -> #app(app(f,x),h)
   #13: #app^4_insert(f,g,app^2_cons(h,t),x) -> #app(f,x)
   #14: #app^4_insert(f,g,app^2_cons(h,t),x) -> #app^4_insert(f,g,t,app(app(g,x),h))
   #15: #app^4_insert(f,g,app^2_cons(h,t),x) -> #app(app(g,x),h)
   #16: #app^4_insert(f,g,app^2_cons(h,t),x) -> #app(g,x)
   #17: #app(app^1_max(_1),_2) ->? #app^2_max(_1,_2)
Number of SCCs: 3, DPs: 15
  SCC { #1 }
POLO(Sum)... succeeded.
      app^4_insert	w: 0
      app^1_max	w: 0
      app^3_sort	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^1_descending_sort	w: 0
      app^1_min	w: 0
      insert	w: 0
      app^2_min	w: 0
      descending_sort	w: 0
      #app^2_max	w: 0
      app^1_sort	w: 0
      #app^1_ascending_sort	w: 0
      app^2_max	w: 0
      #app^4_insert	w: 0
      app^1_descending_sort	w: 0
      0 	w: 0
      app^3_insert	w: 0
      max	w: 0
      #app^3_sort	w: 0
      nil	w: 0
      #app	w: 0
      #app^2_min	w: x1 + x2
      sort	w: 0
      ascending_sort	w: 0
      min	w: 0
      app^2_sort	w: 0
      cons	w: 0
      app^1_insert	w: 0
      app^2_cons	w: 0
      app^2_insert	w: 0
      app^1_s	w: x1 + 1
      app^1_ascending_sort	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 14
  SCC { #11 }
POLO(Sum)... succeeded.
      app^4_insert	w: 0
      app^1_max	w: 0
      app^3_sort	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^1_descending_sort	w: 0
      app^1_min	w: 0
      insert	w: 0
      app^2_min	w: 0
      descending_sort	w: 0
      #app^2_max	w: x2
      app^1_sort	w: 0
      #app^1_ascending_sort	w: 0
      app^2_max	w: 0
      #app^4_insert	w: 0
      app^1_descending_sort	w: 0
      0 	w: 0
      app^3_insert	w: 0
      max	w: 0
      #app^3_sort	w: 0
      nil	w: 0
      #app	w: 0
      #app^2_min	w: 0
      sort	w: 0
      ascending_sort	w: 0
      min	w: 0
      app^2_sort	w: 0
      cons	w: 0
      app^1_insert	w: 0
      app^2_cons	w: 0
      app^2_insert	w: 0
      app^1_s	w: x1 + 1
      app^1_ascending_sort	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 1, DPs: 13
  SCC { #2..5 #7..10 #12..16 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.