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


--------------------------------------------------------------------------------


YES
Input TRS:
    1: app(app(plus(),0()),y) -> y
    2: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    3: app(app(times(),0()),y) -> 0()
    4: app(app(times(),app(s(),x)),y) -> app(app(plus(),app(app(times(),x),y)),y)
    5: app(app(app(comp(),f),g),x) -> app(f,app(g,x))
    6: app(twice(),f) -> app(app(comp(),f),f)
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^2_plus(0(),y) -> y
2: app^2_plus(app^1_s(x),y) -> app^1_s(app^2_plus(x,y))
3: app^2_times(0(),y) -> 0()
4: app^2_times(app^1_s(x),y) -> app^2_plus(app^2_times(x,y),y)
5: app^3_comp(f,g,x) -> app(f,app(g,x))
6: app^1_twice(f) -> app^2_comp(f,f)
7: app(plus(),_1) ->= app^1_plus(_1)
8: app(app^1_plus(_1),_2) ->= app^2_plus(_1,_2)
9: app(times(),_1) ->= app^1_times(_1)
10: app(app^1_times(_1),_2) ->= app^2_times(_1,_2)
11: app(s(),_1) ->= app^1_s(_1)
12: app(twice(),_1) ->= app^1_twice(_1)
13: app(comp(),_1) ->= app^1_comp(_1)
14: app(app^1_comp(_1),_2) ->= app^2_comp(_1,_2)
15: app(app^2_comp(_1,_2),_3) ->= app^3_comp(_1,_2,_3)
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^2_plus(app^1_s(x),y) -> #app^2_plus(x,y)
   #2: #app(twice(),_1) ->? #app^1_twice(_1)
   #3: #app(app^1_times(_1),_2) ->? #app^2_times(_1,_2)
   #4: #app^3_comp(f,g,x) -> #app(f,app(g,x))
   #5: #app^3_comp(f,g,x) -> #app(g,x)
   #6: #app(app^1_plus(_1),_2) ->? #app^2_plus(_1,_2)
   #7: #app(app^2_comp(_1,_2),_3) ->? #app^3_comp(_1,_2,_3)
   #8: #app^2_times(app^1_s(x),y) -> #app^2_plus(app^2_times(x,y),y)
   #9: #app^2_times(app^1_s(x),y) -> #app^2_times(x,y)
Number of SCCs: 3, DPs: 5
  SCC { #9 }
POLO(Sum)... succeeded.
      app^1_twice	w: 0
      s 	w: 0
      app^1_plus	w: 0
      app^2_comp	w: 0
      twice	w: 0
      app^1_comp	w: 0
      #app^2_plus	w: 0
      app^2_plus	w: 0
      0 	w: 0
      times	w: 0
      #app	w: 0
      app^3_comp	w: 0
      #app^3_comp	w: 0
      plus	w: 0
      app^1_times	w: 0
      #app^2_times	w: x1
      #app^1_twice	w: 0
      app^1_s	w: x1 + 1
      comp	w: 0
      app	w: 0
      app^2_times	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 2, DPs: 4
  SCC { #1 }
POLO(Sum)... succeeded.
      app^1_twice	w: 0
      s 	w: 0
      app^1_plus	w: 0
      app^2_comp	w: 0
      twice	w: 0
      app^1_comp	w: 0
      #app^2_plus	w: x1
      app^2_plus	w: 0
      0 	w: 0
      times	w: 0
      #app	w: 0
      app^3_comp	w: 0
      #app^3_comp	w: 0
      plus	w: 0
      app^1_times	w: 0
      #app^2_times	w: 0
      #app^1_twice	w: 0
      app^1_s	w: x1 + 1
      comp	w: 0
      app	w: 0
      app^2_times	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 3
  SCC { #4 #5 #7 }
POLO(Sum)... succeeded.
      app^1_twice	w: x1
      s 	w: 1
      app^1_plus	w: x1 + 1
      app^2_comp	w: x1 + x2 + 2
      twice	w: 1
      app^1_comp	w: x1 + 2
      #app^2_plus	w: 0
      app^2_plus	w: x2 + 1
      0 	w: 2
      times	w: 1
      #app	w: x1
      app^3_comp	w: x1 + x2 + x3 + 2
      #app^3_comp	w: x1 + x2 + 1
      plus	w: 1
      app^1_times	w: x1 + 1
      #app^2_times	w: 0
      #app^1_twice	w: 0
      app^1_s	w: x1 + 1
      comp	w: 1
      app	w: x1 + x2 + 1
      app^2_times	w: x2 + 1
    USABLE RULES: { }
    Removed DPs: #4 #5 #7
Number of SCCs: 0, DPs: 0