/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: plus(0(),x) -> x
    2: plus(s(x),y) -> s(plus(p(s(x)),y))
    3: times(0(),y) -> 0()
    4: times(s(x),y) -> plus(y,times(p(s(x)),y))
    5: p(s(0())) -> 0()
    6: p(s(s(x))) -> s(p(s(x)))
    7: fac(0(),x) -> x
    8: fac(s(x),y) -> fac(p(s(x)),times(s(x),y))
    9: factorial(x) -> fac(x,s(0()))
Number of strict rules: 9
Direct poly ... failed.
Freezing times p
1: plus(0(),x) -> x
2: plus(s(x),y) -> s(plus(p❆1_s(x),y))
3: times❆1_0(y) -> 0()
4: times❆1_s(x,y) -> plus(y,times(p❆1_s(x),y))
5: p❆1_s(0()) -> 0()
6: p❆1_s(s(x)) -> s(p❆1_s(x))
7: fac(0(),x) -> x
8: fac(s(x),y) -> fac(p❆1_s(x),times❆1_s(x,y))
9: factorial(x) -> fac(x,s(0()))
10: p(s(_1)) ->= p❆1_s(_1)
11: times(0(),_1) ->= times❆1_0(_1)
12: times(s(_1),_2) ->= times❆1_s(_1,_2)
Number of strict rules: 9
Direct poly ... failed.
Dependency Pairs:
   #1: #plus(s(x),y) -> #plus(p❆1_s(x),y)
   #2: #plus(s(x),y) -> #p❆1_s(x)
   #3: #p❆1_s(s(x)) -> #p❆1_s(x)
   #4: #factorial(x) -> #fac(x,s(0()))
   #5: #times(0(),_1) ->? #times❆1_0(_1)
   #6: #times(s(_1),_2) ->? #times❆1_s(_1,_2)
   #7: #p(s(_1)) ->? #p❆1_s(_1)
   #8: #fac(s(x),y) -> #fac(p❆1_s(x),times❆1_s(x,y))
   #9: #fac(s(x),y) -> #p❆1_s(x)
   #10: #fac(s(x),y) -> #times❆1_s(x,y)
   #11: #times❆1_s(x,y) -> #plus(y,times(p❆1_s(x),y))
   #12: #times❆1_s(x,y) -> #times(p❆1_s(x),y)
   #13: #times❆1_s(x,y) -> #p❆1_s(x)
Number of SCCs: 4, DPs: 5
	SCC { #3 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  #fac(x1,x2)		w: (0)
  p❆1_s(x1)		w: (0)
  #times❆1_0(x1)		w: (0)
  #plus(x1,x2)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (x1)
  p(x1)		w: (0)
  #times(x1,x2)		w: (0)
  0()		w: (0)
  times❆1_0(x1)		w: (0)
  times(x1,x2)		w: (0)
  fac(x1,x2)		w: (0)
  #times❆1_s(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  factorial(x1)		w: (0)
  times❆1_s(x1,x2)		w: (0)
  #factorial(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 3, DPs: 4
	SCC { #1 }
Sum... succeeded.
  s(x1)		w: (2 + x1)
  #fac(x1,x2)		w: (0)
  p❆1_s(x1)		w: (1 + x1)
  #times❆1_0(x1)		w: (0)
  #plus(x1,x2)		w: (x1)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  #times(x1,x2)		w: (0)
  0()		w: (1)
  times❆1_0(x1)		w: (0)
  times(x1,x2)		w: (0)
  fac(x1,x2)		w: (0)
  #times❆1_s(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  factorial(x1)		w: (0)
  times❆1_s(x1,x2)		w: (0)
  #factorial(x1)		w: (0)
    USABLE RULES: { 5 6 }
    Removed DPs: #1
Number of SCCs: 2, DPs: 3
	SCC { #8 }
Sum... succeeded.
  s(x1)		w: (32289 + x1)
  #fac(x1,x2)		w: (41062 + x1)
  p❆1_s(x1)		w: (3 + x1)
  #times❆1_0(x1)		w: (0)
  #plus(x1,x2)		w: (x1)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  #times(x1,x2)		w: (0)
  0()		w: (3)
  times❆1_0(x1)		w: (2 + x1)
  times(x1,x2)		w: (1)
  fac(x1,x2)		w: (0)
  #times❆1_s(x1,x2)		w: (0)
  plus(x1,x2)		w: (2 + x2 + x1)
  factorial(x1)		w: (0)
  times❆1_s(x1,x2)		w: (2 + x2 + x1)
  #factorial(x1)		w: (0)
    USABLE RULES: { 5 6 }
    Removed DPs: #8
Number of SCCs: 1, DPs: 2
	SCC { #6 #12 }
Sum... succeeded.
  s(x1)		w: (26436 + x1)
  #fac(x1,x2)		w: (41062 + x1)
  p❆1_s(x1)		w: (1 + x1)
  #times❆1_0(x1)		w: (0)
  #plus(x1,x2)		w: (x1)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  #times(x1,x2)		w: (2 + x1)
  0()		w: (3)
  times❆1_0(x1)		w: (2 + x1)
  times(x1,x2)		w: (1)
  fac(x1,x2)		w: (0)
  #times❆1_s(x1,x2)		w: (4 + x1)
  plus(x1,x2)		w: (5855 + x2 + x1)
  factorial(x1)		w: (0)
  times❆1_s(x1,x2)		w: (2 + x2 + x1)
  #factorial(x1)		w: (0)
    USABLE RULES: { 5 6 }
    Removed DPs: #6 #12
Number of SCCs: 0, DPs: 0