/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: exp(x,0()) -> s(0())
    6: exp(x,s(y)) -> times(x,exp(x,y))
    7: p(s(0())) -> 0()
    8: p(s(s(x))) -> s(p(s(x)))
    9: tower(x,y) -> towerIter(x,y,s(0()))
    10: towerIter(0(),y,z) -> z
    11: towerIter(s(x),y,z) -> towerIter(p(s(x)),y,exp(y,z))
Number of strict rules: 11
Direct poly ... failed.
Freezing p
1: plus(0(),x) -> x
2: plus(s(x),y) -> s(plus(p❆1_s(x),y))
3: times(0(),y) -> 0()
4: times(s(x),y) -> plus(y,times(p❆1_s(x),y))
5: exp(x,0()) -> s(0())
6: exp(x,s(y)) -> times(x,exp(x,y))
7: p❆1_s(0()) -> 0()
8: p❆1_s(s(x)) -> s(p❆1_s(x))
9: tower(x,y) -> towerIter(x,y,s(0()))
10: towerIter(0(),y,z) -> z
11: towerIter(s(x),y,z) -> towerIter(p❆1_s(x),y,exp(y,z))
12: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 11
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: #exp(x,s(y)) -> #times(x,exp(x,y))
   #4: #exp(x,s(y)) -> #exp(x,y)
   #5: #tower(x,y) -> #towerIter(x,y,s(0()))
   #6: #towerIter(s(x),y,z) -> #towerIter(p❆1_s(x),y,exp(y,z))
   #7: #towerIter(s(x),y,z) -> #p❆1_s(x)
   #8: #towerIter(s(x),y,z) -> #exp(y,z)
   #9: #p(s(_1)) ->? #p❆1_s(_1)
   #10: #p❆1_s(s(x)) -> #p❆1_s(x)
   #11: #times(s(x),y) -> #plus(y,times(p❆1_s(x),y))
   #12: #times(s(x),y) -> #times(p❆1_s(x),y)
   #13: #times(s(x),y) -> #p❆1_s(x)
Number of SCCs: 5, DPs: 5
	SCC { #10 }
Sum... succeeded.
  tower(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  p❆1_s(x1)		w: (0)
  #plus(x1,x2)		w: (0)
  towerIter(x1,x2,x3)		w: (0)
  #exp(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(x1,x2)		w: (0)
  #tower(x1,x2)		w: (0)
  #towerIter(x1,x2,x3)		w: (0)
  plus(x1,x2)		w: (0)
  exp(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #10
Number of SCCs: 4, DPs: 4
	SCC { #4 }
Sum... succeeded.
  tower(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  p❆1_s(x1)		w: (0)
  #plus(x1,x2)		w: (0)
  towerIter(x1,x2,x3)		w: (0)
  #exp(x1,x2)		w: (x2)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  #times(x1,x2)		w: (0)
  0()		w: (0)
  times(x1,x2)		w: (0)
  #tower(x1,x2)		w: (0)
  #towerIter(x1,x2,x3)		w: (0)
  plus(x1,x2)		w: (0)
  exp(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 3, DPs: 3
	SCC { #12 }
Sum... succeeded.
  tower(x1,x2)		w: (0)
  s(x1)		w: (2 + x1)
  p❆1_s(x1)		w: (1 + x1)
  #plus(x1,x2)		w: (0)
  towerIter(x1,x2,x3)		w: (0)
  #exp(x1,x2)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  #times(x1,x2)		w: (x1)
  0()		w: (1)
  times(x1,x2)		w: (0)
  #tower(x1,x2)		w: (0)
  #towerIter(x1,x2,x3)		w: (0)
  plus(x1,x2)		w: (0)
  exp(x1,x2)		w: (0)
    USABLE RULES: { 7 8 }
    Removed DPs: #12
Number of SCCs: 2, DPs: 2
	SCC { #1 }
Sum... succeeded.
  tower(x1,x2)		w: (0)
  s(x1)		w: (2 + x1)
  p❆1_s(x1)		w: (1 + x1)
  #plus(x1,x2)		w: (x1)
  towerIter(x1,x2,x3)		w: (0)
  #exp(x1,x2)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  #times(x1,x2)		w: (x1)
  0()		w: (1)
  times(x1,x2)		w: (0)
  #tower(x1,x2)		w: (0)
  #towerIter(x1,x2,x3)		w: (0)
  plus(x1,x2)		w: (0)
  exp(x1,x2)		w: (0)
    USABLE RULES: { 7 8 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1
	SCC { #6 }
Sum... succeeded.
  tower(x1,x2)		w: (0)
  s(x1)		w: (2 + x1)
  p❆1_s(x1)		w: (1 + x1)
  #plus(x1,x2)		w: (x1)
  towerIter(x1,x2,x3)		w: (0)
  #exp(x1,x2)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  #times(x1,x2)		w: (x1)
  0()		w: (11798)
  times(x1,x2)		w: (8368 + x2 + x1)
  #tower(x1,x2)		w: (0)
  #towerIter(x1,x2,x3)		w: (10450 + x2 + x1)
  plus(x1,x2)		w: (32287 + x2 + x1)
  exp(x1,x2)		w: (1 + x2 + x1)
    USABLE RULES: { 1 7 8 }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0