/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: times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
    2: times(x,0()) -> 0()
    3: times(x,s(y)) -> plus(times(x,y),x)
    4: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
    5: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
    6: plus(zero(),y) -> y
    7: plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
    8: id(x) -> x
    9: if(true(),x,y) -> x
    10: if(false(),x,y) -> y
    11: not(x) -> if(x,false(),true())
    12: gt(s(x),zero()) -> true()
    13: gt(zero(),y) -> false()
    14: gt(s(x),s(y)) -> gt(x,y)
Number of strict rules: 14
Direct poly ... failed.
Freezing gt
1: times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
2: times(x,0()) -> 0()
3: times(x,s(y)) -> plus(times(x,y),x)
4: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
5: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
6: plus(zero(),y) -> y
7: plus(id(x),s(y)) -> s(plus(x,if(gt❆1_s(y,y),y,s(y))))
8: id(x) -> x
9: if(true(),x,y) -> x
10: if(false(),x,y) -> y
11: not(x) -> if(x,false(),true())
12: gt❆1_s(x,zero()) -> true()
13: gt❆1_zero(y) -> false()
14: gt❆1_s(x,s(y)) -> gt(x,y)
15: gt(zero(),_1) ->= gt❆1_zero(_1)
16: gt(s(_1),_2) ->= gt❆1_s(_1,_2)
Number of strict rules: 14
Direct poly ... failed.
Dependency Pairs:
   #1: #not(x) -> #if(x,false(),true())
   #2: #gt❆1_s(x,s(y)) -> #gt(x,y)
   #3: #plus(id(x),s(y)) -> #plus(x,if(gt❆1_s(y,y),y,s(y)))
   #4: #plus(id(x),s(y)) -> #if(gt❆1_s(y,y),y,s(y))
   #5: #plus(id(x),s(y)) -> #gt❆1_s(y,y)
   #6: #plus(s(x),x) -> #plus(if(gt(x,x),id(x),id(x)),s(x))
   #7: #plus(s(x),x) -> #if(gt(x,x),id(x),id(x))
   #8: #plus(s(x),x) -> #gt(x,x)
   #9: #plus(s(x),x) -> #id(x)
   #10: #plus(s(x),x) -> #id(x)
   #11: #gt(s(_1),_2) ->? #gt❆1_s(_1,_2)
   #12: #times(x,s(y)) -> #plus(times(x,y),x)
   #13: #times(x,s(y)) -> #times(x,y)
   #14: #times(x,plus(y,s(z))) -> #plus(times(x,plus(y,times(s(z),0()))),times(x,s(z)))
   #15: #times(x,plus(y,s(z))) -> #times(x,plus(y,times(s(z),0())))
   #16: #times(x,plus(y,s(z))) -> #plus(y,times(s(z),0()))
   #17: #times(x,plus(y,s(z))) -> #times(s(z),0())
   #18: #times(x,plus(y,s(z))) -> #times(x,s(z))
   #19: #gt(zero(),_1) ->? #gt❆1_zero(_1)
   #20: #plus(s(x),s(y)) -> #plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
   #21: #plus(s(x),s(y)) -> #if(gt(x,y),x,y)
   #22: #plus(s(x),s(y)) -> #gt(x,y)
   #23: #plus(s(x),s(y)) -> #if(not(gt(x,y)),id(x),id(y))
   #24: #plus(s(x),s(y)) -> #not(gt(x,y))
   #25: #plus(s(x),s(y)) -> #gt(x,y)
   #26: #plus(s(x),s(y)) -> #id(x)
   #27: #plus(s(x),s(y)) -> #id(y)
Number of SCCs: 3, DPs: 8
	SCC { #2 #11 }
Sum... succeeded.
  zero()		w: (0)
  s(x1)		w: (2 + x1)
  gt(x1,x2)		w: (0)
  #plus(x1,x2)		w: (0)
  false()		w: (0)
  #id(x1)		w: (0)
  true()		w: (0)
  gt❆1_zero(x1)		w: (0)
  #not(x1)		w: (0)
  #times(x1,x2)		w: (0)
  #gt❆1_zero(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  times(x1,x2)		w: (0)
  #gt(x1,x2)		w: (x1)
  #gt❆1_s(x1,x2)		w: (1 + x1)
  plus(x1,x2)		w: (0)
  #if(x1,x2,x3)		w: (0)
  id(x1)		w: (0)
  gt❆1_s(x1,x2)		w: (0)
  not(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2 #11
Number of SCCs: 2, DPs: 6
	SCC { #13 #15 #18 }
Sum... Max... succeeded.
  zero()		w: (3)
  s(x1)		w: (x1)
  gt(x1,x2)		w: (max{3 + x2, 1 + x1})
  #plus(x1,x2)		w: (0)
  false()		w: (10455)
  #id(x1)		w: (0)
  true()		w: (10456)
  gt❆1_zero(x1)		w: (4)
  #not(x1)		w: (0)
  #times(x1,x2)		w: (max{1 + x2, 0})
  #gt❆1_zero(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (max{x3, x2, 0})
  times(x1,x2)		w: (0)
  #gt(x1,x2)		w: (0)
  #gt❆1_s(x1,x2)		w: (0)
  plus(x1,x2)		w: (max{2 + x2, 2 + x1})
  #if(x1,x2,x3)		w: (0)
  id(x1)		w: (x1)
  gt❆1_s(x1,x2)		w: (max{2 + x2, 0})
  not(x1)		w: (10455 + x1)
    USABLE RULES: { 2 4..10 }
    Removed DPs: #18
Number of SCCs: 2, DPs: 5
	SCC { #13 #15 }
Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... sum_sum_int,sum_neg... heuristic_int,sum_neg... failed.
Finding a loop...  failed.