MAYBE
793.01/297.03	MAYBE
793.01/297.03	
793.01/297.03	We are left with following problem, upon which TcT provides the
793.01/297.03	certificate MAYBE.
793.01/297.03	
793.01/297.03	Strict Trs:
793.01/297.03	  { table() -> gen(s(0()))
793.01/297.03	  , gen(x) -> if1(le(x, 10()), x)
793.01/297.03	  , if1(false(), x) -> nil()
793.01/297.03	  , if1(true(), x) -> if2(x, x)
793.01/297.03	  , le(s(x), s(y)) -> le(x, y)
793.01/297.03	  , le(s(x), 0()) -> false()
793.01/297.03	  , le(0(), y) -> true()
793.01/297.03	  , 10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
793.01/297.03	  , if2(x, y) -> if3(le(y, 10()), x, y)
793.01/297.03	  , if3(false(), x, y) -> gen(s(x))
793.01/297.03	  , if3(true(), x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y)))
793.01/297.03	  , times(s(x), y) -> plus(y, times(x, y))
793.01/297.03	  , times(0(), y) -> 0()
793.01/297.03	  , plus(s(x), y) -> s(plus(x, y))
793.01/297.03	  , plus(0(), y) -> y }
793.01/297.03	Obligation:
793.01/297.03	  runtime complexity
793.01/297.03	Answer:
793.01/297.03	  MAYBE
793.01/297.03	
793.01/297.03	None of the processors succeeded.
793.01/297.03	
793.01/297.03	Details of failed attempt(s):
793.01/297.03	-----------------------------
793.01/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
793.01/297.03	   following reason:
793.01/297.03	   
793.01/297.03	   Computation stopped due to timeout after 297.0 seconds.
793.01/297.03	
793.01/297.03	2) 'Best' failed due to the following reason:
793.01/297.03	   
793.01/297.03	   None of the processors succeeded.
793.01/297.03	   
793.01/297.03	   Details of failed attempt(s):
793.01/297.03	   -----------------------------
793.01/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
793.01/297.03	      seconds)' failed due to the following reason:
793.01/297.03	      
793.01/297.03	      Computation stopped due to timeout after 148.0 seconds.
793.01/297.03	   
793.01/297.03	   2) 'Best' failed due to the following reason:
793.01/297.03	      
793.01/297.03	      None of the processors succeeded.
793.01/297.03	      
793.01/297.03	      Details of failed attempt(s):
793.01/297.03	      -----------------------------
793.01/297.03	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
793.01/297.03	         to the following reason:
793.01/297.03	         
793.01/297.03	         The processor is inapplicable, reason:
793.01/297.03	           Processor only applicable for innermost runtime complexity analysis
793.01/297.03	      
793.01/297.03	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
793.01/297.03	         following reason:
793.01/297.03	         
793.01/297.03	         The processor is inapplicable, reason:
793.01/297.03	           Processor only applicable for innermost runtime complexity analysis
793.01/297.03	      
793.01/297.03	   
793.01/297.03	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
793.01/297.03	      failed due to the following reason:
793.01/297.03	      
793.01/297.03	      None of the processors succeeded.
793.01/297.03	      
793.01/297.03	      Details of failed attempt(s):
793.01/297.03	      -----------------------------
793.01/297.03	      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
793.01/297.03	         failed due to the following reason:
793.01/297.03	         
793.01/297.03	         match-boundness of the problem could not be verified.
793.01/297.03	      
793.01/297.03	      2) 'Bounds with minimal-enrichment and initial automaton 'match''
793.01/297.03	         failed due to the following reason:
793.01/297.03	         
793.01/297.03	         match-boundness of the problem could not be verified.
793.01/297.03	      
793.01/297.03	   
793.01/297.03	
793.01/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
793.01/297.03	   the following reason:
793.01/297.03	   
793.01/297.03	   We add the following weak dependency pairs:
793.01/297.03	   
793.01/297.03	   Strict DPs:
793.01/297.03	     { table^#() -> c_1(gen^#(s(0())))
793.01/297.03	     , gen^#(x) -> c_2(if1^#(le(x, 10()), x))
793.01/297.03	     , if1^#(false(), x) -> c_3()
793.01/297.03	     , if1^#(true(), x) -> c_4(if2^#(x, x))
793.01/297.03	     , if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y))
793.01/297.03	     , le^#(s(x), s(y)) -> c_5(le^#(x, y))
793.01/297.03	     , le^#(s(x), 0()) -> c_6()
793.01/297.03	     , le^#(0(), y) -> c_7()
793.01/297.03	     , 10^#() -> c_8()
793.01/297.03	     , if3^#(false(), x, y) -> c_10(gen^#(s(x)))
793.01/297.03	     , if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y)))
793.01/297.03	     , times^#(s(x), y) -> c_12(plus^#(y, times(x, y)))
793.01/297.03	     , times^#(0(), y) -> c_13()
793.01/297.03	     , plus^#(s(x), y) -> c_14(plus^#(x, y))
793.01/297.03	     , plus^#(0(), y) -> c_15(y) }
793.01/297.03	   
793.01/297.03	   and mark the set of starting terms.
793.01/297.03	   
793.01/297.03	   We are left with following problem, upon which TcT provides the
793.01/297.03	   certificate MAYBE.
793.01/297.03	   
793.01/297.03	   Strict DPs:
793.01/297.03	     { table^#() -> c_1(gen^#(s(0())))
793.01/297.03	     , gen^#(x) -> c_2(if1^#(le(x, 10()), x))
793.01/297.03	     , if1^#(false(), x) -> c_3()
793.01/297.03	     , if1^#(true(), x) -> c_4(if2^#(x, x))
793.01/297.03	     , if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y))
793.01/297.03	     , le^#(s(x), s(y)) -> c_5(le^#(x, y))
793.01/297.03	     , le^#(s(x), 0()) -> c_6()
793.01/297.03	     , le^#(0(), y) -> c_7()
793.01/297.03	     , 10^#() -> c_8()
793.01/297.03	     , if3^#(false(), x, y) -> c_10(gen^#(s(x)))
793.01/297.03	     , if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y)))
793.01/297.03	     , times^#(s(x), y) -> c_12(plus^#(y, times(x, y)))
793.01/297.03	     , times^#(0(), y) -> c_13()
793.01/297.03	     , plus^#(s(x), y) -> c_14(plus^#(x, y))
793.01/297.03	     , plus^#(0(), y) -> c_15(y) }
793.01/297.03	   Strict Trs:
793.01/297.03	     { table() -> gen(s(0()))
793.01/297.03	     , gen(x) -> if1(le(x, 10()), x)
793.01/297.03	     , if1(false(), x) -> nil()
793.01/297.03	     , if1(true(), x) -> if2(x, x)
793.01/297.03	     , le(s(x), s(y)) -> le(x, y)
793.01/297.03	     , le(s(x), 0()) -> false()
793.01/297.03	     , le(0(), y) -> true()
793.01/297.03	     , 10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
793.01/297.03	     , if2(x, y) -> if3(le(y, 10()), x, y)
793.01/297.03	     , if3(false(), x, y) -> gen(s(x))
793.01/297.03	     , if3(true(), x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y)))
793.01/297.03	     , times(s(x), y) -> plus(y, times(x, y))
793.01/297.03	     , times(0(), y) -> 0()
793.01/297.03	     , plus(s(x), y) -> s(plus(x, y))
793.01/297.03	     , plus(0(), y) -> y }
793.01/297.03	   Obligation:
793.01/297.03	     runtime complexity
793.01/297.03	   Answer:
793.01/297.03	     MAYBE
793.01/297.03	   
793.01/297.03	   We estimate the number of application of {3,7,8,9,13} by
793.01/297.03	   applications of Pre({3,7,8,9,13}) = {2,6,11,15}. Here rules are
793.01/297.03	   labeled as follows:
793.01/297.03	   
793.01/297.03	     DPs:
793.01/297.03	       { 1: table^#() -> c_1(gen^#(s(0())))
793.01/297.03	       , 2: gen^#(x) -> c_2(if1^#(le(x, 10()), x))
793.01/297.03	       , 3: if1^#(false(), x) -> c_3()
793.01/297.03	       , 4: if1^#(true(), x) -> c_4(if2^#(x, x))
793.01/297.03	       , 5: if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y))
793.01/297.03	       , 6: le^#(s(x), s(y)) -> c_5(le^#(x, y))
793.01/297.03	       , 7: le^#(s(x), 0()) -> c_6()
793.01/297.03	       , 8: le^#(0(), y) -> c_7()
793.01/297.03	       , 9: 10^#() -> c_8()
793.01/297.03	       , 10: if3^#(false(), x, y) -> c_10(gen^#(s(x)))
793.01/297.03	       , 11: if3^#(true(), x, y) ->
793.01/297.03	             c_11(x, y, times^#(x, y), if2^#(x, s(y)))
793.01/297.03	       , 12: times^#(s(x), y) -> c_12(plus^#(y, times(x, y)))
793.01/297.03	       , 13: times^#(0(), y) -> c_13()
793.01/297.03	       , 14: plus^#(s(x), y) -> c_14(plus^#(x, y))
793.01/297.03	       , 15: plus^#(0(), y) -> c_15(y) }
793.01/297.03	   
793.01/297.03	   We are left with following problem, upon which TcT provides the
793.01/297.03	   certificate MAYBE.
793.01/297.03	   
793.01/297.03	   Strict DPs:
793.01/297.03	     { table^#() -> c_1(gen^#(s(0())))
793.01/297.03	     , gen^#(x) -> c_2(if1^#(le(x, 10()), x))
793.01/297.03	     , if1^#(true(), x) -> c_4(if2^#(x, x))
793.01/297.03	     , if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y))
793.01/297.03	     , le^#(s(x), s(y)) -> c_5(le^#(x, y))
793.01/297.03	     , if3^#(false(), x, y) -> c_10(gen^#(s(x)))
793.01/297.03	     , if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y)))
793.01/297.03	     , times^#(s(x), y) -> c_12(plus^#(y, times(x, y)))
793.01/297.03	     , plus^#(s(x), y) -> c_14(plus^#(x, y))
793.01/297.03	     , plus^#(0(), y) -> c_15(y) }
793.01/297.03	   Strict Trs:
793.01/297.03	     { table() -> gen(s(0()))
793.01/297.03	     , gen(x) -> if1(le(x, 10()), x)
793.01/297.03	     , if1(false(), x) -> nil()
793.01/297.03	     , if1(true(), x) -> if2(x, x)
793.01/297.03	     , le(s(x), s(y)) -> le(x, y)
793.01/297.03	     , le(s(x), 0()) -> false()
793.01/297.03	     , le(0(), y) -> true()
793.01/297.03	     , 10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
793.01/297.03	     , if2(x, y) -> if3(le(y, 10()), x, y)
793.01/297.03	     , if3(false(), x, y) -> gen(s(x))
793.01/297.03	     , if3(true(), x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y)))
793.01/297.03	     , times(s(x), y) -> plus(y, times(x, y))
793.01/297.03	     , times(0(), y) -> 0()
793.01/297.03	     , plus(s(x), y) -> s(plus(x, y))
793.01/297.03	     , plus(0(), y) -> y }
793.01/297.03	   Weak DPs:
793.01/297.03	     { if1^#(false(), x) -> c_3()
793.01/297.03	     , le^#(s(x), 0()) -> c_6()
793.01/297.03	     , le^#(0(), y) -> c_7()
793.01/297.03	     , 10^#() -> c_8()
793.01/297.03	     , times^#(0(), y) -> c_13() }
793.01/297.03	   Obligation:
793.01/297.03	     runtime complexity
793.01/297.03	   Answer:
793.01/297.03	     MAYBE
793.01/297.03	   
793.01/297.03	   Empty strict component of the problem is NOT empty.
793.01/297.03	
793.01/297.03	
793.01/297.03	Arrrr..
793.32/297.30	EOF