MAYBE
1184.50/297.10	MAYBE
1184.50/297.10	
1184.50/297.10	We are left with following problem, upon which TcT provides the
1184.50/297.10	certificate MAYBE.
1184.50/297.10	
1184.50/297.10	Strict Trs:
1184.50/297.10	  { terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
1184.50/297.10	  , terms(X) -> n__terms(X)
1184.50/297.10	  , sqr(s(X)) -> s(n__add(sqr(activate(X)), dbl(activate(X))))
1184.50/297.10	  , sqr(0()) -> 0()
1184.50/297.10	  , s(X) -> n__s(X)
1184.50/297.10	  , activate(X) -> X
1184.50/297.10	  , activate(n__terms(X)) -> terms(X)
1184.50/297.10	  , activate(n__add(X1, X2)) -> add(X1, X2)
1184.50/297.10	  , activate(n__s(X)) -> s(X)
1184.50/297.10	  , activate(n__dbl(X)) -> dbl(X)
1184.50/297.10	  , activate(n__first(X1, X2)) -> first(X1, X2)
1184.50/297.10	  , dbl(X) -> n__dbl(X)
1184.50/297.10	  , dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
1184.50/297.10	  , dbl(0()) -> 0()
1184.50/297.10	  , add(X1, X2) -> n__add(X1, X2)
1184.50/297.10	  , add(s(X), Y) -> s(n__add(activate(X), Y))
1184.50/297.10	  , add(0(), X) -> X
1184.50/297.10	  , first(X1, X2) -> n__first(X1, X2)
1184.50/297.10	  , first(s(X), cons(Y, Z)) ->
1184.50/297.10	    cons(Y, n__first(activate(X), activate(Z)))
1184.50/297.10	  , first(0(), X) -> nil() }
1184.50/297.10	Obligation:
1184.50/297.10	  runtime complexity
1184.50/297.10	Answer:
1184.50/297.10	  MAYBE
1184.50/297.10	
1184.50/297.10	None of the processors succeeded.
1184.50/297.10	
1184.50/297.10	Details of failed attempt(s):
1184.50/297.10	-----------------------------
1184.50/297.10	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
1184.50/297.10	   following reason:
1184.50/297.10	   
1184.50/297.10	   Computation stopped due to timeout after 297.0 seconds.
1184.50/297.10	
1184.50/297.10	2) 'Best' failed due to the following reason:
1184.50/297.10	   
1184.50/297.10	   None of the processors succeeded.
1184.50/297.10	   
1184.50/297.10	   Details of failed attempt(s):
1184.50/297.10	   -----------------------------
1184.50/297.10	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
1184.50/297.10	      seconds)' failed due to the following reason:
1184.50/297.10	      
1184.50/297.10	      Computation stopped due to timeout after 148.0 seconds.
1184.50/297.10	   
1184.50/297.10	   2) 'Best' failed due to the following reason:
1184.50/297.10	      
1184.50/297.10	      None of the processors succeeded.
1184.50/297.10	      
1184.50/297.10	      Details of failed attempt(s):
1184.50/297.10	      -----------------------------
1184.50/297.10	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
1184.50/297.10	         to the following reason:
1184.50/297.10	         
1184.50/297.10	         The processor is inapplicable, reason:
1184.50/297.10	           Processor only applicable for innermost runtime complexity analysis
1184.50/297.10	      
1184.50/297.10	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
1184.50/297.10	         following reason:
1184.50/297.10	         
1184.50/297.10	         The processor is inapplicable, reason:
1184.50/297.10	           Processor only applicable for innermost runtime complexity analysis
1184.50/297.10	      
1184.50/297.10	   
1184.50/297.10	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
1184.50/297.10	      failed due to the following reason:
1184.50/297.10	      
1184.50/297.10	      None of the processors succeeded.
1184.50/297.10	      
1184.50/297.10	      Details of failed attempt(s):
1184.50/297.10	      -----------------------------
1184.50/297.10	      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
1184.50/297.10	         failed due to the following reason:
1184.50/297.10	         
1184.50/297.10	         match-boundness of the problem could not be verified.
1184.50/297.10	      
1184.50/297.10	      2) 'Bounds with minimal-enrichment and initial automaton 'match''
1184.50/297.10	         failed due to the following reason:
1184.50/297.10	         
1184.50/297.10	         match-boundness of the problem could not be verified.
1184.50/297.10	      
1184.50/297.10	   
1184.50/297.10	
1184.50/297.10	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
1184.50/297.10	   the following reason:
1184.50/297.10	   
1184.50/297.10	   We add the following weak dependency pairs:
1184.50/297.10	   
1184.50/297.10	   Strict DPs:
1184.50/297.10	     { terms^#(N) -> c_1(sqr^#(N), s^#(N))
1184.50/297.10	     , terms^#(X) -> c_2(X)
1184.50/297.10	     , sqr^#(s(X)) ->
1184.50/297.10	       c_3(s^#(n__add(sqr(activate(X)), dbl(activate(X)))))
1184.50/297.10	     , sqr^#(0()) -> c_4()
1184.50/297.10	     , s^#(X) -> c_5(X)
1184.50/297.10	     , activate^#(X) -> c_6(X)
1184.50/297.10	     , activate^#(n__terms(X)) -> c_7(terms^#(X))
1184.50/297.10	     , activate^#(n__add(X1, X2)) -> c_8(add^#(X1, X2))
1184.50/297.10	     , activate^#(n__s(X)) -> c_9(s^#(X))
1184.50/297.10	     , activate^#(n__dbl(X)) -> c_10(dbl^#(X))
1184.50/297.10	     , activate^#(n__first(X1, X2)) -> c_11(first^#(X1, X2))
1184.50/297.10	     , add^#(X1, X2) -> c_15(X1, X2)
1184.50/297.10	     , add^#(s(X), Y) -> c_16(s^#(n__add(activate(X), Y)))
1184.50/297.10	     , add^#(0(), X) -> c_17(X)
1184.50/297.10	     , dbl^#(X) -> c_12(X)
1184.50/297.10	     , dbl^#(s(X)) -> c_13(s^#(n__s(n__dbl(activate(X)))))
1184.50/297.10	     , dbl^#(0()) -> c_14()
1184.50/297.10	     , first^#(X1, X2) -> c_18(X1, X2)
1184.50/297.10	     , first^#(s(X), cons(Y, Z)) ->
1184.50/297.10	       c_19(Y, activate^#(X), activate^#(Z))
1184.50/297.10	     , first^#(0(), X) -> c_20() }
1184.50/297.10	   
1184.50/297.10	   and mark the set of starting terms.
1184.50/297.10	   
1184.50/297.10	   We are left with following problem, upon which TcT provides the
1184.50/297.10	   certificate MAYBE.
1184.50/297.10	   
1184.50/297.10	   Strict DPs:
1184.50/297.10	     { terms^#(N) -> c_1(sqr^#(N), s^#(N))
1184.50/297.10	     , terms^#(X) -> c_2(X)
1184.50/297.10	     , sqr^#(s(X)) ->
1184.50/297.10	       c_3(s^#(n__add(sqr(activate(X)), dbl(activate(X)))))
1184.50/297.10	     , sqr^#(0()) -> c_4()
1184.50/297.10	     , s^#(X) -> c_5(X)
1184.50/297.10	     , activate^#(X) -> c_6(X)
1184.50/297.10	     , activate^#(n__terms(X)) -> c_7(terms^#(X))
1184.50/297.10	     , activate^#(n__add(X1, X2)) -> c_8(add^#(X1, X2))
1184.50/297.10	     , activate^#(n__s(X)) -> c_9(s^#(X))
1184.50/297.10	     , activate^#(n__dbl(X)) -> c_10(dbl^#(X))
1184.50/297.10	     , activate^#(n__first(X1, X2)) -> c_11(first^#(X1, X2))
1184.50/297.10	     , add^#(X1, X2) -> c_15(X1, X2)
1184.50/297.10	     , add^#(s(X), Y) -> c_16(s^#(n__add(activate(X), Y)))
1184.50/297.10	     , add^#(0(), X) -> c_17(X)
1184.50/297.10	     , dbl^#(X) -> c_12(X)
1184.50/297.10	     , dbl^#(s(X)) -> c_13(s^#(n__s(n__dbl(activate(X)))))
1184.50/297.10	     , dbl^#(0()) -> c_14()
1184.50/297.10	     , first^#(X1, X2) -> c_18(X1, X2)
1184.50/297.10	     , first^#(s(X), cons(Y, Z)) ->
1184.50/297.10	       c_19(Y, activate^#(X), activate^#(Z))
1184.50/297.10	     , first^#(0(), X) -> c_20() }
1184.50/297.10	   Strict Trs:
1184.50/297.10	     { terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
1184.50/297.10	     , terms(X) -> n__terms(X)
1184.50/297.10	     , sqr(s(X)) -> s(n__add(sqr(activate(X)), dbl(activate(X))))
1184.50/297.10	     , sqr(0()) -> 0()
1184.50/297.10	     , s(X) -> n__s(X)
1184.50/297.10	     , activate(X) -> X
1184.50/297.10	     , activate(n__terms(X)) -> terms(X)
1184.50/297.10	     , activate(n__add(X1, X2)) -> add(X1, X2)
1184.50/297.10	     , activate(n__s(X)) -> s(X)
1184.50/297.10	     , activate(n__dbl(X)) -> dbl(X)
1184.50/297.10	     , activate(n__first(X1, X2)) -> first(X1, X2)
1184.50/297.10	     , dbl(X) -> n__dbl(X)
1184.50/297.10	     , dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
1184.50/297.10	     , dbl(0()) -> 0()
1184.50/297.10	     , add(X1, X2) -> n__add(X1, X2)
1184.50/297.10	     , add(s(X), Y) -> s(n__add(activate(X), Y))
1184.50/297.10	     , add(0(), X) -> X
1184.50/297.10	     , first(X1, X2) -> n__first(X1, X2)
1184.50/297.10	     , first(s(X), cons(Y, Z)) ->
1184.50/297.10	       cons(Y, n__first(activate(X), activate(Z)))
1184.50/297.10	     , first(0(), X) -> nil() }
1184.50/297.10	   Obligation:
1184.50/297.10	     runtime complexity
1184.50/297.10	   Answer:
1184.50/297.10	     MAYBE
1184.50/297.10	   
1184.50/297.10	   We estimate the number of application of {4,17,20} by applications
1184.50/297.10	   of Pre({4,17,20}) = {1,2,5,6,10,11,12,14,15,18,19}. Here rules are
1184.50/297.10	   labeled as follows:
1184.50/297.10	   
1184.50/297.10	     DPs:
1184.50/297.10	       { 1: terms^#(N) -> c_1(sqr^#(N), s^#(N))
1184.50/297.10	       , 2: terms^#(X) -> c_2(X)
1184.50/297.10	       , 3: sqr^#(s(X)) ->
1184.50/297.10	            c_3(s^#(n__add(sqr(activate(X)), dbl(activate(X)))))
1184.50/297.10	       , 4: sqr^#(0()) -> c_4()
1184.50/297.10	       , 5: s^#(X) -> c_5(X)
1184.50/297.10	       , 6: activate^#(X) -> c_6(X)
1184.50/297.10	       , 7: activate^#(n__terms(X)) -> c_7(terms^#(X))
1184.50/297.10	       , 8: activate^#(n__add(X1, X2)) -> c_8(add^#(X1, X2))
1184.50/297.10	       , 9: activate^#(n__s(X)) -> c_9(s^#(X))
1184.50/297.10	       , 10: activate^#(n__dbl(X)) -> c_10(dbl^#(X))
1184.50/297.10	       , 11: activate^#(n__first(X1, X2)) -> c_11(first^#(X1, X2))
1184.50/297.10	       , 12: add^#(X1, X2) -> c_15(X1, X2)
1184.50/297.10	       , 13: add^#(s(X), Y) -> c_16(s^#(n__add(activate(X), Y)))
1184.50/297.10	       , 14: add^#(0(), X) -> c_17(X)
1184.50/297.10	       , 15: dbl^#(X) -> c_12(X)
1184.50/297.10	       , 16: dbl^#(s(X)) -> c_13(s^#(n__s(n__dbl(activate(X)))))
1184.50/297.10	       , 17: dbl^#(0()) -> c_14()
1184.50/297.10	       , 18: first^#(X1, X2) -> c_18(X1, X2)
1184.50/297.10	       , 19: first^#(s(X), cons(Y, Z)) ->
1184.50/297.10	             c_19(Y, activate^#(X), activate^#(Z))
1184.50/297.10	       , 20: first^#(0(), X) -> c_20() }
1184.50/297.10	   
1184.50/297.10	   We are left with following problem, upon which TcT provides the
1184.50/297.10	   certificate MAYBE.
1184.50/297.10	   
1184.50/297.10	   Strict DPs:
1184.50/297.10	     { terms^#(N) -> c_1(sqr^#(N), s^#(N))
1184.50/297.10	     , terms^#(X) -> c_2(X)
1184.50/297.10	     , sqr^#(s(X)) ->
1184.50/297.10	       c_3(s^#(n__add(sqr(activate(X)), dbl(activate(X)))))
1184.50/297.10	     , s^#(X) -> c_5(X)
1184.50/297.10	     , activate^#(X) -> c_6(X)
1184.50/297.10	     , activate^#(n__terms(X)) -> c_7(terms^#(X))
1184.50/297.10	     , activate^#(n__add(X1, X2)) -> c_8(add^#(X1, X2))
1184.50/297.10	     , activate^#(n__s(X)) -> c_9(s^#(X))
1184.50/297.10	     , activate^#(n__dbl(X)) -> c_10(dbl^#(X))
1184.50/297.10	     , activate^#(n__first(X1, X2)) -> c_11(first^#(X1, X2))
1184.50/297.10	     , add^#(X1, X2) -> c_15(X1, X2)
1184.50/297.10	     , add^#(s(X), Y) -> c_16(s^#(n__add(activate(X), Y)))
1184.50/297.10	     , add^#(0(), X) -> c_17(X)
1184.50/297.10	     , dbl^#(X) -> c_12(X)
1184.50/297.10	     , dbl^#(s(X)) -> c_13(s^#(n__s(n__dbl(activate(X)))))
1184.50/297.10	     , first^#(X1, X2) -> c_18(X1, X2)
1184.50/297.10	     , first^#(s(X), cons(Y, Z)) ->
1184.50/297.10	       c_19(Y, activate^#(X), activate^#(Z)) }
1184.50/297.10	   Strict Trs:
1184.50/297.10	     { terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
1184.50/297.10	     , terms(X) -> n__terms(X)
1184.50/297.10	     , sqr(s(X)) -> s(n__add(sqr(activate(X)), dbl(activate(X))))
1184.50/297.10	     , sqr(0()) -> 0()
1184.50/297.10	     , s(X) -> n__s(X)
1184.50/297.10	     , activate(X) -> X
1184.50/297.10	     , activate(n__terms(X)) -> terms(X)
1184.50/297.10	     , activate(n__add(X1, X2)) -> add(X1, X2)
1184.50/297.10	     , activate(n__s(X)) -> s(X)
1184.50/297.10	     , activate(n__dbl(X)) -> dbl(X)
1184.50/297.10	     , activate(n__first(X1, X2)) -> first(X1, X2)
1184.50/297.10	     , dbl(X) -> n__dbl(X)
1184.50/297.10	     , dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
1184.50/297.10	     , dbl(0()) -> 0()
1184.50/297.10	     , add(X1, X2) -> n__add(X1, X2)
1184.50/297.10	     , add(s(X), Y) -> s(n__add(activate(X), Y))
1184.50/297.10	     , add(0(), X) -> X
1184.50/297.10	     , first(X1, X2) -> n__first(X1, X2)
1184.50/297.10	     , first(s(X), cons(Y, Z)) ->
1184.50/297.10	       cons(Y, n__first(activate(X), activate(Z)))
1184.50/297.10	     , first(0(), X) -> nil() }
1184.50/297.10	   Weak DPs:
1184.50/297.10	     { sqr^#(0()) -> c_4()
1184.50/297.10	     , dbl^#(0()) -> c_14()
1184.50/297.10	     , first^#(0(), X) -> c_20() }
1184.50/297.10	   Obligation:
1184.50/297.10	     runtime complexity
1184.50/297.10	   Answer:
1184.50/297.10	     MAYBE
1184.50/297.10	   
1184.50/297.10	   Empty strict component of the problem is NOT empty.
1184.50/297.10	
1184.50/297.10	
1184.50/297.10	Arrrr..
1185.21/297.82	EOF