MAYBE
1184.39/297.09	MAYBE
1184.39/297.09	
1184.39/297.09	We are left with following problem, upon which TcT provides the
1184.39/297.09	certificate MAYBE.
1184.39/297.09	
1184.39/297.09	Strict Trs:
1184.39/297.09	  { from(X) -> cons(X, n__from(n__s(X)))
1184.39/297.09	  , from(X) -> n__from(X)
1184.39/297.09	  , 2ndspos(0(), Z) -> rnil()
1184.39/297.09	  , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z)))
1184.39/297.09	  , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	    rcons(posrecip(Y), 2ndsneg(N, activate(Z)))
1184.39/297.09	  , s(X) -> n__s(X)
1184.39/297.09	  , activate(X) -> X
1184.39/297.09	  , activate(n__from(X)) -> from(activate(X))
1184.39/297.09	  , activate(n__s(X)) -> s(activate(X))
1184.39/297.09	  , 2ndsneg(0(), Z) -> rnil()
1184.39/297.09	  , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z)))
1184.39/297.09	  , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	    rcons(negrecip(Y), 2ndspos(N, activate(Z)))
1184.39/297.09	  , pi(X) -> 2ndspos(X, from(0()))
1184.39/297.09	  , plus(0(), Y) -> Y
1184.39/297.09	  , plus(s(X), Y) -> s(plus(X, Y))
1184.39/297.09	  , times(0(), Y) -> 0()
1184.39/297.09	  , times(s(X), Y) -> plus(Y, times(X, Y))
1184.39/297.09	  , square(X) -> times(X, X) }
1184.39/297.09	Obligation:
1184.39/297.09	  runtime complexity
1184.39/297.09	Answer:
1184.39/297.09	  MAYBE
1184.39/297.09	
1184.39/297.09	None of the processors succeeded.
1184.39/297.09	
1184.39/297.09	Details of failed attempt(s):
1184.39/297.09	-----------------------------
1184.39/297.09	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
1184.39/297.09	   following reason:
1184.39/297.09	   
1184.39/297.09	   Computation stopped due to timeout after 297.0 seconds.
1184.39/297.09	
1184.39/297.09	2) 'Best' failed due to the following reason:
1184.39/297.09	   
1184.39/297.09	   None of the processors succeeded.
1184.39/297.09	   
1184.39/297.09	   Details of failed attempt(s):
1184.39/297.09	   -----------------------------
1184.39/297.09	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
1184.39/297.09	      seconds)' failed due to the following reason:
1184.39/297.09	      
1184.39/297.09	      None of the processors succeeded.
1184.39/297.09	      
1184.39/297.09	      Details of failed attempt(s):
1184.39/297.09	      -----------------------------
1184.39/297.09	      1) 'empty' failed due to the following reason:
1184.39/297.09	         
1184.39/297.09	         Empty strict component of the problem is NOT empty.
1184.39/297.09	      
1184.39/297.09	      2) 'With Problem ...' failed due to the following reason:
1184.39/297.09	         
1184.39/297.09	         None of the processors succeeded.
1184.39/297.09	         
1184.39/297.09	         Details of failed attempt(s):
1184.39/297.09	         -----------------------------
1184.39/297.09	         1) 'empty' failed due to the following reason:
1184.39/297.09	            
1184.39/297.09	            Empty strict component of the problem is NOT empty.
1184.39/297.09	         
1184.39/297.09	         2) 'Fastest' failed due to the following reason:
1184.39/297.09	            
1184.39/297.09	            None of the processors succeeded.
1184.39/297.09	            
1184.39/297.09	            Details of failed attempt(s):
1184.39/297.09	            -----------------------------
1184.39/297.09	            1) 'With Problem ...' failed due to the following reason:
1184.39/297.09	               
1184.39/297.09	               None of the processors succeeded.
1184.39/297.09	               
1184.39/297.09	               Details of failed attempt(s):
1184.39/297.09	               -----------------------------
1184.39/297.09	               1) 'empty' failed due to the following reason:
1184.39/297.09	                  
1184.39/297.09	                  Empty strict component of the problem is NOT empty.
1184.39/297.09	               
1184.39/297.09	               2) 'With Problem ...' failed due to the following reason:
1184.39/297.09	                  
1184.39/297.09	                  None of the processors succeeded.
1184.39/297.09	                  
1184.39/297.09	                  Details of failed attempt(s):
1184.39/297.09	                  -----------------------------
1184.39/297.09	                  1) 'empty' failed due to the following reason:
1184.39/297.09	                     
1184.39/297.09	                     Empty strict component of the problem is NOT empty.
1184.39/297.09	                  
1184.39/297.09	                  2) 'With Problem ...' failed due to the following reason:
1184.39/297.09	                     
1184.39/297.09	                     None of the processors succeeded.
1184.39/297.09	                     
1184.39/297.09	                     Details of failed attempt(s):
1184.39/297.09	                     -----------------------------
1184.39/297.09	                     1) 'empty' failed due to the following reason:
1184.39/297.09	                        
1184.39/297.09	                        Empty strict component of the problem is NOT empty.
1184.39/297.09	                     
1184.39/297.09	                     2) 'With Problem ...' failed due to the following reason:
1184.39/297.09	                        
1184.39/297.09	                        Empty strict component of the problem is NOT empty.
1184.39/297.09	                     
1184.39/297.09	                  
1184.39/297.09	               
1184.39/297.09	            
1184.39/297.09	            2) 'With Problem ...' failed due to the following reason:
1184.39/297.09	               
1184.39/297.09	               None of the processors succeeded.
1184.39/297.09	               
1184.39/297.09	               Details of failed attempt(s):
1184.39/297.09	               -----------------------------
1184.39/297.09	               1) 'empty' failed due to the following reason:
1184.39/297.09	                  
1184.39/297.09	                  Empty strict component of the problem is NOT empty.
1184.39/297.09	               
1184.39/297.09	               2) 'With Problem ...' failed due to the following reason:
1184.39/297.09	                  
1184.39/297.09	                  Empty strict component of the problem is NOT empty.
1184.39/297.09	               
1184.39/297.09	            
1184.39/297.09	         
1184.39/297.09	      
1184.39/297.09	   
1184.39/297.09	   2) 'Best' failed due to the following reason:
1184.39/297.09	      
1184.39/297.09	      None of the processors succeeded.
1184.39/297.09	      
1184.39/297.09	      Details of failed attempt(s):
1184.39/297.09	      -----------------------------
1184.39/297.09	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
1184.39/297.09	         following reason:
1184.39/297.09	         
1184.39/297.09	         The processor is inapplicable, reason:
1184.39/297.09	           Processor only applicable for innermost runtime complexity analysis
1184.39/297.09	      
1184.39/297.09	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
1184.39/297.09	         to the following reason:
1184.39/297.09	         
1184.39/297.09	         The processor is inapplicable, reason:
1184.39/297.09	           Processor only applicable for innermost runtime complexity analysis
1184.39/297.09	      
1184.39/297.09	   
1184.39/297.09	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
1184.39/297.09	      failed due to the following reason:
1184.39/297.09	      
1184.39/297.09	      None of the processors succeeded.
1184.39/297.09	      
1184.39/297.09	      Details of failed attempt(s):
1184.39/297.09	      -----------------------------
1184.39/297.09	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
1184.39/297.09	         failed due to the following reason:
1184.39/297.09	         
1184.39/297.09	         match-boundness of the problem could not be verified.
1184.39/297.09	      
1184.39/297.09	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
1184.39/297.09	         failed due to the following reason:
1184.39/297.09	         
1184.39/297.09	         match-boundness of the problem could not be verified.
1184.39/297.09	      
1184.39/297.09	   
1184.39/297.09	
1184.39/297.09	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
1184.39/297.09	   the following reason:
1184.39/297.09	   
1184.39/297.09	   We add the following weak dependency pairs:
1184.39/297.09	   
1184.39/297.09	   Strict DPs:
1184.39/297.09	     { from^#(X) -> c_1(X, X)
1184.39/297.09	     , from^#(X) -> c_2(X)
1184.39/297.09	     , 2ndspos^#(0(), Z) -> c_3()
1184.39/297.09	     , 2ndspos^#(s(N), cons(X, Z)) ->
1184.39/297.09	       c_4(2ndspos^#(s(N), cons2(X, activate(Z))))
1184.39/297.09	     , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       c_5(Y, 2ndsneg^#(N, activate(Z)))
1184.39/297.09	     , 2ndsneg^#(0(), Z) -> c_10()
1184.39/297.09	     , 2ndsneg^#(s(N), cons(X, Z)) ->
1184.39/297.09	       c_11(2ndsneg^#(s(N), cons2(X, activate(Z))))
1184.39/297.09	     , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       c_12(Y, 2ndspos^#(N, activate(Z)))
1184.39/297.09	     , s^#(X) -> c_6(X)
1184.39/297.09	     , activate^#(X) -> c_7(X)
1184.39/297.09	     , activate^#(n__from(X)) -> c_8(from^#(activate(X)))
1184.39/297.09	     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
1184.39/297.09	     , pi^#(X) -> c_13(2ndspos^#(X, from(0())))
1184.39/297.09	     , plus^#(0(), Y) -> c_14(Y)
1184.39/297.09	     , plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
1184.39/297.09	     , times^#(0(), Y) -> c_16()
1184.39/297.09	     , times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
1184.39/297.09	     , square^#(X) -> c_18(times^#(X, X)) }
1184.39/297.09	   
1184.39/297.09	   and mark the set of starting terms.
1184.39/297.09	   
1184.39/297.09	   We are left with following problem, upon which TcT provides the
1184.39/297.09	   certificate MAYBE.
1184.39/297.09	   
1184.39/297.09	   Strict DPs:
1184.39/297.09	     { from^#(X) -> c_1(X, X)
1184.39/297.09	     , from^#(X) -> c_2(X)
1184.39/297.09	     , 2ndspos^#(0(), Z) -> c_3()
1184.39/297.09	     , 2ndspos^#(s(N), cons(X, Z)) ->
1184.39/297.09	       c_4(2ndspos^#(s(N), cons2(X, activate(Z))))
1184.39/297.09	     , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       c_5(Y, 2ndsneg^#(N, activate(Z)))
1184.39/297.09	     , 2ndsneg^#(0(), Z) -> c_10()
1184.39/297.09	     , 2ndsneg^#(s(N), cons(X, Z)) ->
1184.39/297.09	       c_11(2ndsneg^#(s(N), cons2(X, activate(Z))))
1184.39/297.09	     , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       c_12(Y, 2ndspos^#(N, activate(Z)))
1184.39/297.09	     , s^#(X) -> c_6(X)
1184.39/297.09	     , activate^#(X) -> c_7(X)
1184.39/297.09	     , activate^#(n__from(X)) -> c_8(from^#(activate(X)))
1184.39/297.09	     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
1184.39/297.09	     , pi^#(X) -> c_13(2ndspos^#(X, from(0())))
1184.39/297.09	     , plus^#(0(), Y) -> c_14(Y)
1184.39/297.09	     , plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
1184.39/297.09	     , times^#(0(), Y) -> c_16()
1184.39/297.09	     , times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
1184.39/297.09	     , square^#(X) -> c_18(times^#(X, X)) }
1184.39/297.09	   Strict Trs:
1184.39/297.09	     { from(X) -> cons(X, n__from(n__s(X)))
1184.39/297.09	     , from(X) -> n__from(X)
1184.39/297.09	     , 2ndspos(0(), Z) -> rnil()
1184.39/297.09	     , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z)))
1184.39/297.09	     , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       rcons(posrecip(Y), 2ndsneg(N, activate(Z)))
1184.39/297.09	     , s(X) -> n__s(X)
1184.39/297.09	     , activate(X) -> X
1184.39/297.09	     , activate(n__from(X)) -> from(activate(X))
1184.39/297.09	     , activate(n__s(X)) -> s(activate(X))
1184.39/297.09	     , 2ndsneg(0(), Z) -> rnil()
1184.39/297.09	     , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z)))
1184.39/297.09	     , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       rcons(negrecip(Y), 2ndspos(N, activate(Z)))
1184.39/297.09	     , pi(X) -> 2ndspos(X, from(0()))
1184.39/297.09	     , plus(0(), Y) -> Y
1184.39/297.09	     , plus(s(X), Y) -> s(plus(X, Y))
1184.39/297.09	     , times(0(), Y) -> 0()
1184.39/297.09	     , times(s(X), Y) -> plus(Y, times(X, Y))
1184.39/297.09	     , square(X) -> times(X, X) }
1184.39/297.09	   Obligation:
1184.39/297.09	     runtime complexity
1184.39/297.09	   Answer:
1184.39/297.09	     MAYBE
1184.39/297.09	   
1184.39/297.09	   We estimate the number of application of {3,6,16} by applications
1184.39/297.09	   of Pre({3,6,16}) = {1,2,4,5,7,8,9,10,13,14,18}. Here rules are
1184.39/297.09	   labeled as follows:
1184.39/297.09	   
1184.39/297.09	     DPs:
1184.39/297.09	       { 1: from^#(X) -> c_1(X, X)
1184.39/297.09	       , 2: from^#(X) -> c_2(X)
1184.39/297.09	       , 3: 2ndspos^#(0(), Z) -> c_3()
1184.39/297.09	       , 4: 2ndspos^#(s(N), cons(X, Z)) ->
1184.39/297.09	            c_4(2ndspos^#(s(N), cons2(X, activate(Z))))
1184.39/297.09	       , 5: 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	            c_5(Y, 2ndsneg^#(N, activate(Z)))
1184.39/297.09	       , 6: 2ndsneg^#(0(), Z) -> c_10()
1184.39/297.09	       , 7: 2ndsneg^#(s(N), cons(X, Z)) ->
1184.39/297.09	            c_11(2ndsneg^#(s(N), cons2(X, activate(Z))))
1184.39/297.09	       , 8: 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	            c_12(Y, 2ndspos^#(N, activate(Z)))
1184.39/297.09	       , 9: s^#(X) -> c_6(X)
1184.39/297.09	       , 10: activate^#(X) -> c_7(X)
1184.39/297.09	       , 11: activate^#(n__from(X)) -> c_8(from^#(activate(X)))
1184.39/297.09	       , 12: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
1184.39/297.09	       , 13: pi^#(X) -> c_13(2ndspos^#(X, from(0())))
1184.39/297.09	       , 14: plus^#(0(), Y) -> c_14(Y)
1184.39/297.09	       , 15: plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
1184.39/297.09	       , 16: times^#(0(), Y) -> c_16()
1184.39/297.09	       , 17: times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
1184.39/297.09	       , 18: square^#(X) -> c_18(times^#(X, X)) }
1184.39/297.09	   
1184.39/297.09	   We are left with following problem, upon which TcT provides the
1184.39/297.09	   certificate MAYBE.
1184.39/297.09	   
1184.39/297.09	   Strict DPs:
1184.39/297.09	     { from^#(X) -> c_1(X, X)
1184.39/297.09	     , from^#(X) -> c_2(X)
1184.39/297.09	     , 2ndspos^#(s(N), cons(X, Z)) ->
1184.39/297.09	       c_4(2ndspos^#(s(N), cons2(X, activate(Z))))
1184.39/297.09	     , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       c_5(Y, 2ndsneg^#(N, activate(Z)))
1184.39/297.09	     , 2ndsneg^#(s(N), cons(X, Z)) ->
1184.39/297.09	       c_11(2ndsneg^#(s(N), cons2(X, activate(Z))))
1184.39/297.09	     , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       c_12(Y, 2ndspos^#(N, activate(Z)))
1184.39/297.09	     , s^#(X) -> c_6(X)
1184.39/297.09	     , activate^#(X) -> c_7(X)
1184.39/297.09	     , activate^#(n__from(X)) -> c_8(from^#(activate(X)))
1184.39/297.09	     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
1184.39/297.09	     , pi^#(X) -> c_13(2ndspos^#(X, from(0())))
1184.39/297.09	     , plus^#(0(), Y) -> c_14(Y)
1184.39/297.09	     , plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
1184.39/297.09	     , times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
1184.39/297.09	     , square^#(X) -> c_18(times^#(X, X)) }
1184.39/297.09	   Strict Trs:
1184.39/297.09	     { from(X) -> cons(X, n__from(n__s(X)))
1184.39/297.09	     , from(X) -> n__from(X)
1184.39/297.09	     , 2ndspos(0(), Z) -> rnil()
1184.39/297.09	     , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z)))
1184.39/297.09	     , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       rcons(posrecip(Y), 2ndsneg(N, activate(Z)))
1184.39/297.09	     , s(X) -> n__s(X)
1184.39/297.09	     , activate(X) -> X
1184.39/297.09	     , activate(n__from(X)) -> from(activate(X))
1184.39/297.09	     , activate(n__s(X)) -> s(activate(X))
1184.39/297.09	     , 2ndsneg(0(), Z) -> rnil()
1184.39/297.09	     , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z)))
1184.39/297.09	     , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
1184.39/297.09	       rcons(negrecip(Y), 2ndspos(N, activate(Z)))
1184.39/297.09	     , pi(X) -> 2ndspos(X, from(0()))
1184.39/297.09	     , plus(0(), Y) -> Y
1184.39/297.09	     , plus(s(X), Y) -> s(plus(X, Y))
1184.39/297.09	     , times(0(), Y) -> 0()
1184.39/297.09	     , times(s(X), Y) -> plus(Y, times(X, Y))
1184.39/297.09	     , square(X) -> times(X, X) }
1184.39/297.09	   Weak DPs:
1184.39/297.09	     { 2ndspos^#(0(), Z) -> c_3()
1184.39/297.09	     , 2ndsneg^#(0(), Z) -> c_10()
1184.39/297.09	     , times^#(0(), Y) -> c_16() }
1184.39/297.09	   Obligation:
1184.39/297.09	     runtime complexity
1184.39/297.09	   Answer:
1184.39/297.09	     MAYBE
1184.39/297.09	   
1184.39/297.09	   Empty strict component of the problem is NOT empty.
1184.39/297.09	
1184.39/297.09	
1184.39/297.09	Arrrr..
1185.54/297.95	EOF