MAYBE
1179.21/297.03	MAYBE
1179.21/297.03	
1179.21/297.03	We are left with following problem, upon which TcT provides the
1179.21/297.03	certificate MAYBE.
1179.21/297.03	
1179.21/297.03	Strict Trs:
1179.21/297.03	  { from(X) -> cons(X, n__from(n__s(X)))
1179.21/297.03	  , from(X) -> n__from(X)
1179.21/297.03	  , cons(X1, X2) -> n__cons(X1, X2)
1179.21/297.03	  , 2ndspos(0(), Z) -> rnil()
1179.21/297.03	  , 2ndspos(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	    rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z)))
1179.21/297.03	  , s(X) -> n__s(X)
1179.21/297.03	  , activate(X) -> X
1179.21/297.03	  , activate(n__from(X)) -> from(activate(X))
1179.21/297.03	  , activate(n__s(X)) -> s(activate(X))
1179.21/297.03	  , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
1179.21/297.03	  , 2ndsneg(0(), Z) -> rnil()
1179.21/297.03	  , 2ndsneg(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	    rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z)))
1179.21/297.03	  , pi(X) -> 2ndspos(X, from(0()))
1179.21/297.03	  , plus(0(), Y) -> Y
1179.21/297.03	  , plus(s(X), Y) -> s(plus(X, Y))
1179.21/297.03	  , times(0(), Y) -> 0()
1179.21/297.03	  , times(s(X), Y) -> plus(Y, times(X, Y))
1179.21/297.03	  , square(X) -> times(X, X) }
1179.21/297.03	Obligation:
1179.21/297.03	  runtime complexity
1179.21/297.03	Answer:
1179.21/297.03	  MAYBE
1179.21/297.03	
1179.21/297.03	None of the processors succeeded.
1179.21/297.03	
1179.21/297.03	Details of failed attempt(s):
1179.21/297.03	-----------------------------
1179.21/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
1179.21/297.03	   following reason:
1179.21/297.03	   
1179.21/297.03	   Computation stopped due to timeout after 297.0 seconds.
1179.21/297.03	
1179.21/297.03	2) 'Best' failed due to the following reason:
1179.21/297.03	   
1179.21/297.03	   None of the processors succeeded.
1179.21/297.03	   
1179.21/297.03	   Details of failed attempt(s):
1179.21/297.03	   -----------------------------
1179.21/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
1179.21/297.03	      seconds)' failed due to the following reason:
1179.21/297.03	      
1179.21/297.03	      None of the processors succeeded.
1179.21/297.03	      
1179.21/297.03	      Details of failed attempt(s):
1179.21/297.03	      -----------------------------
1179.21/297.03	      1) 'empty' failed due to the following reason:
1179.21/297.03	         
1179.21/297.03	         Empty strict component of the problem is NOT empty.
1179.21/297.03	      
1179.21/297.03	      2) 'With Problem ...' failed due to the following reason:
1179.21/297.03	         
1179.21/297.03	         None of the processors succeeded.
1179.21/297.03	         
1179.21/297.03	         Details of failed attempt(s):
1179.21/297.03	         -----------------------------
1179.21/297.03	         1) 'empty' failed due to the following reason:
1179.21/297.03	            
1179.21/297.03	            Empty strict component of the problem is NOT empty.
1179.21/297.03	         
1179.21/297.03	         2) 'Fastest' failed due to the following reason:
1179.21/297.03	            
1179.21/297.03	            None of the processors succeeded.
1179.21/297.03	            
1179.21/297.03	            Details of failed attempt(s):
1179.21/297.03	            -----------------------------
1179.21/297.03	            1) 'With Problem ...' failed due to the following reason:
1179.21/297.03	               
1179.21/297.03	               None of the processors succeeded.
1179.21/297.03	               
1179.21/297.03	               Details of failed attempt(s):
1179.21/297.03	               -----------------------------
1179.21/297.03	               1) 'empty' failed due to the following reason:
1179.21/297.03	                  
1179.21/297.03	                  Empty strict component of the problem is NOT empty.
1179.21/297.03	               
1179.21/297.03	               2) 'With Problem ...' failed due to the following reason:
1179.21/297.03	                  
1179.21/297.03	                  None of the processors succeeded.
1179.21/297.03	                  
1179.21/297.03	                  Details of failed attempt(s):
1179.21/297.03	                  -----------------------------
1179.21/297.03	                  1) 'empty' failed due to the following reason:
1179.21/297.03	                     
1179.21/297.03	                     Empty strict component of the problem is NOT empty.
1179.21/297.03	                  
1179.21/297.03	                  2) 'With Problem ...' failed due to the following reason:
1179.21/297.03	                     
1179.21/297.03	                     None of the processors succeeded.
1179.21/297.03	                     
1179.21/297.03	                     Details of failed attempt(s):
1179.21/297.03	                     -----------------------------
1179.21/297.03	                     1) 'empty' failed due to the following reason:
1179.21/297.03	                        
1179.21/297.03	                        Empty strict component of the problem is NOT empty.
1179.21/297.03	                     
1179.21/297.03	                     2) 'With Problem ...' failed due to the following reason:
1179.21/297.03	                        
1179.21/297.03	                        Empty strict component of the problem is NOT empty.
1179.21/297.03	                     
1179.21/297.03	                  
1179.21/297.03	               
1179.21/297.03	            
1179.21/297.03	            2) 'With Problem ...' failed due to the following reason:
1179.21/297.03	               
1179.21/297.03	               None of the processors succeeded.
1179.21/297.03	               
1179.21/297.03	               Details of failed attempt(s):
1179.21/297.03	               -----------------------------
1179.21/297.03	               1) 'empty' failed due to the following reason:
1179.21/297.03	                  
1179.21/297.03	                  Empty strict component of the problem is NOT empty.
1179.21/297.03	               
1179.21/297.03	               2) 'With Problem ...' failed due to the following reason:
1179.21/297.03	                  
1179.21/297.03	                  Empty strict component of the problem is NOT empty.
1179.21/297.03	               
1179.21/297.03	            
1179.21/297.03	         
1179.21/297.03	      
1179.21/297.03	   
1179.21/297.03	   2) 'Best' failed due to the following reason:
1179.21/297.03	      
1179.21/297.03	      None of the processors succeeded.
1179.21/297.03	      
1179.21/297.03	      Details of failed attempt(s):
1179.21/297.03	      -----------------------------
1179.21/297.03	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
1179.21/297.03	         to the following reason:
1179.21/297.03	         
1179.21/297.03	         The processor is inapplicable, reason:
1179.21/297.03	           Processor only applicable for innermost runtime complexity analysis
1179.21/297.03	      
1179.21/297.03	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
1179.21/297.03	         following reason:
1179.21/297.03	         
1179.21/297.03	         The processor is inapplicable, reason:
1179.21/297.03	           Processor only applicable for innermost runtime complexity analysis
1179.21/297.03	      
1179.21/297.03	   
1179.21/297.03	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
1179.21/297.03	      failed due to the following reason:
1179.21/297.03	      
1179.21/297.03	      None of the processors succeeded.
1179.21/297.03	      
1179.21/297.03	      Details of failed attempt(s):
1179.21/297.03	      -----------------------------
1179.21/297.03	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
1179.21/297.03	         failed due to the following reason:
1179.21/297.03	         
1179.21/297.03	         match-boundness of the problem could not be verified.
1179.21/297.03	      
1179.21/297.03	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
1179.21/297.03	         failed due to the following reason:
1179.21/297.03	         
1179.21/297.03	         match-boundness of the problem could not be verified.
1179.21/297.03	      
1179.21/297.03	   
1179.21/297.03	
1179.21/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
1179.21/297.03	   the following reason:
1179.21/297.03	   
1179.21/297.03	   We add the following weak dependency pairs:
1179.21/297.03	   
1179.21/297.03	   Strict DPs:
1179.21/297.03	     { from^#(X) -> c_1(cons^#(X, n__from(n__s(X))))
1179.21/297.03	     , from^#(X) -> c_2(X)
1179.21/297.03	     , cons^#(X1, X2) -> c_3(X1, X2)
1179.21/297.03	     , 2ndspos^#(0(), Z) -> c_4()
1179.21/297.03	     , 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       c_5(activate^#(Y), 2ndsneg^#(N, activate(Z)))
1179.21/297.03	     , activate^#(X) -> c_7(X)
1179.21/297.03	     , activate^#(n__from(X)) -> c_8(from^#(activate(X)))
1179.21/297.03	     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
1179.21/297.03	     , activate^#(n__cons(X1, X2)) -> c_10(cons^#(activate(X1), X2))
1179.21/297.03	     , 2ndsneg^#(0(), Z) -> c_11()
1179.21/297.03	     , 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       c_12(activate^#(Y), 2ndspos^#(N, activate(Z)))
1179.21/297.03	     , s^#(X) -> c_6(X)
1179.21/297.03	     , pi^#(X) -> c_13(2ndspos^#(X, from(0())))
1179.21/297.03	     , plus^#(0(), Y) -> c_14(Y)
1179.21/297.03	     , plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
1179.21/297.03	     , times^#(0(), Y) -> c_16()
1179.21/297.03	     , times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
1179.21/297.03	     , square^#(X) -> c_18(times^#(X, X)) }
1179.21/297.03	   
1179.21/297.03	   and mark the set of starting terms.
1179.21/297.03	   
1179.21/297.03	   We are left with following problem, upon which TcT provides the
1179.21/297.03	   certificate MAYBE.
1179.21/297.03	   
1179.21/297.03	   Strict DPs:
1179.21/297.03	     { from^#(X) -> c_1(cons^#(X, n__from(n__s(X))))
1179.21/297.03	     , from^#(X) -> c_2(X)
1179.21/297.03	     , cons^#(X1, X2) -> c_3(X1, X2)
1179.21/297.03	     , 2ndspos^#(0(), Z) -> c_4()
1179.21/297.03	     , 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       c_5(activate^#(Y), 2ndsneg^#(N, activate(Z)))
1179.21/297.03	     , activate^#(X) -> c_7(X)
1179.21/297.03	     , activate^#(n__from(X)) -> c_8(from^#(activate(X)))
1179.21/297.03	     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
1179.21/297.03	     , activate^#(n__cons(X1, X2)) -> c_10(cons^#(activate(X1), X2))
1179.21/297.03	     , 2ndsneg^#(0(), Z) -> c_11()
1179.21/297.03	     , 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       c_12(activate^#(Y), 2ndspos^#(N, activate(Z)))
1179.21/297.03	     , s^#(X) -> c_6(X)
1179.21/297.03	     , pi^#(X) -> c_13(2ndspos^#(X, from(0())))
1179.21/297.03	     , plus^#(0(), Y) -> c_14(Y)
1179.21/297.03	     , plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
1179.21/297.03	     , times^#(0(), Y) -> c_16()
1179.21/297.03	     , times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
1179.21/297.03	     , square^#(X) -> c_18(times^#(X, X)) }
1179.21/297.03	   Strict Trs:
1179.21/297.03	     { from(X) -> cons(X, n__from(n__s(X)))
1179.21/297.03	     , from(X) -> n__from(X)
1179.21/297.03	     , cons(X1, X2) -> n__cons(X1, X2)
1179.21/297.03	     , 2ndspos(0(), Z) -> rnil()
1179.21/297.03	     , 2ndspos(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z)))
1179.21/297.03	     , s(X) -> n__s(X)
1179.21/297.03	     , activate(X) -> X
1179.21/297.03	     , activate(n__from(X)) -> from(activate(X))
1179.21/297.03	     , activate(n__s(X)) -> s(activate(X))
1179.21/297.03	     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
1179.21/297.03	     , 2ndsneg(0(), Z) -> rnil()
1179.21/297.03	     , 2ndsneg(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z)))
1179.21/297.03	     , pi(X) -> 2ndspos(X, from(0()))
1179.21/297.03	     , plus(0(), Y) -> Y
1179.21/297.03	     , plus(s(X), Y) -> s(plus(X, Y))
1179.21/297.03	     , times(0(), Y) -> 0()
1179.21/297.03	     , times(s(X), Y) -> plus(Y, times(X, Y))
1179.21/297.03	     , square(X) -> times(X, X) }
1179.21/297.03	   Obligation:
1179.21/297.03	     runtime complexity
1179.21/297.03	   Answer:
1179.21/297.03	     MAYBE
1179.21/297.03	   
1179.21/297.03	   We estimate the number of application of {4,10,16} by applications
1179.21/297.03	   of Pre({4,10,16}) = {2,3,5,6,11,12,13,14,18}. Here rules are
1179.21/297.03	   labeled as follows:
1179.21/297.03	   
1179.21/297.03	     DPs:
1179.21/297.03	       { 1: from^#(X) -> c_1(cons^#(X, n__from(n__s(X))))
1179.21/297.03	       , 2: from^#(X) -> c_2(X)
1179.21/297.03	       , 3: cons^#(X1, X2) -> c_3(X1, X2)
1179.21/297.03	       , 4: 2ndspos^#(0(), Z) -> c_4()
1179.21/297.03	       , 5: 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	            c_5(activate^#(Y), 2ndsneg^#(N, activate(Z)))
1179.21/297.03	       , 6: activate^#(X) -> c_7(X)
1179.21/297.03	       , 7: activate^#(n__from(X)) -> c_8(from^#(activate(X)))
1179.21/297.03	       , 8: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
1179.21/297.03	       , 9: activate^#(n__cons(X1, X2)) -> c_10(cons^#(activate(X1), X2))
1179.21/297.03	       , 10: 2ndsneg^#(0(), Z) -> c_11()
1179.21/297.03	       , 11: 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	             c_12(activate^#(Y), 2ndspos^#(N, activate(Z)))
1179.21/297.03	       , 12: s^#(X) -> c_6(X)
1179.21/297.03	       , 13: pi^#(X) -> c_13(2ndspos^#(X, from(0())))
1179.21/297.03	       , 14: plus^#(0(), Y) -> c_14(Y)
1179.21/297.03	       , 15: plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
1179.21/297.03	       , 16: times^#(0(), Y) -> c_16()
1179.21/297.03	       , 17: times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
1179.21/297.03	       , 18: square^#(X) -> c_18(times^#(X, X)) }
1179.21/297.03	   
1179.21/297.03	   We are left with following problem, upon which TcT provides the
1179.21/297.03	   certificate MAYBE.
1179.21/297.03	   
1179.21/297.03	   Strict DPs:
1179.21/297.03	     { from^#(X) -> c_1(cons^#(X, n__from(n__s(X))))
1179.21/297.03	     , from^#(X) -> c_2(X)
1179.21/297.03	     , cons^#(X1, X2) -> c_3(X1, X2)
1179.21/297.03	     , 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       c_5(activate^#(Y), 2ndsneg^#(N, activate(Z)))
1179.21/297.03	     , activate^#(X) -> c_7(X)
1179.21/297.03	     , activate^#(n__from(X)) -> c_8(from^#(activate(X)))
1179.21/297.03	     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
1179.21/297.03	     , activate^#(n__cons(X1, X2)) -> c_10(cons^#(activate(X1), X2))
1179.21/297.03	     , 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       c_12(activate^#(Y), 2ndspos^#(N, activate(Z)))
1179.21/297.03	     , s^#(X) -> c_6(X)
1179.21/297.03	     , pi^#(X) -> c_13(2ndspos^#(X, from(0())))
1179.21/297.03	     , plus^#(0(), Y) -> c_14(Y)
1179.21/297.03	     , plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
1179.21/297.03	     , times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
1179.21/297.03	     , square^#(X) -> c_18(times^#(X, X)) }
1179.21/297.03	   Strict Trs:
1179.21/297.03	     { from(X) -> cons(X, n__from(n__s(X)))
1179.21/297.03	     , from(X) -> n__from(X)
1179.21/297.03	     , cons(X1, X2) -> n__cons(X1, X2)
1179.21/297.03	     , 2ndspos(0(), Z) -> rnil()
1179.21/297.03	     , 2ndspos(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z)))
1179.21/297.03	     , s(X) -> n__s(X)
1179.21/297.03	     , activate(X) -> X
1179.21/297.03	     , activate(n__from(X)) -> from(activate(X))
1179.21/297.03	     , activate(n__s(X)) -> s(activate(X))
1179.21/297.03	     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
1179.21/297.03	     , 2ndsneg(0(), Z) -> rnil()
1179.21/297.03	     , 2ndsneg(s(N), cons(X, n__cons(Y, Z))) ->
1179.21/297.03	       rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z)))
1179.21/297.03	     , pi(X) -> 2ndspos(X, from(0()))
1179.21/297.03	     , plus(0(), Y) -> Y
1179.21/297.03	     , plus(s(X), Y) -> s(plus(X, Y))
1179.21/297.03	     , times(0(), Y) -> 0()
1179.21/297.03	     , times(s(X), Y) -> plus(Y, times(X, Y))
1179.21/297.03	     , square(X) -> times(X, X) }
1179.21/297.03	   Weak DPs:
1179.21/297.03	     { 2ndspos^#(0(), Z) -> c_4()
1179.21/297.03	     , 2ndsneg^#(0(), Z) -> c_11()
1179.21/297.03	     , times^#(0(), Y) -> c_16() }
1179.21/297.03	   Obligation:
1179.21/297.03	     runtime complexity
1179.21/297.03	   Answer:
1179.21/297.03	     MAYBE
1179.21/297.03	   
1179.21/297.03	   Empty strict component of the problem is NOT empty.
1179.21/297.03	
1179.21/297.03	
1179.21/297.03	Arrrr..
1179.78/297.56	EOF