MAYBE
835.37/297.03	MAYBE
835.37/297.03	
835.37/297.03	We are left with following problem, upon which TcT provides the
835.37/297.03	certificate MAYBE.
835.37/297.03	
835.37/297.03	Strict Trs:
835.37/297.03	  { f(g(x)) -> g(f(f(x)))
835.37/297.03	  , f(h(x)) -> h(g(x))
835.37/297.03	  , f'(s(x), y, y) -> f'(y, x, s(x)) }
835.37/297.03	Obligation:
835.37/297.03	  runtime complexity
835.37/297.03	Answer:
835.37/297.03	  MAYBE
835.37/297.03	
835.37/297.03	None of the processors succeeded.
835.37/297.03	
835.37/297.03	Details of failed attempt(s):
835.37/297.03	-----------------------------
835.37/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
835.37/297.03	   following reason:
835.37/297.03	   
835.37/297.03	   Computation stopped due to timeout after 297.0 seconds.
835.37/297.03	
835.37/297.03	2) 'Best' failed due to the following reason:
835.37/297.03	   
835.37/297.03	   None of the processors succeeded.
835.37/297.03	   
835.37/297.03	   Details of failed attempt(s):
835.37/297.03	   -----------------------------
835.37/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
835.37/297.03	      seconds)' failed due to the following reason:
835.37/297.03	      
835.37/297.03	      The weightgap principle applies (using the following nonconstant
835.37/297.03	      growth matrix-interpretation)
835.37/297.03	      
835.37/297.03	      The following argument positions are usable:
835.37/297.03	        Uargs(f) = {1}, Uargs(g) = {1}
835.37/297.03	      
835.37/297.03	      TcT has computed the following matrix interpretation satisfying
835.37/297.03	      not(EDA) and not(IDA(1)).
835.37/297.03	      
835.37/297.03	                 [f](x1) = [1] x1 + [0]         
835.37/297.03	                                                
835.37/297.03	                 [g](x1) = [1] x1 + [0]         
835.37/297.03	                                                
835.37/297.03	                 [h](x1) = [1] x1 + [0]         
835.37/297.03	                                                
835.37/297.03	        [f'](x1, x2, x3) = [1] x1 + [1] x2 + [0]
835.37/297.03	                                                
835.37/297.03	                 [s](x1) = [1] x1 + [4]         
835.37/297.03	      
835.37/297.03	      The order satisfies the following ordering constraints:
835.37/297.03	      
835.37/297.03	               [f(g(x))] =  [1] x + [0]        
835.37/297.03	                         >= [1] x + [0]        
835.37/297.03	                         =  [g(f(f(x)))]       
835.37/297.03	                                               
835.37/297.03	               [f(h(x))] =  [1] x + [0]        
835.37/297.03	                         >= [1] x + [0]        
835.37/297.03	                         =  [h(g(x))]          
835.37/297.03	                                               
835.37/297.03	        [f'(s(x), y, y)] =  [1] x + [1] y + [4]
835.37/297.03	                         >  [1] x + [1] y + [0]
835.37/297.03	                         =  [f'(y, x, s(x))]   
835.37/297.03	                                               
835.37/297.03	      
835.37/297.03	      Further, it can be verified that all rules not oriented are covered by the weightgap condition.
835.37/297.03	      
835.37/297.03	      We are left with following problem, upon which TcT provides the
835.37/297.03	      certificate MAYBE.
835.37/297.03	      
835.37/297.03	      Strict Trs:
835.37/297.03	        { f(g(x)) -> g(f(f(x)))
835.37/297.03	        , f(h(x)) -> h(g(x)) }
835.37/297.03	      Weak Trs: { f'(s(x), y, y) -> f'(y, x, s(x)) }
835.37/297.03	      Obligation:
835.37/297.03	        runtime complexity
835.37/297.03	      Answer:
835.37/297.03	        MAYBE
835.37/297.03	      
835.37/297.03	      The weightgap principle applies (using the following nonconstant
835.37/297.03	      growth matrix-interpretation)
835.37/297.03	      
835.37/297.03	      The following argument positions are usable:
835.37/297.03	        Uargs(f) = {1}, Uargs(g) = {1}
835.37/297.03	      
835.37/297.03	      TcT has computed the following matrix interpretation satisfying
835.37/297.03	      not(EDA) and not(IDA(1)).
835.37/297.03	      
835.37/297.03	                 [f](x1) = [1] x1 + [4]         
835.37/297.03	                                                
835.37/297.03	                 [g](x1) = [1] x1 + [0]         
835.37/297.03	                                                
835.37/297.03	                 [h](x1) = [1] x1 + [4]         
835.37/297.03	                                                
835.37/297.03	        [f'](x1, x2, x3) = [1] x1 + [1] x2 + [4]
835.37/297.03	                                                
835.37/297.03	                 [s](x1) = [1] x1 + [1]         
835.37/297.03	      
835.37/297.03	      The order satisfies the following ordering constraints:
835.37/297.03	      
835.37/297.03	               [f(g(x))] = [1] x + [4]        
835.37/297.03	                         ? [1] x + [8]        
835.37/297.03	                         = [g(f(f(x)))]       
835.37/297.03	                                              
835.37/297.03	               [f(h(x))] = [1] x + [8]        
835.37/297.03	                         > [1] x + [4]        
835.37/297.03	                         = [h(g(x))]          
835.37/297.03	                                              
835.37/297.03	        [f'(s(x), y, y)] = [1] x + [1] y + [5]
835.37/297.03	                         > [1] x + [1] y + [4]
835.37/297.03	                         = [f'(y, x, s(x))]   
835.37/297.03	                                              
835.37/297.03	      
835.37/297.03	      Further, it can be verified that all rules not oriented are covered by the weightgap condition.
835.37/297.03	      
835.37/297.03	      We are left with following problem, upon which TcT provides the
835.37/297.03	      certificate MAYBE.
835.37/297.03	      
835.37/297.03	      Strict Trs: { f(g(x)) -> g(f(f(x))) }
835.37/297.03	      Weak Trs:
835.37/297.03	        { f(h(x)) -> h(g(x))
835.37/297.03	        , f'(s(x), y, y) -> f'(y, x, s(x)) }
835.37/297.03	      Obligation:
835.37/297.03	        runtime complexity
835.37/297.03	      Answer:
835.37/297.03	        MAYBE
835.37/297.03	      
835.37/297.03	      None of the processors succeeded.
835.37/297.03	      
835.37/297.03	      Details of failed attempt(s):
835.37/297.03	      -----------------------------
835.37/297.03	      1) 'empty' failed due to the following reason:
835.37/297.03	         
835.37/297.03	         Empty strict component of the problem is NOT empty.
835.37/297.03	      
835.37/297.03	      2) 'With Problem ...' failed due to the following reason:
835.37/297.03	         
835.37/297.03	         None of the processors succeeded.
835.37/297.03	         
835.37/297.03	         Details of failed attempt(s):
835.37/297.03	         -----------------------------
835.37/297.03	         1) 'empty' failed due to the following reason:
835.37/297.03	            
835.37/297.03	            Empty strict component of the problem is NOT empty.
835.37/297.03	         
835.37/297.03	         2) 'Fastest' failed due to the following reason:
835.37/297.03	            
835.37/297.03	            None of the processors succeeded.
835.37/297.03	            
835.37/297.03	            Details of failed attempt(s):
835.37/297.03	            -----------------------------
835.37/297.03	            1) 'With Problem ...' failed due to the following reason:
835.37/297.03	               
835.37/297.03	               None of the processors succeeded.
835.37/297.03	               
835.37/297.03	               Details of failed attempt(s):
835.37/297.03	               -----------------------------
835.37/297.03	               1) 'empty' failed due to the following reason:
835.37/297.03	                  
835.37/297.03	                  Empty strict component of the problem is NOT empty.
835.37/297.03	               
835.37/297.03	               2) 'With Problem ...' failed due to the following reason:
835.37/297.03	                  
835.37/297.03	                  None of the processors succeeded.
835.37/297.03	                  
835.37/297.03	                  Details of failed attempt(s):
835.37/297.03	                  -----------------------------
835.37/297.03	                  1) 'empty' failed due to the following reason:
835.37/297.03	                     
835.37/297.03	                     Empty strict component of the problem is NOT empty.
835.37/297.03	                  
835.37/297.03	                  2) 'With Problem ...' failed due to the following reason:
835.37/297.03	                     
835.37/297.03	                     None of the processors succeeded.
835.37/297.03	                     
835.37/297.03	                     Details of failed attempt(s):
835.37/297.03	                     -----------------------------
835.37/297.03	                     1) 'empty' failed due to the following reason:
835.37/297.03	                        
835.37/297.03	                        Empty strict component of the problem is NOT empty.
835.37/297.03	                     
835.37/297.03	                     2) 'With Problem ...' failed due to the following reason:
835.37/297.03	                        
835.37/297.03	                        Empty strict component of the problem is NOT empty.
835.37/297.03	                     
835.37/297.03	                  
835.37/297.03	               
835.37/297.03	            
835.37/297.03	            2) 'With Problem ...' failed due to the following reason:
835.37/297.03	               
835.37/297.03	               None of the processors succeeded.
835.37/297.03	               
835.37/297.03	               Details of failed attempt(s):
835.37/297.03	               -----------------------------
835.37/297.03	               1) 'empty' failed due to the following reason:
835.37/297.03	                  
835.37/297.03	                  Empty strict component of the problem is NOT empty.
835.37/297.03	               
835.37/297.03	               2) 'With Problem ...' failed due to the following reason:
835.37/297.03	                  
835.37/297.03	                  Empty strict component of the problem is NOT empty.
835.37/297.03	               
835.37/297.03	            
835.37/297.03	         
835.37/297.03	      
835.37/297.03	   
835.37/297.03	   2) 'Best' failed due to the following reason:
835.37/297.03	      
835.37/297.03	      None of the processors succeeded.
835.37/297.03	      
835.37/297.03	      Details of failed attempt(s):
835.37/297.03	      -----------------------------
835.37/297.03	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
835.37/297.03	         to the following reason:
835.37/297.03	         
835.37/297.03	         The processor is inapplicable, reason:
835.37/297.03	           Processor only applicable for innermost runtime complexity analysis
835.37/297.03	      
835.37/297.03	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
835.37/297.03	         following reason:
835.37/297.03	         
835.37/297.03	         The processor is inapplicable, reason:
835.37/297.03	           Processor only applicable for innermost runtime complexity analysis
835.37/297.03	      
835.37/297.03	   
835.37/297.03	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
835.37/297.03	      failed due to the following reason:
835.37/297.03	      
835.37/297.03	      None of the processors succeeded.
835.37/297.03	      
835.37/297.03	      Details of failed attempt(s):
835.37/297.03	      -----------------------------
835.37/297.03	      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
835.37/297.03	         failed due to the following reason:
835.37/297.03	         
835.37/297.03	         match-boundness of the problem could not be verified.
835.37/297.03	      
835.37/297.03	      2) 'Bounds with minimal-enrichment and initial automaton 'match''
835.37/297.03	         failed due to the following reason:
835.37/297.03	         
835.37/297.03	         match-boundness of the problem could not be verified.
835.37/297.03	      
835.37/297.03	   
835.37/297.03	
835.37/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
835.37/297.03	   the following reason:
835.37/297.03	   
835.37/297.03	   We add the following weak dependency pairs:
835.37/297.03	   
835.37/297.03	   Strict DPs:
835.37/297.03	     { f^#(g(x)) -> c_1(f^#(f(x)))
835.37/297.03	     , f^#(h(x)) -> c_2(x)
835.37/297.03	     , f'^#(s(x), y, y) -> c_3(f'^#(y, x, s(x))) }
835.37/297.03	   
835.37/297.03	   and mark the set of starting terms.
835.37/297.03	   
835.37/297.03	   We are left with following problem, upon which TcT provides the
835.37/297.03	   certificate MAYBE.
835.37/297.03	   
835.37/297.03	   Strict DPs:
835.37/297.03	     { f^#(g(x)) -> c_1(f^#(f(x)))
835.37/297.03	     , f^#(h(x)) -> c_2(x)
835.37/297.03	     , f'^#(s(x), y, y) -> c_3(f'^#(y, x, s(x))) }
835.37/297.03	   Strict Trs:
835.37/297.03	     { f(g(x)) -> g(f(f(x)))
835.37/297.03	     , f(h(x)) -> h(g(x))
835.37/297.03	     , f'(s(x), y, y) -> f'(y, x, s(x)) }
835.37/297.03	   Obligation:
835.37/297.03	     runtime complexity
835.37/297.03	   Answer:
835.37/297.03	     MAYBE
835.37/297.03	   
835.37/297.03	   Empty strict component of the problem is NOT empty.
835.37/297.03	
835.37/297.03	
835.37/297.03	Arrrr..
835.58/297.28	EOF