MAYBE
97.81/24.78	MAYBE
97.81/24.78	
97.81/24.78	We are left with following problem, upon which TcT provides the
97.81/24.78	certificate MAYBE.
97.81/24.78	
97.81/24.78	Strict Trs:
97.81/24.78	  { f(S(x)) -> x
97.81/24.78	  , f(0()) -> 0()
97.81/24.78	  , g(x) -> g(x) }
97.81/24.78	Obligation:
97.81/24.78	  innermost runtime complexity
97.81/24.78	Answer:
97.81/24.78	  MAYBE
97.81/24.78	
97.81/24.78	None of the processors succeeded.
97.81/24.78	
97.81/24.78	Details of failed attempt(s):
97.81/24.78	-----------------------------
97.81/24.78	1) 'empty' failed due to the following reason:
97.81/24.78	   
97.81/24.78	   Empty strict component of the problem is NOT empty.
97.81/24.78	
97.81/24.78	2) 'Best' failed due to the following reason:
97.81/24.78	   
97.81/24.78	   None of the processors succeeded.
97.81/24.78	   
97.81/24.78	   Details of failed attempt(s):
97.81/24.78	   -----------------------------
97.81/24.78	   1) 'With Problem ... (timeout of 297 seconds)' failed due to the
97.81/24.78	      following reason:
97.81/24.78	      
97.81/24.78	      We add the following weak dependency pairs:
97.81/24.78	      
97.81/24.78	      Strict DPs:
97.81/24.78	        { f^#(S(x)) -> c_1()
97.81/24.78	        , f^#(0()) -> c_2()
97.81/24.78	        , g^#(x) -> c_3(g^#(x)) }
97.81/24.78	      
97.81/24.78	      and mark the set of starting terms.
97.81/24.78	      
97.81/24.78	      We are left with following problem, upon which TcT provides the
97.81/24.78	      certificate MAYBE.
97.81/24.78	      
97.81/24.78	      Strict DPs:
97.81/24.78	        { f^#(S(x)) -> c_1()
97.81/24.78	        , f^#(0()) -> c_2()
97.81/24.78	        , g^#(x) -> c_3(g^#(x)) }
97.81/24.78	      Strict Trs:
97.81/24.78	        { f(S(x)) -> x
97.81/24.78	        , f(0()) -> 0()
97.81/24.78	        , g(x) -> g(x) }
97.81/24.78	      Obligation:
97.81/24.78	        innermost runtime complexity
97.81/24.78	      Answer:
97.81/24.78	        MAYBE
97.81/24.78	      
97.81/24.78	      No rule is usable, rules are removed from the input problem.
97.81/24.78	      
97.81/24.78	      We are left with following problem, upon which TcT provides the
97.81/24.78	      certificate MAYBE.
97.81/24.78	      
97.81/24.78	      Strict DPs:
97.81/24.78	        { f^#(S(x)) -> c_1()
97.81/24.78	        , f^#(0()) -> c_2()
97.81/24.78	        , g^#(x) -> c_3(g^#(x)) }
97.81/24.78	      Obligation:
97.81/24.78	        innermost runtime complexity
97.81/24.78	      Answer:
97.81/24.78	        MAYBE
97.81/24.78	      
97.81/24.78	      The weightgap principle applies (using the following constant
97.81/24.78	      growth matrix-interpretation)
97.81/24.78	      
97.81/24.78	      The following argument positions are usable:
97.81/24.78	        Uargs(c_3) = {1}
97.81/24.78	      
97.81/24.78	      TcT has computed the following constructor-restricted matrix
97.81/24.78	      interpretation.
97.81/24.78	      
97.81/24.78	          [S](x1) = [1]           
97.81/24.78	                    [2]           
97.81/24.78	                                  
97.81/24.78	              [0] = [1]           
97.81/24.78	                    [1]           
97.81/24.78	                                  
97.81/24.78	        [f^#](x1) = [1 1] x1 + [2]
97.81/24.78	                    [1 1]      [1]
97.81/24.78	                                  
97.81/24.78	            [c_1] = [0]           
97.81/24.78	                    [0]           
97.81/24.78	                                  
97.81/24.78	            [c_2] = [1]           
97.81/24.78	                    [1]           
97.81/24.78	                                  
97.81/24.78	        [g^#](x1) = [2 1] x1 + [2]
97.81/24.78	                    [1 1]      [2]
97.81/24.78	                                  
97.81/24.78	        [c_3](x1) = [1 0] x1 + [1]
97.81/24.78	                    [0 1]      [2]
97.81/24.78	      
97.81/24.78	      The order satisfies the following ordering constraints:
97.81/24.78	      
97.81/24.78	        [f^#(S(x))] = [5]          
97.81/24.78	                      [4]          
97.81/24.78	                    > [0]          
97.81/24.78	                      [0]          
97.81/24.78	                    = [c_1()]      
97.81/24.78	                                   
97.81/24.78	         [f^#(0())] = [4]          
97.81/24.78	                      [3]          
97.81/24.78	                    > [1]          
97.81/24.78	                      [1]          
97.81/24.78	                    = [c_2()]      
97.81/24.78	                                   
97.81/24.78	           [g^#(x)] = [2 1] x + [2]
97.81/24.78	                      [1 1]     [2]
97.81/24.78	                    ? [2 1] x + [3]
97.81/24.78	                      [1 1]     [4]
97.81/24.78	                    = [c_3(g^#(x))]
97.81/24.78	                                   
97.81/24.78	      
97.81/24.78	      Further, it can be verified that all rules not oriented are covered by the weightgap condition.
97.81/24.78	      
97.81/24.78	      We are left with following problem, upon which TcT provides the
97.81/24.78	      certificate MAYBE.
97.81/24.78	      
97.81/24.78	      Strict DPs: { g^#(x) -> c_3(g^#(x)) }
97.81/24.78	      Weak DPs:
97.81/24.78	        { f^#(S(x)) -> c_1()
97.81/24.78	        , f^#(0()) -> c_2() }
97.81/24.78	      Obligation:
97.81/24.78	        innermost runtime complexity
97.81/24.78	      Answer:
97.81/24.78	        MAYBE
97.81/24.78	      
97.81/24.78	      The following weak DPs constitute a sub-graph of the DG that is
97.81/24.78	      closed under successors. The DPs are removed.
97.81/24.78	      
97.81/24.78	      { f^#(S(x)) -> c_1()
97.81/24.78	      , f^#(0()) -> c_2() }
97.81/24.78	      
97.81/24.78	      We are left with following problem, upon which TcT provides the
97.81/24.78	      certificate MAYBE.
97.81/24.78	      
97.81/24.78	      Strict DPs: { g^#(x) -> c_3(g^#(x)) }
97.81/24.78	      Obligation:
97.81/24.78	        innermost runtime complexity
97.81/24.78	      Answer:
97.81/24.78	        MAYBE
97.81/24.78	      
97.81/24.78	      None of the processors succeeded.
97.81/24.78	      
97.81/24.78	      Details of failed attempt(s):
97.81/24.78	      -----------------------------
97.81/24.78	      1) 'empty' failed due to the following reason:
97.81/24.78	         
97.81/24.78	         Empty strict component of the problem is NOT empty.
97.81/24.78	      
97.81/24.78	      2) 'With Problem ...' failed due to the following reason:
97.81/24.78	         
97.81/24.78	         None of the processors succeeded.
97.81/24.78	         
97.81/24.78	         Details of failed attempt(s):
97.81/24.78	         -----------------------------
97.81/24.78	         1) 'empty' failed due to the following reason:
97.81/24.78	            
97.81/24.78	            Empty strict component of the problem is NOT empty.
97.81/24.78	         
97.81/24.78	         2) 'Fastest' failed due to the following reason:
97.81/24.78	            
97.81/24.78	            None of the processors succeeded.
97.81/24.78	            
97.81/24.78	            Details of failed attempt(s):
97.81/24.78	            -----------------------------
97.81/24.78	            1) 'Fastest (timeout of 24 seconds)' failed due to the following
97.81/24.78	               reason:
97.81/24.78	               
97.81/24.78	               Computation stopped due to timeout after 24.0 seconds.
97.81/24.78	            
97.81/24.78	            2) 'With Problem ...' failed due to the following reason:
97.81/24.78	               
97.81/24.78	               None of the processors succeeded.
97.81/24.78	               
97.81/24.78	               Details of failed attempt(s):
97.81/24.78	               -----------------------------
97.81/24.78	               1) 'empty' failed due to the following reason:
97.81/24.78	                  
97.81/24.78	                  Empty strict component of the problem is NOT empty.
97.81/24.78	               
97.81/24.78	               2) 'Polynomial Path Order (PS)' failed due to the following reason:
97.81/24.78	                  
97.81/24.78	                  The input cannot be shown compatible
97.81/24.78	               
97.81/24.78	            
97.81/24.78	            3) 'Polynomial Path Order (PS)' failed due to the following reason:
97.81/24.78	               
97.81/24.78	               The input cannot be shown compatible
97.81/24.78	            
97.81/24.78	         
97.81/24.78	      
97.81/24.78	   
97.81/24.78	   2) 'Best' failed due to the following reason:
97.81/24.78	      
97.81/24.78	      None of the processors succeeded.
97.81/24.78	      
97.81/24.78	      Details of failed attempt(s):
97.81/24.78	      -----------------------------
97.81/24.78	      1) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
97.81/24.78	         failed due to the following reason:
97.81/24.78	         
97.81/24.78	         Computation stopped due to timeout after 24.0 seconds.
97.81/24.78	      
97.81/24.78	      2) 'With Problem ... (timeout of 148 seconds) (timeout of 297
97.81/24.78	         seconds)' failed due to the following reason:
97.81/24.78	         
97.81/24.78	         The weightgap principle applies (using the following nonconstant
97.81/24.78	         growth matrix-interpretation)
97.81/24.78	         
97.81/24.78	         The following argument positions are usable:
97.81/24.78	           none
97.81/24.78	         
97.81/24.78	         TcT has computed the following matrix interpretation satisfying
97.81/24.78	         not(EDA) and not(IDA(1)).
97.81/24.78	         
97.81/24.78	           [f](x1) = [1] x1 + [7]
97.81/24.78	                                 
97.81/24.78	           [S](x1) = [1] x1 + [7]
97.81/24.78	                                 
97.81/24.78	               [0] = [7]         
97.81/24.78	                                 
97.81/24.78	           [g](x1) = [1] x1 + [0]
97.81/24.78	         
97.81/24.78	         The order satisfies the following ordering constraints:
97.81/24.78	         
97.81/24.78	           [f(S(x))] =  [1] x + [14]
97.81/24.78	                     >  [1] x + [0] 
97.81/24.78	                     =  [x]         
97.81/24.78	                                    
97.81/24.78	            [f(0())] =  [14]        
97.81/24.78	                     >  [7]         
97.81/24.78	                     =  [0()]       
97.81/24.78	                                    
97.81/24.78	              [g(x)] =  [1] x + [0] 
97.81/24.78	                     >= [1] x + [0] 
97.81/24.78	                     =  [g(x)]      
97.81/24.78	                                    
97.81/24.78	         
97.81/24.78	         Further, it can be verified that all rules not oriented are covered by the weightgap condition.
97.81/24.78	         
97.81/24.78	         We are left with following problem, upon which TcT provides the
97.81/24.78	         certificate MAYBE.
97.81/24.78	         
97.81/24.78	         Strict Trs: { g(x) -> g(x) }
97.81/24.78	         Weak Trs:
97.81/24.78	           { f(S(x)) -> x
97.81/24.78	           , f(0()) -> 0() }
97.81/24.78	         Obligation:
97.81/24.78	           innermost runtime complexity
97.81/24.78	         Answer:
97.81/24.78	           MAYBE
97.81/24.78	         
97.81/24.78	         None of the processors succeeded.
97.81/24.78	         
97.81/24.78	         Details of failed attempt(s):
97.81/24.78	         -----------------------------
97.81/24.78	         1) 'empty' failed due to the following reason:
97.81/24.78	            
97.81/24.78	            Empty strict component of the problem is NOT empty.
97.81/24.78	         
97.81/24.78	         2) 'With Problem ...' failed due to the following reason:
97.81/24.78	            
97.81/24.78	            None of the processors succeeded.
97.81/24.78	            
97.81/24.78	            Details of failed attempt(s):
97.81/24.78	            -----------------------------
97.81/24.78	            1) 'empty' failed due to the following reason:
97.81/24.78	               
97.81/24.78	               Empty strict component of the problem is NOT empty.
97.81/24.78	            
97.81/24.78	            2) 'Fastest' failed due to the following reason:
97.81/24.78	               
97.81/24.78	               None of the processors succeeded.
97.81/24.78	               
97.81/24.78	               Details of failed attempt(s):
97.81/24.78	               -----------------------------
97.81/24.78	               1) 'With Problem ...' failed due to the following reason:
97.81/24.78	                  
97.81/24.78	                  None of the processors succeeded.
97.81/24.78	                  
97.81/24.78	                  Details of failed attempt(s):
97.81/24.78	                  -----------------------------
97.81/24.78	                  1) 'empty' failed due to the following reason:
97.81/24.78	                     
97.81/24.78	                     Empty strict component of the problem is NOT empty.
97.81/24.78	                  
97.81/24.78	                  2) 'With Problem ...' failed due to the following reason:
97.81/24.78	                     
97.81/24.78	                     None of the processors succeeded.
97.81/24.78	                     
97.81/24.78	                     Details of failed attempt(s):
97.81/24.78	                     -----------------------------
97.81/24.78	                     1) 'empty' failed due to the following reason:
97.81/24.78	                        
97.81/24.78	                        Empty strict component of the problem is NOT empty.
97.81/24.78	                     
97.81/24.78	                     2) 'With Problem ...' failed due to the following reason:
97.81/24.78	                        
97.81/24.78	                        None of the processors succeeded.
97.81/24.78	                        
97.81/24.78	                        Details of failed attempt(s):
97.81/24.78	                        -----------------------------
97.81/24.78	                        1) 'empty' failed due to the following reason:
97.81/24.78	                           
97.81/24.78	                           Empty strict component of the problem is NOT empty.
97.81/24.78	                        
97.81/24.78	                        2) 'With Problem ...' failed due to the following reason:
97.81/24.78	                           
97.81/24.78	                           Empty strict component of the problem is NOT empty.
97.81/24.78	                        
97.81/24.78	                     
97.81/24.78	                  
97.81/24.78	               
97.81/24.78	               2) 'With Problem ...' failed due to the following reason:
97.81/24.78	                  
97.81/24.78	                  None of the processors succeeded.
97.81/24.78	                  
97.81/24.78	                  Details of failed attempt(s):
97.81/24.78	                  -----------------------------
97.81/24.78	                  1) 'empty' failed due to the following reason:
97.81/24.78	                     
97.81/24.78	                     Empty strict component of the problem is NOT empty.
97.81/24.78	                  
97.81/24.78	                  2) 'With Problem ...' failed due to the following reason:
97.81/24.78	                     
97.81/24.78	                     Empty strict component of the problem is NOT empty.
97.81/24.78	                  
97.81/24.78	               
97.81/24.78	            
97.81/24.78	         
97.81/24.78	      
97.81/24.78	      3) 'Best' failed due to the following reason:
97.81/24.78	         
97.81/24.78	         None of the processors succeeded.
97.81/24.78	         
97.81/24.78	         Details of failed attempt(s):
97.81/24.78	         -----------------------------
97.81/24.78	         1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
97.81/24.78	            to the following reason:
97.81/24.78	            
97.81/24.78	            The input cannot be shown compatible
97.81/24.78	         
97.81/24.78	         2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
97.81/24.78	            following reason:
97.81/24.78	            
97.81/24.78	            The input cannot be shown compatible
97.81/24.78	         
97.81/24.78	      
97.81/24.78	   
97.81/24.78	
97.81/24.78	
97.81/24.78	Arrrr..
97.81/24.79	EOF