YES(?,O(n^1))
14.94/8.16	YES(?,O(n^1))
14.94/8.16	
14.94/8.16	We are left with following problem, upon which TcT provides the
14.94/8.16	certificate YES(?,O(n^1)).
14.94/8.16	
14.94/8.16	Strict Trs:
14.94/8.16	  { f(f(a(), a()), x) -> f(a(), f(x, f(a(), f(a(), a())))) }
14.94/8.16	Obligation:
14.94/8.16	  derivational complexity
14.94/8.16	Answer:
14.94/8.16	  YES(?,O(n^1))
14.94/8.16	
14.94/8.16	We uncurry the input using the following uncurry rules.
14.94/8.16	
14.94/8.16	  { f(a(), x_1) -> a_1(x_1)
14.94/8.16	  , f(a_1(x_1), x_2) -> a_2(x_1, x_2) }
14.94/8.16	
14.94/8.16	We are left with following problem, upon which TcT provides the
14.94/8.16	certificate YES(?,O(n^1)).
14.94/8.16	
14.94/8.16	Strict Trs: { a_2(a(), x) -> a_1(f(x, a_1(a_1(a())))) }
14.94/8.16	Weak Trs:
14.94/8.16	  { f(a(), x_1) -> a_1(x_1)
14.94/8.16	  , f(a_1(x_1), x_2) -> a_2(x_1, x_2) }
14.94/8.16	Obligation:
14.94/8.16	  derivational complexity
14.94/8.16	Answer:
14.94/8.16	  YES(?,O(n^1))
14.94/8.16	
14.94/8.16	TcT has computed the following matrix interpretation satisfying
14.94/8.16	not(EDA) and not(IDA(1)).
14.94/8.16	
14.94/8.16	                  [1 1 0 0]      [1 1 0 0]      [0]
14.94/8.16	    [f](x1, x2) = [0 0 0 0] x1 + [0 0 0 1] x2 + [0]
14.94/8.16	                  [0 0 0 0]      [0 0 0 0]      [0]
14.94/8.16	                  [0 0 0 0]      [0 0 0 0]      [0]
14.94/8.16	                                                   
14.94/8.16	                  [1 0 0 1]      [1 1 0 0]      [0]
14.94/8.16	  [a_2](x1, x2) = [0 0 0 0] x1 + [0 0 0 1] x2 + [0]
14.94/8.16	                  [0 0 0 0]      [0 0 0 0]      [0]
14.94/8.16	                  [0 0 0 0]      [0 0 0 0]      [0]
14.94/8.16	                                                   
14.94/8.16	                  [0]                              
14.94/8.16	            [a] = [0]                              
14.94/8.16	                  [0]                              
14.94/8.16	                  [1]                              
14.94/8.16	                                                   
14.94/8.16	                  [1 0 0 0]      [0]               
14.94/8.16	      [a_1](x1) = [0 0 0 1] x1 + [0]               
14.94/8.16	                  [0 0 0 0]      [0]               
14.94/8.16	                  [0 0 0 0]      [0]               
14.94/8.16	
14.94/8.16	The order satisfies the following ordering constraints:
14.94/8.16	
14.94/8.16	       [f(a(), x_1)] =  [1 1 0 0]       [0]                
14.94/8.16	                        [0 0 0 1] x_1 + [0]                
14.94/8.16	                        [0 0 0 0]       [0]                
14.94/8.16	                        [0 0 0 0]       [0]                
14.94/8.16	                     >= [1 0 0 0]       [0]                
14.94/8.16	                        [0 0 0 1] x_1 + [0]                
14.94/8.16	                        [0 0 0 0]       [0]                
14.94/8.16	                        [0 0 0 0]       [0]                
14.94/8.16	                     =  [a_1(x_1)]                         
14.94/8.16	                                                           
14.94/8.16	  [f(a_1(x_1), x_2)] =  [1 0 0 1]       [1 1 0 0]       [0]
14.94/8.16	                        [0 0 0 0] x_1 + [0 0 0 1] x_2 + [0]
14.94/8.16	                        [0 0 0 0]       [0 0 0 0]       [0]
14.94/8.16	                        [0 0 0 0]       [0 0 0 0]       [0]
14.94/8.16	                     >= [1 0 0 1]       [1 1 0 0]       [0]
14.94/8.16	                        [0 0 0 0] x_1 + [0 0 0 1] x_2 + [0]
14.94/8.16	                        [0 0 0 0]       [0 0 0 0]       [0]
14.94/8.16	                        [0 0 0 0]       [0 0 0 0]       [0]
14.94/8.16	                     =  [a_2(x_1, x_2)]                    
14.94/8.16	                                                           
14.94/8.16	       [a_2(a(), x)] =  [1 1 0 0]     [1]                  
14.94/8.16	                        [0 0 0 1] x + [0]                  
14.94/8.16	                        [0 0 0 0]     [0]                  
14.94/8.16	                        [0 0 0 0]     [0]                  
14.94/8.16	                     >  [1 1 0 0]     [0]                  
14.94/8.16	                        [0 0 0 0] x + [0]                  
14.94/8.16	                        [0 0 0 0]     [0]                  
14.94/8.16	                        [0 0 0 0]     [0]                  
14.94/8.16	                     =  [a_1(f(x, a_1(a_1(a()))))]         
14.94/8.16	                                                           
14.94/8.16	
14.94/8.16	Hurray, we answered YES(?,O(n^1))
14.94/8.18	EOF