YES(?,O(n^1))
7.37/4.29	YES(?,O(n^1))
7.37/4.29	
7.37/4.29	We are left with following problem, upon which TcT provides the
7.37/4.29	certificate YES(?,O(n^1)).
7.37/4.29	
7.37/4.29	Strict Trs:
7.37/4.29	  { f(f(a(), f(a(), a())), x) -> f(x, f(f(a(), a()), a())) }
7.37/4.29	Obligation:
7.37/4.29	  derivational complexity
7.37/4.29	Answer:
7.37/4.29	  YES(?,O(n^1))
7.37/4.29	
7.37/4.29	We uncurry the input using the following uncurry rules.
7.37/4.29	
7.37/4.29	  { f(a_1(x_1), x_2) -> a_2(x_1, x_2)
7.37/4.29	  , f(a(), x_1) -> a_1(x_1) }
7.37/4.29	
7.37/4.29	We are left with following problem, upon which TcT provides the
7.37/4.29	certificate YES(?,O(n^1)).
7.37/4.29	
7.37/4.29	Strict Trs: { a_2(a_1(a()), x) -> f(x, a_2(a(), a())) }
7.37/4.29	Weak Trs:
7.37/4.29	  { f(a_1(x_1), x_2) -> a_2(x_1, x_2)
7.37/4.29	  , f(a(), x_1) -> a_1(x_1) }
7.37/4.29	Obligation:
7.37/4.29	  derivational complexity
7.37/4.29	Answer:
7.37/4.29	  YES(?,O(n^1))
7.37/4.29	
7.37/4.29	TcT has computed the following matrix interpretation satisfying
7.37/4.29	not(EDA) and not(IDA(1)).
7.37/4.29	
7.37/4.29	                  [1 0 0 0]      [1 1 0 0]      [0]
7.37/4.29	    [f](x1, x2) = [0 0 0 0] x1 + [0 0 0 0] x2 + [0]
7.37/4.29	                  [0 0 0 0]      [0 0 0 0]      [0]
7.37/4.29	                  [0 0 0 0]      [0 0 0 0]      [0]
7.37/4.29	                                                   
7.37/4.29	                  [1 0 0 0]      [1 0 0 0]      [0]
7.37/4.29	  [a_2](x1, x2) = [0 0 0 0] x1 + [0 0 0 0] x2 + [0]
7.37/4.29	                  [0 0 0 0]      [0 0 0 0]      [0]
7.37/4.29	                  [0 0 0 0]      [0 0 0 0]      [0]
7.37/4.29	                                                   
7.37/4.29	                  [1 1 0 0]      [0]               
7.37/4.29	      [a_1](x1) = [0 0 0 0] x1 + [0]               
7.37/4.29	                  [0 0 0 0]      [0]               
7.37/4.29	                  [0 0 0 0]      [0]               
7.37/4.29	                                                   
7.37/4.29	                  [0]                              
7.37/4.29	            [a] = [1]                              
7.37/4.29	                  [0]                              
7.37/4.29	                  [0]                              
7.37/4.29	
7.37/4.29	The order satisfies the following ordering constraints:
7.37/4.29	
7.37/4.29	  [f(a_1(x_1), x_2)] =  [1 1 0 0]       [1 1 0 0]       [0]
7.37/4.29	                        [0 0 0 0] x_1 + [0 0 0 0] x_2 + [0]
7.37/4.29	                        [0 0 0 0]       [0 0 0 0]       [0]
7.37/4.29	                        [0 0 0 0]       [0 0 0 0]       [0]
7.37/4.29	                     >= [1 0 0 0]       [1 0 0 0]       [0]
7.37/4.29	                        [0 0 0 0] x_1 + [0 0 0 0] x_2 + [0]
7.37/4.29	                        [0 0 0 0]       [0 0 0 0]       [0]
7.37/4.29	                        [0 0 0 0]       [0 0 0 0]       [0]
7.37/4.29	                     =  [a_2(x_1, x_2)]                    
7.37/4.29	                                                           
7.37/4.29	       [f(a(), x_1)] =  [1 1 0 0]       [0]                
7.37/4.29	                        [0 0 0 0] x_1 + [0]                
7.37/4.29	                        [0 0 0 0]       [0]                
7.37/4.29	                        [0 0 0 0]       [0]                
7.37/4.29	                     >= [1 1 0 0]       [0]                
7.37/4.29	                        [0 0 0 0] x_1 + [0]                
7.37/4.29	                        [0 0 0 0]       [0]                
7.37/4.29	                        [0 0 0 0]       [0]                
7.37/4.29	                     =  [a_1(x_1)]                         
7.37/4.29	                                                           
7.37/4.29	  [a_2(a_1(a()), x)] =  [1 0 0 0]     [1]                  
7.37/4.29	                        [0 0 0 0] x + [0]                  
7.37/4.29	                        [0 0 0 0]     [0]                  
7.37/4.29	                        [0 0 0 0]     [0]                  
7.37/4.29	                     >  [1 0 0 0]     [0]                  
7.37/4.29	                        [0 0 0 0] x + [0]                  
7.37/4.29	                        [0 0 0 0]     [0]                  
7.37/4.29	                        [0 0 0 0]     [0]                  
7.37/4.29	                     =  [f(x, a_2(a(), a()))]              
7.37/4.29	                                                           
7.37/4.29	
7.37/4.29	Hurray, we answered YES(?,O(n^1))
7.37/4.30	EOF