YES(?,O(n^1))

We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).

Strict Trs:
  { decrease(Cons(x, xs)) -> decrease(xs)
  , decrease(Nil()) -> number42(Nil())
  , number42(x) ->
    Cons(Nil(),
         Cons(Nil(),
              Cons(Nil(),
                   Cons(Nil(),
                        Cons(Nil(),
                             Cons(Nil(),
                                  Cons(Nil(),
                                       Cons(Nil(),
                                            Cons(Nil(),
                                                 Cons(Nil(),
                                                      Cons(Nil(),
                                                           Cons(Nil(),
                                                                Cons(Nil(),
                                                                     Cons(Nil(),
                                                                          Cons(Nil(),
                                                                               Cons(Nil(),
                                                                                    Cons(Nil(),
                                                                                         Cons(Nil(),
                                                                                              Cons(Nil(),
                                                                                                   Cons(Nil(),
                                                                                                        Cons(Nil(),
                                                                                                             Cons(Nil(),
                                                                                                                  Cons(Nil(),
                                                                                                                       Cons(Nil(),
                                                                                                                            Cons(Nil(),
                                                                                                                                 Cons(Nil(),
                                                                                                                                      Cons(Nil(),
                                                                                                                                           Cons(Nil(),
                                                                                                                                                Cons(Nil(),
                                                                                                                                                     Cons(Nil(),
                                                                                                                                                          Cons(Nil(),
                                                                                                                                                               Cons(Nil(),
                                                                                                                                                                    Cons(Nil(),
                                                                                                                                                                         Cons(Nil(),
                                                                                                                                                                              Cons(Nil(),
                                                                                                                                                                                   Cons(Nil(),
                                                                                                                                                                                        Cons(Nil(),
                                                                                                                                                                                             Cons(Nil(),
                                                                                                                                                                                                  Cons(Nil(),
                                                                                                                                                                                                       Cons(Nil(),
                                                                                                                                                                                                            Cons(Nil(),
                                                                                                                                                                                                                 Cons(Nil(),
                                                                                                                                                                                                                      Nil()))))))))))))))))))))))))))))))))))))))))))
  , goal(x) -> decrease(x) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

The input was oriented with the instance of 'Small Polynomial Path
Order (PS,1-bounded)' as induced by the safe mapping

 safe(decrease) = {}, safe(Cons) = {1, 2}, safe(Nil) = {},
 safe(number42) = {1}, safe(goal) = {}

and precedence

 decrease > number42, goal > decrease, goal > number42 .

Following symbols are considered recursive:

 {decrease}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

  decrease(Cons(; x,  xs);) > decrease(xs;)                                                                                                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                                                                                                                                                   
           decrease(Nil();) > number42(; Nil())                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                                   
              number42(; x) > Cons(; Nil(),                                                                                                                                                                                                                                                                                                                                        
                                     Cons(; Nil(),                                                                                                                                                                                                                                                                                                                                 
                                            Cons(; Nil(),                                                                                                                                                                                                                                                                                                                          
                                                   Cons(; Nil(),                                                                                                                                                                                                                                                                                                                   
                                                          Cons(; Nil(),                                                                                                                                                                                                                                                                                                            
                                                                 Cons(; Nil(),                                                                                                                                                                                                                                                                                                     
                                                                        Cons(; Nil(),                                                                                                                                                                                                                                                                                              
                                                                               Cons(; Nil(),                                                                                                                                                                                                                                                                                       
                                                                                      Cons(; Nil(),                                                                                                                                                                                                                                                                                
                                                                                             Cons(; Nil(),                                                                                                                                                                                                                                                                         
                                                                                                    Cons(; Nil(),                                                                                                                                                                                                                                                                  
                                                                                                           Cons(; Nil(),                                                                                                                                                                                                                                                           
                                                                                                                  Cons(; Nil(),                                                                                                                                                                                                                                                    
                                                                                                                         Cons(; Nil(),                                                                                                                                                                                                                                             
                                                                                                                                Cons(; Nil(),                                                                                                                                                                                                                                      
                                                                                                                                       Cons(; Nil(),                                                                                                                                                                                                                               
                                                                                                                                              Cons(; Nil(),                                                                                                                                                                                                                        
                                                                                                                                                     Cons(; Nil(),                                                                                                                                                                                                                 
                                                                                                                                                            Cons(; Nil(),                                                                                                                                                                                                          
                                                                                                                                                                   Cons(; Nil(),                                                                                                                                                                                                   
                                                                                                                                                                          Cons(; Nil(),                                                                                                                                                                                            
                                                                                                                                                                                 Cons(; Nil(),                                                                                                                                                                                     
                                                                                                                                                                                        Cons(; Nil(),                                                                                                                                                                              
                                                                                                                                                                                               Cons(; Nil(),                                                                                                                                                                       
                                                                                                                                                                                                      Cons(; Nil(),                                                                                                                                                                
                                                                                                                                                                                                             Cons(; Nil(),                                                                                                                                                         
                                                                                                                                                                                                                    Cons(; Nil(),                                                                                                                                                  
                                                                                                                                                                                                                           Cons(; Nil(),                                                                                                                                           
                                                                                                                                                                                                                                  Cons(; Nil(),                                                                                                                                    
                                                                                                                                                                                                                                         Cons(; Nil(),                                                                                                                             
                                                                                                                                                                                                                                                Cons(; Nil(),                                                                                                                      
                                                                                                                                                                                                                                                       Cons(; Nil(),                                                                                                               
                                                                                                                                                                                                                                                              Cons(; Nil(),                                                                                                        
                                                                                                                                                                                                                                                                     Cons(; Nil(),                                                                                                 
                                                                                                                                                                                                                                                                            Cons(; Nil(),                                                                                          
                                                                                                                                                                                                                                                                                   Cons(; Nil(),                                                                                   
                                                                                                                                                                                                                                                                                          Cons(; Nil(),                                                                            
                                                                                                                                                                                                                                                                                                 Cons(; Nil(),                                                                     
                                                                                                                                                                                                                                                                                                        Cons(; Nil(),                                                              
                                                                                                                                                                                                                                                                                                               Cons(; Nil(),                                                       
                                                                                                                                                                                                                                                                                                                      Cons(; Nil(),                                                
                                                                                                                                                                                                                                                                                                                             Cons(; Nil(),                                         
                                                                                                                                                                                                                                                                                                                                    Nil()))))))))))))))))))))))))))))))))))))))))))
                                                                                                                                                                                                                                                                                                                                                                                   
                   goal(x;) > decrease(x;)                                                                                                                                                                                                                                                                                                                                         
                                                                                                                                                                                                                                                                                                                                                                                   

Hurray, we answered YES(?,O(n^1))