YES(O(1),O(n^1))

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

Strict Trs:
  { app(nil(), xs) -> nil()
  , app(cons(x, xs), ys) -> cons(x, app(xs, ys)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^1))

We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.

Trs: { app(cons(x, xs), ys) -> cons(x, app(xs, ys)) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
  TcT has computed the following constructor-based matrix
  interpretation satisfying not(EDA).
  
     [app](x1, x2) = [2] x1 + [3] x2 + [0]
                                          
             [nil] = [0]                  
                                          
    [cons](x1, x2) = [1] x1 + [1] x2 + [2]
  
  This order satisfies the following ordering constraints:
  
          [app(nil(), xs)] =  [3] xs + [0]                 
                           >= [0]                          
                           =  [nil()]                      
                                                           
    [app(cons(x, xs), ys)] =  [2] xs + [2] x + [3] ys + [4]
                           >  [2] xs + [1] x + [3] ys + [2]
                           =  [cons(x, app(xs, ys))]       
                                                           

We return to the main proof.

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

Strict Trs: { app(nil(), xs) -> nil() }
Weak Trs: { app(cons(x, xs), ys) -> cons(x, app(xs, ys)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^1))

We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.

Trs: { app(nil(), xs) -> nil() }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
  TcT has computed the following constructor-based matrix
  interpretation satisfying not(EDA).
  
     [app](x1, x2) = [2] x1 + [3] x2 + [1]
                                          
             [nil] = [0]                  
                                          
    [cons](x1, x2) = [1] x1 + [1] x2 + [0]
  
  This order satisfies the following ordering constraints:
  
          [app(nil(), xs)] =  [3] xs + [1]                 
                           >  [0]                          
                           =  [nil()]                      
                                                           
    [app(cons(x, xs), ys)] =  [2] xs + [2] x + [3] ys + [1]
                           >= [2] xs + [1] x + [3] ys + [1]
                           =  [cons(x, app(xs, ys))]       
                                                           

We return to the main proof.

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

Weak Trs:
  { app(nil(), xs) -> nil()
  , app(cons(x, xs), ys) -> cons(x, app(xs, ys)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

Empty rules are trivially bounded

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