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:
  { rev(ls) -> r1(ls, empty())
  , r1(empty(), a) -> a
  , r1(cons(x, k), a) -> r1(k, cons(x, a)) }
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: { rev(ls) -> r1(ls, empty()) }

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).
  
         [rev](x1) = [3] x1 + [3]         
                                          
      [r1](x1, x2) = [2] x1 + [2] x2 + [0]
                                          
           [empty] = [0]                  
                                          
    [cons](x1, x2) = [1] x1 + [1] x2 + [0]
  
  This order satisfies the following ordering constraints:
  
              [rev(ls)] =  [3] ls + [3]               
                        >  [2] ls + [0]               
                        =  [r1(ls, empty())]          
                                                      
       [r1(empty(), a)] =  [2] a + [0]                
                        >= [1] a + [0]                
                        =  [a]                        
                                                      
    [r1(cons(x, k), a)] =  [2] a + [2] x + [2] k + [0]
                        >= [2] a + [2] x + [2] k + [0]
                        =  [r1(k, cons(x, a))]        
                                                      

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:
  { r1(empty(), a) -> a
  , r1(cons(x, k), a) -> r1(k, cons(x, a)) }
Weak Trs: { rev(ls) -> r1(ls, empty()) }
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: { r1(empty(), a) -> a }

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).
  
         [rev](x1) = [3] x1 + [3]         
                                          
      [r1](x1, x2) = [2] x1 + [2] x2 + [1]
                                          
           [empty] = [0]                  
                                          
    [cons](x1, x2) = [1] x1 + [1] x2 + [0]
  
  This order satisfies the following ordering constraints:
  
              [rev(ls)] =  [3] ls + [3]               
                        >  [2] ls + [1]               
                        =  [r1(ls, empty())]          
                                                      
       [r1(empty(), a)] =  [2] a + [1]                
                        >  [1] a + [0]                
                        =  [a]                        
                                                      
    [r1(cons(x, k), a)] =  [2] a + [2] x + [2] k + [1]
                        >= [2] a + [2] x + [2] k + [1]
                        =  [r1(k, cons(x, a))]        
                                                      

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: { r1(cons(x, k), a) -> r1(k, cons(x, a)) }
Weak Trs:
  { rev(ls) -> r1(ls, empty())
  , r1(empty(), a) -> a }
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: { r1(cons(x, k), a) -> r1(k, cons(x, a)) }

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).
  
         [rev](x1) = [3] x1 + [3]         
                                          
      [r1](x1, x2) = [2] x1 + [1] x2 + [0]
                                          
           [empty] = [3]                  
                                          
    [cons](x1, x2) = [1] x1 + [1] x2 + [2]
  
  This order satisfies the following ordering constraints:
  
              [rev(ls)] =  [3] ls + [3]               
                        >= [2] ls + [3]               
                        =  [r1(ls, empty())]          
                                                      
       [r1(empty(), a)] =  [1] a + [6]                
                        >  [1] a + [0]                
                        =  [a]                        
                                                      
    [r1(cons(x, k), a)] =  [1] a + [2] x + [2] k + [4]
                        >  [1] a + [1] x + [2] k + [2]
                        =  [r1(k, cons(x, a))]        
                                                      

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:
  { rev(ls) -> r1(ls, empty())
  , r1(empty(), a) -> a
  , r1(cons(x, k), a) -> r1(k, cons(x, a)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

Empty rules are trivially bounded

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