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

Strict Trs:
  { and(not(not(x)), y, not(z)) -> and(y, band(x, z), x) }
Obligation:
  runtime complexity
Answer:
  YES(O(1),O(n^1))

We add the following weak dependency pairs:

Strict DPs:
  { and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }

and mark the set of starting terms.

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

Strict DPs:
  { and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }
Strict Trs:
  { and(not(not(x)), y, not(z)) -> and(y, band(x, z), x) }
Obligation:
  runtime complexity
Answer:
  YES(O(1),O(n^1))

No rule is usable, rules are removed from the input problem.

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

Strict DPs:
  { and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }
Obligation:
  runtime complexity
Answer:
  YES(O(1),O(n^1))

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(c_1) = {1}

TcT has computed the following constructor-restricted matrix
interpretation.

            [not](x1) = [0]                      
                        [2]                      
                                                 
       [band](x1, x2) = [1]                      
                        [0]                      
                                                 
  [and^#](x1, x2, x3) = [0 1] x1 + [1 2] x2 + [0]
                        [0 0]      [0 0]      [0]
                                                 
            [c_1](x1) = [1 0] x1 + [0]           
                        [0 1]      [0]           

The order satisfies the following ordering constraints:

  [and^#(not(not(x)), y, not(z))] = [1 2] y + [2]                 
                                    [0 0]     [0]                 
                                  > [0 1] y + [1]                 
                                    [0 0]     [0]                 
                                  = [c_1(and^#(y, band(x, z), x))]
                                                                  

Further, it can be verified that all rules not oriented are covered by the weightgap condition.

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

Weak DPs:
  { and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }
Obligation:
  runtime complexity
Answer:
  YES(?,O(n^1))

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }

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

Rules: Empty
Obligation:
  runtime complexity
Answer:
  YES(?,O(n^1))

We employ 'linear path analysis' using the following approximated
dependency graph:
empty


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