YES(O(1),O(n^1))
0.00/0.19	YES(O(1),O(n^1))
0.00/0.19	
0.00/0.19	We are left with following problem, upon which TcT provides the
0.00/0.19	certificate YES(O(1),O(n^1)).
0.00/0.19	
0.00/0.19	Strict Trs:
0.00/0.19	  { and(not(not(x)), y, not(z)) -> and(y, band(x, z), x) }
0.00/0.19	Obligation:
0.00/0.19	  innermost runtime complexity
0.00/0.19	Answer:
0.00/0.19	  YES(O(1),O(n^1))
0.00/0.19	
0.00/0.19	We add the following weak dependency pairs:
0.00/0.19	
0.00/0.19	Strict DPs:
0.00/0.19	  { and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }
0.00/0.19	
0.00/0.19	and mark the set of starting terms.
0.00/0.19	
0.00/0.19	We are left with following problem, upon which TcT provides the
0.00/0.19	certificate YES(O(1),O(n^1)).
0.00/0.19	
0.00/0.19	Strict DPs:
0.00/0.19	  { and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }
0.00/0.19	Strict Trs:
0.00/0.19	  { and(not(not(x)), y, not(z)) -> and(y, band(x, z), x) }
0.00/0.19	Obligation:
0.00/0.19	  innermost runtime complexity
0.00/0.19	Answer:
0.00/0.19	  YES(O(1),O(n^1))
0.00/0.19	
0.00/0.19	No rule is usable, rules are removed from the input problem.
0.00/0.19	
0.00/0.19	We are left with following problem, upon which TcT provides the
0.00/0.19	certificate YES(O(1),O(n^1)).
0.00/0.19	
0.00/0.19	Strict DPs:
0.00/0.19	  { and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }
0.00/0.19	Obligation:
0.00/0.19	  innermost runtime complexity
0.00/0.19	Answer:
0.00/0.19	  YES(O(1),O(n^1))
0.00/0.19	
0.00/0.19	The weightgap principle applies (using the following constant
0.00/0.19	growth matrix-interpretation)
0.00/0.19	
0.00/0.19	The following argument positions are usable:
0.00/0.19	  Uargs(c_1) = {1}
0.00/0.19	
0.00/0.19	TcT has computed the following constructor-restricted matrix
0.00/0.19	interpretation.
0.00/0.19	
0.00/0.19	            [not](x1) = [0]                      
0.00/0.19	                        [2]                      
0.00/0.19	                                                 
0.00/0.19	       [band](x1, x2) = [1 0] x1 + [1 0] x2 + [0]
0.00/0.19	                        [0 0]      [0 0]      [0]
0.00/0.19	                                                 
0.00/0.19	  [and^#](x1, x2, x3) = [0 1] x1 + [0 1] x2 + [0]
0.00/0.19	                        [0 0]      [0 0]      [0]
0.00/0.19	                                                 
0.00/0.19	            [c_1](x1) = [1 0] x1 + [1]           
0.00/0.19	                        [0 1]      [0]           
0.00/0.19	
0.00/0.19	The order satisfies the following ordering constraints:
0.00/0.19	
0.00/0.19	  [and^#(not(not(x)), y, not(z))] = [0 1] y + [2]                 
0.00/0.19	                                    [0 0]     [0]                 
0.00/0.19	                                  > [0 1] y + [1]                 
0.00/0.19	                                    [0 0]     [0]                 
0.00/0.19	                                  = [c_1(and^#(y, band(x, z), x))]
0.00/0.19	                                                                  
0.00/0.19	
0.00/0.19	Further, it can be verified that all rules not oriented are covered by the weightgap condition.
0.00/0.19	
0.00/0.19	We are left with following problem, upon which TcT provides the
0.00/0.19	certificate YES(O(1),O(1)).
0.00/0.19	
0.00/0.19	Weak DPs:
0.00/0.19	  { and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }
0.00/0.19	Obligation:
0.00/0.19	  innermost runtime complexity
0.00/0.19	Answer:
0.00/0.19	  YES(O(1),O(1))
0.00/0.19	
0.00/0.19	The following weak DPs constitute a sub-graph of the DG that is
0.00/0.19	closed under successors. The DPs are removed.
0.00/0.19	
0.00/0.19	{ and^#(not(not(x)), y, not(z)) -> c_1(and^#(y, band(x, z), x)) }
0.00/0.19	
0.00/0.19	We are left with following problem, upon which TcT provides the
0.00/0.19	certificate YES(O(1),O(1)).
0.00/0.19	
0.00/0.19	Rules: Empty
0.00/0.19	Obligation:
0.00/0.19	  innermost runtime complexity
0.00/0.19	Answer:
0.00/0.19	  YES(O(1),O(1))
0.00/0.19	
0.00/0.19	Empty rules are trivially bounded
0.00/0.19	
0.00/0.19	Hurray, we answered YES(O(1),O(n^1))
0.38/0.20	EOF