YES(O(1),O(n^1))
0.00/0.10	YES(O(1),O(n^1))
0.00/0.10	
0.00/0.10	We are left with following problem, upon which TcT provides the
0.00/0.10	certificate YES(O(1),O(n^1)).
0.00/0.10	
0.00/0.10	Strict Trs: { f(g(x), y, y) -> g(f(x, x, y)) }
0.00/0.10	Obligation:
0.00/0.10	  innermost runtime complexity
0.00/0.10	Answer:
0.00/0.10	  YES(O(1),O(n^1))
0.00/0.10	
0.00/0.10	We add the following weak dependency pairs:
0.00/0.10	
0.00/0.10	Strict DPs: { f^#(g(x), y, y) -> c_1(f^#(x, x, y)) }
0.00/0.10	
0.00/0.10	and mark the set of starting terms.
0.00/0.10	
0.00/0.10	We are left with following problem, upon which TcT provides the
0.00/0.10	certificate YES(O(1),O(n^1)).
0.00/0.10	
0.00/0.10	Strict DPs: { f^#(g(x), y, y) -> c_1(f^#(x, x, y)) }
0.00/0.10	Strict Trs: { f(g(x), y, y) -> g(f(x, x, y)) }
0.00/0.10	Obligation:
0.00/0.10	  innermost runtime complexity
0.00/0.10	Answer:
0.00/0.10	  YES(O(1),O(n^1))
0.00/0.10	
0.00/0.10	No rule is usable, rules are removed from the input problem.
0.00/0.10	
0.00/0.10	We are left with following problem, upon which TcT provides the
0.00/0.10	certificate YES(O(1),O(n^1)).
0.00/0.10	
0.00/0.10	Strict DPs: { f^#(g(x), y, y) -> c_1(f^#(x, x, y)) }
0.00/0.10	Obligation:
0.00/0.10	  innermost runtime complexity
0.00/0.10	Answer:
0.00/0.10	  YES(O(1),O(n^1))
0.00/0.10	
0.00/0.10	The weightgap principle applies (using the following constant
0.00/0.10	growth matrix-interpretation)
0.00/0.10	
0.00/0.10	The following argument positions are usable:
0.00/0.10	  Uargs(c_1) = {1}
0.00/0.10	
0.00/0.10	TcT has computed the following constructor-restricted matrix
0.00/0.10	interpretation.
0.00/0.10	
0.00/0.10	            [g](x1) = [1 0] x1 + [2]           
0.00/0.10	                      [0 1]      [1]           
0.00/0.10	                                               
0.00/0.10	  [f^#](x1, x2, x3) = [1 0] x1 + [2 2] x3 + [2]
0.00/0.10	                      [2 2]      [2 2]      [1]
0.00/0.10	                                               
0.00/0.10	          [c_1](x1) = [1 0] x1 + [1]           
0.00/0.10	                      [0 1]      [1]           
0.00/0.10	
0.00/0.10	The order satisfies the following ordering constraints:
0.00/0.10	
0.00/0.10	  [f^#(g(x), y, y)] = [1 0] x + [2 2] y + [4]
0.00/0.10	                      [2 2]     [2 2]     [7]
0.00/0.10	                    > [1 0] x + [2 2] y + [3]
0.00/0.10	                      [2 2]     [2 2]     [2]
0.00/0.10	                    = [c_1(f^#(x, x, y))]    
0.00/0.10	                                             
0.00/0.10	
0.00/0.10	Further, it can be verified that all rules not oriented are covered by the weightgap condition.
0.00/0.10	
0.00/0.10	We are left with following problem, upon which TcT provides the
0.00/0.10	certificate YES(O(1),O(1)).
0.00/0.10	
0.00/0.10	Weak DPs: { f^#(g(x), y, y) -> c_1(f^#(x, x, y)) }
0.00/0.10	Obligation:
0.00/0.10	  innermost runtime complexity
0.00/0.10	Answer:
0.00/0.10	  YES(O(1),O(1))
0.00/0.10	
0.00/0.10	The following weak DPs constitute a sub-graph of the DG that is
0.00/0.10	closed under successors. The DPs are removed.
0.00/0.10	
0.00/0.10	{ f^#(g(x), y, y) -> c_1(f^#(x, x, y)) }
0.00/0.10	
0.00/0.10	We are left with following problem, upon which TcT provides the
0.00/0.10	certificate YES(O(1),O(1)).
0.00/0.10	
0.00/0.10	Rules: Empty
0.00/0.10	Obligation:
0.00/0.10	  innermost runtime complexity
0.00/0.10	Answer:
0.00/0.10	  YES(O(1),O(1))
0.00/0.10	
0.00/0.10	Empty rules are trivially bounded
0.00/0.10	
0.00/0.10	Hurray, we answered YES(O(1),O(n^1))
0.00/0.10	EOF