YES(O(1),O(1))
0.00/0.03	YES(O(1),O(1))
0.00/0.03	
0.00/0.03	We are left with following problem, upon which TcT provides the
0.00/0.03	certificate YES(O(1),O(1)).
0.00/0.03	
0.00/0.03	Strict Trs:
0.00/0.03	  { h(x, c(y, z), t(w)) -> h(c(s(y), x), z, t(c(t(w), w)))
0.00/0.03	  , h(c(x, y), c(s(z), z), t(w)) ->
0.00/0.03	    h(z, c(y, x), t(t(c(x, c(y, t(w))))))
0.00/0.03	  , h(c(s(x), c(s(0()), y)), z, t(x)) ->
0.00/0.03	    h(y, c(s(0()), c(x, z)), t(t(c(x, s(x)))))
0.00/0.03	  , t(x) -> x
0.00/0.03	  , t(x) -> c(0(), c(0(), c(0(), c(0(), c(0(), x)))))
0.00/0.03	  , t(t(x)) -> t(c(t(x), x)) }
0.00/0.03	Obligation:
0.00/0.03	  innermost runtime complexity
0.00/0.03	Answer:
0.00/0.03	  YES(O(1),O(1))
0.00/0.03	
0.00/0.03	Arguments of following rules are not normal-forms:
0.00/0.03	
0.00/0.03	{ h(x, c(y, z), t(w)) -> h(c(s(y), x), z, t(c(t(w), w)))
0.00/0.03	, h(c(x, y), c(s(z), z), t(w)) ->
0.00/0.03	  h(z, c(y, x), t(t(c(x, c(y, t(w))))))
0.00/0.03	, h(c(s(x), c(s(0()), y)), z, t(x)) ->
0.00/0.03	  h(y, c(s(0()), c(x, z)), t(t(c(x, s(x)))))
0.00/0.03	, t(t(x)) -> t(c(t(x), x)) }
0.00/0.03	
0.00/0.03	All above mentioned rules can be savely removed.
0.00/0.03	
0.00/0.03	We are left with following problem, upon which TcT provides the
0.00/0.03	certificate YES(O(1),O(1)).
0.00/0.03	
0.00/0.03	Strict Trs:
0.00/0.03	  { t(x) -> x
0.00/0.03	  , t(x) -> c(0(), c(0(), c(0(), c(0(), c(0(), x))))) }
0.00/0.03	Obligation:
0.00/0.03	  innermost runtime complexity
0.00/0.03	Answer:
0.00/0.03	  YES(O(1),O(1))
0.00/0.03	
0.00/0.03	We add the following weak dependency pairs:
0.00/0.03	
0.00/0.03	Strict DPs:
0.00/0.03	  { t^#(x) -> c_1()
0.00/0.03	  , t^#(x) -> c_2() }
0.00/0.03	
0.00/0.03	and mark the set of starting terms.
0.00/0.03	
0.00/0.03	We are left with following problem, upon which TcT provides the
0.00/0.03	certificate YES(O(1),O(1)).
0.00/0.03	
0.00/0.03	Strict DPs:
0.00/0.03	  { t^#(x) -> c_1()
0.00/0.03	  , t^#(x) -> c_2() }
0.00/0.03	Strict Trs:
0.00/0.03	  { t(x) -> x
0.00/0.03	  , t(x) -> c(0(), c(0(), c(0(), c(0(), c(0(), x))))) }
0.00/0.03	Obligation:
0.00/0.03	  innermost runtime complexity
0.00/0.03	Answer:
0.00/0.03	  YES(O(1),O(1))
0.00/0.03	
0.00/0.03	No rule is usable, rules are removed from the input problem.
0.00/0.03	
0.00/0.03	We are left with following problem, upon which TcT provides the
0.00/0.03	certificate YES(O(1),O(1)).
0.00/0.03	
0.00/0.03	Strict DPs:
0.00/0.03	  { t^#(x) -> c_1()
0.00/0.03	  , t^#(x) -> c_2() }
0.00/0.03	Obligation:
0.00/0.03	  innermost runtime complexity
0.00/0.03	Answer:
0.00/0.03	  YES(O(1),O(1))
0.00/0.03	
0.00/0.03	The weightgap principle applies (using the following constant
0.00/0.03	growth matrix-interpretation)
0.00/0.03	
0.00/0.03	The following argument positions are usable:
0.00/0.03	  none
0.00/0.03	
0.00/0.03	TcT has computed the following constructor-restricted matrix
0.00/0.03	interpretation.
0.00/0.03	
0.00/0.03	  [t^#](x1) = [2]
0.00/0.03	              [2]
0.00/0.03	                 
0.00/0.03	      [c_1] = [1]
0.00/0.03	              [2]
0.00/0.03	                 
0.00/0.03	      [c_2] = [1]
0.00/0.03	              [1]
0.00/0.03	
0.00/0.03	The order satisfies the following ordering constraints:
0.00/0.03	
0.00/0.03	  [t^#(x)] = [2]    
0.00/0.03	             [2]    
0.00/0.03	           > [1]    
0.00/0.03	             [2]    
0.00/0.03	           = [c_1()]
0.00/0.03	                    
0.00/0.03	  [t^#(x)] = [2]    
0.00/0.03	             [2]    
0.00/0.03	           > [1]    
0.00/0.03	             [1]    
0.00/0.03	           = [c_2()]
0.00/0.03	                    
0.00/0.03	
0.00/0.03	Further, it can be verified that all rules not oriented are covered by the weightgap condition.
0.00/0.03	
0.00/0.03	We are left with following problem, upon which TcT provides the
0.00/0.03	certificate YES(O(1),O(1)).
0.00/0.03	
0.00/0.03	Weak DPs:
0.00/0.03	  { t^#(x) -> c_1()
0.00/0.03	  , t^#(x) -> c_2() }
0.00/0.03	Obligation:
0.00/0.03	  innermost runtime complexity
0.00/0.03	Answer:
0.00/0.03	  YES(O(1),O(1))
0.00/0.03	
0.00/0.03	The following weak DPs constitute a sub-graph of the DG that is
0.00/0.03	closed under successors. The DPs are removed.
0.00/0.03	
0.00/0.03	{ t^#(x) -> c_1()
0.00/0.03	, t^#(x) -> c_2() }
0.00/0.03	
0.00/0.03	We are left with following problem, upon which TcT provides the
0.00/0.03	certificate YES(O(1),O(1)).
0.00/0.03	
0.00/0.03	Rules: Empty
0.00/0.03	Obligation:
0.00/0.03	  innermost runtime complexity
0.00/0.03	Answer:
0.00/0.03	  YES(O(1),O(1))
0.00/0.03	
0.00/0.03	Empty rules are trivially bounded
0.00/0.03	
0.00/0.03	Hurray, we answered YES(O(1),O(1))
0.00/0.03	EOF