WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l3 0: l0 -> l1 : x^0'=x^post_1, y^0'=y^post_1, [ 1+x^0<=y^0 && 1+y^0<=x^0 && x^0==x^post_1 && y^0==y^post_1 ], cost: 1 1: l1 -> l0 : x^0'=x^post_2, y^0'=y^post_2, [ x^0==x^post_2 && y^0==y^post_2 ], cost: 1 2: l2 -> l0 : x^0'=x^post_3, y^0'=y^post_3, [ x^0==x^post_3 && y^0==y^post_3 ], cost: 1 3: l3 -> l2 : x^0'=x^post_4, y^0'=y^post_4, [ x^0==x^post_4 && y^0==y^post_4 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: l3 -> l2 : x^0'=x^post_4, y^0'=y^post_4, [ x^0==x^post_4 && y^0==y^post_4 ], cost: 1 Removed rules with unsatisfiable guard: Start location: l3 1: l1 -> l0 : x^0'=x^post_2, y^0'=y^post_2, [ x^0==x^post_2 && y^0==y^post_2 ], cost: 1 2: l2 -> l0 : x^0'=x^post_3, y^0'=y^post_3, [ x^0==x^post_3 && y^0==y^post_3 ], cost: 1 3: l3 -> l2 : x^0'=x^post_4, y^0'=y^post_4, [ x^0==x^post_4 && y^0==y^post_4 ], cost: 1 Removed unreachable and leaf rules: Start location: l3 Empty problem, aborting Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [ x^0==x^post_4 && y^0==y^post_4 ] WORST_CASE(Omega(1),?)