WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l4 0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, tmp1^0'=tmp1^post_1, tmp2^0'=tmp2^post_1, tmp3^0'=tmp3^post_1, [ i^0==i^post_1 && j^0==j^post_1 && tmp1^0==tmp1^post_1 && tmp2^0==tmp2^post_1 && tmp3^0==tmp3^post_1 ], cost: 1 1: l2 -> l0 : i^0'=i^post_2, j^0'=j^post_2, tmp1^0'=tmp1^post_2, tmp2^0'=tmp2^post_2, tmp3^0'=tmp3^post_2, [ i^0==i^post_2 && j^0==j^post_2 && tmp1^0==tmp1^post_2 && tmp2^0==tmp2^post_2 && tmp3^0==tmp3^post_2 ], cost: 1 2: l2 -> l0 : i^0'=i^post_3, j^0'=j^post_3, tmp1^0'=tmp1^post_3, tmp2^0'=tmp2^post_3, tmp3^0'=tmp3^post_3, [ i^0==i^post_3 && j^0==j^post_3 && tmp1^0==tmp1^post_3 && tmp2^0==tmp2^post_3 && tmp3^0==tmp3^post_3 ], cost: 1 3: l3 -> l2 : i^0'=i^post_4, j^0'=j^post_4, tmp1^0'=tmp1^post_4, tmp2^0'=tmp2^post_4, tmp3^0'=tmp3^post_4, [ i^post_4==0 && j^post_4==1 && tmp1^post_4==tmp1^post_4 && tmp2^post_4==tmp2^post_4 && tmp3^post_4==tmp3^post_4 ], cost: 1 4: l4 -> l3 : i^0'=i^post_5, j^0'=j^post_5, tmp1^0'=tmp1^post_5, tmp2^0'=tmp2^post_5, tmp3^0'=tmp3^post_5, [ i^0==i^post_5 && j^0==j^post_5 && tmp1^0==tmp1^post_5 && tmp2^0==tmp2^post_5 && tmp3^0==tmp3^post_5 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: l4 -> l3 : i^0'=i^post_5, j^0'=j^post_5, tmp1^0'=tmp1^post_5, tmp2^0'=tmp2^post_5, tmp3^0'=tmp3^post_5, [ i^0==i^post_5 && j^0==j^post_5 && tmp1^0==tmp1^post_5 && tmp2^0==tmp2^post_5 && tmp3^0==tmp3^post_5 ], cost: 1 Removed unreachable and leaf rules: Start location: l4 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: [ i^0==i^post_5 && j^0==j^post_5 && tmp1^0==tmp1^post_5 && tmp2^0==tmp2^post_5 && tmp3^0==tmp3^post_5 ] WORST_CASE(Omega(1),?)