WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l6 0: l0 -> l1 : a^0'=a^post_1, ret_returnOne3^0'=ret_returnOne3^post_1, tmp^0'=tmp^post_1, [ 3<=a^0 && a^0==a^post_1 && ret_returnOne3^0==ret_returnOne3^post_1 && tmp^0==tmp^post_1 ], cost: 1 1: l0 -> l1 : a^0'=a^post_2, ret_returnOne3^0'=ret_returnOne3^post_2, tmp^0'=tmp^post_2, [ 1+a^0<=2 && a^0==a^post_2 && ret_returnOne3^0==ret_returnOne3^post_2 && tmp^0==tmp^post_2 ], cost: 1 2: l0 -> l2 : a^0'=a^post_3, ret_returnOne3^0'=ret_returnOne3^post_3, tmp^0'=tmp^post_3, [ a^0<=2 && 2<=a^0 && tmp^post_3==1 && a^0==a^post_3 && ret_returnOne3^0==ret_returnOne3^post_3 ], cost: 1 7: l1 -> l2 : a^0'=a^post_8, ret_returnOne3^0'=ret_returnOne3^post_8, tmp^0'=tmp^post_8, [ tmp^post_8==0 && a^0==a^post_8 && ret_returnOne3^0==ret_returnOne3^post_8 ], cost: 1 3: l2 -> l3 : a^0'=a^post_4, ret_returnOne3^0'=ret_returnOne3^post_4, tmp^0'=tmp^post_4, [ a^0==a^post_4 && ret_returnOne3^0==ret_returnOne3^post_4 && tmp^0==tmp^post_4 ], cost: 1 4: l4 -> l0 : a^0'=a^post_5, ret_returnOne3^0'=ret_returnOne3^post_5, tmp^0'=tmp^post_5, [ 2<=a^0 && a^0==a^post_5 && ret_returnOne3^0==ret_returnOne3^post_5 && tmp^0==tmp^post_5 ], cost: 1 5: l4 -> l0 : a^0'=a^post_6, ret_returnOne3^0'=ret_returnOne3^post_6, tmp^0'=tmp^post_6, [ 1+a^0<=1 && a^0==a^post_6 && ret_returnOne3^0==ret_returnOne3^post_6 && tmp^0==tmp^post_6 ], cost: 1 6: l4 -> l2 : a^0'=a^post_7, ret_returnOne3^0'=ret_returnOne3^post_7, tmp^0'=tmp^post_7, [ a^0<=1 && 1<=a^0 && tmp^post_7==1 && a^0==a^post_7 && ret_returnOne3^0==ret_returnOne3^post_7 ], cost: 1 8: l5 -> l4 : a^0'=a^post_9, ret_returnOne3^0'=ret_returnOne3^post_9, tmp^0'=tmp^post_9, [ a^1_1==-1 && ret_returnOne3^post_9==1 && a^post_9==ret_returnOne3^post_9 && tmp^0==tmp^post_9 ], cost: 1 9: l6 -> l5 : a^0'=a^post_10, ret_returnOne3^0'=ret_returnOne3^post_10, tmp^0'=tmp^post_10, [ a^0==a^post_10 && ret_returnOne3^0==ret_returnOne3^post_10 && tmp^0==tmp^post_10 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 9: l6 -> l5 : a^0'=a^post_10, ret_returnOne3^0'=ret_returnOne3^post_10, tmp^0'=tmp^post_10, [ a^0==a^post_10 && ret_returnOne3^0==ret_returnOne3^post_10 && tmp^0==tmp^post_10 ], cost: 1 Removed unreachable and leaf rules: Start location: l6 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: [ a^0==a^post_10 && ret_returnOne3^0==ret_returnOne3^post_10 && tmp^0==tmp^post_10 ] WORST_CASE(Omega(1),?)