WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f297_0_createIntList_Return -> f508_0_random_ArrayAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1<=arg1 && arg1>-1 && arg1P_1>-1 ], cost: 1 2: f508_0_random_ArrayAccess -> f698_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3>-1 && x7_1>0 && arg1P_3<=arg1 && arg1>0 && arg1P_3>0 ], cost: 1 1: f1_0_main_Load -> f508_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f658_0_createIntList_LE : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>-1 && arg1P_7>-1 && arg1>0 && 1==arg2P_7 ], cost: 1 3: f698_0_nth_LE -> f746_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>0 && arg2<2 && 2+arg1P_4<=arg1 ], cost: 1 4: f698_0_nth_LE -> f698_0_nth_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ 1+arg1P_5<=arg1 && arg2>1 && arg1>0 && arg1P_5>-1 && -1+arg2==arg2P_5 ], cost: 1 5: f746_0_main_LE -> f746_0_main_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>0 && -1+arg1==arg1P_6 ], cost: 1 7: f658_0_createIntList_LE -> f658_0_createIntList_LE : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>0 && arg2>0 && -1+arg1==arg1P_8 && 1+arg2==arg2P_8 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 2: f508_0_random_ArrayAccess -> f698_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3>-1 && x7_1>0 && arg1P_3<=arg1 && arg1>0 && arg1P_3>0 ], cost: 1 1: f1_0_main_Load -> f508_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f658_0_createIntList_LE : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>-1 && arg1P_7>-1 && arg1>0 && 1==arg2P_7 ], cost: 1 3: f698_0_nth_LE -> f746_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>0 && arg2<2 && 2+arg1P_4<=arg1 ], cost: 1 4: f698_0_nth_LE -> f698_0_nth_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ 1+arg1P_5<=arg1 && arg2>1 && arg1>0 && arg1P_5>-1 && -1+arg2==arg2P_5 ], cost: 1 5: f746_0_main_LE -> f746_0_main_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>0 && -1+arg1==arg1P_6 ], cost: 1 7: f658_0_createIntList_LE -> f658_0_createIntList_LE : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>0 && arg2>0 && -1+arg1==arg1P_8 && 1+arg2==arg2P_8 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Simplified all rules, resulting in: Start location: __init 2: f508_0_random_ArrayAccess -> f698_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3>-1 && arg1P_3<=arg1 && arg1>0 && arg1P_3>0 ], cost: 1 1: f1_0_main_Load -> f508_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f658_0_createIntList_LE : arg1'=arg1P_7, arg2'=1, [ arg2>-1 && arg1P_7>-1 && arg1>0 ], cost: 1 3: f698_0_nth_LE -> f746_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>0 && arg2<2 && 2+arg1P_4<=arg1 ], cost: 1 4: f698_0_nth_LE -> f698_0_nth_LE : arg1'=arg1P_5, arg2'=-1+arg2, [ 1+arg1P_5<=arg1 && arg2>1 && arg1>0 && arg1P_5>-1 ], cost: 1 5: f746_0_main_LE -> f746_0_main_LE : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1>0 ], cost: 1 7: f658_0_createIntList_LE -> f658_0_createIntList_LE : arg1'=-1+arg1, arg2'=1+arg2, [ arg1>0 && arg2>0 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 3. Accelerating the following rules: 4: f698_0_nth_LE -> f698_0_nth_LE : arg1'=arg1P_5, arg2'=-1+arg2, [ 1+arg1P_5<=arg1 && arg2>1 && arg1>0 && arg1P_5>-1 ], cost: 1 Failed to prove monotonicity of the guard of rule 4. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerating simple loops of location 4. Accelerating the following rules: 5: f746_0_main_LE -> f746_0_main_LE : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1>0 ], cost: 1 Accelerated rule 5 with backward acceleration, yielding the new rule 9. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 5. Accelerating simple loops of location 5. Accelerating the following rules: 7: f658_0_createIntList_LE -> f658_0_createIntList_LE : arg1'=-1+arg1, arg2'=1+arg2, [ arg1>0 && arg2>0 ], cost: 1 Accelerated rule 7 with backward acceleration, yielding the new rule 10. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 7. Accelerated all simple loops using metering functions (where possible): Start location: __init 2: f508_0_random_ArrayAccess -> f698_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3>-1 && arg1P_3<=arg1 && arg1>0 && arg1P_3>0 ], cost: 1 1: f1_0_main_Load -> f508_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f658_0_createIntList_LE : arg1'=arg1P_7, arg2'=1, [ arg2>-1 && arg1P_7>-1 && arg1>0 ], cost: 1 3: f698_0_nth_LE -> f746_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>0 && arg2<2 && 2+arg1P_4<=arg1 ], cost: 1 4: f698_0_nth_LE -> f698_0_nth_LE : arg1'=arg1P_5, arg2'=-1+arg2, [ 1+arg1P_5<=arg1 && arg2>1 && arg1>0 && arg1P_5>-1 ], cost: 1 9: f746_0_main_LE -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1>=1 ], cost: arg1 10: f658_0_createIntList_LE -> f658_0_createIntList_LE : arg1'=0, arg2'=arg2+arg1, [ arg2>0 && arg1>=0 ], cost: arg1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 2: f508_0_random_ArrayAccess -> f698_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3>-1 && arg1P_3<=arg1 && arg1>0 && arg1P_3>0 ], cost: 1 11: f508_0_random_ArrayAccess -> f698_0_nth_LE : arg1'=arg1P_5, arg2'=-1+arg2P_3, [ arg1>0 && arg2P_3>1 && arg1P_5>-1 && 1+arg1P_5<=arg1 ], cost: 2 1: f1_0_main_Load -> f508_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f658_0_createIntList_LE : arg1'=arg1P_7, arg2'=1, [ arg2>-1 && arg1P_7>-1 && arg1>0 ], cost: 1 13: f1_0_main_Load -> f658_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2>-1 && arg1P_7>-1 && arg1>0 ], cost: 1+arg1P_7 3: f698_0_nth_LE -> f746_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>0 && arg2<2 && 2+arg1P_4<=arg1 ], cost: 1 12: f698_0_nth_LE -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1>0 && arg2<2 && 2+arg1P_4<=arg1 && arg1P_4>=1 ], cost: 1+arg1P_4 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 2: f508_0_random_ArrayAccess -> f698_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3>-1 && arg1P_3<=arg1 && arg1>0 && arg1P_3>0 ], cost: 1 11: f508_0_random_ArrayAccess -> f698_0_nth_LE : arg1'=arg1P_5, arg2'=-1+arg2P_3, [ arg1>0 && arg2P_3>1 && arg1P_5>-1 && 1+arg1P_5<=arg1 ], cost: 2 1: f1_0_main_Load -> f508_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 13: f1_0_main_Load -> f658_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2>-1 && arg1P_7>-1 && arg1>0 ], cost: 1+arg1P_7 12: f698_0_nth_LE -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1>0 && arg2<2 && 2+arg1P_4<=arg1 && arg1P_4>=1 ], cost: 1+arg1P_4 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 16: f508_0_random_ArrayAccess -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg2P_3>-1 && arg1P_3<=arg1 && arg1>0 && arg1P_3>0 && arg2P_3<2 && 2+arg1P_4<=arg1P_3 && arg1P_4>=1 ], cost: 2+arg1P_4 17: f508_0_random_ArrayAccess -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1>0 && arg2P_3>1 && 1+arg1P_5<=arg1 && arg1P_5>0 && -1+arg2P_3<2 && 2+arg1P_4<=arg1P_5 && arg1P_4>=1 ], cost: 3+arg1P_4 14: __init -> f508_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_9>0 && arg1P_2>-1 ], cost: 2 15: __init -> f658_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2P_9>-1 && arg1P_7>-1 && arg1P_9>0 ], cost: 2+arg1P_7 Eliminated locations (on tree-shaped paths): Start location: __init 15: __init -> f658_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2P_9>-1 && arg1P_7>-1 && arg1P_9>0 ], cost: 2+arg1P_7 18: __init -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1P_9>0 && arg2P_3>-1 && arg1P_3<=arg1P_2 && arg1P_2>0 && arg1P_3>0 && arg2P_3<2 && 2+arg1P_4<=arg1P_3 && arg1P_4>=1 ], cost: 4+arg1P_4 19: __init -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1P_9>0 && arg1P_2>0 && arg2P_3>1 && 1+arg1P_5<=arg1P_2 && arg1P_5>0 && -1+arg2P_3<2 && 2+arg1P_4<=arg1P_5 && arg1P_4>=1 ], cost: 5+arg1P_4 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 15: __init -> f658_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2P_9>-1 && arg1P_7>-1 && arg1P_9>0 ], cost: 2+arg1P_7 18: __init -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1P_9>0 && arg2P_3>-1 && arg1P_3<=arg1P_2 && arg1P_2>0 && arg1P_3>0 && arg2P_3<2 && 2+arg1P_4<=arg1P_3 && arg1P_4>=1 ], cost: 4+arg1P_4 19: __init -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1P_9>0 && arg1P_2>0 && arg2P_3>1 && 1+arg1P_5<=arg1P_2 && arg1P_5>0 && -1+arg2P_3<2 && 2+arg1P_4<=arg1P_5 && arg1P_4>=1 ], cost: 5+arg1P_4 Computing asymptotic complexity for rule 15 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 18 Simplified the guard: 18: __init -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1P_9>0 && arg2P_3>-1 && arg1P_3<=arg1P_2 && arg1P_2>0 && arg2P_3<2 && 2+arg1P_4<=arg1P_3 && arg1P_4>=1 ], cost: 4+arg1P_4 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 19 Simplified the guard: 19: __init -> f746_0_main_LE : arg1'=0, arg2'=arg2P_6, [ arg1P_9>0 && arg2P_3>1 && 1+arg1P_5<=arg1P_2 && -1+arg2P_3<2 && 2+arg1P_4<=arg1P_5 && arg1P_4>=1 ], cost: 5+arg1P_4 Resulting cost 0 has complexity: Unknown 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: [] WORST_CASE(Omega(1),?)