WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>0 && x2_1>-1 && arg1>0 && arg1==arg1P_1 && arg2==arg2P_1 ], cost: 1 1: f1_0_main_Load\' -> f126_0_test_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>0 && x6_1>-1 && arg1>0 && x6_1-100*x7_1<100 && x6_1-100*x7_1>=0 && x6_1-100*x7_1==arg1P_2 ], cost: 1 2: f126_0_test_LE -> f126_0_test_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>0 && -1+arg1==arg1P_3 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f126_0_test_LE : arg1'=x6_1-100*x7_1, arg2'=arg2P_2, [ arg2>0 && x6_1>-1 && arg1>0 && x6_1-100*x7_1<100 && x6_1-100*x7_1>=0 ], cost: 1 2: f126_0_test_LE -> f126_0_test_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>0 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 2: f126_0_test_LE -> f126_0_test_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>0 ], cost: 1 Accelerated rule 2 with backward acceleration, yielding the new rule 4. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 2. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f126_0_test_LE : arg1'=x6_1-100*x7_1, arg2'=arg2P_2, [ arg2>0 && x6_1>-1 && arg1>0 && x6_1-100*x7_1<100 && x6_1-100*x7_1>=0 ], cost: 1 4: f126_0_test_LE -> f126_0_test_LE : arg1'=0, arg2'=arg2P_3, [ arg1>=1 ], cost: arg1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f126_0_test_LE : arg1'=x6_1-100*x7_1, arg2'=arg2P_2, [ arg2>0 && x6_1>-1 && arg1>0 && x6_1-100*x7_1<100 && x6_1-100*x7_1>=0 ], cost: 1 5: f1_0_main_Load\' -> f126_0_test_LE : arg1'=0, arg2'=arg2P_3, [ arg2>0 && x6_1>-1 && arg1>0 && x6_1-100*x7_1<100 && x6_1-100*x7_1>=1 ], cost: 1+x6_1-100*x7_1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>0 && arg1>0 ], cost: 1 5: f1_0_main_Load\' -> f126_0_test_LE : arg1'=0, arg2'=arg2P_3, [ arg2>0 && x6_1>-1 && arg1>0 && x6_1-100*x7_1<100 && x6_1-100*x7_1>=1 ], cost: 1+x6_1-100*x7_1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 7: __init -> f126_0_test_LE : arg1'=0, arg2'=arg2P_3, [ arg2P_4>0 && arg1P_4>0 && x6_1>-1 && x6_1-100*x7_1<100 && x6_1-100*x7_1>=1 ], cost: 3+x6_1-100*x7_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 7: __init -> f126_0_test_LE : arg1'=0, arg2'=arg2P_3, [ arg2P_4>0 && arg1P_4>0 && x6_1>-1 && x6_1-100*x7_1<100 && x6_1-100*x7_1>=1 ], cost: 3+x6_1-100*x7_1 Computing asymptotic complexity for rule 7 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),?)