WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f127_0_times_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f127_0_times_NE -> f127_0_times_NE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>0 && -1+arg2 f469_0_times_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ 1==arg2 && 1==arg1P_3 && 0==arg2P_3 && arg1==arg3P_3 ], cost: 1 3: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2>0 && -1+arg2 f469_0_times_InvokeMethod : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>0 && -1+arg2 f469_0_times_InvokeMethod : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2>0 && -1+arg2 f484_0_plus_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1>0 && arg2==arg1P_8 && arg3==arg2P_8 ], cost: 1 6: f218_0_times_Return -> f469_0_times_InvokeMethod : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1==arg1P_7 && arg3==arg2P_7 && arg2==arg3P_7 ], cost: 1 8: f484_0_plus_LE -> f484_0_plus_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2>0 && -1+arg2 f484_0_plus_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2<1 && -1+arg10 && -1+arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1_0_main_Load -> f127_0_times_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f127_0_times_NE -> f127_0_times_NE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>0 && -1+arg2 f469_0_times_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ 1==arg2 && 1==arg1P_3 && 0==arg2P_3 && arg1==arg3P_3 ], cost: 1 3: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2>0 && -1+arg2 f469_0_times_InvokeMethod : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>0 && -1+arg2 f469_0_times_InvokeMethod : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2>0 && -1+arg2 f484_0_plus_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1>0 && arg2==arg1P_8 && arg3==arg2P_8 ], cost: 1 8: f484_0_plus_LE -> f484_0_plus_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2>0 && -1+arg2 f484_0_plus_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2<1 && -1+arg10 && -1+arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f127_0_times_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f127_0_times_NE -> f127_0_times_NE : arg2'=-1+arg2, arg3'=arg3P_2, [ arg2>0 ], cost: 1 2: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=1, arg2'=0, arg3'=arg1, [ 1==arg2 ], cost: 1 3: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=0, arg3'=0, [ arg2>0 && 0==arg1 ], cost: 1 4: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=arg2P_5, arg3'=arg1, [ arg2>0 ], cost: 1 5: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=arg2P_6, arg3'=0, [ arg2>0 && 0==arg1 ], cost: 1 7: f469_0_times_InvokeMethod -> f484_0_plus_LE : arg1'=arg2, arg2'=arg3, arg3'=arg3P_8, [ arg1>0 ], cost: 1 8: f484_0_plus_LE -> f484_0_plus_LE : arg2'=-1+arg2, arg3'=arg3P_9, [ arg2>0 ], cost: 1 9: f484_0_plus_LE -> f484_0_plus_LE : arg1'=-1+arg1, arg3'=arg3P_10, [ arg2<1 && arg1>0 ], cost: 1 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f127_0_times_NE -> f127_0_times_NE : arg2'=-1+arg2, arg3'=arg3P_2, [ arg2>0 ], cost: 1 Accelerated rule 1 with backward acceleration, yielding the new rule 11. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 1. Accelerating simple loops of location 4. Accelerating the following rules: 8: f484_0_plus_LE -> f484_0_plus_LE : arg2'=-1+arg2, arg3'=arg3P_9, [ arg2>0 ], cost: 1 9: f484_0_plus_LE -> f484_0_plus_LE : arg1'=-1+arg1, arg3'=arg3P_10, [ arg2<1 && arg1>0 ], cost: 1 Accelerated rule 8 with backward acceleration, yielding the new rule 12. Accelerated rule 9 with backward acceleration, yielding the new rule 13. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 8 9. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f127_0_times_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 2: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=1, arg2'=0, arg3'=arg1, [ 1==arg2 ], cost: 1 3: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=0, arg3'=0, [ arg2>0 && 0==arg1 ], cost: 1 4: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=arg2P_5, arg3'=arg1, [ arg2>0 ], cost: 1 5: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=arg2P_6, arg3'=0, [ arg2>0 && 0==arg1 ], cost: 1 11: f127_0_times_NE -> f127_0_times_NE : arg2'=0, arg3'=arg3P_2, [ arg2>=1 ], cost: arg2 7: f469_0_times_InvokeMethod -> f484_0_plus_LE : arg1'=arg2, arg2'=arg3, arg3'=arg3P_8, [ arg1>0 ], cost: 1 12: f484_0_plus_LE -> f484_0_plus_LE : arg2'=0, arg3'=arg3P_9, [ arg2>=1 ], cost: arg2 13: f484_0_plus_LE -> f484_0_plus_LE : arg1'=0, arg3'=arg3P_10, [ arg2<1 && arg1>=1 ], cost: arg1 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f127_0_times_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 14: f1_0_main_Load -> f127_0_times_NE : arg1'=arg1P_1, arg2'=0, arg3'=arg3P_2, [ arg2>1 && arg1P_1>-1 && arg1>0 && arg2P_1>=1 ], cost: 1+arg2P_1 2: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=1, arg2'=0, arg3'=arg1, [ 1==arg2 ], cost: 1 3: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=0, arg3'=0, [ arg2>0 && 0==arg1 ], cost: 1 4: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=arg2P_5, arg3'=arg1, [ arg2>0 ], cost: 1 5: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=arg2P_6, arg3'=0, [ arg2>0 && 0==arg1 ], cost: 1 7: f469_0_times_InvokeMethod -> f484_0_plus_LE : arg1'=arg2, arg2'=arg3, arg3'=arg3P_8, [ arg1>0 ], cost: 1 15: f469_0_times_InvokeMethod -> f484_0_plus_LE : arg1'=arg2, arg2'=0, arg3'=arg3P_9, [ arg1>0 && arg3>=1 ], cost: 1+arg3 16: f469_0_times_InvokeMethod -> f484_0_plus_LE : arg1'=0, arg2'=arg3, arg3'=arg3P_10, [ arg1>0 && arg3<1 && arg2>=1 ], cost: 1+arg2 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f127_0_times_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 14: f1_0_main_Load -> f127_0_times_NE : arg1'=arg1P_1, arg2'=0, arg3'=arg3P_2, [ arg2>1 && arg1P_1>-1 && arg1>0 && arg2P_1>=1 ], cost: 1+arg2P_1 2: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=1, arg2'=0, arg3'=arg1, [ 1==arg2 ], cost: 1 3: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=0, arg3'=0, [ arg2>0 && 0==arg1 ], cost: 1 4: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=arg2P_5, arg3'=arg1, [ arg2>0 ], cost: 1 5: f127_0_times_NE -> f469_0_times_InvokeMethod : arg1'=arg2, arg2'=arg2P_6, arg3'=0, [ arg2>0 && 0==arg1 ], cost: 1 15: f469_0_times_InvokeMethod -> f484_0_plus_LE : arg1'=arg2, arg2'=0, arg3'=arg3P_9, [ arg1>0 && arg3>=1 ], cost: 1+arg3 16: f469_0_times_InvokeMethod -> f484_0_plus_LE : arg1'=0, arg2'=arg3, arg3'=arg3P_10, [ arg1>0 && arg3<1 && arg2>=1 ], cost: 1+arg2 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 19: f127_0_times_NE -> f484_0_plus_LE : arg1'=0, arg2'=0, arg3'=arg3P_9, [ 1==arg2 && arg1>=1 ], cost: 2+arg1 20: f127_0_times_NE -> f484_0_plus_LE : arg1'=arg2P_5, arg2'=0, arg3'=arg3P_9, [ arg2>0 && arg1>=1 ], cost: 2+arg1 21: f127_0_times_NE -> f484_0_plus_LE : arg1'=0, arg2'=arg1, arg3'=arg3P_10, [ arg2>0 && arg1<1 && arg2P_5>=1 ], cost: 2+arg2P_5 22: f127_0_times_NE -> f484_0_plus_LE : arg1'=0, arg2'=0, arg3'=arg3P_10, [ arg2>0 && 0==arg1 && arg2P_6>=1 ], cost: 2+arg2P_6 17: __init -> f127_0_times_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_1>-1 && arg2P_11>1 && arg1P_1>-1 && arg1P_11>0 ], cost: 2 18: __init -> f127_0_times_NE : arg1'=arg1P_1, arg2'=0, arg3'=arg3P_2, [ arg2P_11>1 && arg1P_1>-1 && arg1P_11>0 && arg2P_1>=1 ], cost: 2+arg2P_1 Eliminated locations (on tree-shaped paths): Start location: __init 23: __init -> f484_0_plus_LE : arg1'=0, arg2'=0, arg3'=arg3P_9, [ arg2P_11>1 && arg1P_11>0 && 1==arg2P_1 && arg1P_1>=1 ], cost: 4+arg1P_1 24: __init -> f484_0_plus_LE : arg1'=arg2P_5, arg2'=0, arg3'=arg3P_9, [ arg2P_11>1 && arg1P_11>0 && arg2P_1>0 && arg1P_1>=1 ], cost: 4+arg1P_1 25: __init -> f484_0_plus_LE : arg1'=0, arg2'=arg1P_1, arg3'=arg3P_10, [ arg2P_11>1 && arg1P_1>-1 && arg1P_11>0 && arg2P_1>0 && arg1P_1<1 && arg2P_5>=1 ], cost: 4+arg2P_5 26: __init -> f484_0_plus_LE : arg1'=0, arg2'=0, arg3'=arg3P_10, [ arg2P_11>1 && arg1P_11>0 && arg2P_1>0 && 0==arg1P_1 && arg2P_6>=1 ], cost: 4+arg2P_6 27: __init -> [8] : [ arg2P_11>1 && arg1P_1>-1 && arg1P_11>0 && arg2P_1>=1 ], cost: 2+arg2P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 23: __init -> f484_0_plus_LE : arg1'=0, arg2'=0, arg3'=arg3P_9, [ arg2P_11>1 && arg1P_11>0 && 1==arg2P_1 && arg1P_1>=1 ], cost: 4+arg1P_1 24: __init -> f484_0_plus_LE : arg1'=arg2P_5, arg2'=0, arg3'=arg3P_9, [ arg2P_11>1 && arg1P_11>0 && arg2P_1>0 && arg1P_1>=1 ], cost: 4+arg1P_1 25: __init -> f484_0_plus_LE : arg1'=0, arg2'=arg1P_1, arg3'=arg3P_10, [ arg2P_11>1 && arg1P_1>-1 && arg1P_11>0 && arg2P_1>0 && arg1P_1<1 && arg2P_5>=1 ], cost: 4+arg2P_5 26: __init -> f484_0_plus_LE : arg1'=0, arg2'=0, arg3'=arg3P_10, [ arg2P_11>1 && arg1P_11>0 && arg2P_1>0 && 0==arg1P_1 && arg2P_6>=1 ], cost: 4+arg2P_6 27: __init -> [8] : [ arg2P_11>1 && arg1P_1>-1 && arg1P_11>0 && arg2P_1>=1 ], cost: 2+arg2P_1 Computing asymptotic complexity for rule 23 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 24 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 27 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 26 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 25 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),?)