WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_New -> f262_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>2 ], cost: 1 1: f1_0_main_New -> f262_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2>1 ], cost: 1 2: f1_0_main_New -> f76_0__init__LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ 5==arg1P_3 && 5==arg2P_3 && 5==arg3P_3 ], cost: 1 7: f262_0_main_InvokeMethod -> f194_0_height_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1P_8<=arg1 && 1+arg2P_8<=arg1 && arg1>0 && arg1P_8>0 && arg2P_8>-1 ], cost: 1 3: f76_0__init__LE -> f76_0__init__LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg20 && arg2>1 && arg2==arg3 && -1+arg2==arg1P_4 && -1+arg2==arg2P_4 && -1+arg2==arg3P_4 ], cost: 1 4: f76_0__init__LE -> f288_0__init__InvokeMethod : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ -1+arg21 && arg2P_5>4 && arg1>0 && arg2==arg3 && arg1==arg1P_5 && -1+arg2==arg3P_5 ], cost: 1 5: f76_0__init__LE -> f288_0__init__InvokeMethod : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ -1+arg21 && arg2P_6>3 && arg1>0 && arg2==arg3 && arg1==arg1P_6 && -1+arg2==arg3P_6 ], cost: 1 6: f288_0__init__InvokeMethod -> f76_0__init__LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3>0 && arg1>0 && arg2>2 && arg3==arg1P_7 && arg3==arg2P_7 && arg3==arg3P_7 ], cost: 1 8: f194_0_height_NONNULL -> f194_0_height_NONNULL : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ 2+arg1P_9<=arg1 && arg1P_9<=arg2 && 3+arg2P_9<=arg1 && 1+arg2P_9<=arg2 && arg1>2 && arg2>0 && arg1P_9>0 && arg2P_9>-1 ], cost: 1 9: f194_0_height_NONNULL -> f194_0_height_NONNULL : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ 2+arg1P_10<=arg1 && 3+arg2P_10<=arg1 && arg1>2 && arg2>-1 && arg1P_10>0 && arg2P_10>-1 ], cost: 1 10: __init -> f1_0_main_New : 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_New : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_New -> f262_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>2 ], cost: 1 1: f1_0_main_New -> f262_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2>1 ], cost: 1 2: f1_0_main_New -> f76_0__init__LE : arg1'=5, arg2'=5, arg3'=5, [], cost: 1 7: f262_0_main_InvokeMethod -> f194_0_height_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1P_8<=arg1 && 1+arg2P_8<=arg1 && arg1>0 && arg1P_8>0 && arg2P_8>-1 ], cost: 1 3: f76_0__init__LE -> f76_0__init__LE : arg1'=-1+arg2, arg2'=-1+arg2, arg3'=-1+arg2, [ arg1>0 && arg2>1 && arg2==arg3 ], cost: 1 4: f76_0__init__LE -> f288_0__init__InvokeMethod : arg2'=arg2P_5, arg3'=-1+arg2, [ arg2>1 && arg2P_5>4 && arg1>0 && arg2==arg3 ], cost: 1 5: f76_0__init__LE -> f288_0__init__InvokeMethod : arg2'=arg2P_6, arg3'=-1+arg2, [ arg2>1 && arg2P_6>3 && arg1>0 && arg2==arg3 ], cost: 1 6: f288_0__init__InvokeMethod -> f76_0__init__LE : arg1'=arg3, arg2'=arg3, [ arg3>0 && arg1>0 && arg2>2 ], cost: 1 8: f194_0_height_NONNULL -> f194_0_height_NONNULL : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ 2+arg1P_9<=arg1 && arg1P_9<=arg2 && 3+arg2P_9<=arg1 && 1+arg2P_9<=arg2 && arg1>2 && arg2>0 && arg1P_9>0 && arg2P_9>-1 ], cost: 1 9: f194_0_height_NONNULL -> f194_0_height_NONNULL : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ 2+arg1P_10<=arg1 && 3+arg2P_10<=arg1 && arg1>2 && arg2>-1 && arg1P_10>0 && arg2P_10>-1 ], cost: 1 10: __init -> f1_0_main_New : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 3: f76_0__init__LE -> f76_0__init__LE : arg1'=-1+arg2, arg2'=-1+arg2, arg3'=-1+arg2, [ arg1>0 && arg2>1 && arg2==arg3 ], cost: 1 Accelerated rule 3 with backward acceleration, yielding the new rule 11. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 3. Accelerating simple loops of location 4. Accelerating the following rules: 8: f194_0_height_NONNULL -> f194_0_height_NONNULL : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ 2+arg1P_9<=arg1 && arg1P_9<=arg2 && 3+arg2P_9<=arg1 && 1+arg2P_9<=arg2 && arg1>2 && arg2>0 && arg1P_9>0 && arg2P_9>-1 ], cost: 1 9: f194_0_height_NONNULL -> f194_0_height_NONNULL : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ 2+arg1P_10<=arg1 && 3+arg2P_10<=arg1 && arg1>2 && arg2>-1 && arg1P_10>0 && arg2P_10>-1 ], cost: 1 Failed to prove monotonicity of the guard of rule 8. Failed to prove monotonicity of the guard of rule 9. [accelerate] Nesting with 2 inner and 2 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_New -> f262_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>2 ], cost: 1 1: f1_0_main_New -> f262_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2>1 ], cost: 1 2: f1_0_main_New -> f76_0__init__LE : arg1'=5, arg2'=5, arg3'=5, [], cost: 1 7: f262_0_main_InvokeMethod -> f194_0_height_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1P_8<=arg1 && 1+arg2P_8<=arg1 && arg1>0 && arg1P_8>0 && arg2P_8>-1 ], cost: 1 4: f76_0__init__LE -> f288_0__init__InvokeMethod : arg2'=arg2P_5, arg3'=-1+arg2, [ arg2>1 && arg2P_5>4 && arg1>0 && arg2==arg3 ], cost: 1 5: f76_0__init__LE -> f288_0__init__InvokeMethod : arg2'=arg2P_6, arg3'=-1+arg2, [ arg2>1 && arg2P_6>3 && arg1>0 && arg2==arg3 ], cost: 1 11: f76_0__init__LE -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [ arg1>0 && arg2==arg3 && -1+arg2>=1 ], cost: -1+arg2 6: f288_0__init__InvokeMethod -> f76_0__init__LE : arg1'=arg3, arg2'=arg3, [ arg3>0 && arg1>0 && arg2>2 ], cost: 1 8: f194_0_height_NONNULL -> f194_0_height_NONNULL : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ 2+arg1P_9<=arg1 && arg1P_9<=arg2 && 3+arg2P_9<=arg1 && 1+arg2P_9<=arg2 && arg1>2 && arg2>0 && arg1P_9>0 && arg2P_9>-1 ], cost: 1 9: f194_0_height_NONNULL -> f194_0_height_NONNULL : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ 2+arg1P_10<=arg1 && 3+arg2P_10<=arg1 && arg1>2 && arg2>-1 && arg1P_10>0 && arg2P_10>-1 ], cost: 1 10: __init -> f1_0_main_New : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_New -> f262_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>2 ], cost: 1 1: f1_0_main_New -> f262_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2>1 ], cost: 1 2: f1_0_main_New -> f76_0__init__LE : arg1'=5, arg2'=5, arg3'=5, [], cost: 1 12: f1_0_main_New -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [], cost: 5 7: f262_0_main_InvokeMethod -> f194_0_height_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1P_8<=arg1 && 1+arg2P_8<=arg1 && arg1>0 && arg1P_8>0 && arg2P_8>-1 ], cost: 1 14: f262_0_main_InvokeMethod -> f194_0_height_NONNULL : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1P_9>0 && arg2P_9>-1 && 2+arg1P_9<=arg1 && 3+arg2P_9<=arg1 && 3<=arg1 ], cost: 2 15: f262_0_main_InvokeMethod -> f194_0_height_NONNULL : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1P_10>0 && arg2P_10>-1 && 2+arg1P_10<=arg1 && 3+arg2P_10<=arg1 && 3<=arg1 ], cost: 2 4: f76_0__init__LE -> f288_0__init__InvokeMethod : arg2'=arg2P_5, arg3'=-1+arg2, [ arg2>1 && arg2P_5>4 && arg1>0 && arg2==arg3 ], cost: 1 5: f76_0__init__LE -> f288_0__init__InvokeMethod : arg2'=arg2P_6, arg3'=-1+arg2, [ arg2>1 && arg2P_6>3 && arg1>0 && arg2==arg3 ], cost: 1 6: f288_0__init__InvokeMethod -> f76_0__init__LE : arg1'=arg3, arg2'=arg3, [ arg3>0 && arg1>0 && arg2>2 ], cost: 1 13: f288_0__init__InvokeMethod -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [ arg1>0 && arg2>2 && -1+arg3>=1 ], cost: arg3 10: __init -> f1_0_main_New : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 2: f1_0_main_New -> f76_0__init__LE : arg1'=5, arg2'=5, arg3'=5, [], cost: 1 12: f1_0_main_New -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [], cost: 5 4: f76_0__init__LE -> f288_0__init__InvokeMethod : arg2'=arg2P_5, arg3'=-1+arg2, [ arg2>1 && arg2P_5>4 && arg1>0 && arg2==arg3 ], cost: 1 5: f76_0__init__LE -> f288_0__init__InvokeMethod : arg2'=arg2P_6, arg3'=-1+arg2, [ arg2>1 && arg2P_6>3 && arg1>0 && arg2==arg3 ], cost: 1 6: f288_0__init__InvokeMethod -> f76_0__init__LE : arg1'=arg3, arg2'=arg3, [ arg3>0 && arg1>0 && arg2>2 ], cost: 1 13: f288_0__init__InvokeMethod -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [ arg1>0 && arg2>2 && -1+arg3>=1 ], cost: arg3 10: __init -> f1_0_main_New : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 18: f76_0__init__LE -> f76_0__init__LE : arg1'=-1+arg2, arg2'=-1+arg2, arg3'=-1+arg2, [ arg2>1 && arg2P_5>4 && arg1>0 && arg2==arg3 ], cost: 2 19: f76_0__init__LE -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [ arg2P_5>4 && arg1>0 && arg2==arg3 && -2+arg2>=1 ], cost: arg2 20: f76_0__init__LE -> f76_0__init__LE : arg1'=-1+arg2, arg2'=-1+arg2, arg3'=-1+arg2, [ arg2>1 && arg2P_6>3 && arg1>0 && arg2==arg3 ], cost: 2 21: f76_0__init__LE -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [ arg2P_6>3 && arg1>0 && arg2==arg3 && -2+arg2>=1 ], cost: arg2 16: __init -> f76_0__init__LE : arg1'=5, arg2'=5, arg3'=5, [], cost: 2 17: __init -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [], cost: 6 Accelerating simple loops of location 2. [accelerate] Removed some duplicate simple loops Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 20: f76_0__init__LE -> f76_0__init__LE : arg1'=-1+arg2, arg2'=-1+arg2, arg3'=-1+arg2, [ arg2>1 && arg1>0 && arg2==arg3 ], cost: 2 21: f76_0__init__LE -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [ arg1>0 && arg2==arg3 && -2+arg2>=1 ], cost: arg2 Accelerated rule 20 with backward acceleration, yielding the new rule 22. Failed to prove monotonicity of the guard of rule 21. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 20. Accelerated all simple loops using metering functions (where possible): Start location: __init 21: f76_0__init__LE -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [ arg1>0 && arg2==arg3 && -2+arg2>=1 ], cost: arg2 22: f76_0__init__LE -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [ arg1>0 && arg2==arg3 && -1+arg2>=1 ], cost: -2+2*arg2 16: __init -> f76_0__init__LE : arg1'=5, arg2'=5, arg3'=5, [], cost: 2 17: __init -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [], cost: 6 Chained accelerated rules (with incoming rules): Start location: __init 16: __init -> f76_0__init__LE : arg1'=5, arg2'=5, arg3'=5, [], cost: 2 17: __init -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [], cost: 6 23: __init -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [], cost: 7 24: __init -> f76_0__init__LE : arg1'=1, arg2'=1, arg3'=1, [], cost: 10 Removed unreachable locations (and leaf rules with constant cost): Start location: __init ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 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),?)