WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f191_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 && -1+arg2==arg1P_1 && arg2==arg2P_1 && 0==arg3P_1 ], cost: 1 1: f191_0_main_LE -> f191_0_main_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>0 && arg3>0 && -1+arg1==arg1P_2 && arg1==arg2P_2 ], cost: 1 2: f191_0_main_LE -> f191_0_main_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && -1+arg1==arg1P_3 && arg1==arg2P_3 && 1==arg3P_3 ], cost: 1 3: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2<1 && arg1P_4>0 ], cost: 1 4: f270_0_length_FieldAccess -> f270_0_length_FieldAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ 1+arg1P_5<=arg1 && arg1>0 && arg1P_5>-1 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f191_0_main_LE : arg1'=-1+arg2, arg3'=0, [ arg1>0 && arg2>-1 ], cost: 1 1: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=arg3P_2, [ arg2>0 && arg3>0 ], cost: 1 2: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=1, [ arg2>0 ], cost: 1 3: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2<1 && arg1P_4>0 ], cost: 1 4: f270_0_length_FieldAccess -> f270_0_length_FieldAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ 1+arg1P_5<=arg1 && arg1>0 && arg1P_5>-1 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=arg3P_2, [ arg2>0 && arg3>0 ], cost: 1 2: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=1, [ arg2>0 ], cost: 1 Failed to prove monotonicity of the guard of rule 1. [test] deduced invariant 1-arg2+arg1<=0 Accelerated rule 2 with backward acceleration, yielding the new rule 6. [accelerate] Nesting with 2 inner and 2 outer candidates Accelerating simple loops of location 2. Accelerating the following rules: 4: f270_0_length_FieldAccess -> f270_0_length_FieldAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ 1+arg1P_5<=arg1 && 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 Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f191_0_main_LE : arg1'=-1+arg2, arg3'=0, [ arg1>0 && arg2>-1 ], cost: 1 1: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=arg3P_2, [ arg2>0 && arg3>0 ], cost: 1 2: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=1, [ arg2>0 ], cost: 1 3: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2<1 && arg1P_4>0 ], cost: 1 6: f191_0_main_LE -> f191_0_main_LE : arg1'=-1, arg2'=0, arg3'=1, [ 1-arg2+arg1<=0 && 1+arg1>=1 ], cost: 1+arg1 4: f270_0_length_FieldAccess -> f270_0_length_FieldAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ 1+arg1P_5<=arg1 && arg1>0 && arg1P_5>-1 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f191_0_main_LE : arg1'=-1+arg2, arg3'=0, [ arg1>0 && arg2>-1 ], cost: 1 7: f1_0_main_Load -> f191_0_main_LE : arg1'=-2+arg2, arg2'=-1+arg2, arg3'=1, [ arg1>0 && arg2>0 ], cost: 2 8: f1_0_main_Load -> f191_0_main_LE : arg1'=-1, arg2'=0, arg3'=1, [ arg1>0 && arg2>=1 ], cost: 1+arg2 3: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2<1 && arg1P_4>0 ], cost: 1 9: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2<1 && arg1P_5>-1 ], cost: 2 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 8: f1_0_main_Load -> f191_0_main_LE : arg1'=-1, arg2'=0, arg3'=1, [ arg1>0 && arg2>=1 ], cost: 1+arg2 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 10: __init -> f191_0_main_LE : arg1'=-1, arg2'=0, arg3'=1, [ arg1P_6>0 && arg2P_6>=1 ], cost: 2+arg2P_6 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 10: __init -> f191_0_main_LE : arg1'=-1, arg2'=0, arg3'=1, [ arg1P_6>0 && arg2P_6>=1 ], cost: 2+arg2P_6 Computing asymptotic complexity for rule 10 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),?)