WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_ConstantStackPush -> f64_0_main_LT : arg1'=arg1P_1, [ 3==arg1P_1 ], cost: 1 1: f64_0_main_LT -> f64_0_main_LT : arg1'=arg1P_2, [ arg1>5 && 3+arg1==arg1P_2 ], cost: 1 2: f64_0_main_LT -> f64_0_main_LT : arg1'=arg1P_3, [ arg1<11 && arg1<6 && arg1>2 && 1+arg1==arg1P_3 ], cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_ConstantStackPush -> f64_0_main_LT : arg1'=3, [], cost: 1 1: f64_0_main_LT -> f64_0_main_LT : arg1'=3+arg1, [ arg1>5 ], cost: 1 2: f64_0_main_LT -> f64_0_main_LT : arg1'=1+arg1, [ arg1<6 && arg1>2 ], cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f64_0_main_LT -> f64_0_main_LT : arg1'=3+arg1, [ arg1>5 ], cost: 1 2: f64_0_main_LT -> f64_0_main_LT : arg1'=1+arg1, [ arg1<6 && arg1>2 ], cost: 1 Accelerated rule 1 with non-termination, yielding the new rule 4. Accelerated rule 2 with backward acceleration, yielding the new rule 5. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 1 2. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_ConstantStackPush -> f64_0_main_LT : arg1'=3, [], cost: 1 4: f64_0_main_LT -> [3] : [ arg1>5 ], cost: NONTERM 5: f64_0_main_LT -> f64_0_main_LT : arg1'=6, [ arg1>2 && 6-arg1>=0 ], cost: 6-arg1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_ConstantStackPush -> f64_0_main_LT : arg1'=3, [], cost: 1 6: f1_0_main_ConstantStackPush -> f64_0_main_LT : arg1'=6, [], cost: 4 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, [], cost: 1 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),?)