WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_ConstantStackPush -> f79_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, [ 0==arg1P_1 && 100==arg2P_1 ], cost: 1 1: f79_0_main_GE -> f79_0_main_GE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2<52 && arg2>arg1 && -1+arg1==arg1P_2 && 1+arg2==arg2P_2 ], cost: 1 2: f79_0_main_GE -> f79_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2>51 && arg2>arg1 && 1+arg1==arg1P_3 && -1+arg2==arg2P_3 ], cost: 1 3: __init -> f1_0_main_ConstantStackPush : 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_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_ConstantStackPush -> f79_0_main_GE : arg1'=0, arg2'=100, [], cost: 1 1: f79_0_main_GE -> f79_0_main_GE : arg1'=-1+arg1, arg2'=1+arg2, [ arg2<52 && arg2>arg1 ], cost: 1 2: f79_0_main_GE -> f79_0_main_GE : arg1'=1+arg1, arg2'=-1+arg2, [ arg2>51 && arg2>arg1 ], cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f79_0_main_GE -> f79_0_main_GE : arg1'=-1+arg1, arg2'=1+arg2, [ arg2<52 && arg2>arg1 ], cost: 1 2: f79_0_main_GE -> f79_0_main_GE : arg1'=1+arg1, arg2'=-1+arg2, [ arg2>51 && arg2>arg1 ], cost: 1 Accelerated rule 1 with metering function 52-arg2, yielding the new rule 4. Found no metering function for rule 2. Nested simple loops 2 (outer loop) and 4 (inner loop) with NONTERM, resulting in the new rules: 5, 6. Removing the simple loops: 1 2. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_ConstantStackPush -> f79_0_main_GE : arg1'=0, arg2'=100, [], cost: 1 4: f79_0_main_GE -> f79_0_main_GE : arg1'=-52+arg1+arg2, arg2'=52, [ arg2<52 && arg2>arg1 ], cost: 52-arg2 5: f79_0_main_GE -> [3] : [ arg2<52 && arg2>arg1 && 52>-52+arg1+arg2 ], cost: NONTERM 6: f79_0_main_GE -> [3] : arg1'=1+arg1, arg2'=-1+arg2, [ arg2>51 && -1+arg2<52 && -1+arg2>1+arg1 && 52>-52+arg1+arg2 ], cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_ConstantStackPush -> f79_0_main_GE : arg1'=0, arg2'=100, [], cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_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),?)