WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P_1, arg2'=arg2P_1, [ x9_1>-1 && arg2>0 && x9_1-2*x10_1==1 && arg1>0 && arg1==arg1P_1 && arg2==arg2P_1 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P_3, arg2'=arg2P_3, [ x17_1>-1 && arg2>0 && -2*x18_1+x17_1==0 && arg1>0 && arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1 1: f1_0_main_Load\' -> f174_0_test_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ x13_1>-1 && arg2>0 && -2*x14_1+x13_1==1 && arg1>0 && -2*x14_1+x13_1<2 && -2*x14_1+x13_1>=0 && 1==arg1P_2 && 0==arg2P_2 ], cost: 1 3: f1_0_main_Load\' -> f174_0_test_EQ : arg1'=arg1P_4, arg2'=arg2P_4, [ x21_1>-1 && arg2>0 && x21_1-2*x22_1==0 && arg1>0 && x21_1-2*x22_1<2 && x21_1-2*x22_1>=0 && 0==arg1P_4 && 1==arg2P_4 ], cost: 1 4: f174_0_test_EQ -> f174_0_test_EQ : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1==arg2 && -1+arg1==arg1P_5 && -1+arg1==arg2P_5 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_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, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ 1+2*x10_1>-1 && arg2>0 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ 2*x18_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f174_0_test_EQ : arg1'=1, arg2'=0, [ 1+2*x14_1>-1 && arg2>0 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f174_0_test_EQ : arg1'=0, arg2'=1, [ 2*x22_1>-1 && arg2>0 && arg1>0 ], cost: 1 4: f174_0_test_EQ -> f174_0_test_EQ : arg1'=-1+arg1, arg2'=-1+arg1, [ arg1==arg2 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 4: f174_0_test_EQ -> f174_0_test_EQ : arg1'=-1+arg1, arg2'=-1+arg1, [ arg1==arg2 ], cost: 1 Accelerated rule 4 with non-termination, yielding the new rule 6. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 4. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ 1+2*x10_1>-1 && arg2>0 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ 2*x18_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f174_0_test_EQ : arg1'=1, arg2'=0, [ 1+2*x14_1>-1 && arg2>0 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f174_0_test_EQ : arg1'=0, arg2'=1, [ 2*x22_1>-1 && arg2>0 && arg1>0 ], cost: 1 6: f174_0_test_EQ -> [4] : [ arg1==arg2 ], cost: NONTERM 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ 1+2*x10_1>-1 && arg2>0 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ 2*x18_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f174_0_test_EQ : arg1'=1, arg2'=0, [ 1+2*x14_1>-1 && arg2>0 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f174_0_test_EQ : arg1'=0, arg2'=1, [ 2*x22_1>-1 && arg2>0 && arg1>0 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], 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),?)