NO ### 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, [ x11_1>-1 && arg2>1 && x12_1-2*x13_1==1 && x12_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, [ x21_1>-1 && arg2>1 && -2*x23_1+x22_1==0 && x22_1>-1 && arg1>0 && arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1 1: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>-1 && arg2>1 && x17_1-2*x18_1==1 && x17_1>-1 && arg1>0 && x17_1-2*x18_1<2 && x17_1-2*x18_1>=0 ], cost: 1 3: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P_4, arg2'=arg2P_4, [ x26_1>-1 && arg2>1 && -2*x28_1+x27_1==0 && x27_1>-1 && arg1>0 && -2*x28_1+x27_1<2 && -2*x28_1+x27_1>=0 && -x26_1==arg1P_4 ], cost: 1 4: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<0 && -1+arg1==arg1P_5 ], cost: 1 5: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>0 && -1+arg1==arg1P_6 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 1+2*x13_1>-1 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x23_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>-1 && arg2>1 && 1+2*x18_1>-1 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x26_1, arg2'=arg2P_4, [ x26_1>-1 && arg2>1 && 2*x28_1>-1 && arg1>0 ], cost: 1 4: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P_5, [ arg1<0 ], cost: 1 5: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1>0 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 4: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P_5, [ arg1<0 ], cost: 1 5: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1>0 ], cost: 1 Accelerated rule 4 with non-termination, yielding the new rule 7. Accelerated rule 5 with backward acceleration, yielding the new rule 8. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 4 5. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 1+2*x13_1>-1 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x23_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>-1 && arg2>1 && 1+2*x18_1>-1 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x26_1, arg2'=arg2P_4, [ x26_1>-1 && arg2>1 && 2*x28_1>-1 && arg1>0 ], cost: 1 7: f171_0_sum_EQ -> [4] : [ arg1<0 ], cost: NONTERM 8: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P_6, [ arg1>=1 ], cost: arg1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 1+2*x13_1>-1 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x23_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>-1 && arg2>1 && 1+2*x18_1>-1 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x26_1, arg2'=arg2P_4, [ x26_1>-1 && arg2>1 && 2*x28_1>-1 && arg1>0 ], cost: 1 9: f1_0_main_Load\' -> [4] : [ arg2>1 && 2*x28_1>-1 && arg1>0 ], cost: NONTERM 10: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P_6, [ arg2>1 && 1+2*x18_1>-1 && arg1>0 && arg1P_2>=1 ], cost: 1+arg1P_2 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 1+2*x13_1>-1 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x23_1>-1 && arg1>0 ], cost: 1 9: f1_0_main_Load\' -> [4] : [ arg2>1 && 2*x28_1>-1 && arg1>0 ], cost: NONTERM 10: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P_6, [ arg2>1 && 1+2*x18_1>-1 && arg1>0 && arg1P_2>=1 ], cost: 1+arg1P_2 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 9: f1_0_main_Load\' -> [4] : [ arg2>1 && 2*x28_1>-1 && arg1>0 ], cost: NONTERM 10: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P_6, [ arg2>1 && 1+2*x18_1>-1 && arg1>0 && arg1P_2>=1 ], cost: 1+arg1P_2 11: __init -> f1_0_main_Load\' : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2P_7>1 && 1+2*x13_1>-1 && arg1P_7>0 ], cost: 2 12: __init -> f1_0_main_Load\' : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2P_7>1 && 2*x23_1>-1 && arg1P_7>0 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 13: __init -> [4] : [ arg2P_7>1 && 1+2*x13_1>-1 && arg1P_7>0 && 2*x28_1>-1 ], cost: NONTERM 14: __init -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P_6, [ arg2P_7>1 && 1+2*x13_1>-1 && arg1P_7>0 && 1+2*x18_1>-1 && arg1P_2>=1 ], cost: 3+arg1P_2 15: __init -> [4] : [ arg2P_7>1 && 2*x23_1>-1 && arg1P_7>0 && 2*x28_1>-1 ], cost: NONTERM 16: __init -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P_6, [ arg2P_7>1 && 2*x23_1>-1 && arg1P_7>0 && 1+2*x18_1>-1 && arg1P_2>=1 ], cost: 3+arg1P_2 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 13: __init -> [4] : [ arg2P_7>1 && 1+2*x13_1>-1 && arg1P_7>0 && 2*x28_1>-1 ], cost: NONTERM 14: __init -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P_6, [ arg2P_7>1 && 1+2*x13_1>-1 && arg1P_7>0 && 1+2*x18_1>-1 && arg1P_2>=1 ], cost: 3+arg1P_2 15: __init -> [4] : [ arg2P_7>1 && 2*x23_1>-1 && arg1P_7>0 && 2*x28_1>-1 ], cost: NONTERM 16: __init -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P_6, [ arg2P_7>1 && 2*x23_1>-1 && arg1P_7>0 && 1+2*x18_1>-1 && arg1P_2>=1 ], cost: 3+arg1P_2 Computing asymptotic complexity for rule 13 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [ arg2P_7>1 && 1+2*x13_1>-1 && arg1P_7>0 && 2*x28_1>-1 ] NO