NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f181_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ -1+arg2P_1<=arg1 && arg2>-1 && arg1>0 && arg2P_1>1 && -1+arg2==arg1P_1 && arg2==arg3P_1 ], cost: 1 1: f181_0_main_LE -> f181_0_main_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ -2+arg2P_2<=arg2 && arg3>0 && arg2>0 && arg2P_2>2 && -1+arg1==arg1P_2 && arg1==arg3P_2 ], cost: 1 2: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg3<1 && arg1P_3>0 ], cost: 1 3: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg1P_4<=arg2 && arg3<1 && arg2>1 && arg1P_4>2 ], cost: 1 4: f168_0_visit_NULL -> f168_0_visit_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ 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 -> f181_0_main_LE : arg1'=-1+arg2, arg2'=arg2P_1, arg3'=arg2, [ -1+arg2P_1<=arg1 && arg2>-1 && arg1>0 && arg2P_1>1 ], cost: 1 1: f181_0_main_LE -> f181_0_main_LE : arg1'=-1+arg1, arg2'=arg2P_2, arg3'=arg1, [ -2+arg2P_2<=arg2 && arg3>0 && arg2>0 && arg2P_2>2 ], cost: 1 2: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg3<1 && arg1P_3>0 ], cost: 1 3: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg1P_4<=arg2 && arg3<1 && arg2>1 && arg1P_4>2 ], cost: 1 4: f168_0_visit_NULL -> f168_0_visit_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ 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: f181_0_main_LE -> f181_0_main_LE : arg1'=-1+arg1, arg2'=arg2P_2, arg3'=arg1, [ -2+arg2P_2<=arg2 && arg3>0 && arg2>0 && arg2P_2>2 ], cost: 1 Found no metering function for rule 1. Removing the simple loops:. Accelerating simple loops of location 2. Accelerating the following rules: 4: f168_0_visit_NULL -> f168_0_visit_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1>0 && arg1P_5>-1 ], cost: 1 Accelerated rule 4 with NONTERM (after strengthening guard), yielding the new rule 6. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f181_0_main_LE : arg1'=-1+arg2, arg2'=arg2P_1, arg3'=arg2, [ -1+arg2P_1<=arg1 && arg2>-1 && arg1>0 && arg2P_1>1 ], cost: 1 1: f181_0_main_LE -> f181_0_main_LE : arg1'=-1+arg1, arg2'=arg2P_2, arg3'=arg1, [ -2+arg2P_2<=arg2 && arg3>0 && arg2>0 && arg2P_2>2 ], cost: 1 2: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg3<1 && arg1P_3>0 ], cost: 1 3: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg1P_4<=arg2 && arg3<1 && arg2>1 && arg1P_4>2 ], cost: 1 4: f168_0_visit_NULL -> f168_0_visit_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1>0 && arg1P_5>-1 ], cost: 1 6: f168_0_visit_NULL -> [5] : [ arg1>0 && arg1P_5>0 ], cost: NONTERM 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 -> f181_0_main_LE : arg1'=-1+arg2, arg2'=arg2P_1, arg3'=arg2, [ -1+arg2P_1<=arg1 && arg2>-1 && arg1>0 && arg2P_1>1 ], cost: 1 7: f1_0_main_Load -> f181_0_main_LE : arg1'=-2+arg2, arg2'=arg2P_2, arg3'=-1+arg2, [ arg1>0 && arg2>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1 ], cost: 2 2: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg3<1 && arg1P_3>0 ], cost: 1 3: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg1P_4<=arg2 && arg3<1 && arg2>1 && arg1P_4>2 ], cost: 1 8: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>0 && arg3<1 && arg1P_5>-1 ], cost: 2 9: f181_0_main_LE -> f168_0_visit_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3<1 && arg2>1 && arg1P_5>-1 ], cost: 2 10: f181_0_main_LE -> [5] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg3<1 && arg1P_3>0 ], cost: NONTERM 11: f181_0_main_LE -> [5] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg1P_4<=arg2 && arg3<1 && arg2>1 && arg1P_4>2 ], cost: NONTERM 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 0: f1_0_main_Load -> f181_0_main_LE : arg1'=-1+arg2, arg2'=arg2P_1, arg3'=arg2, [ -1+arg2P_1<=arg1 && arg2>-1 && arg1>0 && arg2P_1>1 ], cost: 1 7: f1_0_main_Load -> f181_0_main_LE : arg1'=-2+arg2, arg2'=arg2P_2, arg3'=-1+arg2, [ arg1>0 && arg2>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1 ], cost: 2 10: f181_0_main_LE -> [5] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg3<1 && arg1P_3>0 ], cost: NONTERM 11: f181_0_main_LE -> [5] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg1P_4<=arg2 && arg3<1 && arg2>1 && arg1P_4>2 ], cost: NONTERM 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 10: f181_0_main_LE -> [5] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg3<1 && arg1P_3>0 ], cost: NONTERM 11: f181_0_main_LE -> [5] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg1P_4<=arg2 && arg3<1 && arg2>1 && arg1P_4>2 ], cost: NONTERM 12: __init -> f181_0_main_LE : arg1'=-1+arg2P_6, arg2'=arg2P_1, arg3'=arg2P_6, [ -1+arg2P_1<=arg1P_6 && arg2P_6>-1 && arg1P_6>0 && arg2P_1>1 ], cost: 2 13: __init -> f181_0_main_LE : arg1'=-2+arg2P_6, arg2'=arg2P_2, arg3'=-1+arg2P_6, [ arg1P_6>0 && arg2P_6>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1P_6 ], cost: 3 Eliminated locations (on tree-shaped paths): Start location: __init 14: __init -> [5] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ -1+arg2P_1<=arg1P_6 && arg2P_6>-1 && arg1P_6>0 && arg2P_1>1 && arg2P_6<1 && arg1P_3>0 ], cost: NONTERM 15: __init -> [5] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg2P_1<=arg1P_6 && arg2P_6>-1 && arg1P_6>0 && arg2P_1>1 && -1+arg1P_4<=arg2P_1 && arg2P_6<1 && arg1P_4>2 ], cost: NONTERM 16: __init -> [5] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1P_6>0 && arg2P_6>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1P_6 && -1+arg2P_6<1 && arg1P_3>0 ], cost: NONTERM 17: __init -> [5] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_6>0 && arg2P_6>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1P_6 && -1+arg1P_4<=arg2P_2 && -1+arg2P_6<1 && arg1P_4>2 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 14: __init -> [5] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ -1+arg2P_1<=arg1P_6 && arg2P_6>-1 && arg1P_6>0 && arg2P_1>1 && arg2P_6<1 && arg1P_3>0 ], cost: NONTERM 15: __init -> [5] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -1+arg2P_1<=arg1P_6 && arg2P_6>-1 && arg1P_6>0 && arg2P_1>1 && -1+arg1P_4<=arg2P_1 && arg2P_6<1 && arg1P_4>2 ], cost: NONTERM 16: __init -> [5] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1P_6>0 && arg2P_6>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1P_6 && -1+arg2P_6<1 && arg1P_3>0 ], cost: NONTERM 17: __init -> [5] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_6>0 && arg2P_6>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1P_6 && -1+arg1P_4<=arg2P_2 && -1+arg2P_6<1 && arg1P_4>2 ], cost: NONTERM Computing asymptotic complexity for rule 14 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: [ -1+arg2P_1<=arg1P_6 && arg2P_6>-1 && arg1P_6>0 && arg2P_1>1 && arg2P_6<1 && arg1P_3>0 ] NO