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 [test] deduced pseudo-invariant 1-arg3+arg1<=0, also trying -1+arg3-arg1<=-1 Accelerated rule 1 with backward acceleration, yielding the new rule 6. [accelerate] Nesting with 1 inner and 1 outer candidates 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 [test] deduced pseudo-invariant -arg1P_5+arg1<=0, also trying arg1P_5-arg1<=-1 Accelerated rule 4 with non-termination, yielding the new rule 7. Accelerated rule 4 with non-termination, yielding the new rule 8. Accelerated rule 4 with backward acceleration, yielding the new rule 9. [accelerate] Nesting with 0 inner and 1 outer candidates Also removing duplicate rules: 8. 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 6: f181_0_main_LE -> f181_0_main_LE : arg1'=-1, arg2'=arg2P_2, arg3'=0, [ -2+arg2P_2<=arg2 && arg2>0 && arg2P_2>2 && 1-arg3+arg1<=0 && 1+arg1>=1 ], cost: 1+arg1 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 7: f168_0_visit_NULL -> [5] : [ arg1>0 && arg1P_5>0 ], cost: NONTERM 9: f168_0_visit_NULL -> [5] : [ arg1>0 && arg1P_5>-1 && -arg1P_5+arg1<=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 10: 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 11: f1_0_main_Load -> f181_0_main_LE : arg1'=-1, arg2'=arg2P_2, arg3'=0, [ arg1>0 && arg2P_2>2 && arg2>=1 && -2+arg2P_2<=1+arg1 ], cost: 1+arg2 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 12: 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 13: 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 14: f181_0_main_LE -> [5] : [ arg2>0 && arg3<1 ], cost: NONTERM 15: f181_0_main_LE -> [5] : [ arg3<1 && arg2>1 ], cost: NONTERM 16: f181_0_main_LE -> [5] : [ arg2>0 && arg3<1 ], cost: NONTERM 17: f181_0_main_LE -> [5] : [ arg3<1 && arg2>1 ], 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 10: 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 11: f1_0_main_Load -> f181_0_main_LE : arg1'=-1, arg2'=arg2P_2, arg3'=0, [ arg1>0 && arg2P_2>2 && arg2>=1 && -2+arg2P_2<=1+arg1 ], cost: 1+arg2 14: f181_0_main_LE -> [5] : [ arg2>0 && arg3<1 ], cost: NONTERM 15: f181_0_main_LE -> [5] : [ arg3<1 && arg2>1 ], cost: NONTERM 16: f181_0_main_LE -> [5] : [ arg2>0 && arg3<1 ], cost: NONTERM 17: f181_0_main_LE -> [5] : [ arg3<1 && arg2>1 ], 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 14: f181_0_main_LE -> [5] : [ arg2>0 && arg3<1 ], cost: NONTERM 15: f181_0_main_LE -> [5] : [ arg3<1 && arg2>1 ], cost: NONTERM 16: f181_0_main_LE -> [5] : [ arg2>0 && arg3<1 ], cost: NONTERM 17: f181_0_main_LE -> [5] : [ arg3<1 && arg2>1 ], cost: NONTERM 18: __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 19: __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 20: __init -> f181_0_main_LE : arg1'=-1, arg2'=arg2P_2, arg3'=0, [ arg1P_6>0 && arg2P_2>2 && arg2P_6>=1 && -2+arg2P_2<=1+arg1P_6 ], cost: 2+arg2P_6 Merged rules: Start location: __init 21: f181_0_main_LE -> [5] : [ arg2>0 && arg3<1 ], cost: NONTERM 22: f181_0_main_LE -> [5] : [ arg3<1 && arg2>1 ], cost: NONTERM 18: __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 19: __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 20: __init -> f181_0_main_LE : arg1'=-1, arg2'=arg2P_2, arg3'=0, [ arg1P_6>0 && arg2P_2>2 && arg2P_6>=1 && -2+arg2P_2<=1+arg1P_6 ], cost: 2+arg2P_6 Eliminated locations (on tree-shaped paths): Start location: __init 23: __init -> [5] : [ -1+arg2P_1<=arg1P_6 && arg2P_6>-1 && arg1P_6>0 && arg2P_1>1 && arg2P_6<1 ], cost: NONTERM 24: __init -> [5] : [ -1+arg2P_1<=arg1P_6 && arg2P_6>-1 && arg1P_6>0 && arg2P_1>1 && arg2P_6<1 ], cost: NONTERM 25: __init -> [5] : [ arg1P_6>0 && arg2P_6>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1P_6 && -1+arg2P_6<1 ], cost: NONTERM 26: __init -> [5] : [ arg1P_6>0 && arg2P_6>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1P_6 && -1+arg2P_6<1 ], cost: NONTERM 27: __init -> [5] : [ arg1P_6>0 && arg2P_2>2 && arg2P_6>=1 && -2+arg2P_2<=1+arg1P_6 ], cost: NONTERM 28: __init -> [5] : [ arg1P_6>0 && arg2P_2>2 && arg2P_6>=1 && -2+arg2P_2<=1+arg1P_6 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 24: __init -> [5] : [ -1+arg2P_1<=arg1P_6 && arg2P_6>-1 && arg1P_6>0 && arg2P_1>1 && arg2P_6<1 ], cost: NONTERM 26: __init -> [5] : [ arg1P_6>0 && arg2P_6>0 && arg2P_2>2 && -2+arg2P_2<=1+arg1P_6 && -1+arg2P_6<1 ], cost: NONTERM 28: __init -> [5] : [ arg1P_6>0 && arg2P_2>2 && arg2P_6>=1 && -2+arg2P_2<=1+arg1P_6 ], cost: NONTERM Computing asymptotic complexity for rule 28 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: [ arg1P_6>0 && arg2P_2>2 && arg2P_6>=1 && -2+arg2P_2<=1+arg1P_6 ] NO