NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg3P_1>0 && arg2>-1 && -1+arg1P_1<=arg1 && -3+arg2P_1<=arg1 && arg1>0 && arg1P_1>1 && arg2P_1>3 ], cost: 1 1: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ -3+arg1P_2<=arg1 && arg2>-1 && -1+arg2P_2<=arg1 && arg1>0 && arg1P_2>3 && arg2P_2>1 && 0==arg3P_2 ], cost: 1 2: f192_0_main_NE -> f192_0_main_NE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1>=arg1P_3 && arg3>0 && arg1>=-3+arg2P_3 && -3+arg2P_3<=arg2 && arg1>0 && arg2>0 && arg1P_3>0 && arg2P_3>3 && arg3==arg3P_3 ], cost: 1 3: f192_0_main_NE -> f192_0_main_NE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ -3+arg1P_4<=arg1 && -3+arg1P_4<=arg2 && arg2P_4<=arg2 && arg1>0 && arg2>0 && arg1P_4>3 && arg2P_4>0 && 0==arg3 && 0==arg3P_4 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg3P_1>0 && arg2>-1 && -1+arg1P_1<=arg1 && -3+arg2P_1<=arg1 && arg1>0 && arg1P_1>1 && arg2P_1>3 ], cost: 1 1: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=0, [ -3+arg1P_2<=arg1 && arg2>-1 && -1+arg2P_2<=arg1 && arg1>0 && arg1P_2>3 && arg2P_2>1 ], cost: 1 2: f192_0_main_NE -> f192_0_main_NE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>=arg1P_3 && arg3>0 && arg1>=-3+arg2P_3 && -3+arg2P_3<=arg2 && arg1>0 && arg2>0 && arg1P_3>0 && arg2P_3>3 ], cost: 1 3: f192_0_main_NE -> f192_0_main_NE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ -3+arg1P_4<=arg1 && -3+arg1P_4<=arg2 && arg2P_4<=arg2 && arg1>0 && arg2>0 && arg1P_4>3 && arg2P_4>0 && 0==arg3 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 2: f192_0_main_NE -> f192_0_main_NE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>=arg1P_3 && arg3>0 && arg1>=-3+arg2P_3 && -3+arg2P_3<=arg2 && arg1>0 && arg2>0 && arg1P_3>0 && arg2P_3>3 ], cost: 1 3: f192_0_main_NE -> f192_0_main_NE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ -3+arg1P_4<=arg1 && -3+arg1P_4<=arg2 && arg2P_4<=arg2 && arg1>0 && arg2>0 && arg1P_4>3 && arg2P_4>0 && 0==arg3 ], cost: 1 Accelerated rule 2 with non-termination, yielding the new rule 5. Accelerated rule 2 with backward acceleration, yielding the new rule 6. Accelerated rule 3 with non-termination, yielding the new rule 7. Accelerated rule 3 with backward acceleration, yielding the new rule 8. [accelerate] Nesting with 2 inner and 0 outer candidates Removing the simple loops: 2 3. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg3P_1>0 && arg2>-1 && -1+arg1P_1<=arg1 && -3+arg2P_1<=arg1 && arg1>0 && arg1P_1>1 && arg2P_1>3 ], cost: 1 1: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=0, [ -3+arg1P_2<=arg1 && arg2>-1 && -1+arg2P_2<=arg1 && arg1>0 && arg1P_2>3 && arg2P_2>1 ], cost: 1 5: f192_0_main_NE -> [3] : [ arg1>=arg1P_3 && arg3>0 && arg1>=-3+arg2P_3 && -3+arg2P_3<=arg2 && arg1>0 && arg2>0 && arg1P_3>0 && arg2P_3>3 && arg1P_3>=-3+arg2P_3 ], cost: NONTERM 6: f192_0_main_NE -> f192_0_main_NE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>=arg1P_3 && arg3>0 && -3+arg2P_3<=arg2 && arg1>0 && arg2>0 && arg1P_3>0 && arg2P_3>3 && k>=1 && arg1P_3>=-3+arg2P_3 ], cost: k 7: f192_0_main_NE -> [3] : [ -3+arg1P_4<=arg1 && -3+arg1P_4<=arg2 && arg2P_4<=arg2 && arg1>0 && arg2>0 && arg1P_4>3 && arg2P_4>0 && 0==arg3 && -3+arg1P_4<=arg2P_4 ], cost: NONTERM 8: f192_0_main_NE -> f192_0_main_NE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ -3+arg1P_4<=arg1 && arg2P_4<=arg2 && arg1>0 && arg2>0 && arg1P_4>3 && arg2P_4>0 && 0==arg3 && k_1>=1 && -3+arg1P_4<=arg2P_4 ], cost: k_1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg3P_1>0 && arg2>-1 && -1+arg1P_1<=arg1 && -3+arg2P_1<=arg1 && arg1>0 && arg1P_1>1 && arg2P_1>3 ], cost: 1 1: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=0, [ -3+arg1P_2<=arg1 && arg2>-1 && -1+arg2P_2<=arg1 && arg1>0 && arg1P_2>3 && arg2P_2>1 ], cost: 1 9: f1_0_main_Load -> [3] : [ arg2>-1 && arg1>0 ], cost: NONTERM 10: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_1, [ arg3P_1>0 && arg2>-1 && arg1>0 && arg1P_3>0 && arg2P_3>3 && k>=1 && arg1P_3>=-3+arg2P_3 && arg1P_3<=1+arg1 && -3+arg2P_3<=3+arg1 ], cost: 1+k 11: f1_0_main_Load -> [3] : [ arg2>-1 && arg1>0 ], cost: NONTERM 12: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ arg2>-1 && arg1>0 && arg1P_4>3 && arg2P_4>0 && k_1>=1 && -3+arg1P_4<=arg2P_4 && -3+arg1P_4<=3+arg1 && arg2P_4<=1+arg1 ], cost: 1+k_1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 9: f1_0_main_Load -> [3] : [ arg2>-1 && arg1>0 ], cost: NONTERM 10: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_1, [ arg3P_1>0 && arg2>-1 && arg1>0 && arg1P_3>0 && arg2P_3>3 && k>=1 && arg1P_3>=-3+arg2P_3 && arg1P_3<=1+arg1 && -3+arg2P_3<=3+arg1 ], cost: 1+k 11: f1_0_main_Load -> [3] : [ arg2>-1 && arg1>0 ], cost: NONTERM 12: f1_0_main_Load -> f192_0_main_NE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ arg2>-1 && arg1>0 && arg1P_4>3 && arg2P_4>0 && k_1>=1 && -3+arg1P_4<=arg2P_4 && -3+arg1P_4<=3+arg1 && arg2P_4<=1+arg1 ], cost: 1+k_1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 13: __init -> [3] : [ arg2P_5>-1 && arg1P_5>0 ], cost: NONTERM 14: __init -> f192_0_main_NE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_1, [ arg3P_1>0 && arg2P_5>-1 && arg1P_5>0 && arg1P_3>0 && arg2P_3>3 && k>=1 && arg1P_3>=-3+arg2P_3 && arg1P_3<=1+arg1P_5 && -3+arg2P_3<=3+arg1P_5 ], cost: 2+k 15: __init -> [3] : [ arg2P_5>-1 && arg1P_5>0 ], cost: NONTERM 16: __init -> f192_0_main_NE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ arg2P_5>-1 && arg1P_5>0 && arg1P_4>3 && arg2P_4>0 && k_1>=1 && -3+arg1P_4<=arg2P_4 && -3+arg1P_4<=3+arg1P_5 && arg2P_4<=1+arg1P_5 ], cost: 2+k_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 14: __init -> f192_0_main_NE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_1, [ arg3P_1>0 && arg2P_5>-1 && arg1P_5>0 && arg1P_3>0 && arg2P_3>3 && k>=1 && arg1P_3>=-3+arg2P_3 && arg1P_3<=1+arg1P_5 && -3+arg2P_3<=3+arg1P_5 ], cost: 2+k 15: __init -> [3] : [ arg2P_5>-1 && arg1P_5>0 ], cost: NONTERM 16: __init -> f192_0_main_NE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ arg2P_5>-1 && arg1P_5>0 && arg1P_4>3 && arg2P_4>0 && k_1>=1 && -3+arg1P_4<=arg2P_4 && -3+arg1P_4<=3+arg1P_5 && arg2P_4<=1+arg1P_5 ], cost: 2+k_1 Computing asymptotic complexity for rule 15 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_5>-1 && arg1P_5>0 ] NO