NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f31_0_loop_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1 1: f31_0_loop_LE -> f31_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ 5==arg1 && 5==arg1P_2 ], cost: 1 2: f31_0_loop_LE -> f31_0_loop_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1<5 && arg1>0 && -1+arg1==arg1P_3 ], cost: 1 3: f31_0_loop_LE -> f31_0_loop_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>5 && -1+arg1==arg1P_4 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_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, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f31_0_loop_LE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f31_0_loop_LE -> f31_0_loop_LE : arg1'=5, arg2'=arg2P_2, [ 5==arg1 ], cost: 1 2: f31_0_loop_LE -> f31_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1<5 && arg1>0 ], cost: 1 3: f31_0_loop_LE -> f31_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1>5 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f31_0_loop_LE -> f31_0_loop_LE : arg1'=5, arg2'=arg2P_2, [ 5==arg1 ], cost: 1 2: f31_0_loop_LE -> f31_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1<5 && arg1>0 ], cost: 1 3: f31_0_loop_LE -> f31_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1>5 ], cost: 1 Accelerated rule 1 with non-termination, yielding the new rule 5. Accelerated rule 2 with backward acceleration, yielding the new rule 6. Accelerated rule 3 with backward acceleration, yielding the new rule 7. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 1 2 3. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f31_0_loop_LE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 5: f31_0_loop_LE -> [3] : [ 5==arg1 ], cost: NONTERM 6: f31_0_loop_LE -> f31_0_loop_LE : arg1'=0, arg2'=arg2P_3, [ arg1<5 && arg1>=1 ], cost: arg1 7: f31_0_loop_LE -> f31_0_loop_LE : arg1'=5, arg2'=arg2P_4, [ -5+arg1>=1 ], cost: -5+arg1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f31_0_loop_LE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 8: f1_0_main_Load -> [3] : [ arg1>0 && 5==arg2 ], cost: NONTERM 9: f1_0_main_Load -> f31_0_loop_LE : arg1'=0, arg2'=arg2P_3, [ arg1>0 && arg2<5 && arg2>=1 ], cost: 1+arg2 10: f1_0_main_Load -> f31_0_loop_LE : arg1'=5, arg2'=arg2P_4, [ arg1>0 && -5+arg2>=1 ], cost: -4+arg2 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 8: f1_0_main_Load -> [3] : [ arg1>0 && 5==arg2 ], cost: NONTERM 9: f1_0_main_Load -> f31_0_loop_LE : arg1'=0, arg2'=arg2P_3, [ arg1>0 && arg2<5 && arg2>=1 ], cost: 1+arg2 10: f1_0_main_Load -> f31_0_loop_LE : arg1'=5, arg2'=arg2P_4, [ arg1>0 && -5+arg2>=1 ], cost: -4+arg2 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 11: __init -> [3] : [ arg1P_5>0 && 5==arg2P_5 ], cost: NONTERM 12: __init -> f31_0_loop_LE : arg1'=0, arg2'=arg2P_3, [ arg1P_5>0 && arg2P_5<5 && arg2P_5>=1 ], cost: 2+arg2P_5 13: __init -> f31_0_loop_LE : arg1'=5, arg2'=arg2P_4, [ arg1P_5>0 && -5+arg2P_5>=1 ], cost: -3+arg2P_5 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 11: __init -> [3] : [ arg1P_5>0 && 5==arg2P_5 ], cost: NONTERM 12: __init -> f31_0_loop_LE : arg1'=0, arg2'=arg2P_3, [ arg1P_5>0 && arg2P_5<5 && arg2P_5>=1 ], cost: 2+arg2P_5 13: __init -> f31_0_loop_LE : arg1'=5, arg2'=arg2P_4, [ arg1P_5>0 && -5+arg2P_5>=1 ], cost: -3+arg2P_5 Computing asymptotic complexity for rule 11 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_5>0 && 5==arg2P_5 ] NO