NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f172_0_even_NE : arg1'=arg1P_1, arg2'=arg2P_1, [ -5+arg2-1 && arg1>0 && -5+arg2==arg1P_1 ], cost: 1 1: f172_0_even_NE -> f137_0_odd_NE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1<1 && arg1<0 && -1+arg1 f137_0_odd_NE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>1 && -1+arg1 f172_0_even_NE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1<1 && arg1<0 && -1+arg1 f172_0_even_NE : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>1 && -1+arg1 f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_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, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f172_0_even_NE : arg1'=-5+arg2, arg2'=arg2P_1, [ arg2>-1 && arg1>0 ], cost: 1 1: f172_0_even_NE -> f137_0_odd_NE : arg1'=-1+arg1, arg2'=arg2P_2, [ arg1<0 ], cost: 1 2: f172_0_even_NE -> f137_0_odd_NE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>1 ], cost: 1 3: f137_0_odd_NE -> f172_0_even_NE : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1<0 ], cost: 1 4: f137_0_odd_NE -> f172_0_even_NE : arg1'=-1+arg1, arg2'=arg2P_5, [ arg1>1 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 1: f172_0_even_NE -> f137_0_odd_NE : arg1'=-1+arg1, arg2'=arg2P_2, [ arg1<0 ], cost: 1 2: f172_0_even_NE -> f137_0_odd_NE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>1 ], cost: 1 3: f137_0_odd_NE -> f172_0_even_NE : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1<0 ], cost: 1 4: f137_0_odd_NE -> f172_0_even_NE : arg1'=-1+arg1, arg2'=arg2P_5, [ arg1>1 ], cost: 1 6: __init -> f172_0_even_NE : arg1'=-5+arg2P_6, arg2'=arg2P_1, [ arg2P_6>-1 && arg1P_6>0 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 7: f172_0_even_NE -> f172_0_even_NE : arg1'=-2+arg1, arg2'=arg2P_4, [ arg1<0 ], cost: 2 8: f172_0_even_NE -> f172_0_even_NE : arg1'=-2+arg1, arg2'=arg2P_5, [ -1+arg1>1 ], cost: 2 6: __init -> f172_0_even_NE : arg1'=-5+arg2P_6, arg2'=arg2P_1, [ arg2P_6>-1 && arg1P_6>0 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 7: f172_0_even_NE -> f172_0_even_NE : arg1'=-2+arg1, arg2'=arg2P_4, [ arg1<0 ], cost: 2 8: f172_0_even_NE -> f172_0_even_NE : arg1'=-2+arg1, arg2'=arg2P_5, [ -1+arg1>1 ], cost: 2 Accelerated rule 7 with non-termination, yielding the new rule 9. Accelerated rule 8 with backward acceleration, yielding the new rule 10. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 7 8. Accelerated all simple loops using metering functions (where possible): Start location: __init 9: f172_0_even_NE -> [4] : [ arg1<0 ], cost: NONTERM 10: f172_0_even_NE -> f172_0_even_NE : arg1'=-2*k+arg1, arg2'=arg2P_5, [ k>=1 && 1-2*k+arg1>1 ], cost: 2*k 6: __init -> f172_0_even_NE : arg1'=-5+arg2P_6, arg2'=arg2P_1, [ arg2P_6>-1 && arg1P_6>0 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 6: __init -> f172_0_even_NE : arg1'=-5+arg2P_6, arg2'=arg2P_1, [ arg2P_6>-1 && arg1P_6>0 ], cost: 2 11: __init -> [4] : [], cost: NONTERM 12: __init -> f172_0_even_NE : arg1'=-5+arg2P_6-2*k, arg2'=arg2P_5, [ arg2P_6>-1 && k>=1 && -4+arg2P_6-2*k>1 ], cost: 2+2*k Removed unreachable locations (and leaf rules with constant cost): Start location: __init 11: __init -> [4] : [], cost: NONTERM 12: __init -> f172_0_even_NE : arg1'=-5+arg2P_6-2*k, arg2'=arg2P_5, [ arg2P_6>-1 && k>=1 && -4+arg2P_6-2*k>1 ], cost: 2+2*k ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 11: __init -> [4] : [], cost: NONTERM 12: __init -> f172_0_even_NE : arg1'=-5+arg2P_6-2*k, arg2'=arg2P_5, [ arg2P_6>-1 && k>=1 && -4+arg2P_6-2*k>1 ], cost: 2+2*k 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: [] NO