NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f89_0_loop_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1 1: f89_0_loop_LE -> f131_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1<50 && arg1>19 && arg1==arg1P_2 ], cost: 1 2: f89_0_loop_LE -> f131_0_loop_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1<20 && arg1<50 && arg1>0 && -1+arg1==arg1P_3 ], cost: 1 3: f131_0_loop_LE -> f89_0_loop_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1<30 && arg1<11 && arg1==arg1P_4 ], cost: 1 4: f131_0_loop_LE -> f89_0_loop_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<29 && arg1>10 && 1+arg1==arg1P_5 ], cost: 1 5: f131_0_loop_LE -> f89_0_loop_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>39 && 1+arg1==arg1P_6 ], cost: 1 6: f131_0_loop_LE -> f89_0_loop_LE : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1<40 && arg1>28 && arg1==arg1P_7 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f89_0_loop_LE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f89_0_loop_LE -> f131_0_loop_LE : arg2'=arg2P_2, [ arg1<50 && arg1>19 ], cost: 1 2: f89_0_loop_LE -> f131_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1<20 && arg1>0 ], cost: 1 3: f131_0_loop_LE -> f89_0_loop_LE : arg2'=arg2P_4, [ arg1<11 ], cost: 1 4: f131_0_loop_LE -> f89_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_5, [ arg1<29 && arg1>10 ], cost: 1 5: f131_0_loop_LE -> f89_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_6, [ arg1>39 ], cost: 1 6: f131_0_loop_LE -> f89_0_loop_LE : arg2'=arg2P_7, [ arg1<40 && arg1>28 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 1: f89_0_loop_LE -> f131_0_loop_LE : arg2'=arg2P_2, [ arg1<50 && arg1>19 ], cost: 1 2: f89_0_loop_LE -> f131_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1<20 && arg1>0 ], cost: 1 3: f131_0_loop_LE -> f89_0_loop_LE : arg2'=arg2P_4, [ arg1<11 ], cost: 1 4: f131_0_loop_LE -> f89_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_5, [ arg1<29 && arg1>10 ], cost: 1 5: f131_0_loop_LE -> f89_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_6, [ arg1>39 ], cost: 1 6: f131_0_loop_LE -> f89_0_loop_LE : arg2'=arg2P_7, [ arg1<40 && arg1>28 ], cost: 1 8: __init -> f89_0_loop_LE : arg1'=arg2P_8, arg2'=arg2P_1, [ arg1P_8>0 && arg2P_8>-1 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 9: f89_0_loop_LE -> f89_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_5, [ arg1>19 && arg1<29 ], cost: 2 10: f89_0_loop_LE -> f89_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_6, [ arg1<50 && arg1>39 ], cost: 2 11: f89_0_loop_LE -> f89_0_loop_LE : arg2'=arg2P_7, [ arg1<40 && arg1>28 ], cost: 2 12: f89_0_loop_LE -> f89_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1>0 && -1+arg1<11 ], cost: 2 13: f89_0_loop_LE -> f89_0_loop_LE : arg1'=arg1, arg2'=arg2P_5, [ arg1<20 && -1+arg1>10 ], cost: 2 8: __init -> f89_0_loop_LE : arg1'=arg2P_8, arg2'=arg2P_1, [ arg1P_8>0 && arg2P_8>-1 ], cost: 2 Accelerating simple loops of location 1. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 9: f89_0_loop_LE -> f89_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_5, [ arg1>19 && arg1<29 ], cost: 2 10: f89_0_loop_LE -> f89_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_6, [ arg1<50 && arg1>39 ], cost: 2 11: f89_0_loop_LE -> f89_0_loop_LE : arg2'=arg2P_7, [ arg1<40 && arg1>28 ], cost: 2 12: f89_0_loop_LE -> f89_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1>0 && -1+arg1<11 ], cost: 2 13: f89_0_loop_LE -> f89_0_loop_LE : arg2'=arg2P_5, [ arg1<20 && -1+arg1>10 ], cost: 2 Accelerated rule 9 with backward acceleration, yielding the new rule 14. Accelerated rule 10 with backward acceleration, yielding the new rule 15. Accelerated rule 11 with non-termination, yielding the new rule 16. Accelerated rule 12 with backward acceleration, yielding the new rule 17. Accelerated rule 13 with non-termination, yielding the new rule 18. [accelerate] Nesting with 3 inner and 3 outer candidates Removing the simple loops: 9 10 11 12 13. Accelerated all simple loops using metering functions (where possible): Start location: __init 14: f89_0_loop_LE -> f89_0_loop_LE : arg1'=29, arg2'=arg2P_5, [ arg1>19 && 29-arg1>=1 ], cost: 58-2*arg1 15: f89_0_loop_LE -> f89_0_loop_LE : arg1'=50, arg2'=arg2P_6, [ arg1>39 && 50-arg1>=1 ], cost: 100-2*arg1 16: f89_0_loop_LE -> [4] : [ arg1<40 && arg1>28 ], cost: NONTERM 17: f89_0_loop_LE -> f89_0_loop_LE : arg1'=0, arg2'=arg2P_4, [ -1+arg1<11 && arg1>=1 ], cost: 2*arg1 18: f89_0_loop_LE -> [4] : [ arg1<20 && -1+arg1>10 ], cost: NONTERM 8: __init -> f89_0_loop_LE : arg1'=arg2P_8, arg2'=arg2P_1, [ arg1P_8>0 && arg2P_8>-1 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 8: __init -> f89_0_loop_LE : arg1'=arg2P_8, arg2'=arg2P_1, [ arg1P_8>0 && arg2P_8>-1 ], cost: 2 19: __init -> f89_0_loop_LE : arg1'=29, arg2'=arg2P_5, [ arg2P_8>19 && 29-arg2P_8>=1 ], cost: 60-2*arg2P_8 20: __init -> f89_0_loop_LE : arg1'=50, arg2'=arg2P_6, [ arg2P_8>39 && 50-arg2P_8>=1 ], cost: 102-2*arg2P_8 21: __init -> [4] : [], cost: NONTERM 22: __init -> f89_0_loop_LE : arg1'=0, arg2'=arg2P_4, [ -1+arg2P_8<11 && arg2P_8>=1 ], cost: 2+2*arg2P_8 23: __init -> [4] : [], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: __init 19: __init -> f89_0_loop_LE : arg1'=29, arg2'=arg2P_5, [ arg2P_8>19 && 29-arg2P_8>=1 ], cost: 60-2*arg2P_8 20: __init -> f89_0_loop_LE : arg1'=50, arg2'=arg2P_6, [ arg2P_8>39 && 50-arg2P_8>=1 ], cost: 102-2*arg2P_8 21: __init -> [4] : [], cost: NONTERM 22: __init -> f89_0_loop_LE : arg1'=0, arg2'=arg2P_4, [ -1+arg2P_8<11 && arg2P_8>=1 ], cost: 2+2*arg2P_8 23: __init -> [4] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 19: __init -> f89_0_loop_LE : arg1'=29, arg2'=arg2P_5, [ arg2P_8>19 && 29-arg2P_8>=1 ], cost: 60-2*arg2P_8 20: __init -> f89_0_loop_LE : arg1'=50, arg2'=arg2P_6, [ arg2P_8>39 && 50-arg2P_8>=1 ], cost: 102-2*arg2P_8 22: __init -> f89_0_loop_LE : arg1'=0, arg2'=arg2P_4, [ -1+arg2P_8<11 && arg2P_8>=1 ], cost: 2+2*arg2P_8 23: __init -> [4] : [], cost: NONTERM Computing asymptotic complexity for rule 23 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