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 metering function 29-arg1, yielding the new rule 14. Accelerated rule 10 with metering function 50-arg1, yielding the new rule 15. Accelerated rule 11 with NONTERM, yielding the new rule 16. Accelerated rule 12 with metering function arg1, yielding the new rule 17. Accelerated rule 13 with NONTERM, yielding the new rule 18. 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 && arg1<29 ], cost: 58-2*arg1 15: f89_0_loop_LE -> f89_0_loop_LE : arg1'=50, arg2'=arg2P_6, [ arg1<50 && arg1>39 ], 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, [ arg1>0 && -1+arg1<11 ], 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 && arg2P_8<29 ], cost: 60-2*arg2P_8 20: __init -> f89_0_loop_LE : arg1'=50, arg2'=arg2P_6, [ arg2P_8<50 && arg2P_8>39 ], cost: 102-2*arg2P_8 21: __init -> [4] : arg1'=arg2P_8, arg2'=arg2P_1, [ arg2P_8<40 && arg2P_8>28 ], cost: NONTERM 22: __init -> f89_0_loop_LE : arg1'=0, arg2'=arg2P_4, [ arg2P_8>0 && -1+arg2P_8<11 ], cost: 2+2*arg2P_8 23: __init -> [4] : arg1'=arg2P_8, arg2'=arg2P_1, [ arg2P_8<20 && -1+arg2P_8>10 ], 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 && arg2P_8<29 ], cost: 60-2*arg2P_8 20: __init -> f89_0_loop_LE : arg1'=50, arg2'=arg2P_6, [ arg2P_8<50 && arg2P_8>39 ], cost: 102-2*arg2P_8 21: __init -> [4] : arg1'=arg2P_8, arg2'=arg2P_1, [ arg2P_8<40 && arg2P_8>28 ], cost: NONTERM 22: __init -> f89_0_loop_LE : arg1'=0, arg2'=arg2P_4, [ arg2P_8>0 && -1+arg2P_8<11 ], cost: 2+2*arg2P_8 23: __init -> [4] : arg1'=arg2P_8, arg2'=arg2P_1, [ arg2P_8<20 && -1+arg2P_8>10 ], 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 && arg2P_8<29 ], cost: 60-2*arg2P_8 20: __init -> f89_0_loop_LE : arg1'=50, arg2'=arg2P_6, [ arg2P_8<50 && arg2P_8>39 ], cost: 102-2*arg2P_8 21: __init -> [4] : arg1'=arg2P_8, arg2'=arg2P_1, [ arg2P_8<40 && arg2P_8>28 ], cost: NONTERM 22: __init -> f89_0_loop_LE : arg1'=0, arg2'=arg2P_4, [ arg2P_8>0 && -1+arg2P_8<11 ], cost: 2+2*arg2P_8 23: __init -> [4] : arg1'=arg2P_8, arg2'=arg2P_1, [ arg2P_8<20 && -1+arg2P_8>10 ], cost: NONTERM Computing asymptotic complexity for rule 19 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 20 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 21 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_8<40 && arg2P_8>28 ] NO