NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f66_0_loop_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1 1: f66_0_loop_LE -> f66_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1<31 && arg1<25 && arg1>10 && -1+arg1==arg1P_2 ], cost: 1 2: f66_0_loop_LE -> f66_0_loop_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1<31 && arg1>25 && -1+arg1==arg1P_3 ], cost: 1 3: f66_0_loop_LE -> f66_0_loop_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ 25==arg1 && 29==arg1P_4 ], cost: 1 4: f66_0_loop_LE -> f66_0_loop_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>30 && 20==arg1P_5 ], cost: 1 5: __init -> 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 -> f66_0_loop_LE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f66_0_loop_LE -> f66_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_2, [ arg1<25 && arg1>10 ], cost: 1 2: f66_0_loop_LE -> f66_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1<31 && arg1>25 ], cost: 1 3: f66_0_loop_LE -> f66_0_loop_LE : arg1'=29, arg2'=arg2P_4, [ 25==arg1 ], cost: 1 4: f66_0_loop_LE -> f66_0_loop_LE : arg1'=20, arg2'=arg2P_5, [ arg1>30 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f66_0_loop_LE -> f66_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_2, [ arg1<25 && arg1>10 ], cost: 1 2: f66_0_loop_LE -> f66_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1<31 && arg1>25 ], cost: 1 3: f66_0_loop_LE -> f66_0_loop_LE : arg1'=29, arg2'=arg2P_4, [ 25==arg1 ], cost: 1 4: f66_0_loop_LE -> f66_0_loop_LE : arg1'=20, arg2'=arg2P_5, [ arg1>30 ], cost: 1 Accelerated rule 1 with metering function -10+arg1, yielding the new rule 6. Accelerated rule 2 with metering function -25+arg1, yielding the new rule 7. Accelerated rule 3 with metering function meter (where 4*meter==25-arg1), yielding the new rule 8. Found no metering function for rule 4. Nested simple loops 3 (outer loop) and 7 (inner loop) with NONTERM, resulting in the new rules: 9, 10. Removing the simple loops: 1 2 3. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f66_0_loop_LE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 4: f66_0_loop_LE -> f66_0_loop_LE : arg1'=20, arg2'=arg2P_5, [ arg1>30 ], cost: 1 6: f66_0_loop_LE -> f66_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg1<25 && arg1>10 ], cost: -10+arg1 7: f66_0_loop_LE -> f66_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1<31 && arg1>25 ], cost: -25+arg1 8: f66_0_loop_LE -> f66_0_loop_LE : arg1'=29, arg2'=arg2P_4, [ 25==arg1 && 4*meter==25-arg1 && meter>=1 ], cost: meter 9: f66_0_loop_LE -> [3] : [ arg1<31 && arg1>25 ], cost: NONTERM 10: f66_0_loop_LE -> [3] : arg1'=29, arg2'=arg2P_4, [ 25==arg1 ], cost: NONTERM 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f66_0_loop_LE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 11: f1_0_main_Load -> f66_0_loop_LE : arg1'=20, arg2'=arg2P_5, [ arg1>0 && arg2>30 ], cost: 2 12: f1_0_main_Load -> f66_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg1>0 && arg2<25 && arg2>10 ], cost: -9+arg2 13: f1_0_main_Load -> f66_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1>0 && arg2<31 && arg2>25 ], cost: -24+arg2 14: f1_0_main_Load -> [3] : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2<31 && arg2>25 ], cost: NONTERM 15: f1_0_main_Load -> [3] : arg1'=29, arg2'=arg2P_4, [ arg1>0 && 25==arg2 ], cost: NONTERM 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 12: f1_0_main_Load -> f66_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg1>0 && arg2<25 && arg2>10 ], cost: -9+arg2 13: f1_0_main_Load -> f66_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1>0 && arg2<31 && arg2>25 ], cost: -24+arg2 14: f1_0_main_Load -> [3] : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2<31 && arg2>25 ], cost: NONTERM 15: f1_0_main_Load -> [3] : arg1'=29, arg2'=arg2P_4, [ arg1>0 && 25==arg2 ], cost: NONTERM 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 16: __init -> f66_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg1P_6>0 && arg2P_6<25 && arg2P_6>10 ], cost: -8+arg2P_6 17: __init -> f66_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1P_6>0 && arg2P_6<31 && arg2P_6>25 ], cost: -23+arg2P_6 18: __init -> [3] : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6<31 && arg2P_6>25 ], cost: NONTERM 19: __init -> [3] : arg1'=29, arg2'=arg2P_4, [ arg1P_6>0 && 25==arg2P_6 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 16: __init -> f66_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg1P_6>0 && arg2P_6<25 && arg2P_6>10 ], cost: -8+arg2P_6 17: __init -> f66_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1P_6>0 && arg2P_6<31 && arg2P_6>25 ], cost: -23+arg2P_6 18: __init -> [3] : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6<31 && arg2P_6>25 ], cost: NONTERM 19: __init -> [3] : arg1'=29, arg2'=arg2P_4, [ arg1P_6>0 && 25==arg2P_6 ], cost: NONTERM Computing asymptotic complexity for rule 16 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 17 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 18 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_6>0 && arg2P_6<31 && arg2P_6>25 ] NO