NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f53_0_loop_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1 1: f53_0_loop_LE -> f74_0_loop_NE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1<21 && arg1>10 && -1+arg1==arg1P_2 ], cost: 1 2: f53_0_loop_LE -> f74_0_loop_NE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>20 && 1+arg1==arg1P_3 ], cost: 1 3: f74_0_loop_NE -> f53_0_loop_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1<30 && arg1==arg1P_4 ], cost: 1 4: f74_0_loop_NE -> f53_0_loop_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>30 && arg1==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 -> f53_0_loop_LE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f53_0_loop_LE -> f74_0_loop_NE : arg1'=-1+arg1, arg2'=arg2P_2, [ arg1<21 && arg1>10 ], cost: 1 2: f53_0_loop_LE -> f74_0_loop_NE : arg1'=1+arg1, arg2'=arg2P_3, [ arg1>20 ], cost: 1 3: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P_4, [ arg1<30 ], cost: 1 4: f74_0_loop_NE -> f53_0_loop_LE : 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 ### Eliminated locations (on linear paths): Start location: __init 1: f53_0_loop_LE -> f74_0_loop_NE : arg1'=-1+arg1, arg2'=arg2P_2, [ arg1<21 && arg1>10 ], cost: 1 2: f53_0_loop_LE -> f74_0_loop_NE : arg1'=1+arg1, arg2'=arg2P_3, [ arg1>20 ], cost: 1 3: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P_4, [ arg1<30 ], cost: 1 4: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P_5, [ arg1>30 ], cost: 1 6: __init -> f53_0_loop_LE : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6>-1 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 7: f53_0_loop_LE -> f53_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1<21 && arg1>10 ], cost: 2 8: f53_0_loop_LE -> f53_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_4, [ arg1>20 && 1+arg1<30 ], cost: 2 9: f53_0_loop_LE -> f53_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_5, [ 1+arg1>30 ], cost: 2 6: __init -> f53_0_loop_LE : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6>-1 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 7: f53_0_loop_LE -> f53_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1<21 && arg1>10 ], cost: 2 8: f53_0_loop_LE -> f53_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_4, [ arg1>20 && 1+arg1<30 ], cost: 2 9: f53_0_loop_LE -> f53_0_loop_LE : arg1'=1+arg1, arg2'=arg2P_5, [ 1+arg1>30 ], cost: 2 Accelerated rule 7 with backward acceleration, yielding the new rule 10. Accelerated rule 8 with backward acceleration, yielding the new rule 11. Accelerated rule 9 with non-termination, yielding the new rule 12. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 7 8 9. Accelerated all simple loops using metering functions (where possible): Start location: __init 10: f53_0_loop_LE -> f53_0_loop_LE : arg1'=10, arg2'=arg2P_4, [ arg1<21 && -10+arg1>=1 ], cost: -20+2*arg1 11: f53_0_loop_LE -> f53_0_loop_LE : arg1'=29, arg2'=arg2P_4, [ arg1>20 && 29-arg1>=1 ], cost: 58-2*arg1 12: f53_0_loop_LE -> [4] : [ 1+arg1>30 ], cost: NONTERM 6: __init -> f53_0_loop_LE : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6>-1 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 6: __init -> f53_0_loop_LE : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6>-1 ], cost: 2 13: __init -> f53_0_loop_LE : arg1'=10, arg2'=arg2P_4, [ arg2P_6<21 && -10+arg2P_6>=1 ], cost: -18+2*arg2P_6 14: __init -> f53_0_loop_LE : arg1'=29, arg2'=arg2P_4, [ arg2P_6>20 && 29-arg2P_6>=1 ], cost: 60-2*arg2P_6 15: __init -> [4] : [], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: __init 13: __init -> f53_0_loop_LE : arg1'=10, arg2'=arg2P_4, [ arg2P_6<21 && -10+arg2P_6>=1 ], cost: -18+2*arg2P_6 14: __init -> f53_0_loop_LE : arg1'=29, arg2'=arg2P_4, [ arg2P_6>20 && 29-arg2P_6>=1 ], cost: 60-2*arg2P_6 15: __init -> [4] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 13: __init -> f53_0_loop_LE : arg1'=10, arg2'=arg2P_4, [ arg2P_6<21 && -10+arg2P_6>=1 ], cost: -18+2*arg2P_6 14: __init -> f53_0_loop_LE : arg1'=29, arg2'=arg2P_4, [ arg2P_6>20 && 29-arg2P_6>=1 ], cost: 60-2*arg2P_6 15: __init -> [4] : [], cost: NONTERM Computing asymptotic complexity for rule 15 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