NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f121_0_loop_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ 20+arg2>arg2 && arg2>-1 && arg1>0 && 20+arg2==arg1P_1 ], cost: 1 1: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1<31 && arg1<25 && arg1>10 && -1+arg1==arg1P_2 ], cost: 1 2: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>25 && arg1<31 && -1+arg1==arg1P_3 ], cost: 1 3: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>30 && 20==arg1P_4 ], cost: 1 4: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ 25==arg1 && 29==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 -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P_1, [ arg2>-1 && arg1>0 ], cost: 1 1: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_2, [ arg1<25 && arg1>10 ], cost: 1 2: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>25 && arg1<31 ], cost: 1 3: f121_0_loop_LE -> f121_0_loop_LE : arg1'=20, arg2'=arg2P_4, [ arg1>30 ], cost: 1 4: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P_5, [ 25==arg1 ], 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: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_2, [ arg1<25 && arg1>10 ], cost: 1 2: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>25 && arg1<31 ], cost: 1 3: f121_0_loop_LE -> f121_0_loop_LE : arg1'=20, arg2'=arg2P_4, [ arg1>30 ], cost: 1 4: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P_5, [ 25==arg1 ], cost: 1 Accelerated rule 1 with backward acceleration, yielding the new rule 6. Accelerated rule 2 with backward acceleration, yielding the new rule 7. Failed to prove monotonicity of the guard of rule 3. Failed to prove monotonicity of the guard of rule 4. [accelerate] Nesting with 4 inner and 4 outer candidates Nested simple loops 4 (outer loop) and 7 (inner loop) with Rule(1 | arg1<31, -25+arg1>=1, | NONTERM || 3 | ), resulting in the new rules: 8, 9. Removing the simple loops: 1 2 4. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P_1, [ arg2>-1 && arg1>0 ], cost: 1 3: f121_0_loop_LE -> f121_0_loop_LE : arg1'=20, arg2'=arg2P_4, [ arg1>30 ], cost: 1 6: f121_0_loop_LE -> f121_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg1<25 && -10+arg1>=1 ], cost: -10+arg1 7: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1<31 && -25+arg1>=1 ], cost: -25+arg1 8: f121_0_loop_LE -> [3] : [ arg1<31 && -25+arg1>=1 ], cost: NONTERM 9: f121_0_loop_LE -> [3] : [ 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 -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P_1, [ arg2>-1 && arg1>0 ], cost: 1 10: f1_0_main_Load -> f121_0_loop_LE : arg1'=20, arg2'=arg2P_4, [ arg1>0 && 20+arg2>30 ], cost: 2 11: f1_0_main_Load -> f121_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg2>-1 && arg1>0 && 20+arg2<25 ], cost: 11+arg2 12: f1_0_main_Load -> f121_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1>0 && 20+arg2<31 && -5+arg2>=1 ], cost: -4+arg2 13: f1_0_main_Load -> [3] : [ arg1>0 && 20+arg2<31 && -5+arg2>=1 ], cost: NONTERM 14: f1_0_main_Load -> [3] : [ arg1>0 && 25==20+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 11: f1_0_main_Load -> f121_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg2>-1 && arg1>0 && 20+arg2<25 ], cost: 11+arg2 12: f1_0_main_Load -> f121_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1>0 && 20+arg2<31 && -5+arg2>=1 ], cost: -4+arg2 13: f1_0_main_Load -> [3] : [ arg1>0 && 20+arg2<31 && -5+arg2>=1 ], cost: NONTERM 14: f1_0_main_Load -> [3] : [ arg1>0 && 25==20+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 15: __init -> f121_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg2P_6>-1 && arg1P_6>0 && 20+arg2P_6<25 ], cost: 12+arg2P_6 16: __init -> f121_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1P_6>0 && 20+arg2P_6<31 && -5+arg2P_6>=1 ], cost: -3+arg2P_6 17: __init -> [3] : [ arg1P_6>0 && 20+arg2P_6<31 && -5+arg2P_6>=1 ], cost: NONTERM 18: __init -> [3] : [ arg1P_6>0 && 25==20+arg2P_6 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 15: __init -> f121_0_loop_LE : arg1'=10, arg2'=arg2P_2, [ arg2P_6>-1 && arg1P_6>0 && 20+arg2P_6<25 ], cost: 12+arg2P_6 16: __init -> f121_0_loop_LE : arg1'=25, arg2'=arg2P_3, [ arg1P_6>0 && 20+arg2P_6<31 && -5+arg2P_6>=1 ], cost: -3+arg2P_6 17: __init -> [3] : [ arg1P_6>0 && 20+arg2P_6<31 && -5+arg2P_6>=1 ], cost: NONTERM 18: __init -> [3] : [ arg1P_6>0 && 25==20+arg2P_6 ], cost: NONTERM 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 && 25==20+arg2P_6 ] NO