NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f325_0_loop_GT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 && 20==arg1P_1 && -20==arg2P_1 && arg2==arg3P_1 ], cost: 1 1: f325_0_loop_GT -> f325_0_loop_GT : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ -arg3+arg1<5 && arg3<=arg1 && arg3>=arg2 && arg1==arg1P_2 && -arg1==arg2P_2 && -arg3==arg3P_2 ], cost: 1 2: f325_0_loop_GT -> f325_0_loop_GT : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3<=arg1 && arg3>=arg2 && -arg3+arg1>=5 && arg3+arg1<5 && arg1==arg1P_3 && -arg1==arg2P_3 && -arg3==arg3P_3 ], cost: 1 3: f325_0_loop_GT -> f325_0_loop_GT : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>=arg3 && arg2<=arg3 && -arg3+arg1>=5 && arg3+arg1>=5 && arg3<1 && 1+arg1==arg1P_4 && -1-arg1==arg2P_4 && -1+arg3==arg3P_4 ], cost: 1 4: f325_0_loop_GT -> f325_0_loop_GT : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1>=arg3 && arg2<=arg3 && -arg3+arg1>=5 && arg3+arg1>=5 && arg3>1 && 1+arg1==arg1P_5 && -1-arg1==arg2P_5 && -1+arg3==arg3P_5 ], cost: 1 5: f325_0_loop_GT -> f325_0_loop_GT : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1>5 && arg2<2 && 1==arg3 && -1==arg1P_6 && 1==arg2P_6 && 0==arg3P_6 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f325_0_loop_GT : arg1'=20, arg2'=-20, arg3'=arg2, [ arg1>0 && arg2>-1 ], cost: 1 1: f325_0_loop_GT -> f325_0_loop_GT : arg2'=-arg1, arg3'=-arg3, [ -arg3+arg1<5 && arg3<=arg1 && arg3>=arg2 ], cost: 1 2: f325_0_loop_GT -> f325_0_loop_GT : arg2'=-arg1, arg3'=-arg3, [ arg3>=arg2 && -arg3+arg1>=5 && arg3+arg1<5 ], cost: 1 3: f325_0_loop_GT -> f325_0_loop_GT : arg1'=1+arg1, arg2'=-1-arg1, arg3'=-1+arg3, [ arg2<=arg3 && arg3+arg1>=5 && arg3<1 ], cost: 1 4: f325_0_loop_GT -> f325_0_loop_GT : arg1'=1+arg1, arg2'=-1-arg1, arg3'=-1+arg3, [ arg2<=arg3 && -arg3+arg1>=5 && arg3+arg1>=5 && arg3>1 ], cost: 1 5: f325_0_loop_GT -> f325_0_loop_GT : arg1'=-1, arg2'=1, arg3'=0, [ arg1>5 && arg2<2 && 1==arg3 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f325_0_loop_GT -> f325_0_loop_GT : arg2'=-arg1, arg3'=-arg3, [ -arg3+arg1<5 && arg3<=arg1 && arg3>=arg2 ], cost: 1 2: f325_0_loop_GT -> f325_0_loop_GT : arg2'=-arg1, arg3'=-arg3, [ arg3>=arg2 && -arg3+arg1>=5 && arg3+arg1<5 ], cost: 1 3: f325_0_loop_GT -> f325_0_loop_GT : arg1'=1+arg1, arg2'=-1-arg1, arg3'=-1+arg3, [ arg2<=arg3 && arg3+arg1>=5 && arg3<1 ], cost: 1 4: f325_0_loop_GT -> f325_0_loop_GT : arg1'=1+arg1, arg2'=-1-arg1, arg3'=-1+arg3, [ arg2<=arg3 && -arg3+arg1>=5 && arg3+arg1>=5 && arg3>1 ], cost: 1 5: f325_0_loop_GT -> f325_0_loop_GT : arg1'=-1, arg2'=1, arg3'=0, [ arg1>5 && arg2<2 && 1==arg3 ], cost: 1 Accelerated rule 1 with non-termination, yielding the new rule 7. Failed to prove monotonicity of the guard of rule 2. Accelerated rule 3 with non-termination, yielding the new rule 8. Accelerated rule 4 with backward acceleration, yielding the new rule 9. Failed to prove monotonicity of the guard of rule 5. [accelerate] Nesting with 3 inner and 3 outer candidates Removing the simple loops: 1 3 4. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f325_0_loop_GT : arg1'=20, arg2'=-20, arg3'=arg2, [ arg1>0 && arg2>-1 ], cost: 1 2: f325_0_loop_GT -> f325_0_loop_GT : arg2'=-arg1, arg3'=-arg3, [ arg3>=arg2 && -arg3+arg1>=5 && arg3+arg1<5 ], cost: 1 5: f325_0_loop_GT -> f325_0_loop_GT : arg1'=-1, arg2'=1, arg3'=0, [ arg1>5 && arg2<2 && 1==arg3 ], cost: 1 7: f325_0_loop_GT -> [3] : [ -arg3+arg1<5 && arg3<=arg1 && arg3>=arg2 && arg3+arg1<5 && -arg3<=arg1 ], cost: NONTERM 8: f325_0_loop_GT -> [3] : [ arg2<=arg3 && arg3+arg1>=5 && arg3<1 ], cost: NONTERM 9: f325_0_loop_GT -> f325_0_loop_GT : arg1'=-1+arg3+arg1, arg2'=1-arg3-arg1, arg3'=1, [ arg2<=arg3 && -arg3+arg1>=5 && arg3+arg1>=5 && -1+arg3>=1 ], cost: -1+arg3 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f325_0_loop_GT : arg1'=20, arg2'=-20, arg3'=arg2, [ arg1>0 && arg2>-1 ], cost: 1 10: f1_0_main_Load -> f325_0_loop_GT : arg1'=-1, arg2'=1, arg3'=0, [ arg1>0 && 1==arg2 ], cost: 2 11: f1_0_main_Load -> [3] : [ arg1>0 && -arg2==0 ], cost: NONTERM 12: f1_0_main_Load -> f325_0_loop_GT : arg1'=19+arg2, arg2'=-19-arg2, arg3'=1, [ arg1>0 && 20-arg2>=5 && -1+arg2>=1 ], cost: arg2 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 11: f1_0_main_Load -> [3] : [ arg1>0 && -arg2==0 ], cost: NONTERM 12: f1_0_main_Load -> f325_0_loop_GT : arg1'=19+arg2, arg2'=-19-arg2, arg3'=1, [ arg1>0 && 20-arg2>=5 && -1+arg2>=1 ], cost: arg2 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 13: __init -> [3] : [ arg1P_7>0 && -arg2P_7==0 ], cost: NONTERM 14: __init -> f325_0_loop_GT : arg1'=19+arg2P_7, arg2'=-19-arg2P_7, arg3'=1, [ arg1P_7>0 && 20-arg2P_7>=5 && -1+arg2P_7>=1 ], cost: 1+arg2P_7 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 13: __init -> [3] : [ arg1P_7>0 && -arg2P_7==0 ], cost: NONTERM 14: __init -> f325_0_loop_GT : arg1'=19+arg2P_7, arg2'=-19-arg2P_7, arg3'=1, [ arg1P_7>0 && 20-arg2P_7>=5 && -1+arg2P_7>=1 ], cost: 1+arg2P_7 Computing asymptotic complexity for rule 13 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_7>0 && -arg2P_7==0 ] NO