NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f32_0_increase_GE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1 1: f32_0_increase_GE -> f91_0_increase_aux_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1<10 && arg1==arg1P_2 ], cost: 1 2: f32_0_increase_GE -> f32_0_increase_GE : arg1'=arg1P_3, arg2'=arg2P_3, [ 0==arg1 && 1==arg1P_3 ], cost: 1 3: f91_0_increase_aux_LE -> f91_0_increase_aux_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>0 && 1+arg1>arg1 && 1+arg1==arg1P_4 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f32_0_increase_GE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f32_0_increase_GE -> f91_0_increase_aux_LE : arg2'=arg2P_2, [ arg1<10 ], cost: 1 2: f32_0_increase_GE -> f32_0_increase_GE : arg1'=1, arg2'=arg2P_3, [ 0==arg1 ], cost: 1 3: f91_0_increase_aux_LE -> f91_0_increase_aux_LE : arg1'=1+arg1, arg2'=arg2P_4, [ arg1>0 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 2: f32_0_increase_GE -> f32_0_increase_GE : arg1'=1, arg2'=arg2P_3, [ 0==arg1 ], cost: 1 Failed to prove monotonicity of the guard of rule 2. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerating simple loops of location 2. Accelerating the following rules: 3: f91_0_increase_aux_LE -> f91_0_increase_aux_LE : arg1'=1+arg1, arg2'=arg2P_4, [ arg1>0 ], cost: 1 Accelerated rule 3 with non-termination, yielding the new rule 5. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 3. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f32_0_increase_GE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f32_0_increase_GE -> f91_0_increase_aux_LE : arg2'=arg2P_2, [ arg1<10 ], cost: 1 2: f32_0_increase_GE -> f32_0_increase_GE : arg1'=1, arg2'=arg2P_3, [ 0==arg1 ], cost: 1 5: f91_0_increase_aux_LE -> [5] : [ arg1>0 ], cost: NONTERM 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f32_0_increase_GE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 6: f1_0_main_Load -> f32_0_increase_GE : arg1'=1, arg2'=arg2P_3, [ arg1>0 && 0==arg2 ], cost: 2 1: f32_0_increase_GE -> f91_0_increase_aux_LE : arg2'=arg2P_2, [ arg1<10 ], cost: 1 7: f32_0_increase_GE -> [5] : [ arg1<10 && arg1>0 ], cost: NONTERM 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f32_0_increase_GE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 6: f1_0_main_Load -> f32_0_increase_GE : arg1'=1, arg2'=arg2P_3, [ arg1>0 && 0==arg2 ], cost: 2 7: f32_0_increase_GE -> [5] : [ arg1<10 && arg1>0 ], cost: NONTERM 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 7: f32_0_increase_GE -> [5] : [ arg1<10 && arg1>0 ], cost: NONTERM 8: __init -> f32_0_increase_GE : arg1'=arg2P_5, arg2'=arg2P_1, [ arg1P_5>0 && arg2P_5>-1 ], cost: 2 9: __init -> f32_0_increase_GE : arg1'=1, arg2'=arg2P_3, [ arg1P_5>0 && 0==arg2P_5 ], cost: 3 Eliminated locations (on tree-shaped paths): Start location: __init 10: __init -> [5] : [ arg1P_5>0 && arg2P_5<10 && arg2P_5>0 ], cost: NONTERM 11: __init -> [5] : [ arg1P_5>0 && 0==arg2P_5 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 10: __init -> [5] : [ arg1P_5>0 && arg2P_5<10 && arg2P_5>0 ], cost: NONTERM 11: __init -> [5] : [ arg1P_5>0 && 0==arg2P_5 ], cost: NONTERM Computing asymptotic complexity for rule 11 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_5>0 && 0==arg2P_5 ] NO