NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f51_0_increase_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1 1: f51_0_increase_GE -> f83_0_increase_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1<10 && arg1==arg1P_2 && arg1==arg2P_2 && arg1==arg3P_2 ], cost: 1 2: f83_0_increase_LE -> f51_0_increase_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2<6 && arg2==arg3 && 1+arg1==arg1P_3 ], cost: 1 3: f83_0_increase_LE -> f83_0_increase_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2>5 && arg2==arg3 && arg1==arg1P_4 && 1+arg2==arg2P_4 && 1+arg2==arg3P_4 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_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, arg3'=arg3P_5, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f51_0_increase_GE : arg1'=arg2, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f51_0_increase_GE -> f83_0_increase_LE : arg2'=arg1, arg3'=arg1, [ arg1<10 ], cost: 1 2: f83_0_increase_LE -> f51_0_increase_GE : arg1'=1+arg1, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2<6 && arg2==arg3 ], cost: 1 3: f83_0_increase_LE -> f83_0_increase_LE : arg2'=1+arg2, arg3'=1+arg2, [ arg2>5 && arg2==arg3 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 3: f83_0_increase_LE -> f83_0_increase_LE : arg2'=1+arg2, arg3'=1+arg2, [ arg2>5 && arg2==arg3 ], 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 -> f51_0_increase_GE : arg1'=arg2, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f51_0_increase_GE -> f83_0_increase_LE : arg2'=arg1, arg3'=arg1, [ arg1<10 ], cost: 1 2: f83_0_increase_LE -> f51_0_increase_GE : arg1'=1+arg1, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2<6 && arg2==arg3 ], cost: 1 5: f83_0_increase_LE -> [4] : [ arg2>5 && arg2==arg3 ], cost: NONTERM 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f51_0_increase_GE : arg1'=arg2, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f51_0_increase_GE -> f83_0_increase_LE : arg2'=arg1, arg3'=arg1, [ arg1<10 ], cost: 1 6: f51_0_increase_GE -> [4] : [ arg1<10 && arg1>5 ], cost: NONTERM 2: f83_0_increase_LE -> f51_0_increase_GE : arg1'=1+arg1, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2<6 && arg2==arg3 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 6: f51_0_increase_GE -> [4] : [ arg1<10 && arg1>5 ], cost: NONTERM 8: f51_0_increase_GE -> f51_0_increase_GE : arg1'=1+arg1, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1<6 ], cost: 2 7: __init -> f51_0_increase_GE : arg1'=arg2P_5, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_5>0 && arg2P_5>-1 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 8: f51_0_increase_GE -> f51_0_increase_GE : arg1'=1+arg1, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1<6 ], cost: 2 Accelerated rule 8 with backward acceleration, yielding the new rule 9. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 8. Accelerated all simple loops using metering functions (where possible): Start location: __init 6: f51_0_increase_GE -> [4] : [ arg1<10 && arg1>5 ], cost: NONTERM 9: f51_0_increase_GE -> f51_0_increase_GE : arg1'=6, arg2'=arg2P_3, arg3'=arg3P_3, [ 6-arg1>=1 ], cost: 12-2*arg1 7: __init -> f51_0_increase_GE : arg1'=arg2P_5, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_5>0 && arg2P_5>-1 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 6: f51_0_increase_GE -> [4] : [ arg1<10 && arg1>5 ], cost: NONTERM 7: __init -> f51_0_increase_GE : arg1'=arg2P_5, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_5>0 && arg2P_5>-1 ], cost: 2 10: __init -> f51_0_increase_GE : arg1'=6, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2P_5>-1 && 6-arg2P_5>=1 ], cost: 14-2*arg2P_5 Eliminated locations (on tree-shaped paths): Start location: __init 11: __init -> [4] : [ arg1P_5>0 && arg2P_5<10 && arg2P_5>5 ], cost: NONTERM 12: __init -> [4] : [ arg2P_5>-1 && 6-arg2P_5>=1 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 11: __init -> [4] : [ arg1P_5>0 && arg2P_5<10 && arg2P_5>5 ], cost: NONTERM 12: __init -> [4] : [ arg2P_5>-1 && 6-arg2P_5>=1 ], cost: NONTERM Computing asymptotic complexity for rule 12 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: [ arg2P_5>-1 && 6-arg2P_5>=1 ] NO