NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_ConstantStackPush -> f124_0_main_GT : arg1'=arg1P_1, arg2'=arg2P_1, [ 0==arg1P_1 && 0==arg2P_1 ], cost: 1 1: f124_0_main_GT -> f124_0_main_GT : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>-1 && arg1>-1 && arg2>=arg1 && -arg1+arg2>=1 && 1+arg1==arg1P_2 && arg2==arg2P_2 ], cost: 1 2: f124_0_main_GT -> f124_0_main_GT : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>-1 && -arg1+arg2==0 && arg2>-1 && arg2>=arg1 && 1+arg1==arg1P_3 && 2+arg2==arg2P_3 ], cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_ConstantStackPush -> f124_0_main_GT : arg1'=0, arg2'=0, [], cost: 1 1: f124_0_main_GT -> f124_0_main_GT : arg1'=1+arg1, [ arg1>-1 && -arg1+arg2>=1 ], cost: 1 2: f124_0_main_GT -> f124_0_main_GT : arg1'=1+arg1, arg2'=2+arg2, [ arg1>-1 && -arg1+arg2==0 ], cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f124_0_main_GT -> f124_0_main_GT : arg1'=1+arg1, [ arg1>-1 && -arg1+arg2>=1 ], cost: 1 2: f124_0_main_GT -> f124_0_main_GT : arg1'=1+arg1, arg2'=2+arg2, [ arg1>-1 && -arg1+arg2==0 ], cost: 1 Accelerated rule 1 with metering function -arg1+arg2, yielding the new rule 4. Accelerated rule 2 with metering function 1+arg1-arg2, yielding the new rule 5. Nested simple loops 2 (outer loop) and 4 (inner loop) with NONTERM, resulting in the new rules: 6, 7. Nested simple loops 1 (outer loop) and 5 (inner loop) with NONTERM, resulting in the new rules: 8, 9. Removing the simple loops: 1 2. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_ConstantStackPush -> f124_0_main_GT : arg1'=0, arg2'=0, [], cost: 1 4: f124_0_main_GT -> f124_0_main_GT : arg1'=arg2, [ arg1>-1 && -arg1+arg2>=1 ], cost: -arg1+arg2 5: f124_0_main_GT -> f124_0_main_GT : arg1'=1+2*arg1-arg2, arg2'=2+2*arg1-arg2, [ arg1>-1 && -arg1+arg2==0 ], cost: 1+arg1-arg2 6: f124_0_main_GT -> [3] : [ arg1>-1 && -arg1+arg2>=1 && arg2>-1 ], cost: NONTERM 7: f124_0_main_GT -> [3] : arg1'=1+arg1, arg2'=2+arg2, [ arg1>-1 && -arg1+arg2==0 && 2+arg2>-1 ], cost: NONTERM 8: f124_0_main_GT -> [3] : [ arg1>-1 && -arg1+arg2==0 && 1+2*arg1-arg2>-1 ], cost: NONTERM 9: f124_0_main_GT -> [3] : arg1'=1+arg1, [ arg1>-1 && -1-arg1+arg2==0 && 3+2*arg1-arg2>-1 ], cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_ConstantStackPush -> f124_0_main_GT : arg1'=0, arg2'=0, [], cost: 1 10: f1_0_main_ConstantStackPush -> f124_0_main_GT : arg1'=1, arg2'=2, [], cost: 2 11: f1_0_main_ConstantStackPush -> [3] : arg1'=1, arg2'=2, [], cost: NONTERM 12: f1_0_main_ConstantStackPush -> [3] : arg1'=0, arg2'=0, [], cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 11: f1_0_main_ConstantStackPush -> [3] : arg1'=1, arg2'=2, [], cost: NONTERM 12: f1_0_main_ConstantStackPush -> [3] : arg1'=0, arg2'=0, [], cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 13: __init -> [3] : arg1'=1, arg2'=2, [], cost: NONTERM 14: __init -> [3] : arg1'=0, arg2'=0, [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 14: __init -> [3] : arg1'=0, arg2'=0, [], cost: NONTERM Computing asymptotic complexity for rule 14 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