NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f104_0_loop_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1 1: f104_0_loop_EQ -> f104_0_loop_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1<0 && arg1<5 && 1-arg1==arg1P_2 ], cost: 1 2: f104_0_loop_EQ -> f104_0_loop_EQ : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>0 && arg1<5 && 1-arg1==arg1P_3 ], cost: 1 3: f104_0_loop_EQ -> f104_0_loop_EQ : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>4 && 2>-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 -> f104_0_loop_EQ : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f104_0_loop_EQ -> f104_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P_2, [ arg1<0 ], cost: 1 2: f104_0_loop_EQ -> f104_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P_3, [ arg1>0 && arg1<5 ], cost: 1 3: f104_0_loop_EQ -> f104_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P_4, [ arg1>4 ], 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: 1: f104_0_loop_EQ -> f104_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P_2, [ arg1<0 ], cost: 1 2: f104_0_loop_EQ -> f104_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P_3, [ arg1>0 && arg1<5 ], cost: 1 3: f104_0_loop_EQ -> f104_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P_4, [ arg1>4 ], cost: 1 Failed to prove monotonicity of the guard of rule 1. Failed to prove monotonicity of the guard of rule 2. Failed to prove monotonicity of the guard of rule 3. [accelerate] Nesting with 3 inner and 3 outer candidates Nested simple loops 2 (outer loop) and 1 (inner loop) with Rule(1 | arg1<0, 1-arg1<5, | NONTERM || 3 | ), resulting in the new rules: 5, 6. Nested simple loops 3 (outer loop) and 1 (inner loop) with Rule(1 | 1-arg1>4, | NONTERM || 3 | ), resulting in the new rules: 7, 8. Nested simple loops 1 (outer loop) and 2 (inner loop) with Rule(1 | arg1<5, 1-arg1<0, | NONTERM || 3 | ), resulting in the new rules: 9, 10. Nested simple loops 1 (outer loop) and 3 (inner loop) with Rule(1 | arg1>4, | NONTERM || 3 | ), resulting in the new rules: 11, 12. Removing the simple loops: 1 2 3. Also removing duplicate rules: 5 6 7 8. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f104_0_loop_EQ : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 9: f104_0_loop_EQ -> [3] : [ arg1<5 && 1-arg1<0 ], cost: NONTERM 10: f104_0_loop_EQ -> [3] : [ arg1<0 && 1-arg1<5 ], cost: NONTERM 11: f104_0_loop_EQ -> [3] : [ arg1>4 ], cost: NONTERM 12: f104_0_loop_EQ -> [3] : [ 1-arg1>4 ], 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 -> f104_0_loop_EQ : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 13: f1_0_main_Load -> [3] : [ arg1>0 && arg2<5 && 1-arg2<0 ], cost: NONTERM 14: f1_0_main_Load -> [3] : [ arg1>0 && arg2>4 ], 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 13: f1_0_main_Load -> [3] : [ arg1>0 && arg2<5 && 1-arg2<0 ], cost: NONTERM 14: f1_0_main_Load -> [3] : [ arg1>0 && arg2>4 ], 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 15: __init -> [3] : [ arg1P_5>0 && arg2P_5<5 && 1-arg2P_5<0 ], cost: NONTERM 16: __init -> [3] : [ arg1P_5>0 && arg2P_5>4 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 15: __init -> [3] : [ arg1P_5>0 && arg2P_5<5 && 1-arg2P_5<0 ], cost: NONTERM 16: __init -> [3] : [ arg1P_5>0 && arg2P_5>4 ], cost: NONTERM Computing asymptotic complexity for rule 16 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 && arg2P_5>4 ] NO