NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f142_0_loop_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && 5==arg1P_1 && arg2==arg2P_1 ], cost: 1 1: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2<0 && arg2<-arg1 && 1+arg1==arg1P_2 && 1-arg2==arg2P_2 ], cost: 1 2: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2>0 && arg2<-arg1 && 1+arg1==arg1P_3 && 1-arg2==arg2P_3 ], cost: 1 3: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2<=arg1 && arg2<0 && arg2>=-arg1 && 1+arg1==arg1P_4 && 0==arg2P_4 ], cost: 1 4: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2<=arg1 && arg2>0 && arg2>=-arg1 && 1+arg1==arg1P_5 && 0==arg2P_5 ], cost: 1 5: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2>arg1 && arg2<0 && arg2>=-arg1 && 1+arg1==arg1P_6 && -1-arg2==arg2P_6 ], cost: 1 6: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>arg1 && arg2>0 && arg2>=-arg1 && 1+arg1==arg1P_7 && -1-arg2==arg2P_7 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Removed rules with unsatisfiable guard: Start location: __init 0: f1_0_main_Load -> f142_0_loop_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && 5==arg1P_1 && arg2==arg2P_1 ], cost: 1 1: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2<0 && arg2<-arg1 && 1+arg1==arg1P_2 && 1-arg2==arg2P_2 ], cost: 1 2: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2>0 && arg2<-arg1 && 1+arg1==arg1P_3 && 1-arg2==arg2P_3 ], cost: 1 3: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2<=arg1 && arg2<0 && arg2>=-arg1 && 1+arg1==arg1P_4 && 0==arg2P_4 ], cost: 1 4: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2<=arg1 && arg2>0 && arg2>=-arg1 && 1+arg1==arg1P_5 && 0==arg2P_5 ], cost: 1 6: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>arg1 && arg2>0 && arg2>=-arg1 && 1+arg1==arg1P_7 && -1-arg2==arg2P_7 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, [ arg1>0 && arg2>-1 ], cost: 1 1: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, [ arg2<0 && arg2<-arg1 ], cost: 1 2: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, [ arg2>0 && arg2<-arg1 ], cost: 1 3: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, [ arg2<0 && arg2>=-arg1 ], cost: 1 4: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, [ arg2<=arg1 && arg2>0 ], cost: 1 6: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, [ arg2>arg1 && arg2>0 && arg2>=-arg1 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, [ arg2<0 && arg2<-arg1 ], cost: 1 2: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, [ arg2>0 && arg2<-arg1 ], cost: 1 3: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, [ arg2<0 && arg2>=-arg1 ], cost: 1 4: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, [ arg2<=arg1 && arg2>0 ], cost: 1 6: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, [ arg2>arg1 && arg2>0 && arg2>=-arg1 ], 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. Failed to prove monotonicity of the guard of rule 4. Failed to prove monotonicity of the guard of rule 6. [accelerate] Nesting with 5 inner and 5 outer candidates Nested simple loops 2 (outer loop) and 1 (inner loop) with Rule(1 | arg2<0, arg2<-arg1, k>=0, 1-arg2<1-2*k-arg1, | 2*k || 1 | 0=2*k+arg1, ), resulting in the new rules: 8, 9. Nested simple loops 6 (outer loop) and 1 (inner loop) with Rule(1 | arg2<0, arg2<-arg1, 1-arg2>=-1-arg1, | NONTERM || 3 | ), resulting in the new rules: 10, 11. Nested simple loops 1 (outer loop) and 2 (inner loop) with Rule(1 | 1-arg2<0, 1-arg2<-1-arg1, k_1>=0, arg2<2-2*k_1-arg1, | 2*k_1 || 1 | 0=2*k_1+arg1, ), resulting in the new rules: 12, 13. Nested simple loops 1 (outer loop) and 6 (inner loop) with Rule(1 | arg2>arg1, arg2>0, arg2>=-arg1, | NONTERM || 3 | ), resulting in the new rules: 14, 15. Removing the simple loops: 1 2 6. Also removing duplicate rules: 10 11. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, [ arg1>0 && arg2>-1 ], cost: 1 3: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, [ arg2<0 && arg2>=-arg1 ], cost: 1 4: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, [ arg2<=arg1 && arg2>0 ], cost: 1 8: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=2*k+arg1, [ arg2<0 && arg2<-arg1 && k>=0 && 1-arg2<1-2*k-arg1 ], cost: 2*k 9: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+2*k+arg1, arg2'=1-arg2, [ arg2<-arg1 && 1-arg2<0 && 1-arg2<-1-arg1 && k>=0 && arg2<-2*k-arg1 ], cost: 1+2*k 12: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=2*k_1+arg1, [ 1-arg2<0 && 1-arg2<-1-arg1 && k_1>=0 && arg2<2-2*k_1-arg1 ], cost: 2*k_1 13: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+2*k_1+arg1, arg2'=1-arg2, [ arg2<0 && arg2<-2-arg1 && k_1>=0 && 1-arg2<1-2*k_1-arg1 ], cost: 1+2*k_1 14: f142_0_loop_EQ -> [3] : [ arg2>arg1 && arg2>0 && arg2>=-arg1 ], cost: NONTERM 15: f142_0_loop_EQ -> [3] : [ arg2<0 && arg2<-arg1 && 1-arg2>=-1-arg1 ], cost: NONTERM 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, [ arg1>0 && arg2>-1 ], cost: 1 16: f1_0_main_Load -> f142_0_loop_EQ : arg1'=6, arg2'=0, [ arg1>0 && arg2<=5 && arg2>0 ], cost: 2 17: f1_0_main_Load -> [3] : [ arg1>0 && arg2>5 ], cost: NONTERM 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 17: f1_0_main_Load -> [3] : [ arg1>0 && arg2>5 ], cost: NONTERM 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 18: __init -> [3] : [ arg1P_8>0 && arg2P_8>5 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 18: __init -> [3] : [ arg1P_8>0 && arg2P_8>5 ], cost: NONTERM Computing asymptotic complexity for rule 18 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_8>0 && arg2P_8>5 ] NO