NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=arg1P0, -arg1P0 == 0, cost: 1 1: f41_0_main_GE -> f41_0_main_GE : arg1'=arg1P1, (51-arg1P1 == 0 /\ -50+arg1 < 0), cost: 1 2: f41_0_main_GE -> f41_0_main_GE : arg1'=arg1P2, (49-arg1P2 == 0 /\ -49+arg1 > 0), cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=arg1P0, -arg1P0 == 0, cost: 1 New rule: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=0, TRUE, cost: 1 Applied preprocessing Original rule: f41_0_main_GE -> f41_0_main_GE : arg1'=arg1P1, (51-arg1P1 == 0 /\ -50+arg1 < 0), cost: 1 New rule: f41_0_main_GE -> f41_0_main_GE : arg1'=51, 50-arg1 > 0, cost: 1 Applied preprocessing Original rule: f41_0_main_GE -> f41_0_main_GE : arg1'=arg1P2, (49-arg1P2 == 0 /\ -49+arg1 > 0), cost: 1 New rule: f41_0_main_GE -> f41_0_main_GE : arg1'=49, -49+arg1 > 0, cost: 1 Simplified rules Start location: __init 4: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=0, TRUE, cost: 1 5: f41_0_main_GE -> f41_0_main_GE : arg1'=51, 50-arg1 > 0, cost: 1 6: f41_0_main_GE -> f41_0_main_GE : arg1'=49, -49+arg1 > 0, cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f41_0_main_GE -> f41_0_main_GE : arg1'=49, -49+arg1 > 0, cost: 1 Second rule: f41_0_main_GE -> f41_0_main_GE : arg1'=51, 50-arg1 > 0, cost: 1 New rule: f41_0_main_GE -> f41_0_main_GE : arg1'=51, -49+arg1 > 0, cost: 2 Applied nonterm Original rule: f41_0_main_GE -> f41_0_main_GE : arg1'=51, -49+arg1 > 0, cost: 2 New rule: f41_0_main_GE -> [3] : (-1+n1 >= 0 /\ -49+arg1 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_mcDjcD.txt Applied chaining First rule: f41_0_main_GE -> f41_0_main_GE : arg1'=51, 50-arg1 > 0, cost: 1 Second rule: f41_0_main_GE -> [3] : (-1+n1 >= 0 /\ -49+arg1 > 0), cost: NONTERM New rule: f41_0_main_GE -> [3] : (50-arg1 > 0 /\ 2 > 0 /\ -1+n1 >= 0), cost: NONTERM Applied chaining First rule: f41_0_main_GE -> f41_0_main_GE : arg1'=51, 50-arg1 > 0, cost: 1 Second rule: f41_0_main_GE -> f41_0_main_GE : arg1'=49, -49+arg1 > 0, cost: 1 New rule: f41_0_main_GE -> f41_0_main_GE : arg1'=49, 50-arg1 > 0, cost: 2 Applied nonterm Original rule: f41_0_main_GE -> f41_0_main_GE : arg1'=49, 50-arg1 > 0, cost: 2 New rule: f41_0_main_GE -> [3] : (-1+n2 >= 0 /\ 50-arg1 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_LnaOAN.txt Applied chaining First rule: f41_0_main_GE -> f41_0_main_GE : arg1'=49, -49+arg1 > 0, cost: 1 Second rule: f41_0_main_GE -> [3] : (-1+n2 >= 0 /\ 50-arg1 > 0), cost: NONTERM New rule: f41_0_main_GE -> [3] : (-1+n2 >= 0 /\ 1 > 0 /\ -49+arg1 > 0), cost: NONTERM Applied simplification Original rule: f41_0_main_GE -> [3] : (50-arg1 > 0 /\ 2 > 0 /\ -1+n1 >= 0), cost: NONTERM New rule: f41_0_main_GE -> [3] : (50-arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM Applied simplification Original rule: f41_0_main_GE -> [3] : (-1+n2 >= 0 /\ 1 > 0 /\ -49+arg1 > 0), cost: NONTERM New rule: f41_0_main_GE -> [3] : (-1+n2 >= 0 /\ -49+arg1 > 0), cost: NONTERM Accelerated simple loops Start location: __init 4: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=0, TRUE, cost: 1 5: f41_0_main_GE -> f41_0_main_GE : arg1'=51, 50-arg1 > 0, cost: 1 6: f41_0_main_GE -> f41_0_main_GE : arg1'=49, -49+arg1 > 0, cost: 1 7: f41_0_main_GE -> [3] : (-1+n1 >= 0 /\ -49+arg1 > 0), cost: NONTERM 9: f41_0_main_GE -> [3] : (-1+n2 >= 0 /\ 50-arg1 > 0), cost: NONTERM 11: f41_0_main_GE -> [3] : (50-arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM 12: f41_0_main_GE -> [3] : (-1+n2 >= 0 /\ -49+arg1 > 0), cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=0, TRUE, cost: 1 Second rule: f41_0_main_GE -> f41_0_main_GE : arg1'=51, 50-arg1 > 0, cost: 1 New rule: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=51, 50 > 0, cost: 2 Applied chaining First rule: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=0, TRUE, cost: 1 Second rule: f41_0_main_GE -> [3] : (-1+n2 >= 0 /\ 50-arg1 > 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : 50 > 0, cost: NONTERM Applied chaining First rule: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=0, TRUE, cost: 1 Second rule: f41_0_main_GE -> [3] : (50-arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : 50 > 0, cost: NONTERM Applied deletion Removed the following rules: 5 6 7 9 11 12 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=0, TRUE, cost: 1 13: f1_0_main_ConstantStackPush -> f41_0_main_GE : arg1'=51, 50 > 0, cost: 2 14: f1_0_main_ConstantStackPush -> [3] : 50 > 0, cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 14: f1_0_main_ConstantStackPush -> [3] : 50 > 0, cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : 50 > 0, cost: NONTERM New rule: __init -> [3] : 50 > 0, cost: NONTERM Applied deletion Removed the following rules: 3 14 Eliminated locations on linear paths Start location: __init 15: __init -> [3] : 50 > 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 15 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: 50 > 0