NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=arg1P0, -arg1P0 == 0, cost: 1 1: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1P1, (-20+arg1 < 0 /\ -11+arg1 < 0 /\ 1+arg1-arg1P1 == 0), cost: 1 2: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1P2, (-10+arg1 > 0 /\ arg1-arg1P2 == 0 /\ -20+arg1 < 0), cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=arg1P0, -arg1P0 == 0, cost: 1 New rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 Applied preprocessing Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1P1, (-20+arg1 < 0 /\ -11+arg1 < 0 /\ 1+arg1-arg1P1 == 0), cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 11-arg1 > 0, cost: 1 Applied preprocessing Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1P2, (-10+arg1 > 0 /\ arg1-arg1P2 == 0 /\ -20+arg1 < 0), cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: 1 Simplified rules Start location: __init 4: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 5: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 11-arg1 > 0, cost: 1 6: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Applied acceleration Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 11-arg1 > 0, cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1+n1, (12-arg1-n1 > 0 /\ n1 >= 0), cost: n1 Applied instantiation Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1+n1, (12-arg1-n1 > 0 /\ n1 >= 0), cost: n1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (1 > 0 /\ 11-arg1 >= 0), cost: 11-arg1 Applied nonterm Original rule: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: 1 New rule: f55_0_main_GE -> [3] : (20-arg1 > 0 /\ -10+arg1 > 0), cost: NONTERM Applied acceleration Original rule: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: n3 Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: 1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (1 > 0 /\ 11-arg1 >= 0), cost: 11-arg1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 == 0, cost: 12-arg1 Applied nonterm Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 == 0, cost: 12-arg1 New rule: f55_0_main_GE -> [3] : (11-arg1 >= 0 /\ -11+arg1 >= 0), cost: NONTERM Applied acceleration Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 == 0, cost: 12-arg1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (11-arg1 >= 0 /\ -11+arg1 >= 0), cost: n9 Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (1 > 0 /\ 11-arg1 >= 0), cost: 11-arg1 Second rule: f55_0_main_GE -> [3] : (11-arg1 >= 0 /\ -11+arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (0 >= 0 /\ 1 > 0 /\ 11-arg1 >= 0), cost: NONTERM Heuristically decided not to add the following rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (11-arg1 >= 0 /\ -11+arg1 >= 0), cost: n9 Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (1 > 0 /\ 11-arg1 >= 0), cost: 11-arg1 Second rule: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 <= 0, cost: 12-arg1 Applied nonterm Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 <= 0, cost: 12-arg1 New rule: f55_0_main_GE -> [3] : 11-arg1 >= 0, cost: NONTERM Applied acceleration Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 <= 0, cost: 12-arg1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, 11-arg1 >= 0, cost: n11 Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: 1 Second rule: f55_0_main_GE -> [3] : 11-arg1 >= 0, cost: NONTERM New rule: f55_0_main_GE -> [3] : (20-arg1 > 0 /\ -10+arg1 > 0 /\ 11-arg1 >= 0), cost: NONTERM Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: 1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, 11-arg1 >= 0, cost: n11 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (20-arg1 > 0 /\ -10+arg1 > 0 /\ 11-arg1 >= 0), cost: 1+n11 Applied simplification Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (1 > 0 /\ 11-arg1 >= 0), cost: 11-arg1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 <= 0, cost: 11-arg1 Applied simplification Original rule: f55_0_main_GE -> [3] : (11-arg1 >= 0 /\ -11+arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (-11+arg1 <= 0 /\ -11+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (0 >= 0 /\ 1 > 0 /\ 11-arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : -11+arg1 <= 0, cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : 11-arg1 >= 0, cost: NONTERM New rule: f55_0_main_GE -> [3] : -11+arg1 <= 0, cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (20-arg1 > 0 /\ -10+arg1 > 0 /\ 11-arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (-10+arg1 > 0 /\ -11+arg1 <= 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, 11-arg1 >= 0, cost: n11 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 <= 0, cost: n11 Applied simplification Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (20-arg1 > 0 /\ -10+arg1 > 0 /\ 11-arg1 >= 0), cost: 1+n11 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (-10+arg1 > 0 /\ -11+arg1 <= 0), cost: 1+n11 Applied deletion Removed the following rules: 5 6 Applied deletion Removed the following rules: 18 Accelerated simple loops Start location: __init 4: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 8: f55_0_main_GE -> [3] : (20-arg1 > 0 /\ -10+arg1 > 0), cost: NONTERM 9: f55_0_main_GE -> f55_0_main_GE : (20-arg1 > 0 /\ -10+arg1 > 0), cost: n3 16: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 <= 0, cost: 11-arg1 17: f55_0_main_GE -> [3] : (-11+arg1 <= 0 /\ -11+arg1 >= 0), cost: NONTERM 19: f55_0_main_GE -> [3] : -11+arg1 <= 0, cost: NONTERM 20: f55_0_main_GE -> [3] : (-10+arg1 > 0 /\ -11+arg1 <= 0), cost: NONTERM 21: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 <= 0, cost: n11 22: f55_0_main_GE -> f55_0_main_GE : arg1'=11, (-10+arg1 > 0 /\ -11+arg1 <= 0), cost: 1+n11 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 <= 0, cost: 11-arg1 New rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=11, -11 <= 0, cost: 12 Applied chaining First rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 Second rule: f55_0_main_GE -> [3] : -11+arg1 <= 0, cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : -11 <= 0, cost: NONTERM Applied chaining First rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=11, -11+arg1 <= 0, cost: n11 New rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=11, -11 <= 0, cost: 1+n11 Applied deletion Removed the following rules: 8 9 16 17 19 20 21 22 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 23: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=11, -11 <= 0, cost: 12 24: f1_0_main_ConstantStackPush -> [3] : -11 <= 0, cost: NONTERM 25: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=11, -11 <= 0, cost: 1+n11 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 24: f1_0_main_ConstantStackPush -> [3] : -11 <= 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] : -11 <= 0, cost: NONTERM New rule: __init -> [3] : -11 <= 0, cost: NONTERM Applied deletion Removed the following rules: 3 24 Eliminated locations on linear paths Start location: __init 26: __init -> [3] : -11 <= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 26 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -11 <= 0