NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=arg1P0, arg2'=arg2P0, (-arg1P0 == 0 /\ 100-arg2P0 == 0), cost: 1 1: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1P1, arg2'=arg2P1, (-arg2P1+arg2 == 0 /\ -arg1+arg2 > 0 /\ -2-arg1+arg2 > 0 /\ 1+arg1-arg1P1 == 0), cost: 1 2: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1P2, arg2'=arg2P2, (-2 < 0 /\ -1+arg2-arg1P2 == 0 /\ 1-arg2P2+arg2 == 0 /\ 2+arg1-arg2 == 0), cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=arg1P0, arg2'=arg2P0, (-arg1P0 == 0 /\ 100-arg2P0 == 0), cost: 1 New rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=0, arg2'=100, TRUE, cost: 1 Applied preprocessing Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1P1, arg2'=arg2P1, (-arg2P1+arg2 == 0 /\ -arg1+arg2 > 0 /\ -2-arg1+arg2 > 0 /\ 1+arg1-arg1P1 == 0), cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, -2-arg1+arg2 > 0, cost: 1 Applied preprocessing Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1P2, arg2'=arg2P2, (-2 < 0 /\ -1+arg2-arg1P2 == 0 /\ 1-arg2P2+arg2 == 0 /\ 2+arg1-arg2 == 0), cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 Simplified rules Start location: __init 4: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=0, arg2'=100, TRUE, cost: 1 5: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, -2-arg1+arg2 > 0, cost: 1 6: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied acceleration Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, -2-arg1+arg2 > 0, cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1+n1, (n1 >= 0 /\ -1-arg1-n1+arg2 > 0), cost: n1 Applied instantiation Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1+n1, (n1 >= 0 /\ -1-arg1-n1+arg2 > 0), cost: n1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (1 > 0 /\ -2-arg1+arg2 >= 0), cost: -2-arg1+arg2 Applied nonterm Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 New rule: f162_0_main_GE -> [3] : (-2-arg1+arg2 >= 0 /\ 2+arg1-arg2 >= 0), cost: NONTERM Applied acceleration Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2+n3, arg2'=arg2+n3, (-2-arg1+arg2 >= 0 /\ 2+arg1-arg2 >= 0), cost: n3 Applied chaining First rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 Second rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (1 > 0 /\ -2-arg1+arg2 >= 0), cost: -2-arg1+arg2 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 Applied nonterm Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 New rule: f162_0_main_GE -> [3] : (-2-arg1+arg2 >= 0 /\ 2+arg1-arg2 >= 0), cost: NONTERM Applied acceleration Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2+n7, arg2'=arg2+n7, (-2-arg1+arg2 >= 0 /\ 2+arg1-arg2 >= 0), cost: n7 Applied chaining First rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (1 > 0 /\ -2-arg1+arg2 >= 0), cost: -2-arg1+arg2 Second rule: f162_0_main_GE -> [3] : (-2-arg1+arg2 >= 0 /\ 2+arg1-arg2 >= 0), cost: NONTERM New rule: f162_0_main_GE -> [3] : (0 >= 0 /\ 1 > 0 /\ -2-arg1+arg2 >= 0), cost: NONTERM Heuristically decided not to add the following rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2+n7, arg2'=arg2+n7, (-2-arg1+arg2 >= 0 /\ 2+arg1-arg2 >= 0), cost: n7 Applied chaining First rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (1 > 0 /\ -2-arg1+arg2 >= 0), cost: -2-arg1+arg2 Second rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, -2-arg1+arg2 >= 0, cost: -1-arg1+arg2 Applied nonterm Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, -2-arg1+arg2 >= 0, cost: -1-arg1+arg2 New rule: f162_0_main_GE -> [3] : -2-arg1+arg2 >= 0, cost: NONTERM Applied acceleration Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, -2-arg1+arg2 >= 0, cost: -1-arg1+arg2 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2+n9, arg2'=arg2+n9, -2-arg1+arg2 >= 0, cost: n9 Applied chaining First rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 Second rule: f162_0_main_GE -> [3] : -2-arg1+arg2 >= 0, cost: NONTERM New rule: f162_0_main_GE -> [3] : (0 >= 0 /\ 2+arg1-arg2 == 0), cost: NONTERM Applied chaining First rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, 2+arg1-arg2 == 0, cost: 1 Second rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2+n9, arg2'=arg2+n9, -2-arg1+arg2 >= 0, cost: n9 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2+n9, arg2'=1+arg2+n9, (0 >= 0 /\ 2+arg1-arg2 == 0), cost: 1+n9 Applied simplification Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (1 > 0 /\ -2-arg1+arg2 >= 0), cost: -2-arg1+arg2 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, -2-arg1+arg2 >= 0, cost: -2-arg1+arg2 Applied simplification Original rule: f162_0_main_GE -> [3] : (0 >= 0 /\ 1 > 0 /\ -2-arg1+arg2 >= 0), cost: NONTERM New rule: f162_0_main_GE -> [3] : -2-arg1+arg2 >= 0, cost: NONTERM Applied simplification Original rule: f162_0_main_GE -> [3] : (0 >= 0 /\ 2+arg1-arg2 == 0), cost: NONTERM New rule: f162_0_main_GE -> [3] : 2+arg1-arg2 == 0, cost: NONTERM Applied simplification Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2+n9, arg2'=1+arg2+n9, (0 >= 0 /\ 2+arg1-arg2 == 0), cost: 1+n9 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2+n9, arg2'=1+arg2+n9, 2+arg1-arg2 == 0, cost: 1+n9 Applied deletion Removed the following rules: 5 6 Applied deletion Removed the following rules: 8 12 Accelerated simple loops Start location: __init 4: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=0, arg2'=100, TRUE, cost: 1 9: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2+n3, arg2'=arg2+n3, (-2-arg1+arg2 >= 0 /\ 2+arg1-arg2 >= 0), cost: n3 10: f162_0_main_GE -> [3] : (-2-arg1+arg2 >= 0 /\ 2+arg1-arg2 >= 0), cost: NONTERM 14: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2+n9, arg2'=arg2+n9, -2-arg1+arg2 >= 0, cost: n9 16: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, -2-arg1+arg2 >= 0, cost: -2-arg1+arg2 17: f162_0_main_GE -> [3] : -2-arg1+arg2 >= 0, cost: NONTERM 18: f162_0_main_GE -> [3] : 2+arg1-arg2 == 0, cost: NONTERM 19: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2+n9, arg2'=1+arg2+n9, 2+arg1-arg2 == 0, cost: 1+n9 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=0, arg2'=100, TRUE, cost: 1 Second rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2+n9, arg2'=arg2+n9, -2-arg1+arg2 >= 0, cost: n9 New rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=98+n9, arg2'=100+n9, 98 >= 0, cost: 1+n9 Applied chaining First rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=0, arg2'=100, TRUE, cost: 1 Second rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, -2-arg1+arg2 >= 0, cost: -2-arg1+arg2 New rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=98, arg2'=100, 98 >= 0, cost: 99 Applied chaining First rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=0, arg2'=100, TRUE, cost: 1 Second rule: f162_0_main_GE -> [3] : -2-arg1+arg2 >= 0, cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : 98 >= 0, cost: NONTERM Applied deletion Removed the following rules: 9 10 14 16 17 18 19 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=0, arg2'=100, TRUE, cost: 1 20: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=98+n9, arg2'=100+n9, 98 >= 0, cost: 1+n9 21: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=98, arg2'=100, 98 >= 0, cost: 99 22: f1_0_main_ConstantStackPush -> [3] : 98 >= 0, cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 22: f1_0_main_ConstantStackPush -> [3] : 98 >= 0, cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : 98 >= 0, cost: NONTERM New rule: __init -> [3] : 98 >= 0, cost: NONTERM Applied deletion Removed the following rules: 3 22 Eliminated locations on linear paths Start location: __init 23: __init -> [3] : 98 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 23 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: 98 >= 0