NO Initial ITS Start location: __init Program variables: arg1 arg2 0: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=arg1p1, arg2'=arg2p1, (100-arg2p1 == 0 /\ -arg1p1 == 0), cost: 1 1: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1p2, arg2'=arg2p2, (-2-arg1+arg2 > 0 /\ -arg1+arg2 > 0 /\ -arg2p2+arg2 == 0 /\ 1+arg1-arg1p2 == 0), cost: 1 2: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1p3, arg2'=arg2p3, (-1-arg1p3+arg2 == 0 /\ 2+arg1-arg2 == 0 /\ -2 < 0 /\ 1+arg2-arg2p3 == 0), cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1p4, arg2'=arg2p4, T, cost: 1 Chained Linear Paths Start location: __init Program variables: arg1 arg2 1: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1p2, arg2'=arg2p2, (-2-arg1+arg2 > 0 /\ -arg1+arg2 > 0 /\ -arg2p2+arg2 == 0 /\ 1+arg1-arg1p2 == 0), cost: 1 2: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1p3, arg2'=arg2p3, (-1-arg1p3+arg2 == 0 /\ 2+arg1-arg2 == 0 /\ -2 < 0 /\ 1+arg2-arg2p3 == 0), cost: 1 4: __init -> f162_0_main_GE : arg1'=arg1p1, arg2'=arg2p1, (100-arg2p1 == 0 /\ -arg1p1 == 0), cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg1'=arg1p4, arg2'=arg2p4, T, cost: 1 Second rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg1'=arg1p1, arg2'=arg2p1, (100-arg2p1 == 0 /\ -arg1p1 == 0), cost: 1 New rule: __init -> f162_0_main_GE : arg1'=arg1p1, arg2'=arg2p1, (100-arg2p1 == 0 /\ -arg1p1 == 0), cost: 1 Applied deletion Removed the following rules: 0 3 Simplified Transitions Start location: __init Program variables: arg1 arg2 5: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, (-2-arg1+arg2 > 0 /\ -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 7: __init -> f162_0_main_GE : arg1'=0, arg2'=100, T, cost: 1 Propagated Equalities Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1p2, arg2'=arg2p2, (-2-arg1+arg2 > 0 /\ -arg1+arg2 > 0 /\ -arg2p2+arg2 == 0 /\ 1+arg1-arg1p2 == 0), cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, arg2'=arg2, (0 == 0 /\ -2-arg1+arg2 > 0 /\ -arg1+arg2 > 0), cost: 1 propagated equality arg2p2 = arg2 propagated equality arg1p2 = 1+arg1 Simplified Guard Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, arg2'=arg2, (0 == 0 /\ -2-arg1+arg2 > 0 /\ -arg1+arg2 > 0), cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, arg2'=arg2, (-2-arg1+arg2 > 0 /\ -arg1+arg2 > 0), cost: 1 Removed Trivial Updates Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, arg2'=arg2, (-2-arg1+arg2 > 0 /\ -arg1+arg2 > 0), cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, (-2-arg1+arg2 > 0 /\ -arg1+arg2 > 0), cost: 1 Propagated Equalities Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1p3, arg2'=arg2p3, (-1-arg1p3+arg2 == 0 /\ 2+arg1-arg2 == 0 /\ -2 < 0 /\ 1+arg2-arg2p3 == 0), cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, (0 == 0 /\ 2+arg1-arg2 == 0 /\ -2 < 0), cost: 1 propagated equality arg1p3 = -1+arg2 propagated equality arg2p3 = 1+arg2 Simplified Guard Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-1+arg2, arg2'=1+arg2, (0 == 0 /\ 2+arg1-arg2 == 0 /\ -2 < 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 Propagated Equalities Original rule: __init -> f162_0_main_GE : arg1'=arg1p1, arg2'=arg2p1, (100-arg2p1 == 0 /\ -arg1p1 == 0), cost: 1 New rule: __init -> f162_0_main_GE : arg1'=0, arg2'=100, 0 == 0, cost: 1 propagated equality arg2p1 = 100 propagated equality arg1p1 = 0 Simplified Guard Original rule: __init -> f162_0_main_GE : arg1'=0, arg2'=100, 0 == 0, cost: 1 New rule: __init -> f162_0_main_GE : arg1'=0, arg2'=100, T, cost: 1 Step with 7 Trace 7[T] Blocked [{}, {}] Step with 5 Trace 7[T], 5[(-2-arg1+arg2 > 0 /\ -arg1+arg2 > 0)] Blocked [{}, {}, {}] Accelerate Start location: __init Program variables: arg1 arg2 5: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, (-2-arg1+arg2 > 0 /\ -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 8: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1+n, (-1+n >= 0 /\ -arg1+arg2 > 0 /\ -1-arg1-n+arg2 > 0), cost: 1 7: __init -> f162_0_main_GE : arg1'=0, arg2'=100, T, cost: 1 Loop Acceleration Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, (-2-arg1+arg2 > 0 /\ -arg1+arg2 > 0), cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1+n, (-1+n >= 0 /\ -arg1+arg2 > 0 /\ -1-arg1-n+arg2 > 0), cost: 1 -2-arg1+arg2 > 0 [0]: montonic decrease yields -1-arg1-n+arg2 > 0 -2-arg1+arg2 > 0 [1]: eventual increase yields (1 <= 0 /\ -2-arg1+arg2 > 0) -arg1+arg2 > 0 [0]: monotonic increase yields -arg1+arg2 > 0, dependencies: -2-arg1+arg2 > 0 Replacement map: {-2-arg1+arg2 > 0 -> -1-arg1-n+arg2 > 0, -arg1+arg2 > 0 -> -arg1+arg2 > 0} Trace 7[T], 8[(-1+n >= 0 /\ -arg1+arg2 > 0 /\ -1-arg1-n+arg2 > 0)] Blocked [{}, {}, {5[T], 8[T]}] Step with 6 Trace 7[T], 8[(-1+n >= 0 /\ -arg1+arg2 > 0 /\ -1-arg1-n+arg2 > 0)], 6[(2+arg1-arg2 == 0)] Blocked [{}, {}, {5[T], 8[T]}, {}] Nonterm Start location: __init Program variables: arg1 arg2 5: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, (-2-arg1+arg2 > 0 /\ -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 8: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1+n, (-1+n >= 0 /\ -arg1+arg2 > 0 /\ -1-arg1-n+arg2 > 0), cost: 1 9: f162_0_main_GE -> LoAT_sink : (2+arg1-arg2 >= 0 /\ -2-arg1+arg2 >= 0 /\ -1+n2 >= 0), cost: NONTERM 10: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2+n2, arg2'=arg2+n2, (2+arg1-arg2 >= 0 /\ -2-arg1+arg2 >= 0 /\ -1+n2 >= 0), cost: 1 7: __init -> f162_0_main_GE : arg1'=0, arg2'=100, T, cost: 1 Certificate of Non-Termination 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 -> LoAT_sink : (2+arg1-arg2 >= 0 /\ -2-arg1+arg2 >= 0 /\ -1+n2 >= 0), cost: NONTERM 2+arg1-arg2 >= 0 [0]: monotonic increase yields 2+arg1-arg2 >= 0 -2-arg1+arg2 >= 0 [0]: monotonic increase yields -2-arg1+arg2 >= 0 Replacement map: {2+arg1-arg2 >= 0 -> 2+arg1-arg2 >= 0, -2-arg1+arg2 >= 0 -> -2-arg1+arg2 >= 0} Loop 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+n2, arg2'=arg2+n2, (2+arg1-arg2 >= 0 /\ -2-arg1+arg2 >= 0 /\ -1+n2 >= 0), cost: 1 2+arg1-arg2 >= 0 [0]: monotonic increase yields 2+arg1-arg2 >= 0 -2-arg1+arg2 >= 0 [0]: monotonic increase yields -2-arg1+arg2 >= 0 Replacement map: {2+arg1-arg2 >= 0 -> 2+arg1-arg2 >= 0, -2-arg1+arg2 >= 0 -> -2-arg1+arg2 >= 0} Step with 9 Trace 7[T], 8[(-1+n >= 0 /\ -arg1+arg2 > 0 /\ -1-arg1-n+arg2 > 0)], 9[(2+arg1-arg2 >= 0 /\ -2-arg1+arg2 >= 0 /\ -1+n2 >= 0)] Blocked [{}, {}, {5[T], 8[T]}, {9[T]}] Refute Counterexample [ arg1=0 arg2=100 ] 7 [ arg1=98 arg2=100 ] 8 [ arg1=arg1 arg2=arg2 ] 9 NO Build SHA: a05f16bf13df659c382799650051f91bf6828c7b