NO Initial ITS Start location: __init Program variables: arg1 arg2 0: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=arg1p1, arg2'=arg2p1, (-arg1p1-arg2 == 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 1 1: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1p2, arg2'=arg2p2, (-2+arg1 < 0 /\ -1-arg1p2+arg1 == 0 /\ -1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1p3, arg2'=arg2p3, T, cost: 1 Chained Linear Paths Start location: __init Program variables: arg1 arg2 1: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1p2, arg2'=arg2p2, (-2+arg1 < 0 /\ -1-arg1p2+arg1 == 0 /\ -1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 3: __init -> f33_0_loop_GE : arg1'=arg1p1, arg2'=arg2p1, (1+arg2p3 > 0 /\ arg1p3 > 0 /\ -arg1p1-arg2p3 == 0), cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg1'=arg1p3, arg2'=arg2p3, T, cost: 1 Second rule: f1_0_main_ConstantStackPush -> f33_0_loop_GE : arg1'=arg1p1, arg2'=arg2p1, (-arg1p1-arg2 == 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 1 New rule: __init -> f33_0_loop_GE : arg1'=arg1p1, arg2'=arg2p1, (1+arg2p3 > 0 /\ arg1p3 > 0 /\ -arg1p1-arg2p3 == 0), cost: 1 Applied deletion Removed the following rules: 0 2 Simplified Transitions Start location: __init Program variables: arg1 arg2 4: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-1+arg1, arg2'=arg2p2, (-2+arg1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 5: __init -> f33_0_loop_GE : arg1'=-arg2p3, arg2'=arg2p1, (1+arg2p3 > 0), cost: 1 Propagated Equalities Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=arg1p2, arg2'=arg2p2, (-2+arg1 < 0 /\ -1-arg1p2+arg1 == 0 /\ -1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-1+arg1, arg2'=arg2p2, (0 == 0 /\ -2+arg1 < 0 /\ -1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 propagated equality arg1p2 = -1+arg1 Simplified Guard Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-1+arg1, arg2'=arg2p2, (0 == 0 /\ -2+arg1 < 0 /\ -1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-1+arg1, arg2'=arg2p2, (-2+arg1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 Propagated Equalities Original rule: __init -> f33_0_loop_GE : arg1'=arg1p1, arg2'=arg2p1, (1+arg2p3 > 0 /\ arg1p3 > 0 /\ -arg1p1-arg2p3 == 0), cost: 1 New rule: __init -> f33_0_loop_GE : arg1'=-arg2p3, arg2'=arg2p1, (0 == 0 /\ 1+arg2p3 > 0 /\ arg1p3 > 0), cost: 1 propagated equality arg1p1 = -arg2p3 Simplified Guard Original rule: __init -> f33_0_loop_GE : arg1'=-arg2p3, arg2'=arg2p1, (0 == 0 /\ 1+arg2p3 > 0 /\ arg1p3 > 0), cost: 1 New rule: __init -> f33_0_loop_GE : arg1'=-arg2p3, arg2'=arg2p1, (1+arg2p3 > 0 /\ arg1p3 > 0), cost: 1 Eliminated Temporary Variables via Transitive Closure Original rule: __init -> f33_0_loop_GE : arg1'=-arg2p3, arg2'=arg2p1, (1+arg2p3 > 0 /\ arg1p3 > 0), cost: 1 New rule: __init -> f33_0_loop_GE : arg1'=-arg2p3, arg2'=arg2p1, (1+arg2p3 > 0), cost: 1 Step with 5 Trace 5[(1+arg2p3 > 0)] Blocked [{}, {}] Step with 4 Trace 5[(1+arg2p3 > 0)], 4[(-2+arg1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0)] Blocked [{}, {}, {}] Nonterm Start location: __init Program variables: arg1 arg2 4: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-1+arg1, arg2'=arg2p2, (-2+arg1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 6: f33_0_loop_GE -> LoAT_sink : (2-arg1 > 0 /\ -1+n >= 0 /\ 1-arg1 > 0 /\ -arg1 > 0), cost: NONTERM 7: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-n+arg1, arg2'=arg2p2, (2-arg1 > 0 /\ -1+n >= 0 /\ 1-arg1 > 0 /\ -arg1 > 0), cost: 1 5: __init -> f33_0_loop_GE : arg1'=-arg2p3, arg2'=arg2p1, (1+arg2p3 > 0), cost: 1 Certificate of Non-Termination Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-1+arg1, arg2'=arg2p2, (-2+arg1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 New rule: f33_0_loop_GE -> LoAT_sink : (2-arg1 > 0 /\ -1+n >= 0 /\ 1-arg1 > 0 /\ -arg1 > 0), cost: NONTERM 2-arg1 > 0 [0]: monotonic increase yields 2-arg1 > 0 1-arg1 > 0 [0]: monotonic increase yields 1-arg1 > 0 -arg1 > 0 [0]: monotonic increase yields -arg1 > 0 Replacement map: {2-arg1 > 0 -> 2-arg1 > 0, 1-arg1 > 0 -> 1-arg1 > 0, -arg1 > 0 -> -arg1 > 0} Loop Acceleration Original rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-1+arg1, arg2'=arg2p2, (-2+arg1 < 0 /\ -1+arg1 < 0 /\ arg1 < 0), cost: 1 New rule: f33_0_loop_GE -> f33_0_loop_GE : arg1'=-n+arg1, arg2'=arg2p2, (2-arg1 > 0 /\ -1+n >= 0 /\ 1-arg1 > 0 /\ -arg1 > 0), cost: 1 2-arg1 > 0 [0]: monotonic increase yields 2-arg1 > 0 1-arg1 > 0 [0]: monotonic increase yields 1-arg1 > 0 -arg1 > 0 [0]: monotonic increase yields -arg1 > 0 Replacement map: {2-arg1 > 0 -> 2-arg1 > 0, 1-arg1 > 0 -> 1-arg1 > 0, -arg1 > 0 -> -arg1 > 0} Step with 6 Trace 5[(1+arg2p3 > 0)], 6[(2-arg1 > 0 /\ -1+n >= 0 /\ 1-arg1 > 0 /\ -arg1 > 0)] Blocked [{}, {}, {6[T]}] Refute Counterexample [ arg1=-1 arg2=0 ] 5 [ arg1=arg1 arg2=arg2 ] 6 NO Build SHA: a05f16bf13df659c382799650051f91bf6828c7b