LTS Termination Proof

by AProVE

Input

• Initial Location: l5, l4, l6, l3, l0, l2
• Transitions: (pre-variables and post-variables)

  l0	1	l1:		x1 = ___const_20HAT0 ∧ x2 = _iHAT0 ∧ x1 = ___const_20HATpost ∧ x2 = _iHATpost ∧ _iHAT0 = _iHATpost ∧ ___const_20HAT0 = ___const_20HATpost
  l2	2	l0:		x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x1 = _x3 ∧ _x = _x2 ∧ _x ≤ _x1
  l2	3	l3:		x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ _x4 = _x6 ∧ _x7 = 1 + _x5 ∧ 1 + _x5 ≤ _x4
  l4	4	l0:		x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x9 = _x11 ∧ _x8 = _x10 ∧ _x9 ≤ 0
  l4	5	l3:		x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ _x13 = _x15 ∧ _x12 = _x14 ∧ 1 ≤ _x13
  l3	6	l2:		x1 = _x16 ∧ x2 = _x17 ∧ x1 = _x18 ∧ x2 = _x19 ∧ _x17 = _x19 ∧ _x16 = _x18
  l5	7	l4:		x1 = _x20 ∧ x2 = _x21 ∧ x1 = _x22 ∧ x2 = _x23 ∧ _x24 = 0 ∧ _x23 = _x23 ∧ _x20 = _x22
  l6	8	l5:		x1 = _x25 ∧ x2 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ _x26 = _x28 ∧ _x25 = _x27

Proof

1 Switch to Cooperation Termination Proof

2 SCC Decomposition

We consider subproblems for each of the 1 SCC(s) of the program graph.

2.1 SCC Subproblem 1/1

Here we consider the SCC { l3, l2 }.

2.1.1 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 0.

2.1.2 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by 0.

2.1.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

Tool configuration

AProVE

• version: AProVE Commit ID: unknown
• strategy: Statistics for single proof: 100.00 % (5 real / 0 unknown / 0 assumptions / 5 total proof steps)