LTS Termination Proof

Input

Integer Transition System

Initial Location: l4, l3, l0, l2

Transitions: (pre-variables and post-variables)

l0	1	l1:	x1 = _Result_4HAT0 ∧ x2 = ___cil_tmp4_8HAT0 ∧ x3 = ___const_1000HAT0 ∧ x4 = ___const_101HAT0 ∧ x5 = ___const_9HAT0 ∧ x6 = ___retres3_7HAT0 ∧ x7 = _i_5HAT0 ∧ x8 = _x_6HAT0 ∧ x1 = _Result_4HATpost ∧ x2 = ___cil_tmp4_8HATpost ∧ x3 = ___const_1000HATpost ∧ x4 = ___const_101HATpost ∧ x5 = ___const_9HATpost ∧ x6 = ___retres3_7HATpost ∧ x7 = _i_5HATpost ∧ x8 = _x_6HATpost ∧ _x_6HAT0 = _x_6HATpost ∧ _i_5HAT0 = _i_5HATpost ∧ ___const_9HAT0 = ___const_9HATpost ∧ ___const_101HAT0 = ___const_101HATpost ∧ ___const_1000HAT0 = ___const_1000HATpost ∧ _Result_4HATpost = ___cil_tmp4_8HATpost ∧ ___cil_tmp4_8HATpost = ___retres3_7HATpost ∧ ___retres3_7HATpost = 0 ∧ 1 + ___const_9HAT0 − _x_6HAT0 ≤ 0
l0	2	l1:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x1 = _x8 ∧ x2 = _x9 ∧ x3 = _x10 ∧ x4 = _x11 ∧ x5 = _x12 ∧ x6 = _x13 ∧ x7 = _x14 ∧ x8 = _x15 ∧ _x7 = _x15 ∧ _x6 = _x14 ∧ _x4 = _x12 ∧ _x3 = _x11 ∧ _x2 = _x10 ∧ _x8 = _x9 ∧ _x9 = _x13 ∧ _x13 = 0 ∧ 1 − _x3 + _x6 ≤ 0 ∧ 0 ≤ _x4 − _x7
l0	3	l2:	x1 = _x16 ∧ x2 = _x17 ∧ x3 = _x18 ∧ x4 = _x19 ∧ x5 = _x20 ∧ x6 = _x21 ∧ x7 = _x22 ∧ x8 = _x23 ∧ x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x4 = _x27 ∧ x5 = _x28 ∧ x6 = _x29 ∧ x7 = _x30 ∧ x8 = _x31 ∧ _x23 = _x31 ∧ _x21 = _x29 ∧ _x20 = _x28 ∧ _x19 = _x27 ∧ _x18 = _x26 ∧ _x17 = _x25 ∧ _x16 = _x24 ∧ _x30 = −1 + _x22 ∧ 0 ≤ − _x19 + _x22 ∧ 0 ≤ _x20 − _x23
l2	4	l0:	x1 = _x32 ∧ x2 = _x33 ∧ x3 = _x34 ∧ x4 = _x35 ∧ x5 = _x36 ∧ x6 = _x37 ∧ x7 = _x38 ∧ x8 = _x39 ∧ x1 = _x40 ∧ x2 = _x41 ∧ x3 = _x42 ∧ x4 = _x43 ∧ x5 = _x44 ∧ x6 = _x45 ∧ x7 = _x46 ∧ x8 = _x47 ∧ _x39 = _x47 ∧ _x38 = _x46 ∧ _x37 = _x45 ∧ _x36 = _x44 ∧ _x35 = _x43 ∧ _x34 = _x42 ∧ _x33 = _x41 ∧ _x32 = _x40
l3	5	l0:	x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x4 = _x51 ∧ x5 = _x52 ∧ x6 = _x53 ∧ x7 = _x54 ∧ x8 = _x55 ∧ x1 = _x56 ∧ x2 = _x57 ∧ x3 = _x58 ∧ x4 = _x59 ∧ x5 = _x60 ∧ x6 = _x61 ∧ x7 = _x62 ∧ x8 = _x63 ∧ _x55 = _x63 ∧ _x53 = _x61 ∧ _x52 = _x60 ∧ _x51 = _x59 ∧ _x50 = _x58 ∧ _x49 = _x57 ∧ _x48 = _x56 ∧ _x62 = _x50
l4	6	l3:	x1 = _x64 ∧ x2 = _x65 ∧ x3 = _x66 ∧ x4 = _x67 ∧ x5 = _x68 ∧ x6 = _x69 ∧ x7 = _x70 ∧ x8 = _x71 ∧ x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x4 = _x75 ∧ x5 = _x76 ∧ x6 = _x77 ∧ x7 = _x78 ∧ x8 = _x79 ∧ _x71 = _x79 ∧ _x70 = _x78 ∧ _x69 = _x77 ∧ _x68 = _x76 ∧ _x67 = _x75 ∧ _x66 = _x74 ∧ _x65 = _x73 ∧ _x64 = _x72

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

l4	l4	l4:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8
l3	l3	l3:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8
l0	l0	l0:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8
l2	l2	l2:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8

and for every transition t, a duplicate t is considered.

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 { l0, l2 }.

2.1.1 Transition Removal

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

l0:	− x4 + x5 + x7 − x8
l2:	− x4 + x5 + x7 − x8

2.1.2 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by 0.

l2:	0
l0:	−1

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)