LTS Termination Proof

Input

Integer Transition System

Initial Location: f1332_0_rotateEachNode_FieldAccess, f972_0_createTree_GE, f1142_0_insert_GT, f358_0_createTree_Return, f1007_0_main_InvokeMethod, f1_0_main_Load, __init

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f1007_0_main_InvokeMethod:	x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x6 = _arg6 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ x6 = _arg6P ∧ −1 ≤ _x7 − 1 ∧ 0 ≤ _arg2 − 1 ∧ _arg1P ≤ _arg1 ∧ 0 ≤ _arg1 − 1 ∧ 0 ≤ _arg1P − 1 ∧ 0 ≤ _arg2P − 1
f358_0_createTree_Return	2	f1007_0_main_InvokeMethod:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x1 = _x6 ∧ x2 = _x8 ∧ x3 = _x9 ∧ x4 = _x10 ∧ x5 = _x11 ∧ x6 = _x12 ∧ _x4 = _x11 ∧ _x3 = _x10 ∧ _x2 = _x9 ∧ _x3 + 2 ≤ _x1 ∧ _x4 + 2 ≤ _x1 ∧ _x2 + 2 ≤ _x1 ∧ 0 ≤ _x8 − 1 ∧ 0 ≤ _x6 − 1 ∧ 0 ≤ _x1 − 1 ∧ 0 ≤ _x − 1 ∧ _x8 ≤ _x1 ∧ _x6 ≤ _x1 ∧ _x6 ≤ _x
f1007_0_main_InvokeMethod	3	f1332_0_rotateEachNode_FieldAccess:	x1 = _x13 ∧ x2 = _x14 ∧ x3 = _x15 ∧ x4 = _x17 ∧ x5 = _x18 ∧ x6 = _x19 ∧ x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ x4 = _x23 ∧ x5 = _x24 ∧ x6 = _x25 ∧ _x20 ≤ _x14 ∧ 1 ≤ _x26 − 1 ∧ _x21 ≤ _x14 ∧ 0 ≤ _x13 − 1 ∧ 0 ≤ _x14 − 1 ∧ 0 ≤ _x20 − 1 ∧ 0 ≤ _x21 − 1 ∧ _x15 + 2 ≤ _x14 ∧ _x18 + 2 ≤ _x14 ∧ _x17 + 2 ≤ _x14
f1_0_main_Load	4	f972_0_createTree_GE:	x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ x4 = _x30 ∧ x5 = _x31 ∧ x6 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ x4 = _x36 ∧ x5 = _x38 ∧ x6 = _x39 ∧ 2 = _x38 ∧ _x28 = _x36 ∧ 0 = _x34 ∧ 1 ≤ _x33 − 1 ∧ 0 ≤ _x27 − 1 ∧ −1 ≤ _x35 − 1 ∧ 1 ≤ _x28 − 1 ∧ −1 ≤ _x39 − 1
f972_0_createTree_GE	5	f972_0_createTree_GE:	x1 = _x40 ∧ x2 = _x41 ∧ x3 = _x42 ∧ x4 = _x43 ∧ x5 = _x44 ∧ x6 = _x45 ∧ x1 = _x46 ∧ x2 = _x47 ∧ x3 = _x48 ∧ x4 = _x49 ∧ x5 = _x50 ∧ x6 = _x51 ∧ −1 ≤ _x44 − 1 ∧ _x41 ≤ _x42 − 1 ∧ 0 ≤ _x42 − 1 ∧ 1 ≤ _x43 − 1 ∧ −1 ≤ _x52 − 1 ∧ _x44 ≤ _x43 − 1 ∧ 0 ≤ _x40 − 1 ∧ 3 ≤ _x46 − 1 ∧ _x45 + 2 ≤ _x40 ∧ _x41 + 1 = _x47 ∧ _x42 = _x48 ∧ _x43 = _x49 ∧ _x44 + 1 = _x50
f972_0_createTree_GE	6	f972_0_createTree_GE:	x1 = _x53 ∧ x2 = _x54 ∧ x3 = _x56 ∧ x4 = _x57 ∧ x5 = _x58 ∧ x6 = _x59 ∧ x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x4 = _x63 ∧ x5 = _x64 ∧ x6 = _x65 ∧ −1 ≤ _x58 − 1 ∧ _x54 ≤ _x56 − 1 ∧ 0 ≤ _x56 − 1 ∧ 1 ≤ _x57 − 1 ∧ −1 ≤ _x66 − 1 ∧ _x58 ≤ _x57 − 1 ∧ 0 ≤ _x53 − 1 ∧ 2 ≤ _x60 − 1 ∧ _x59 + 2 ≤ _x53 ∧ _x54 + 1 = _x61 ∧ _x56 = _x62 ∧ _x57 = _x63 ∧ _x58 + 1 = _x64
f1332_0_rotateEachNode_FieldAccess	7	f1332_0_rotateEachNode_FieldAccess:	x1 = _x67 ∧ x2 = _x68 ∧ x3 = _x69 ∧ x4 = _x70 ∧ x5 = _x71 ∧ x6 = _x72 ∧ x1 = _x73 ∧ x2 = _x74 ∧ x3 = _x75 ∧ x4 = _x76 ∧ x5 = _x77 ∧ x6 = _x78 ∧ −1 ≤ _x74 − 1 ∧ −1 ≤ _x73 − 1 ∧ 2 ≤ _x68 − 1 ∧ 2 ≤ _x67 − 1 ∧ _x74 + 3 ≤ _x68 ∧ _x74 + 3 ≤ _x67 ∧ _x73 + 3 ≤ _x68 ∧ _x73 + 3 ≤ _x67
f1332_0_rotateEachNode_FieldAccess	8	f1332_0_rotateEachNode_FieldAccess:	x1 = _x79 ∧ x2 = _x80 ∧ x3 = _x81 ∧ x4 = _x82 ∧ x5 = _x83 ∧ x6 = _x84 ∧ x1 = _x85 ∧ x2 = _x86 ∧ x3 = _x87 ∧ x4 = _x88 ∧ x5 = _x89 ∧ x6 = _x90 ∧ −1 ≤ _x86 − 1 ∧ −1 ≤ _x85 − 1 ∧ 2 ≤ _x80 − 1 ∧ 2 ≤ _x79 − 1 ∧ _x86 + 2 ≤ _x80 ∧ _x86 + 2 ≤ _x79 ∧ _x85 + 2 ≤ _x80 ∧ _x85 + 2 ≤ _x79
f972_0_createTree_GE	9	f1142_0_insert_GT:	x1 = _x91 ∧ x2 = _x92 ∧ x3 = _x93 ∧ x4 = _x94 ∧ x5 = _x95 ∧ x6 = _x96 ∧ x1 = _x97 ∧ x2 = _x98 ∧ x3 = _x99 ∧ x4 = _x100 ∧ x5 = _x101 ∧ x6 = _x102 ∧ _x96 = _x100 ∧ _x94 = _x99 ∧ _x96 + 2 ≤ _x91 ∧ 0 ≤ _x97 − 1 ∧ 0 ≤ _x91 − 1 ∧ _x97 ≤ _x91 ∧ _x95 ≤ _x94 − 1 ∧ −1 ≤ _x98 − 1 ∧ 1 ≤ _x94 − 1 ∧ 0 ≤ _x93 − 1 ∧ _x92 ≤ _x93 − 1 ∧ −1 ≤ _x95 − 1
f1142_0_insert_GT	10	f1142_0_insert_GT:	x1 = _x103 ∧ x2 = _x104 ∧ x3 = _x105 ∧ x4 = _x106 ∧ x5 = _x107 ∧ x6 = _x108 ∧ x1 = _x109 ∧ x2 = _x110 ∧ x3 = _x111 ∧ x4 = _x112 ∧ x5 = _x113 ∧ x6 = _x114 ∧ _x105 = _x111 ∧ _x104 = _x110 ∧ _x112 + 4 ≤ _x103 ∧ _x106 + 2 ≤ _x103 ∧ 0 ≤ _x109 − 1 ∧ 2 ≤ _x103 − 1 ∧ _x109 + 2 ≤ _x103 ∧ _x106 ≤ _x104 − 1 ∧ 1 ≤ _x105 − 1
f1142_0_insert_GT	11	f1142_0_insert_GT:	x1 = _x115 ∧ x2 = _x116 ∧ x3 = _x117 ∧ x4 = _x118 ∧ x5 = _x119 ∧ x6 = _x120 ∧ x1 = _x121 ∧ x2 = _x122 ∧ x3 = _x123 ∧ x4 = _x124 ∧ x5 = _x125 ∧ x6 = _x126 ∧ _x117 = _x123 ∧ _x116 = _x122 ∧ _x124 + 4 ≤ _x115 ∧ _x118 + 2 ≤ _x115 ∧ 0 ≤ _x121 − 1 ∧ 2 ≤ _x115 − 1 ∧ _x121 + 2 ≤ _x115 ∧ _x116 ≤ _x118 ∧ 1 ≤ _x117 − 1
__init	12	f1_0_main_Load:	x1 = _x127 ∧ x2 = _x128 ∧ x3 = _x129 ∧ x4 = _x130 ∧ x5 = _x131 ∧ x6 = _x132 ∧ x1 = _x133 ∧ x2 = _x134 ∧ x3 = _x135 ∧ x4 = _x136 ∧ x5 = _x137 ∧ x6 = _x138 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

f1332_0_rotateEachNode_FieldAccess	f1332_0_rotateEachNode_FieldAccess	f1332_0_rotateEachNode_FieldAccess:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6
f972_0_createTree_GE	f972_0_createTree_GE	f972_0_createTree_GE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6
f1142_0_insert_GT	f1142_0_insert_GT	f1142_0_insert_GT:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6
f358_0_createTree_Return	f358_0_createTree_Return	f358_0_createTree_Return:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6
f1007_0_main_InvokeMethod	f1007_0_main_InvokeMethod	f1007_0_main_InvokeMethod:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6
f1_0_main_Load	f1_0_main_Load	f1_0_main_Load:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6
__init	__init	__init:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6

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

2 SCC Decomposition

We consider subproblems for each of the 3 SCC(s) of the program graph.

2.1 SCC Subproblem 1/3

Here we consider the SCC { f972_0_createTree_GE }.

2.1.1 Transition Removal

We remove transitions 5, 6 using the following ranking functions, which are bounded by 0.

f972_0_createTree_GE:

− x2 + x3

2.1.2 Trivial Cooperation Program

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

2.2 SCC Subproblem 2/3

Here we consider the SCC { f1142_0_insert_GT }.

2.2.1 Transition Removal

We remove transitions 10, 11 using the following ranking functions, which are bounded by 0.

f1142_0_insert_GT:

2.2.2 Trivial Cooperation Program

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

2.3 SCC Subproblem 3/3

Here we consider the SCC { f1332_0_rotateEachNode_FieldAccess }.

2.3.1 Transition Removal

We remove transitions 7, 8 using the following ranking functions, which are bounded by 0.

f1332_0_rotateEachNode_FieldAccess:

2.3.2 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 % (10 real / 0 unknown / 0 assumptions / 10 total proof steps)