(0) Obligation:
Need to prove time_complexity of the following program:
/**
* Example taken from "A Term Rewriting Approach to the Automated Termination
* Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
* and converted to Java.
*/
public class PastaB5 {
public static void main(String[] args) {
Random.args = args;
int x = Random.random();
while (x > 0 && (x % 2) == 0) {
x--;
}
}
}
public class Random {
static String[] args;
static int index = 0;
public static int random() {
String string = args[index];
index++;
return string.length();
}
}
(1) JBCToGraph (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Constructed TerminationGraph.
(2) Obligation:
Termination Graph based on JBC Program:
PastaB5.main([Ljava/lang/String;)V: Graph of 111 nodes with 1 SCC.
(3) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(48)) transformation)
Extracted set of 62 edges for the analysis of TIME complexity. Kept leaves.
(4) Obligation:
Set of 62 edges based on JBC Program.
Performed SCC analyses:
- Used field analysis yielded the following read fields:
Considered paths: nonterm paths and paths from start to sinks
(5) JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID) transformation)
Transformed 62 jbc graph edges to a weighted ITS with 62 rules.
Filtered conditions with variables that do not depend on the variables on the lhs or rhs without taking transitive dependencies into account.
Did no encode lower bounds for putfield and astore.
(6) Obligation:
IntTrs with 62 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{0,0}> main_Load_3(o2, env, static) :|: 0 < o2
main_Load_3(o2, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_5(o2, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_5(o2, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_13(iconst_0, o2, env, static) :|: 0 < o2 && iconst_0 = 0
langle_clinit_rangle_ArrayCreate_13(iconst_0, o2, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_16(a2, o2, iconst_0, env, static) :|: a2 = 2 && 0 < o2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_16(a2, o2, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_17(o2, env, static') :|: 0 <= a2 && 0 < o2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_17(o2, env, static) -{0,0}> langle_clinit_rangle_New_19(o2, env, static) :|: 0 < o2
langle_clinit_rangle_New_19(o2, env, static) -{0,0}> langle_clinit_rangle_New_20(o2, env, static) :|: 0 < o2 && 0 <= static
langle_clinit_rangle_New_20(o2, env, static) -{1,1}> langle_clinit_rangle_Duplicate_21(o4, o2, env, static) :|: o4 = 1 && 0 < o2 && 0 < o4
langle_clinit_rangle_Duplicate_21(o4, o2, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_24(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_clinit_rangle_ConstantStackPush_24(o4, o2, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_26(o4, NULL, o2, env, static) :|: NULL = 0 && 0 < o2 && 0 < o4
langle_clinit_rangle_InvokeMethod_26(o4, NULL, o2, env, static) -{1,1}> langle_init_rangle_Load_27(o4, o2, env, static) :|: NULL = 0 && 0 < o2 && 0 < o4
langle_init_rangle_Load_27(o4, o2, env, static) -{1,1}> langle_init_rangle_InvokeMethod_31(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_InvokeMethod_31(o4, o2, env, static) -{1,1}> langle_init_rangle_Load_33(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_Load_33(o4, o2, env, static) -{1,1}> langle_init_rangle_InvokeMethod_36(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_InvokeMethod_36(o4, o2, env, static) -{1,1}> langle_init_rangle_Return_37(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_Return_37(o4, o2, env, static) -{1,1}> langle_init_rangle_Return_38(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_Return_38(o4, o2, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_39(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_clinit_rangle_FieldAccess_39(o4, o2, env, static) -{1,1}> langle_clinit_rangle_Return_41(o2, env, static') :|: 0 < o2 && 0 <= o4 && 0 < o4 && 0 <= static && static' <= static + o4
langle_clinit_rangle_Return_41(o2, env, static) -{1,1}> main_Load_48(o2, env, static) :|: 0 < o2
main_Load_48(o2, env, static) -{0,0}> main_Load_49(o2, env, static) :|: 0 < o2
main_Load_49(o2, env, static) -{0,0}> main_Load_52(o2, env, static) :|: 0 < o2 && 0 <= static
main_Load_52(o2, env, static) -{0,0}> main_Load_54(o2, env, static) :|: 0 < o2
main_Load_54(o2, env, static) -{0,0}> main_Load_55(o2, env, static) :|: 0 < o2
main_Load_55(o2, env, static) -{1,1}> main_FieldAccess_58(o2, env, static) :|: 0 < o2
main_FieldAccess_58(o2, env, static) -{0,0}> main_FieldAccess_59(o2, env, static) :|: 0 < o2
main_FieldAccess_59(o2, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_61(o2, NULL, iconst_0, env, static) :|: NULL = 0 && 0 < o2 && iconst_0 = 0
langle_clinit_rangle_ConstantStackPush_61(o2, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_62(iconst_0, o2, NULL, env, static) :|: NULL = 0 && 0 < o2 && iconst_0 = 0
langle_clinit_rangle_FieldAccess_62(iconst_0, o2, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_63(o2, NULL, iconst_0, env, static') :|: NULL = 0 && 0 < o2 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0
langle_clinit_rangle_Return_63(o2, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_64(o2, NULL, iconst_0, env, static) :|: NULL = 0 && 0 < o2 && iconst_0 = 0
main_FieldAccess_64(o2, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_65(o2, iconst_0, env, static') :|: NULL = 0 && 0 < o2 && 0 <= o2 && iconst_0 = 0 && 0 <= static && static' <= static + o2
main_InvokeMethod_65(o2, iconst_0, env, static) -{1,1}> random_FieldAccess_66(o2, iconst_0, env, static) :|: 0 < o2 && iconst_0 = 0
random_FieldAccess_66(o2, iconst_0, env, static) -{1,1}> random_FieldAccess_68(o2, iconst_0, env, static) :|: 0 < o2 && o2 <= static && 0 <= o2 && iconst_0 = 0 && 0 <= static
random_FieldAccess_68(o2, iconst_0, env, static) -{1,1}> random_ArrayAccess_69(o2, iconst_0, env, static) :|: 0 < o2 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && iconst_0 <= static
random_ArrayAccess_69(a6, iconst_0, env, static) -{0,0}> random_ArrayAccess_70(a6, iconst_0, i4, env, static) :|: 0 <= i4 && iconst_0 = 0 && 0 < a6 && i4 < a6
random_ArrayAccess_70(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_70(a6, iconst_0, i6, env, static) -{0,0}> random_ArrayAccess_74(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_74(a6, iconst_0, i6, env, static) -{1,1}> random_Store_78(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && o7 < a6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_Store_78(o7, a6, iconst_0, i6, env, static) -{1,1}> random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) -{1,1}> random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) :|: 1 <= i6 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && iconst_0 <= static
random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) -{1,1}> random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) -{1,1}> random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) -{1,1}> random_Load_92(o7, a6, iconst_1, i6, env, static') :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && static' <= static + iconst_1
random_Load_92(o7, a6, iconst_1, i6, env, static) -{1,1}> random_InvokeMethod_96(o7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 <= o7 && 0 < a6
random_InvokeMethod_96(o11, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) :|: 0 <= o11 && 1 <= i6 && iconst_1 = 1 && 0 < o11 && 0 < a6
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) -{1,1}> random_Return_104(i7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && i7 <= o11 && iconst_1 = 1 && 0 < o11 && 0 < a6 && 0 <= i7
random_Return_104(i7, a6, iconst_1, i6, env, static) -{1,1}> main_Store_110(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Store_110(a6, i7, iconst_1, i6, env, static) -{1,1}> main_Load_112(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Load_112(a6, i7, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
main_LE_208(a6, i23, iconst_1, i6, env, static) -{0,0}> main_LE_219(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 <= i23
main_LE_219(a6, i23, iconst_1, i6, env, static) -{1,1}> main_Load_230(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 < i23
main_Load_230(a6, i23, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && iconst_2 = 2
main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) -{1,1}> main_NE_258(a6, i28, i23, iconst_1, i6, env, static) :|: 0 <= i28 && 1 <= i6 && iconst_1 = 1 && i23 % iconst_2 = i28 && 1 <= i23 && 0 < a6 && i28 <= 1 && iconst_2 = 2
main_NE_258(a6, iconst_1, i23, iconst_1, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_NE_258(a6, iconst_0, i23, iconst_1, i6, env, static) -{0,0}> main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_0 <= 1 && iconst_1 = 1 && 1 <= i23 && iconst_0 = 0 && 0 < a6
main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) -{1,1}> main_Inc_266(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 1 <= i23 && 0 < a6
main_Inc_266(a6, i23, iconst_1, i6, env, static) -{1,1}> main_JMP_275(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 1 <= i23 && i23 + -1 = i30 && 0 < a6
main_JMP_275(a6, i30, iconst_1, i6, env, static) -{1,1}> main_Load_287(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
main_Load_287(a6, i30, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
(7) StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
obtained
main_Load_1(
o2,
env,
static) -{23,23}>
random_ArrayAccess_70(
o2,
0,
i4',
env,
static'3) :|:
static'3 <=
static'2 +
o2 &&
i4' <
o2 &&
static'2 <=
static'1 +
0 &&
0 <
o2 &&
0 <=
2 &&
0 <=
i4' &&
0 <=
o2 &&
0 <=
static'2 &&
o2 <=
static'3 &&
static'1 <=
static''' +
1 &&
0 <=
static'1 &&
static''' <=
static +
2 &&
0 <=
static''' &&
-1 *
static'3 <=
0 &&
0 <=
static &&
0 <
1 &&
0 <
2 &&
0 <=
1 &&
0 <=
static'3by chaining
main_Load_1(
o2,
env,
static) -{0,0}>
main_Load_3(
o2,
env,
static) :|:
0 <
o2main_Load_3(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_ConstantStackPush_5(
o2,
env,
static) :|:
0 <
o2langle_clinit_rangle_ConstantStackPush_5(
o2,
env,
static) -{1,1}>
langle_clinit_rangle_ArrayCreate_13(
iconst_0,
o2,
env,
static) :|:
0 <
o2 &&
iconst_0 =
0langle_clinit_rangle_ArrayCreate_13(
iconst_0,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_FieldAccess_16(
a2,
o2,
iconst_0,
env,
static) :|:
a2 =
2 &&
0 <
o2 &&
iconst_0 =
0 &&
0 <
a2langle_clinit_rangle_FieldAccess_16(
a2,
o2,
iconst_0,
env,
static) -{1,1}>
langle_clinit_rangle_New_17(
o2,
env,
static') :|:
0 <=
a2 &&
0 <
o2 &&
iconst_0 =
0 &&
static' <=
static +
a2 &&
0 <=
static &&
0 <
a2langle_clinit_rangle_New_17(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_New_19(
o2,
env,
static) :|:
0 <
o2langle_clinit_rangle_New_19(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_New_20(
o2,
env,
static) :|:
0 <
o2 &&
0 <=
staticlangle_clinit_rangle_New_20(
o2,
env,
static) -{1,1}>
langle_clinit_rangle_Duplicate_21(
o4,
o2,
env,
static) :|:
o4 =
1 &&
0 <
o2 &&
0 <
o4langle_clinit_rangle_Duplicate_21(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_ConstantStackPush_24(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_clinit_rangle_ConstantStackPush_24(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_InvokeMethod_26(
o4,
NULL,
o2,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
0 <
o4langle_clinit_rangle_InvokeMethod_26(
o4,
NULL,
o2,
env,
static) -{1,1}>
langle_init_rangle_Load_27(
o4,
o2,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
0 <
o4langle_init_rangle_Load_27(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_InvokeMethod_31(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_InvokeMethod_31(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_Load_33(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_Load_33(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_InvokeMethod_36(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_InvokeMethod_36(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_Return_37(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_Return_37(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_Return_38(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_Return_38(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_FieldAccess_39(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_clinit_rangle_FieldAccess_39(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_Return_41(
o2,
env,
static') :|:
0 <
o2 &&
0 <=
o4 &&
0 <
o4 &&
0 <=
static &&
static' <=
static +
o4langle_clinit_rangle_Return_41(
o2,
env,
static) -{1,1}>
main_Load_48(
o2,
env,
static) :|:
0 <
o2main_Load_48(
o2,
env,
static) -{0,0}>
main_Load_49(
o2,
env,
static) :|:
0 <
o2main_Load_49(
o2,
env,
static) -{0,0}>
main_Load_52(
o2,
env,
static) :|:
0 <
o2 &&
0 <=
staticmain_Load_52(
o2,
env,
static) -{0,0}>
main_Load_54(
o2,
env,
static) :|:
0 <
o2main_Load_54(
o2,
env,
static) -{0,0}>
main_Load_55(
o2,
env,
static) :|:
0 <
o2main_Load_55(
o2,
env,
static) -{1,1}>
main_FieldAccess_58(
o2,
env,
static) :|:
0 <
o2main_FieldAccess_58(
o2,
env,
static) -{0,0}>
main_FieldAccess_59(
o2,
env,
static) :|:
0 <
o2main_FieldAccess_59(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_ConstantStackPush_61(
o2,
NULL,
iconst_0,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0langle_clinit_rangle_ConstantStackPush_61(
o2,
NULL,
iconst_0,
env,
static) -{1,1}>
langle_clinit_rangle_FieldAccess_62(
iconst_0,
o2,
NULL,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0langle_clinit_rangle_FieldAccess_62(
iconst_0,
o2,
NULL,
env,
static) -{1,1}>
langle_clinit_rangle_Return_63(
o2,
NULL,
iconst_0,
env,
static') :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0 &&
0 <=
static &&
static' <=
static +
iconst_0langle_clinit_rangle_Return_63(
o2,
NULL,
iconst_0,
env,
static) -{1,1}>
main_FieldAccess_64(
o2,
NULL,
iconst_0,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0main_FieldAccess_64(
o2,
NULL,
iconst_0,
env,
static) -{1,1}>
main_InvokeMethod_65(
o2,
iconst_0,
env,
static') :|:
NULL =
0 &&
0 <
o2 &&
0 <=
o2 &&
iconst_0 =
0 &&
0 <=
static &&
static' <=
static +
o2main_InvokeMethod_65(
o2,
iconst_0,
env,
static) -{1,1}>
random_FieldAccess_66(
o2,
iconst_0,
env,
static) :|:
0 <
o2 &&
iconst_0 =
0random_FieldAccess_66(
o2,
iconst_0,
env,
static) -{1,1}>
random_FieldAccess_68(
o2,
iconst_0,
env,
static) :|:
0 <
o2 &&
o2 <=
static &&
0 <=
o2 &&
iconst_0 =
0 &&
0 <=
staticrandom_FieldAccess_68(
o2,
iconst_0,
env,
static) -{1,1}>
random_ArrayAccess_69(
o2,
iconst_0,
env,
static) :|:
0 <
o2 &&
-1 *
static <=
iconst_0 &&
iconst_0 =
0 &&
0 <=
static &&
iconst_0 <=
staticrandom_ArrayAccess_69(
a6,
iconst_0,
env,
static) -{0,0}>
random_ArrayAccess_70(
a6,
iconst_0,
i4,
env,
static) :|:
0 <=
i4 &&
iconst_0 =
0 &&
0 <
a6 &&
i4 <
a6obtained
random_ArrayAccess_70(a6, 0, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1
by chaining
random_ArrayAccess_70(a6, iconst_0, i6, env, static) -{0,0}> random_ArrayAccess_74(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_74(a6, iconst_0, i6, env, static) -{1,1}> random_Store_78(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && o7 < a6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_Store_78(o7, a6, iconst_0, i6, env, static) -{1,1}> random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) -{1,1}> random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) :|: 1 <= i6 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && iconst_0 <= static
random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) -{1,1}> random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) -{1,1}> random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) -{1,1}> random_Load_92(o7, a6, iconst_1, i6, env, static') :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && static' <= static + iconst_1
random_Load_92(o7, a6, iconst_1, i6, env, static) -{1,1}> random_InvokeMethod_96(o7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 <= o7 && 0 < a6
obtained
random_InvokeMethod_96(o11, a6, 1, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11
by chaining
random_InvokeMethod_96(o11, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) :|: 0 <= o11 && 1 <= i6 && iconst_1 = 1 && 0 < o11 && 0 < a6
random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) -{1,1}> random_Return_104(i7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && i7 <= o11 && iconst_1 = 1 && 0 < o11 && 0 < a6 && 0 <= i7
random_Return_104(i7, a6, iconst_1, i6, env, static) -{1,1}> main_Store_110(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Store_110(a6, i7, iconst_1, i6, env, static) -{1,1}> main_Load_112(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Load_112(a6, i7, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
obtained
main_LE_208(a6, i23, 1, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 % 2 = i28' && 0 <= i28'
by chaining
main_LE_208(a6, i23, iconst_1, i6, env, static) -{0,0}> main_LE_219(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 <= i23
main_LE_219(a6, i23, iconst_1, i6, env, static) -{1,1}> main_Load_230(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 < i23
main_Load_230(a6, i23, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && iconst_2 = 2
main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) -{1,1}> main_NE_258(a6, i28, i23, iconst_1, i6, env, static) :|: 0 <= i28 && 1 <= i6 && iconst_1 = 1 && i23 % iconst_2 = i28 && 1 <= i23 && 0 < a6 && i28 <= 1 && iconst_2 = 2
obtained
main_NE_258(a6, 0, i23, 1, i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23
by chaining
main_NE_258(a6, iconst_0, i23, iconst_1, i6, env, static) -{0,0}> main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_0 <= 1 && iconst_1 = 1 && 1 <= i23 && iconst_0 = 0 && 0 < a6
main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) -{1,1}> main_Inc_266(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 1 <= i23 && 0 < a6
main_Inc_266(a6, i23, iconst_1, i6, env, static) -{1,1}> main_JMP_275(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 1 <= i23 && i23 + -1 = i30 && 0 < a6
main_JMP_275(a6, i30, iconst_1, i6, env, static) -{1,1}> main_Load_287(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
main_Load_287(a6, i30, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
(8) Obligation:
IntTrs with 10 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
random_ArrayAccess_70(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_70(a6, 0, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_InvokeMethod_96(o11, a6, 1, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
main_LE_208(a6, i23, 1, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 % 2 = i28' && 0 <= i28'
main_NE_258(a6, iconst_1, i23, iconst_1, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_NE_258(a6, 0, i23, 1, i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23
(9) MovedArithmeticToConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Moved arithmethic from lhss to constraints.
random_InvokeMethod_96(o11, a6, 1, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11
was transformed to
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
main_NE_258(a6, 0, i23, 1, i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23
was transformed to
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
main_LE_208(a6, i23, 1, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 % 2 = i28' && 0 <= i28'
was transformed to
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 % 2 = i28' && 0 <= i28' && x = 1
random_ArrayAccess_70(a6, 0, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1
was transformed to
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
(10) Obligation:
IntTrs with 10 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
random_ArrayAccess_70(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
main_NE_258(a6, iconst_1, i23, iconst_1, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 % 2 = i28' && 0 <= i28' && x = 1
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
(11) LinearizedLhssProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Linearized lhss.
random_ArrayAccess_70(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
was transformed to
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_NE_258(a6, iconst_1, i23, iconst_1, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6
was transformed to
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
(12) Obligation:
IntTrs with 10 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 % 2 = i28' && 0 <= i28' && x = 1
(13) RemoveDivModProof (CONCRETE UPPER BOUND(ID) transformation)
Removed div and mod.
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 % 2 = i28' && 0 <= i28' && x = 1
was transformed to
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_LE_208'(a6, i23, x, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
main_LE_208'(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: i23 - 2 * div < 2 && i23 - 2 * div + 2 > 0 && 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
(14) Obligation:
IntTrs with 11 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_LE_208'(a6, i23, x, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_LE_208'(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: i23 - 2 * div < 2 && i23 - 2 * div + 2 > 0 && 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
(15) MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Moved arithmethic from constraints to rhss.
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
was transformed to
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
was transformed to
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, 1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_LE_208'(a6, i23, x, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
was transformed to
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_LE_208'(a6, i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
main_LE_208'(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: i23 - 2 * div < 2 && i23 - 2 * div + 2 > 0 && 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
was transformed to
main_LE_208'(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i23 - 2 * div, i23, 1, i6, env, static) :|: i23 - 2 * div < 2 && i23 - 2 * div + 2 > 0 && 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
was transformed to
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
was transformed to
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
was transformed to
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 + -1, 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
was transformed to
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, 0, 1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
(16) Obligation:
IntTrs with 11 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, 1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_LE_208'(a6, i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
main_LE_208'(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i23 - 2 * div, i23, 1, i6, env, static) :|: i23 - 2 * div < 2 && i23 - 2 * div + 2 > 0 && 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 + -1, 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, 0, 1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
(17) ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Simplified expressions.
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
was transformed to
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 && 0 < o2 && 0 <= i4' && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 <= static'3
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
was transformed to
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 < o11 && x = 1
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_LE_208'(a6, i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
was transformed to
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_LE_208'(a6, i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && i23 + -2 * div = i28' && 0 <= i28' && x = 1
main_LE_208'(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i23 - 2 * div, i23, 1, i6, env, static) :|: i23 - 2 * div < 2 && i23 - 2 * div + 2 > 0 && 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i23 - 2 * div = i28' && 0 <= i28' && x = 1
was transformed to
main_LE_208'(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i23 + -2 * div, i23, 1, i6, env, static) :|: i23 + -2 * div < 2 && 0 < i23 + -2 * div + 2 && 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && i23 + -2 * div = i28' && 0 <= i28' && x = 1
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 + -1, 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
was transformed to
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 - 1, 1, i6, env, static) :|: 0 < a6 && i23 - 1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
was transformed to
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
(18) Obligation:
IntTrs with 11 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, 0, 1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 - 1, 1, i6, env, static) :|: 0 < a6 && i23 - 1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_LE_208'(a6, i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && i23 + -2 * div = i28' && 0 <= i28' && x = 1
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, 1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208'(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i23 + -2 * div, i23, 1, i6, env, static) :|: i23 + -2 * div < 2 && 0 < i23 + -2 * div + 2 && 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && i23 + -2 * div = i28' && 0 <= i28' && x = 1
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 && 0 < o2 && 0 <= i4' && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 <= static'3
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 < o11 && x = 1
(19) JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID) transformation)
Transformed 62 jbc graph edges to a weighted ITS with 62 rules.
Used simplified encoding of division and modulo.
Filtered conditions with variables that do not depend on the variables on the lhs or rhs without taking transitive dependencies into account.
Did no encode lower bounds for putfield and astore.
(20) Obligation:
IntTrs with 62 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{0,0}> main_Load_3(o2, env, static) :|: 0 < o2
main_Load_3(o2, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_5(o2, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_5(o2, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_13(iconst_0, o2, env, static) :|: 0 < o2 && iconst_0 = 0
langle_clinit_rangle_ArrayCreate_13(iconst_0, o2, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_16(a2, o2, iconst_0, env, static) :|: a2 = 2 && 0 < o2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_16(a2, o2, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_17(o2, env, static') :|: 0 <= a2 && 0 < o2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_17(o2, env, static) -{0,0}> langle_clinit_rangle_New_19(o2, env, static) :|: 0 < o2
langle_clinit_rangle_New_19(o2, env, static) -{0,0}> langle_clinit_rangle_New_20(o2, env, static) :|: 0 < o2 && 0 <= static
langle_clinit_rangle_New_20(o2, env, static) -{1,1}> langle_clinit_rangle_Duplicate_21(o4, o2, env, static) :|: o4 = 1 && 0 < o2 && 0 < o4
langle_clinit_rangle_Duplicate_21(o4, o2, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_24(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_clinit_rangle_ConstantStackPush_24(o4, o2, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_26(o4, NULL, o2, env, static) :|: NULL = 0 && 0 < o2 && 0 < o4
langle_clinit_rangle_InvokeMethod_26(o4, NULL, o2, env, static) -{1,1}> langle_init_rangle_Load_27(o4, o2, env, static) :|: NULL = 0 && 0 < o2 && 0 < o4
langle_init_rangle_Load_27(o4, o2, env, static) -{1,1}> langle_init_rangle_InvokeMethod_31(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_InvokeMethod_31(o4, o2, env, static) -{1,1}> langle_init_rangle_Load_33(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_Load_33(o4, o2, env, static) -{1,1}> langle_init_rangle_InvokeMethod_36(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_InvokeMethod_36(o4, o2, env, static) -{1,1}> langle_init_rangle_Return_37(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_Return_37(o4, o2, env, static) -{1,1}> langle_init_rangle_Return_38(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_Return_38(o4, o2, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_39(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_clinit_rangle_FieldAccess_39(o4, o2, env, static) -{1,1}> langle_clinit_rangle_Return_41(o2, env, static') :|: 0 < o2 && 0 <= o4 && 0 < o4 && 0 <= static && static' <= static + o4
langle_clinit_rangle_Return_41(o2, env, static) -{1,1}> main_Load_48(o2, env, static) :|: 0 < o2
main_Load_48(o2, env, static) -{0,0}> main_Load_49(o2, env, static) :|: 0 < o2
main_Load_49(o2, env, static) -{0,0}> main_Load_52(o2, env, static) :|: 0 < o2 && 0 <= static
main_Load_52(o2, env, static) -{0,0}> main_Load_54(o2, env, static) :|: 0 < o2
main_Load_54(o2, env, static) -{0,0}> main_Load_55(o2, env, static) :|: 0 < o2
main_Load_55(o2, env, static) -{1,1}> main_FieldAccess_58(o2, env, static) :|: 0 < o2
main_FieldAccess_58(o2, env, static) -{0,0}> main_FieldAccess_59(o2, env, static) :|: 0 < o2
main_FieldAccess_59(o2, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_61(o2, NULL, iconst_0, env, static) :|: NULL = 0 && 0 < o2 && iconst_0 = 0
langle_clinit_rangle_ConstantStackPush_61(o2, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_62(iconst_0, o2, NULL, env, static) :|: NULL = 0 && 0 < o2 && iconst_0 = 0
langle_clinit_rangle_FieldAccess_62(iconst_0, o2, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_63(o2, NULL, iconst_0, env, static') :|: NULL = 0 && 0 < o2 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0
langle_clinit_rangle_Return_63(o2, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_64(o2, NULL, iconst_0, env, static) :|: NULL = 0 && 0 < o2 && iconst_0 = 0
main_FieldAccess_64(o2, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_65(o2, iconst_0, env, static') :|: NULL = 0 && 0 < o2 && 0 <= o2 && iconst_0 = 0 && 0 <= static && static' <= static + o2
main_InvokeMethod_65(o2, iconst_0, env, static) -{1,1}> random_FieldAccess_66(o2, iconst_0, env, static) :|: 0 < o2 && iconst_0 = 0
random_FieldAccess_66(o2, iconst_0, env, static) -{1,1}> random_FieldAccess_68(o2, iconst_0, env, static) :|: 0 < o2 && o2 <= static && 0 <= o2 && iconst_0 = 0 && 0 <= static
random_FieldAccess_68(o2, iconst_0, env, static) -{1,1}> random_ArrayAccess_69(o2, iconst_0, env, static) :|: 0 < o2 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && iconst_0 <= static
random_ArrayAccess_69(a6, iconst_0, env, static) -{0,0}> random_ArrayAccess_70(a6, iconst_0, i4, env, static) :|: 0 <= i4 && iconst_0 = 0 && 0 < a6 && i4 < a6
random_ArrayAccess_70(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_70(a6, iconst_0, i6, env, static) -{0,0}> random_ArrayAccess_74(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_74(a6, iconst_0, i6, env, static) -{1,1}> random_Store_78(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && o7 < a6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_Store_78(o7, a6, iconst_0, i6, env, static) -{1,1}> random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) -{1,1}> random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) :|: 1 <= i6 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && iconst_0 <= static
random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) -{1,1}> random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) -{1,1}> random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) -{1,1}> random_Load_92(o7, a6, iconst_1, i6, env, static') :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && static' <= static + iconst_1
random_Load_92(o7, a6, iconst_1, i6, env, static) -{1,1}> random_InvokeMethod_96(o7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 <= o7 && 0 < a6
random_InvokeMethod_96(o11, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) :|: 0 <= o11 && 1 <= i6 && iconst_1 = 1 && 0 < o11 && 0 < a6
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) -{1,1}> random_Return_104(i7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && i7 <= o11 && iconst_1 = 1 && 0 < o11 && 0 < a6 && 0 <= i7
random_Return_104(i7, a6, iconst_1, i6, env, static) -{1,1}> main_Store_110(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Store_110(a6, i7, iconst_1, i6, env, static) -{1,1}> main_Load_112(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Load_112(a6, i7, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
main_LE_208(a6, i23, iconst_1, i6, env, static) -{0,0}> main_LE_219(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 <= i23
main_LE_219(a6, i23, iconst_1, i6, env, static) -{1,1}> main_Load_230(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 < i23
main_Load_230(a6, i23, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && iconst_2 = 2
main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) -{1,1}> main_NE_258(a6, i28, i23, iconst_1, i6, env, static) :|: 0 <= i28 && 1 <= i6 && i28 < iconst_2 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && i28 <= 1 && iconst_2 = 2
main_NE_258(a6, iconst_1, i23, iconst_1, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_NE_258(a6, iconst_0, i23, iconst_1, i6, env, static) -{0,0}> main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_0 <= 1 && iconst_1 = 1 && 1 <= i23 && iconst_0 = 0 && 0 < a6
main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) -{1,1}> main_Inc_266(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 1 <= i23 && 0 < a6
main_Inc_266(a6, i23, iconst_1, i6, env, static) -{1,1}> main_JMP_275(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 1 <= i23 && i23 + -1 = i30 && 0 < a6
main_JMP_275(a6, i30, iconst_1, i6, env, static) -{1,1}> main_Load_287(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
main_Load_287(a6, i30, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
(21) StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
obtained
main_Load_1(
o2,
env,
static) -{23,23}>
random_ArrayAccess_70(
o2,
0,
i4',
env,
static'3) :|:
static'3 <=
static'2 +
o2 &&
i4' <
o2 &&
static'2 <=
static'1 +
0 &&
0 <
o2 &&
0 <=
2 &&
0 <=
i4' &&
0 <=
o2 &&
0 <=
static'2 &&
o2 <=
static'3 &&
static'1 <=
static''' +
1 &&
0 <=
static'1 &&
static''' <=
static +
2 &&
0 <=
static''' &&
-1 *
static'3 <=
0 &&
0 <=
static &&
0 <
1 &&
0 <
2 &&
0 <=
1 &&
0 <=
static'3by chaining
main_Load_1(
o2,
env,
static) -{0,0}>
main_Load_3(
o2,
env,
static) :|:
0 <
o2main_Load_3(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_ConstantStackPush_5(
o2,
env,
static) :|:
0 <
o2langle_clinit_rangle_ConstantStackPush_5(
o2,
env,
static) -{1,1}>
langle_clinit_rangle_ArrayCreate_13(
iconst_0,
o2,
env,
static) :|:
0 <
o2 &&
iconst_0 =
0langle_clinit_rangle_ArrayCreate_13(
iconst_0,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_FieldAccess_16(
a2,
o2,
iconst_0,
env,
static) :|:
a2 =
2 &&
0 <
o2 &&
iconst_0 =
0 &&
0 <
a2langle_clinit_rangle_FieldAccess_16(
a2,
o2,
iconst_0,
env,
static) -{1,1}>
langle_clinit_rangle_New_17(
o2,
env,
static') :|:
0 <=
a2 &&
0 <
o2 &&
iconst_0 =
0 &&
static' <=
static +
a2 &&
0 <=
static &&
0 <
a2langle_clinit_rangle_New_17(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_New_19(
o2,
env,
static) :|:
0 <
o2langle_clinit_rangle_New_19(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_New_20(
o2,
env,
static) :|:
0 <
o2 &&
0 <=
staticlangle_clinit_rangle_New_20(
o2,
env,
static) -{1,1}>
langle_clinit_rangle_Duplicate_21(
o4,
o2,
env,
static) :|:
o4 =
1 &&
0 <
o2 &&
0 <
o4langle_clinit_rangle_Duplicate_21(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_ConstantStackPush_24(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_clinit_rangle_ConstantStackPush_24(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_InvokeMethod_26(
o4,
NULL,
o2,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
0 <
o4langle_clinit_rangle_InvokeMethod_26(
o4,
NULL,
o2,
env,
static) -{1,1}>
langle_init_rangle_Load_27(
o4,
o2,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
0 <
o4langle_init_rangle_Load_27(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_InvokeMethod_31(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_InvokeMethod_31(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_Load_33(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_Load_33(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_InvokeMethod_36(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_InvokeMethod_36(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_Return_37(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_Return_37(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_Return_38(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_Return_38(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_FieldAccess_39(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_clinit_rangle_FieldAccess_39(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_Return_41(
o2,
env,
static') :|:
0 <
o2 &&
0 <=
o4 &&
0 <
o4 &&
0 <=
static &&
static' <=
static +
o4langle_clinit_rangle_Return_41(
o2,
env,
static) -{1,1}>
main_Load_48(
o2,
env,
static) :|:
0 <
o2main_Load_48(
o2,
env,
static) -{0,0}>
main_Load_49(
o2,
env,
static) :|:
0 <
o2main_Load_49(
o2,
env,
static) -{0,0}>
main_Load_52(
o2,
env,
static) :|:
0 <
o2 &&
0 <=
staticmain_Load_52(
o2,
env,
static) -{0,0}>
main_Load_54(
o2,
env,
static) :|:
0 <
o2main_Load_54(
o2,
env,
static) -{0,0}>
main_Load_55(
o2,
env,
static) :|:
0 <
o2main_Load_55(
o2,
env,
static) -{1,1}>
main_FieldAccess_58(
o2,
env,
static) :|:
0 <
o2main_FieldAccess_58(
o2,
env,
static) -{0,0}>
main_FieldAccess_59(
o2,
env,
static) :|:
0 <
o2main_FieldAccess_59(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_ConstantStackPush_61(
o2,
NULL,
iconst_0,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0langle_clinit_rangle_ConstantStackPush_61(
o2,
NULL,
iconst_0,
env,
static) -{1,1}>
langle_clinit_rangle_FieldAccess_62(
iconst_0,
o2,
NULL,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0langle_clinit_rangle_FieldAccess_62(
iconst_0,
o2,
NULL,
env,
static) -{1,1}>
langle_clinit_rangle_Return_63(
o2,
NULL,
iconst_0,
env,
static') :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0 &&
0 <=
static &&
static' <=
static +
iconst_0langle_clinit_rangle_Return_63(
o2,
NULL,
iconst_0,
env,
static) -{1,1}>
main_FieldAccess_64(
o2,
NULL,
iconst_0,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0main_FieldAccess_64(
o2,
NULL,
iconst_0,
env,
static) -{1,1}>
main_InvokeMethod_65(
o2,
iconst_0,
env,
static') :|:
NULL =
0 &&
0 <
o2 &&
0 <=
o2 &&
iconst_0 =
0 &&
0 <=
static &&
static' <=
static +
o2main_InvokeMethod_65(
o2,
iconst_0,
env,
static) -{1,1}>
random_FieldAccess_66(
o2,
iconst_0,
env,
static) :|:
0 <
o2 &&
iconst_0 =
0random_FieldAccess_66(
o2,
iconst_0,
env,
static) -{1,1}>
random_FieldAccess_68(
o2,
iconst_0,
env,
static) :|:
0 <
o2 &&
o2 <=
static &&
0 <=
o2 &&
iconst_0 =
0 &&
0 <=
staticrandom_FieldAccess_68(
o2,
iconst_0,
env,
static) -{1,1}>
random_ArrayAccess_69(
o2,
iconst_0,
env,
static) :|:
0 <
o2 &&
-1 *
static <=
iconst_0 &&
iconst_0 =
0 &&
0 <=
static &&
iconst_0 <=
staticrandom_ArrayAccess_69(
a6,
iconst_0,
env,
static) -{0,0}>
random_ArrayAccess_70(
a6,
iconst_0,
i4,
env,
static) :|:
0 <=
i4 &&
iconst_0 =
0 &&
0 <
a6 &&
i4 <
a6obtained
random_ArrayAccess_70(a6, 0, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1
by chaining
random_ArrayAccess_70(a6, iconst_0, i6, env, static) -{0,0}> random_ArrayAccess_74(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_74(a6, iconst_0, i6, env, static) -{1,1}> random_Store_78(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && o7 < a6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_Store_78(o7, a6, iconst_0, i6, env, static) -{1,1}> random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) -{1,1}> random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) :|: 1 <= i6 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && iconst_0 <= static
random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) -{1,1}> random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) -{1,1}> random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) -{1,1}> random_Load_92(o7, a6, iconst_1, i6, env, static') :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && static' <= static + iconst_1
random_Load_92(o7, a6, iconst_1, i6, env, static) -{1,1}> random_InvokeMethod_96(o7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 <= o7 && 0 < a6
obtained
random_InvokeMethod_96(o11, a6, 1, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11
by chaining
random_InvokeMethod_96(o11, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) :|: 0 <= o11 && 1 <= i6 && iconst_1 = 1 && 0 < o11 && 0 < a6
random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) -{1,1}> random_Return_104(i7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && i7 <= o11 && iconst_1 = 1 && 0 < o11 && 0 < a6 && 0 <= i7
random_Return_104(i7, a6, iconst_1, i6, env, static) -{1,1}> main_Store_110(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Store_110(a6, i7, iconst_1, i6, env, static) -{1,1}> main_Load_112(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Load_112(a6, i7, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
obtained
main_LE_208(a6, i23, 1, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i28' < 2 && 0 <= i28'
by chaining
main_LE_208(a6, i23, iconst_1, i6, env, static) -{0,0}> main_LE_219(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 <= i23
main_LE_219(a6, i23, iconst_1, i6, env, static) -{1,1}> main_Load_230(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 < i23
main_Load_230(a6, i23, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && iconst_2 = 2
main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) -{1,1}> main_NE_258(a6, i28, i23, iconst_1, i6, env, static) :|: 0 <= i28 && 1 <= i6 && i28 < iconst_2 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && i28 <= 1 && iconst_2 = 2
obtained
main_NE_258(a6, 0, i23, 1, i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23
by chaining
main_NE_258(a6, iconst_0, i23, iconst_1, i6, env, static) -{0,0}> main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_0 <= 1 && iconst_1 = 1 && 1 <= i23 && iconst_0 = 0 && 0 < a6
main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) -{1,1}> main_Inc_266(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 1 <= i23 && 0 < a6
main_Inc_266(a6, i23, iconst_1, i6, env, static) -{1,1}> main_JMP_275(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 1 <= i23 && i23 + -1 = i30 && 0 < a6
main_JMP_275(a6, i30, iconst_1, i6, env, static) -{1,1}> main_Load_287(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
main_Load_287(a6, i30, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
(22) Obligation:
IntTrs with 10 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
random_ArrayAccess_70(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_70(a6, 0, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_InvokeMethod_96(o11, a6, 1, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
main_LE_208(a6, i23, 1, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i28' < 2 && 0 <= i28'
main_NE_258(a6, iconst_1, i23, iconst_1, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_NE_258(a6, 0, i23, 1, i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23
(23) MovedArithmeticToConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Moved arithmethic from lhss to constraints.
main_LE_208(a6, i23, 1, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i28' < 2 && 0 <= i28'
was transformed to
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i28' < 2 && 0 <= i28' && x = 1
random_InvokeMethod_96(o11, a6, 1, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11
was transformed to
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
main_NE_258(a6, 0, i23, 1, i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23
was transformed to
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
random_ArrayAccess_70(a6, 0, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1
was transformed to
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
(24) Obligation:
IntTrs with 10 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i28' < 2 && 0 <= i28' && x = 1
random_ArrayAccess_70(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
main_NE_258(a6, iconst_1, i23, iconst_1, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
(25) LinearizedLhssProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Linearized lhss.
random_ArrayAccess_70(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
was transformed to
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_NE_258(a6, iconst_1, i23, iconst_1, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6
was transformed to
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
(26) Obligation:
IntTrs with 10 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i28' < 2 && 0 <= i28' && x = 1
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
(27) MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Moved arithmethic from constraints to rhss.
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, iconst_1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
was transformed to
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
was transformed to
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, 1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
was transformed to
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 + -1, 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
was transformed to
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
was transformed to
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
was transformed to
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, 0, 1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
(28) Obligation:
IntTrs with 10 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i28' < 2 && 0 <= i28' && x = 1
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, 1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 + -1, 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, 0, 1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
(29) ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Simplified expressions.
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 + 0 && 0 < o2 && 0 <= 2 && 0 <= i4' && 0 <= o2 && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 < 1 && 0 < 2 && 0 <= 1 && 0 <= static'3
was transformed to
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 && 0 < o2 && 0 <= i4' && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 <= static'3
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 <= o11 && 0 < o11 && x = 1
was transformed to
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 < o11 && x = 1
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && 0 <= i23 && i28' < 2 && 0 <= i28' && x = 1
was transformed to
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && i28' < 2 && 0 <= i28' && x = 1
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 + -1, 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 <= 1 && i23 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
was transformed to
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 - 1, 1, i6, env, static) :|: 0 < a6 && i23 - 1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && iconst_1 <= 1 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
was transformed to
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
(30) Obligation:
IntTrs with 10 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_208(a6, iconst_0, iconst_1, i6, env, static) -{0,0}> main_LE_218(a6, 0, 1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
main_NE_258(a6, x, i23, x', i6, env, static) -{3,3}> main_Load_197(a6, i23 - 1, 1, i6, env, static) :|: 0 < a6 && i23 - 1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i23 && x = 0 && x' = 1
main_NE_258(a6, iconst_1, i23, x, i6, env, static) -{0,0}> main_NE_261(a6, 1, i23, i6, env, static) :|: 1 <= i6 && 0 <= iconst_1 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && x = iconst_1
random_ArrayAccess_70(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_73(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
random_InvokeMethod_96(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_99(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, 1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
random_ArrayAccess_70(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_96(o7', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 0 <= o7' && 0 <= static && 1 <= i6 && o7' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_Load_1(o2, env, static) -{23,23}> random_ArrayAccess_70(o2, 0, i4', env, static'3) :|: static'3 <= static'2 + o2 && i4' < o2 && static'2 <= static'1 && 0 < o2 && 0 <= i4' && 0 <= static'2 && o2 <= static'3 && static'1 <= static''' + 1 && 0 <= static'1 && static''' <= static + 2 && 0 <= static''' && -1 * static'3 <= 0 && 0 <= static && 0 <= static'3
random_InvokeMethod_96(o11, a6, x, i6, env, static) -{3,3}> main_Load_197(a6, i7', 1, i6, env, static) :|: i7' <= o11 && 0 <= i7' && 1 <= i6 && 0 < a6 && 0 < o11 && x = 1
main_LE_208(a6, i23, x, i6, env, static) -{4,4}> main_NE_258(a6, i28', i23, 1, i6, env, static) :|: 1 <= i6 && 1 <= i23 && i28' <= 1 && 0 < a6 && 0 < i23 && i28' < 2 && 0 <= i28' && x = 1
(31) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(48)) transformation)
Extracted set of 58 edges for the analysis of TIME complexity. Dropped leaves.
(32) Obligation:
Set of 58 edges based on JBC Program.
Performed SCC analyses:
- Used field analysis yielded the following read fields:
Considered paths: all paths from start
(33) JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID) transformation)
Transformed 58 jbc graph edges to a weighted ITS with 58 rules.
Used simplified encoding of division and modulo.
Filtered conditions with variables that do not depend on the variables on the lhs or rhs without taking transitive dependencies into account.
Filtered fields of type java.lang.Object.
Did no encode lower bounds for putfield and astore.
(34) Obligation:
IntTrs with 58 rules
Start term: main_Load_1(args, env, static)
Considered paths: all paths from start
Rules:
main_Load_1(o2, env, static) -{0,0}> main_Load_3(o2, env, static) :|: 0 < o2
main_Load_3(o2, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_5(o2, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_5(o2, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_13(iconst_0, o2, env, static) :|: 0 < o2 && iconst_0 = 0
langle_clinit_rangle_ArrayCreate_13(iconst_0, o2, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_16(a2, o2, iconst_0, env, static) :|: a2 = 2 && 0 < o2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_16(a2, o2, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_17(o2, env, static') :|: 0 <= a2 && 0 < o2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_17(o2, env, static) -{0,0}> langle_clinit_rangle_New_19(o2, env, static) :|: 0 < o2
langle_clinit_rangle_New_19(o2, env, static) -{0,0}> langle_clinit_rangle_New_20(o2, env, static) :|: 0 < o2 && 0 <= static
langle_clinit_rangle_New_20(o2, env, static) -{1,1}> langle_clinit_rangle_Duplicate_21(o4, o2, env, static) :|: o4 = 1 && 0 < o2 && 0 < o4
langle_clinit_rangle_Duplicate_21(o4, o2, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_24(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_clinit_rangle_ConstantStackPush_24(o4, o2, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_26(o4, NULL, o2, env, static) :|: NULL = 0 && 0 < o2 && 0 < o4
langle_clinit_rangle_InvokeMethod_26(o4, NULL, o2, env, static) -{1,1}> langle_init_rangle_Load_27(o4, o2, env, static) :|: NULL = 0 && 0 < o2 && 0 < o4
langle_init_rangle_Load_27(o4, o2, env, static) -{1,1}> langle_init_rangle_InvokeMethod_31(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_InvokeMethod_31(o4, o2, env, static) -{1,1}> langle_init_rangle_Load_33(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_Load_33(o4, o2, env, static) -{1,1}> langle_init_rangle_InvokeMethod_36(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_InvokeMethod_36(o4, o2, env, static) -{1,1}> langle_init_rangle_Return_37(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_Return_37(o4, o2, env, static) -{1,1}> langle_init_rangle_Return_38(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_init_rangle_Return_38(o4, o2, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_39(o4, o2, env, static) :|: 0 < o2 && 0 < o4
langle_clinit_rangle_FieldAccess_39(o4, o2, env, static) -{1,1}> langle_clinit_rangle_Return_41(o2, env, static') :|: 0 < o2 && 0 <= o4 && 0 < o4 && 0 <= static && static' <= static + o4
langle_clinit_rangle_Return_41(o2, env, static) -{1,1}> main_Load_48(o2, env, static) :|: 0 < o2
main_Load_48(o2, env, static) -{0,0}> main_Load_49(o2, env, static) :|: 0 < o2
main_Load_49(o2, env, static) -{0,0}> main_Load_52(o2, env, static) :|: 0 < o2 && 0 <= static
main_Load_52(o2, env, static) -{0,0}> main_Load_54(o2, env, static) :|: 0 < o2
main_Load_54(o2, env, static) -{0,0}> main_Load_55(o2, env, static) :|: 0 < o2
main_Load_55(o2, env, static) -{1,1}> main_FieldAccess_58(o2, env, static) :|: 0 < o2
main_FieldAccess_58(o2, env, static) -{0,0}> main_FieldAccess_59(o2, env, static) :|: 0 < o2
main_FieldAccess_59(o2, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_61(o2, NULL, iconst_0, env, static) :|: NULL = 0 && 0 < o2 && iconst_0 = 0
langle_clinit_rangle_ConstantStackPush_61(o2, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_62(iconst_0, o2, NULL, env, static) :|: NULL = 0 && 0 < o2 && iconst_0 = 0
langle_clinit_rangle_FieldAccess_62(iconst_0, o2, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_63(o2, NULL, iconst_0, env, static') :|: NULL = 0 && 0 < o2 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0
langle_clinit_rangle_Return_63(o2, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_64(o2, NULL, iconst_0, env, static) :|: NULL = 0 && 0 < o2 && iconst_0 = 0
main_FieldAccess_64(o2, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_65(o2, iconst_0, env, static') :|: NULL = 0 && 0 < o2 && 0 <= o2 && iconst_0 = 0 && 0 <= static && static' <= static + o2
main_InvokeMethod_65(o2, iconst_0, env, static) -{1,1}> random_FieldAccess_66(o2, iconst_0, env, static) :|: 0 < o2 && iconst_0 = 0
random_FieldAccess_66(o2, iconst_0, env, static) -{1,1}> random_FieldAccess_68(o2, iconst_0, env, static) :|: 0 < o2 && o2 <= static && 0 <= o2 && iconst_0 = 0 && 0 <= static
random_FieldAccess_68(o2, iconst_0, env, static) -{1,1}> random_ArrayAccess_69(o2, iconst_0, env, static) :|: 0 < o2 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && iconst_0 <= static
random_ArrayAccess_69(a6, iconst_0, env, static) -{0,0}> random_ArrayAccess_70(a6, iconst_0, i4, env, static) :|: 0 <= i4 && iconst_0 = 0 && 0 < a6 && i4 < a6
random_ArrayAccess_70(a6, iconst_0, i6, env, static) -{0,0}> random_ArrayAccess_74(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_74(a6, iconst_0, i6, env, static) -{1,1}> random_Store_78(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && o7 < a6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_Store_78(o7, a6, iconst_0, i6, env, static) -{1,1}> random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_80(o7, a6, iconst_0, i6, env, static) -{1,1}> random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) :|: 1 <= i6 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && iconst_0 <= static
random_ConstantStackPush_84(iconst_0, o7, a6, i6, env, static) -{1,1}> random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_IntArithmetic_87(iconst_0, iconst_1, o7, a6, i6, env, static) -{1,1}> random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 < a6
random_FieldAccess_89(iconst_1, o7, a6, iconst_0, i6, env, static) -{1,1}> random_Load_92(o7, a6, iconst_1, i6, env, static') :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 0 <= o7 && 0 <= static && 0 < a6 && static' <= static + iconst_1
random_Load_92(o7, a6, iconst_1, i6, env, static) -{1,1}> random_InvokeMethod_96(o7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 <= o7 && 0 < a6
random_InvokeMethod_96(o11, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) :|: 0 <= o11 && 1 <= i6 && iconst_1 = 1 && 0 < o11 && 0 < a6
random_InvokeMethod_98(o11, a6, iconst_1, i6, env, static) -{1,1}> random_Return_104(i7, a6, iconst_1, i6, env, static) :|: 1 <= i6 && i7 <= o11 && iconst_1 = 1 && 0 < o11 && 0 < a6 && 0 <= i7
random_Return_104(i7, a6, iconst_1, i6, env, static) -{1,1}> main_Store_110(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Store_110(a6, i7, iconst_1, i6, env, static) -{1,1}> main_Load_112(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Load_112(a6, i7, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i7, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i7
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208(a6, i23, iconst_1, i6, env, static) -{0,0}> main_LE_219(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 <= i23
main_LE_219(a6, i23, iconst_1, i6, env, static) -{1,1}> main_Load_230(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 < i23
main_Load_230(a6, i23, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && iconst_2 = 2
main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) -{1,1}> main_NE_258(a6, i28, i23, iconst_1, i6, env, static) :|: 0 <= i28 && 1 <= i6 && i28 < iconst_2 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && i28 <= 1 && iconst_2 = 2
main_NE_258(a6, iconst_0, i23, iconst_1, i6, env, static) -{0,0}> main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_0 <= 1 && iconst_1 = 1 && 1 <= i23 && iconst_0 = 0 && 0 < a6
main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) -{1,1}> main_Inc_266(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 1 <= i23 && 0 < a6
main_Inc_266(a6, i23, iconst_1, i6, env, static) -{1,1}> main_JMP_275(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 1 <= i23 && i23 + -1 = i30 && 0 < a6
main_JMP_275(a6, i30, iconst_1, i6, env, static) -{1,1}> main_Load_287(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
main_Load_287(a6, i30, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
(35) StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
obtained
main_Load_1(
o2,
env,
static) -{33,33}>
main_Load_197(
o2,
i7',
1,
i4',
env,
static'4) :|:
static'4 <=
static'3 +
1 &&
0 <=
i7' &&
0 <=
1 &&
0 <
o2 &&
0 <
2 &&
1 <=
i4' &&
0 <=
i4' &&
0 <=
o7' &&
0 <=
static'3 &&
0 <
1 &&
0 <=
static &&
0 <=
static''' &&
static''' <=
static +
2 &&
0 <=
static'1 &&
static'1 <=
static''' +
1 &&
o2 <=
static'3 &&
0 <=
static'2 &&
-1 *
static'3 <=
0 &&
0 <=
o2 &&
i7' <=
o7' &&
o7' <
o2 &&
0 <=
2 &&
0 <
o7' &&
static'2 <=
static'1 +
0 &&
static'3 <=
static'2 +
o2 &&
i4' <
o2by chaining
main_Load_1(
o2,
env,
static) -{0,0}>
main_Load_3(
o2,
env,
static) :|:
0 <
o2main_Load_3(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_ConstantStackPush_5(
o2,
env,
static) :|:
0 <
o2langle_clinit_rangle_ConstantStackPush_5(
o2,
env,
static) -{1,1}>
langle_clinit_rangle_ArrayCreate_13(
iconst_0,
o2,
env,
static) :|:
0 <
o2 &&
iconst_0 =
0langle_clinit_rangle_ArrayCreate_13(
iconst_0,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_FieldAccess_16(
a2,
o2,
iconst_0,
env,
static) :|:
a2 =
2 &&
0 <
o2 &&
iconst_0 =
0 &&
0 <
a2langle_clinit_rangle_FieldAccess_16(
a2,
o2,
iconst_0,
env,
static) -{1,1}>
langle_clinit_rangle_New_17(
o2,
env,
static') :|:
0 <=
a2 &&
0 <
o2 &&
iconst_0 =
0 &&
static' <=
static +
a2 &&
0 <=
static &&
0 <
a2langle_clinit_rangle_New_17(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_New_19(
o2,
env,
static) :|:
0 <
o2langle_clinit_rangle_New_19(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_New_20(
o2,
env,
static) :|:
0 <
o2 &&
0 <=
staticlangle_clinit_rangle_New_20(
o2,
env,
static) -{1,1}>
langle_clinit_rangle_Duplicate_21(
o4,
o2,
env,
static) :|:
o4 =
1 &&
0 <
o2 &&
0 <
o4langle_clinit_rangle_Duplicate_21(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_ConstantStackPush_24(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_clinit_rangle_ConstantStackPush_24(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_InvokeMethod_26(
o4,
NULL,
o2,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
0 <
o4langle_clinit_rangle_InvokeMethod_26(
o4,
NULL,
o2,
env,
static) -{1,1}>
langle_init_rangle_Load_27(
o4,
o2,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
0 <
o4langle_init_rangle_Load_27(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_InvokeMethod_31(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_InvokeMethod_31(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_Load_33(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_Load_33(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_InvokeMethod_36(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_InvokeMethod_36(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_Return_37(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_Return_37(
o4,
o2,
env,
static) -{1,1}>
langle_init_rangle_Return_38(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_init_rangle_Return_38(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_FieldAccess_39(
o4,
o2,
env,
static) :|:
0 <
o2 &&
0 <
o4langle_clinit_rangle_FieldAccess_39(
o4,
o2,
env,
static) -{1,1}>
langle_clinit_rangle_Return_41(
o2,
env,
static') :|:
0 <
o2 &&
0 <=
o4 &&
0 <
o4 &&
0 <=
static &&
static' <=
static +
o4langle_clinit_rangle_Return_41(
o2,
env,
static) -{1,1}>
main_Load_48(
o2,
env,
static) :|:
0 <
o2main_Load_48(
o2,
env,
static) -{0,0}>
main_Load_49(
o2,
env,
static) :|:
0 <
o2main_Load_49(
o2,
env,
static) -{0,0}>
main_Load_52(
o2,
env,
static) :|:
0 <
o2 &&
0 <=
staticmain_Load_52(
o2,
env,
static) -{0,0}>
main_Load_54(
o2,
env,
static) :|:
0 <
o2main_Load_54(
o2,
env,
static) -{0,0}>
main_Load_55(
o2,
env,
static) :|:
0 <
o2main_Load_55(
o2,
env,
static) -{1,1}>
main_FieldAccess_58(
o2,
env,
static) :|:
0 <
o2main_FieldAccess_58(
o2,
env,
static) -{0,0}>
main_FieldAccess_59(
o2,
env,
static) :|:
0 <
o2main_FieldAccess_59(
o2,
env,
static) -{0,0}>
langle_clinit_rangle_ConstantStackPush_61(
o2,
NULL,
iconst_0,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0langle_clinit_rangle_ConstantStackPush_61(
o2,
NULL,
iconst_0,
env,
static) -{1,1}>
langle_clinit_rangle_FieldAccess_62(
iconst_0,
o2,
NULL,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0langle_clinit_rangle_FieldAccess_62(
iconst_0,
o2,
NULL,
env,
static) -{1,1}>
langle_clinit_rangle_Return_63(
o2,
NULL,
iconst_0,
env,
static') :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0 &&
0 <=
static &&
static' <=
static +
iconst_0langle_clinit_rangle_Return_63(
o2,
NULL,
iconst_0,
env,
static) -{1,1}>
main_FieldAccess_64(
o2,
NULL,
iconst_0,
env,
static) :|:
NULL =
0 &&
0 <
o2 &&
iconst_0 =
0main_FieldAccess_64(
o2,
NULL,
iconst_0,
env,
static) -{1,1}>
main_InvokeMethod_65(
o2,
iconst_0,
env,
static') :|:
NULL =
0 &&
0 <
o2 &&
0 <=
o2 &&
iconst_0 =
0 &&
0 <=
static &&
static' <=
static +
o2main_InvokeMethod_65(
o2,
iconst_0,
env,
static) -{1,1}>
random_FieldAccess_66(
o2,
iconst_0,
env,
static) :|:
0 <
o2 &&
iconst_0 =
0random_FieldAccess_66(
o2,
iconst_0,
env,
static) -{1,1}>
random_FieldAccess_68(
o2,
iconst_0,
env,
static) :|:
0 <
o2 &&
o2 <=
static &&
0 <=
o2 &&
iconst_0 =
0 &&
0 <=
staticrandom_FieldAccess_68(
o2,
iconst_0,
env,
static) -{1,1}>
random_ArrayAccess_69(
o2,
iconst_0,
env,
static) :|:
0 <
o2 &&
-1 *
static <=
iconst_0 &&
iconst_0 =
0 &&
0 <=
static &&
iconst_0 <=
staticrandom_ArrayAccess_69(
a6,
iconst_0,
env,
static) -{0,0}>
random_ArrayAccess_70(
a6,
iconst_0,
i4,
env,
static) :|:
0 <=
i4 &&
iconst_0 =
0 &&
0 <
a6 &&
i4 <
a6random_ArrayAccess_70(
a6,
iconst_0,
i6,
env,
static) -{0,0}>
random_ArrayAccess_74(
a6,
iconst_0,
i6,
env,
static) :|:
0 <=
i6 &&
1 <=
i6 &&
iconst_0 =
0 &&
0 <
a6random_ArrayAccess_74(
a6,
iconst_0,
i6,
env,
static) -{1,1}>
random_Store_78(
o7,
a6,
iconst_0,
i6,
env,
static) :|:
1 <=
i6 &&
o7 <
a6 &&
iconst_0 =
0 &&
0 <=
o7 &&
0 <
a6random_Store_78(
o7,
a6,
iconst_0,
i6,
env,
static) -{1,1}>
random_FieldAccess_80(
o7,
a6,
iconst_0,
i6,
env,
static) :|:
1 <=
i6 &&
iconst_0 =
0 &&
0 <=
o7 &&
0 <
a6random_FieldAccess_80(
o7,
a6,
iconst_0,
i6,
env,
static) -{1,1}>
random_ConstantStackPush_84(
iconst_0,
o7,
a6,
i6,
env,
static) :|:
1 <=
i6 &&
-1 *
static <=
iconst_0 &&
iconst_0 =
0 &&
0 <=
o7 &&
0 <=
static &&
0 <
a6 &&
iconst_0 <=
staticrandom_ConstantStackPush_84(
iconst_0,
o7,
a6,
i6,
env,
static) -{1,1}>
random_IntArithmetic_87(
iconst_0,
iconst_1,
o7,
a6,
i6,
env,
static) :|:
1 <=
i6 &&
iconst_1 =
1 &&
iconst_0 =
0 &&
0 <=
o7 &&
0 <
a6random_IntArithmetic_87(
iconst_0,
iconst_1,
o7,
a6,
i6,
env,
static) -{1,1}>
random_FieldAccess_89(
iconst_1,
o7,
a6,
iconst_0,
i6,
env,
static) :|:
1 <=
i6 &&
iconst_1 =
1 &&
iconst_0 =
0 &&
0 <=
o7 &&
0 <
a6random_FieldAccess_89(
iconst_1,
o7,
a6,
iconst_0,
i6,
env,
static) -{1,1}>
random_Load_92(
o7,
a6,
iconst_1,
i6,
env,
static') :|:
1 <=
i6 &&
iconst_1 =
1 &&
iconst_0 =
0 &&
0 <=
o7 &&
0 <=
static &&
0 <
a6 &&
static' <=
static +
iconst_1random_Load_92(
o7,
a6,
iconst_1,
i6,
env,
static) -{1,1}>
random_InvokeMethod_96(
o7,
a6,
iconst_1,
i6,
env,
static) :|:
1 <=
i6 &&
iconst_1 =
1 &&
0 <=
o7 &&
0 <
a6random_InvokeMethod_96(
o11,
a6,
iconst_1,
i6,
env,
static) -{0,0}>
random_InvokeMethod_98(
o11,
a6,
iconst_1,
i6,
env,
static) :|:
0 <=
o11 &&
1 <=
i6 &&
iconst_1 =
1 &&
0 <
o11 &&
0 <
a6random_InvokeMethod_98(
o11,
a6,
iconst_1,
i6,
env,
static) -{1,1}>
random_Return_104(
i7,
a6,
iconst_1,
i6,
env,
static) :|:
1 <=
i6 &&
i7 <=
o11 &&
iconst_1 =
1 &&
0 <
o11 &&
0 <
a6 &&
0 <=
i7random_Return_104(
i7,
a6,
iconst_1,
i6,
env,
static) -{1,1}>
main_Store_110(
a6,
i7,
iconst_1,
i6,
env,
static) :|:
1 <=
i6 &&
iconst_1 =
1 &&
0 <
a6 &&
0 <=
i7main_Store_110(
a6,
i7,
iconst_1,
i6,
env,
static) -{1,1}>
main_Load_112(
a6,
i7,
iconst_1,
i6,
env,
static) :|:
1 <=
i6 &&
iconst_1 =
1 &&
0 <
a6 &&
0 <=
i7main_Load_112(
a6,
i7,
iconst_1,
i6,
env,
static) -{0,0}>
main_Load_197(
a6,
i7,
iconst_1,
i6,
env,
static) :|:
1 <=
i6 &&
iconst_1 =
1 &&
0 <
a6 &&
0 <=
i7obtained
main_Load_197(a6, i17, 1, i6, env, static) -{8,8}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 < 2 && i17 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i17 && 0 < i17 && 0 <= 1 && 0 <= i17
by chaining
main_Load_197(a6, i17, iconst_1, i6, env, static) -{1,1}> main_LE_208(a6, i17, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i17 && iconst_1 = 1 && 0 < a6
main_LE_208(a6, i23, iconst_1, i6, env, static) -{0,0}> main_LE_219(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 <= i23
main_LE_219(a6, i23, iconst_1, i6, env, static) -{1,1}> main_Load_230(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && 0 < i23
main_Load_230(a6, i23, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6
main_ConstantStackPush_240(a6, i23, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && iconst_2 = 2
main_IntArithmetic_255(a6, i23, iconst_2, iconst_1, i6, env, static) -{1,1}> main_NE_258(a6, i28, i23, iconst_1, i6, env, static) :|: 0 <= i28 && 1 <= i6 && i28 < iconst_2 && iconst_1 = 1 && 1 <= i23 && 0 < a6 && i28 <= 1 && iconst_2 = 2
main_NE_258(a6, iconst_0, i23, iconst_1, i6, env, static) -{0,0}> main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && iconst_0 <= 1 && iconst_1 = 1 && 1 <= i23 && iconst_0 = 0 && 0 < a6
main_NE_262(a6, iconst_0, i23, iconst_1, i6, env, static) -{1,1}> main_Inc_266(a6, i23, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && iconst_0 = 0 && 1 <= i23 && 0 < a6
main_Inc_266(a6, i23, iconst_1, i6, env, static) -{1,1}> main_JMP_275(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 1 <= i23 && i23 + -1 = i30 && 0 < a6
main_JMP_275(a6, i30, iconst_1, i6, env, static) -{1,1}> main_Load_287(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
main_Load_287(a6, i30, iconst_1, i6, env, static) -{0,0}> main_Load_197(a6, i30, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= i30 && iconst_1 = 1 && 0 < a6
(36) Obligation:
IntTrs with 2 rules
Start term: main_Load_1(args, env, static)
Considered paths: all paths from start
Rules:
main_Load_1(o2, env, static) -{33,33}> main_Load_197(o2, i7', 1, i4', env, static'4) :|: static'4 <= static'3 + 1 && 0 <= i7' && 0 <= 1 && 0 < o2 && 0 < 2 && 1 <= i4' && 0 <= i4' && 0 <= o7' && 0 <= static'3 && 0 < 1 && 0 <= static && 0 <= static''' && static''' <= static + 2 && 0 <= static'1 && static'1 <= static''' + 1 && o2 <= static'3 && 0 <= static'2 && -1 * static'3 <= 0 && 0 <= o2 && i7' <= o7' && o7' < o2 && 0 <= 2 && 0 < o7' && static'2 <= static'1 + 0 && static'3 <= static'2 + o2 && i4' < o2
main_Load_197(a6, i17, 1, i6, env, static) -{8,8}> main_Load_197(a6, i30', 1, i6, env, static) :|: 0 <= 0 && 0 < a6 && 0 < 2 && i17 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i17 && 0 < i17 && 0 <= 1 && 0 <= i17
(37) WeightedIntTrsUnneededArgumentFilterProof (CONCRETE UPPER BOUND(ID) transformation)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
main_Load_1(x1, x2, x3) → main_Load_1(x1, x3)
main_Load_197(x1, x2, x3, x4, x5, x6) → main_Load_197(x1, x2, x4)
(38) Obligation:
IntTrs with 2 rules
Start term: main_Load_1(args, static)
Considered paths: all paths from start
Rules:
main_Load_1(o2, static) -{33,33}> main_Load_197(o2, i7', i4') :|: static'4 <= static'3 + 1 && 0 <= i7' && 0 <= 1 && 0 < o2 && 0 < 2 && 1 <= i4' && 0 <= i4' && 0 <= o7' && 0 <= static'3 && 0 < 1 && 0 <= static && 0 <= static''' && static''' <= static + 2 && 0 <= static'1 && static'1 <= static''' + 1 && o2 <= static'3 && 0 <= static'2 && -1 * static'3 <= 0 && 0 <= o2 && i7' <= o7' && o7' < o2 && 0 <= 2 && 0 < o7' && static'2 <= static'1 + 0 && static'3 <= static'2 + o2 && i4' < o2
main_Load_197(a6, i17, i6) -{8,8}> main_Load_197(a6, i30', i6) :|: 0 <= 0 && 0 < a6 && 0 < 2 && i17 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i17 && 0 < i17 && 0 <= 1 && 0 <= i17
(39) MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Moved arithmethic from constraints to rhss.
main_Load_197(a6, i17, i6) -{8,8}> main_Load_197(a6, i30', i6) :|: 0 <= 0 && 0 < a6 && 0 < 2 && i17 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i17 && 0 < i17 && 0 <= 1 && 0 <= i17
was transformed to
main_Load_197(a6, i17, i6) -{8,8}> main_Load_197(a6, i17 + -1, i6) :|: 0 <= 0 && 0 < a6 && 0 < 2 && i17 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i17 && 0 < i17 && 0 <= 1 && 0 <= i17
(40) Obligation:
IntTrs with 2 rules
Start term: main_Load_1(args, static)
Considered paths: all paths from start
Rules:
main_Load_1(o2, static) -{33,33}> main_Load_197(o2, i7', i4') :|: static'4 <= static'3 + 1 && 0 <= i7' && 0 <= 1 && 0 < o2 && 0 < 2 && 1 <= i4' && 0 <= i4' && 0 <= o7' && 0 <= static'3 && 0 < 1 && 0 <= static && 0 <= static''' && static''' <= static + 2 && 0 <= static'1 && static'1 <= static''' + 1 && o2 <= static'3 && 0 <= static'2 && -1 * static'3 <= 0 && 0 <= o2 && i7' <= o7' && o7' < o2 && 0 <= 2 && 0 < o7' && static'2 <= static'1 + 0 && static'3 <= static'2 + o2 && i4' < o2
main_Load_197(a6, i17, i6) -{8,8}> main_Load_197(a6, i17 + -1, i6) :|: 0 <= 0 && 0 < a6 && 0 < 2 && i17 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i17 && 0 < i17 && 0 <= 1 && 0 <= i17
(41) ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)
Simplified expressions.
main_Load_1(o2, static) -{33,33}> main_Load_197(o2, i7', i4') :|: static'4 <= static'3 + 1 && 0 <= i7' && 0 <= 1 && 0 < o2 && 0 < 2 && 1 <= i4' && 0 <= i4' && 0 <= o7' && 0 <= static'3 && 0 < 1 && 0 <= static && 0 <= static''' && static''' <= static + 2 && 0 <= static'1 && static'1 <= static''' + 1 && o2 <= static'3 && 0 <= static'2 && -1 * static'3 <= 0 && 0 <= o2 && i7' <= o7' && o7' < o2 && 0 <= 2 && 0 < o7' && static'2 <= static'1 + 0 && static'3 <= static'2 + o2 && i4' < o2
was transformed to
main_Load_1(o2, static) -{33,33}> main_Load_197(o2, i7', i4') :|: static'4 <= static'3 + 1 && 0 <= i7' && 0 < o2 && 1 <= i4' && 0 <= i4' && 0 <= static'3 && 0 <= static && 0 <= static''' && static''' <= static + 2 && 0 <= static'1 && static'1 <= static''' + 1 && o2 <= static'3 && 0 <= static'2 && -1 * static'3 <= 0 && i7' <= o7' && o7' < o2 && 0 < o7' && static'2 <= static'1 && static'3 <= static'2 + o2 && i4' < o2
main_Load_197(a6, i17, i6) -{8,8}> main_Load_197(a6, i17 + -1, i6) :|: 0 <= 0 && 0 < a6 && 0 < 2 && i17 + -1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i17 && 0 < i17 && 0 <= 1 && 0 <= i17
was transformed to
main_Load_197(a6, i17, i6) -{8,8}> main_Load_197(a6, i17 - 1, i6) :|: 0 < a6 && i17 - 1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i17 && 0 < i17
(42) Obligation:
IntTrs with 2 rules
Start term: main_Load_1(args, static)
Considered paths: all paths from start
Rules:
main_Load_197(a6, i17, i6) -{8,8}> main_Load_197(a6, i17 - 1, i6) :|: 0 < a6 && i17 - 1 = i30' && 1 <= i6 && 0 <= i30' && 1 <= i17 && 0 < i17
main_Load_1(o2, static) -{33,33}> main_Load_197(o2, i7', i4') :|: static'4 <= static'3 + 1 && 0 <= i7' && 0 < o2 && 1 <= i4' && 0 <= i4' && 0 <= static'3 && 0 <= static && 0 <= static''' && static''' <= static + 2 && 0 <= static'1 && static'1 <= static''' + 1 && o2 <= static'3 && 0 <= static'2 && -1 * static'3 <= 0 && i7' <= o7' && o7' < o2 && 0 < o7' && static'2 <= static'1 && static'3 <= static'2 + o2 && i4' < o2
(43) koat Proof (EQUIVALENT transformation)
YES(?, 8*ar_0 + 33)
Initial complexity problem:
1: T:
(Comp: ?, Cost: 8) main_Load_197(ar_0, ar_1, ar_2) -> Com_1(main_Load_197(ar_0, ar_1 - 1, ar_2)) [ 0 < ar_0 /\ ar_1 - 1 = i30' /\ 1 <= ar_2 /\ 0 <= i30' /\ 1 <= ar_1 /\ 0 < ar_1 ]
(Comp: ?, Cost: 33) main_Load_1(ar_0, ar_1, ar_2) -> Com_1(main_Load_197(ar_0, i7', i4')) [ static'4 <= static'3 + 1 /\ 0 <= i7' /\ 0 < ar_0 /\ 1 <= i4' /\ 0 <= i4' /\ 0 <= static'3 /\ 0 <= ar_1 /\ 0 <= static''' /\ static''' <= ar_1 + 2 /\ 0 <= static'1 /\ static'1 <= static''' + 1 /\ ar_0 <= static'3 /\ 0 <= static'2 /\ -static'3 <= 0 /\ i7' <= o7' /\ o7' < ar_0 /\ 0 < o7' /\ static'2 <= static'1 /\ static'3 <= static'2 + ar_0 /\ i4' < ar_0 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(main_Load_1(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0
Repeatedly propagating knowledge in problem 1 produces the following problem:
2: T:
(Comp: ?, Cost: 8) main_Load_197(ar_0, ar_1, ar_2) -> Com_1(main_Load_197(ar_0, ar_1 - 1, ar_2)) [ 0 < ar_0 /\ ar_1 - 1 = i30' /\ 1 <= ar_2 /\ 0 <= i30' /\ 1 <= ar_1 /\ 0 < ar_1 ]
(Comp: 1, Cost: 33) main_Load_1(ar_0, ar_1, ar_2) -> Com_1(main_Load_197(ar_0, i7', i4')) [ static'4 <= static'3 + 1 /\ 0 <= i7' /\ 0 < ar_0 /\ 1 <= i4' /\ 0 <= i4' /\ 0 <= static'3 /\ 0 <= ar_1 /\ 0 <= static''' /\ static''' <= ar_1 + 2 /\ 0 <= static'1 /\ static'1 <= static''' + 1 /\ ar_0 <= static'3 /\ 0 <= static'2 /\ -static'3 <= 0 /\ i7' <= o7' /\ o7' < ar_0 /\ 0 < o7' /\ static'2 <= static'1 /\ static'3 <= static'2 + ar_0 /\ i4' < ar_0 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(main_Load_1(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0
A polynomial rank function with
Pol(main_Load_197) = V_2
Pol(main_Load_1) = V_1
Pol(koat_start) = V_1
orients all transitions weakly and the transition
main_Load_197(ar_0, ar_1, ar_2) -> Com_1(main_Load_197(ar_0, ar_1 - 1, ar_2)) [ 0 < ar_0 /\ ar_1 - 1 = i30' /\ 1 <= ar_2 /\ 0 <= i30' /\ 1 <= ar_1 /\ 0 < ar_1 ]
strictly and produces the following problem:
3: T:
(Comp: ar_0, Cost: 8) main_Load_197(ar_0, ar_1, ar_2) -> Com_1(main_Load_197(ar_0, ar_1 - 1, ar_2)) [ 0 < ar_0 /\ ar_1 - 1 = i30' /\ 1 <= ar_2 /\ 0 <= i30' /\ 1 <= ar_1 /\ 0 < ar_1 ]
(Comp: 1, Cost: 33) main_Load_1(ar_0, ar_1, ar_2) -> Com_1(main_Load_197(ar_0, i7', i4')) [ static'4 <= static'3 + 1 /\ 0 <= i7' /\ 0 < ar_0 /\ 1 <= i4' /\ 0 <= i4' /\ 0 <= static'3 /\ 0 <= ar_1 /\ 0 <= static''' /\ static''' <= ar_1 + 2 /\ 0 <= static'1 /\ static'1 <= static''' + 1 /\ ar_0 <= static'3 /\ 0 <= static'2 /\ -static'3 <= 0 /\ i7' <= o7' /\ o7' < ar_0 /\ 0 < o7' /\ static'2 <= static'1 /\ static'3 <= static'2 + ar_0 /\ i4' < ar_0 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(main_Load_1(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0
Complexity upper bound 8*ar_0 + 33
Time: 0.123 sec (SMT: 0.115 sec)
(44) BOUNDS(CONSTANT, 33 + 8 * |args|)