time complexity proof of /tmp/tmp2ZLQki/PastaA1.jar

The time complexity of the given JBC problem could be proven to be BOUNDS(CONSTANT, 80 + 18 * |args| + 10 * |args|^2).

0 JBC problem

↳1 JBCToGraph (BOTH CONCRETE BOUNDS(ID, ID), 483 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(47)), 0 ms)

↳4 JBCComplexityEdges

    ↳5 JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID), 117 ms)

    ↳6 WeightedIntTrs

        ↳7 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 37 ms)

        ↳8 WeightedIntTrs

        ↳9 MovedArithmeticToConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

        ↳10 WeightedIntTrs

        ↳11 LinearizedLhssProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

        ↳12 WeightedIntTrs

        ↳13 MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

        ↳14 WeightedIntTrs

        ↳15 ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

        ↳16 WeightedIntTrs

    ↳17 JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID), 133 ms)

    ↳18 WeightedIntTrs

        ↳19 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 26 ms)

        ↳20 WeightedIntTrs

        ↳21 MovedArithmeticToConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

        ↳22 WeightedIntTrs

        ↳23 LinearizedLhssProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

        ↳24 WeightedIntTrs

        ↳25 MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

        ↳26 WeightedIntTrs

        ↳27 ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

        ↳28 WeightedIntTrs

↳29 TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(47)), 0 ms)

↳30 JBCComplexityEdges

    ↳31 JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID), 100 ms)

    ↳32 WeightedIntTrs

    ↳33 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 24 ms)

    ↳34 WeightedIntTrs

    ↳35 WeightedIntTrsUnneededArgumentFilterProof (CONCRETE UPPER BOUND(ID), 0 ms)

    ↳36 WeightedIntTrs

    ↳37 MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

    ↳38 WeightedIntTrs

    ↳39 ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID), 0 ms)

    ↳40 WeightedIntTrs

    ↳41 koat Proof (⇔, 163 ms)

    ↳42 BOUNDS(CONSTANT, 33 + 18 * |args| + 10 * |args|^2)

(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 PastaA1 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        while (x > 0) {
            int y = 0;
            while (y < x) {
                y++;
            }
            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:
PastaA1.main([Ljava/lang/String;)V: Graph of 117 nodes with 1 SCC.

(3) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(47)) transformation)

Extracted set of 70 edges for the analysis of TIME complexity. Kept leaves.

(4) Obligation:

Set of 70 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 70 jbc graph edges to a weighted ITS with 70 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.

(6) Obligation:

IntTrs with 70 rules
Start term: main_Load_1(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(o1, env, static) -{0,0}> main_Load_3(o1, env, static) :|: 0 < o1
main_Load_3(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(o1, env, static) :|: 0 < o1
langle_clinit_rangle_ConstantStackPush_6(o1, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_9(iconst_0, o1, env, static) :|: iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ArrayCreate_9(iconst_0, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_11(a2, o1, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2 && 0 < o1
langle_clinit_rangle_FieldAccess_11(a2, o1, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_14(o1, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2 && 0 < o1
langle_clinit_rangle_New_14(o1, env, static) -{0,0}> langle_clinit_rangle_New_15(o1, env, static) :|: 0 < o1
langle_clinit_rangle_New_15(o1, env, static) -{0,0}> langle_clinit_rangle_New_16(o1, env, static) :|: 0 <= static && 0 < o1
langle_clinit_rangle_New_16(o1, env, static) -{1,1}> langle_clinit_rangle_Duplicate_18(o4, o1, env, static) :|: o4 = 1 && 0 < o4 && 0 < o1
langle_clinit_rangle_Duplicate_18(o4, o1, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_20(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_ConstantStackPush_20(o4, o1, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_22(o4, NULL, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_clinit_rangle_InvokeMethod_22(o4, NULL, o1, env, static) -{1,1}> langle_init_rangle_Load_24(o4, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_init_rangle_Load_24(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_26(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_26(o4, o1, env, static) -{1,1}> langle_init_rangle_Load_28(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Load_28(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_30(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_30(o4, o1, env, static) -{1,1}> langle_init_rangle_Return_33(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_33(o4, o1, env, static) -{1,1}> langle_init_rangle_Return_36(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_36(o4, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_38(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_FieldAccess_38(o4, o1, env, static) -{1,1}> langle_clinit_rangle_Return_43(o1, env, static') :|: 0 <= o4 && 0 < o4 && 0 <= static && 0 < o1 && static' <= static + o4
langle_clinit_rangle_Return_43(o1, env, static) -{1,1}> main_Load_54(o1, env, static) :|: 0 < o1
main_Load_54(o1, env, static) -{0,0}> main_Load_55(o1, env, static) :|: 0 < o1
main_Load_55(o1, env, static) -{0,0}> main_Load_56(o1, env, static) :|: 0 <= static && 0 < o1
main_Load_56(o1, env, static) -{0,0}> main_Load_57(o1, env, static) :|: 0 < o1
main_Load_57(o1, env, static) -{0,0}> main_Load_58(o1, env, static) :|: 0 < o1
main_Load_58(o1, env, static) -{1,1}> main_FieldAccess_59(o1, env, static) :|: 0 < o1
main_FieldAccess_59(o1, env, static) -{0,0}> main_FieldAccess_60(o1, env, static) :|: 0 < o1
main_FieldAccess_60(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_61(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ConstantStackPush_61(o1, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_63(iconst_0, o1, NULL, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_FieldAccess_63(iconst_0, o1, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_64(o1, NULL, iconst_0, env, static') :|: NULL = 0 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0 && 0 < o1
langle_clinit_rangle_Return_64(o1, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_65(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
main_FieldAccess_65(o1, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_66(o1, iconst_0, env, static') :|: static' <= static + o1 && NULL = 0 && 0 <= o1 && iconst_0 = 0 && 0 <= static && 0 < o1
main_InvokeMethod_66(o1, iconst_0, env, static) -{1,1}> random_FieldAccess_69(o1, iconst_0, env, static) :|: iconst_0 = 0 && 0 < o1
random_FieldAccess_69(o1, iconst_0, env, static) -{1,1}> random_FieldAccess_70(o1, iconst_0, env, static) :|: 0 <= o1 && o1 <= static && iconst_0 = 0 && 0 <= static && 0 < o1
random_FieldAccess_70(o1, iconst_0, env, static) -{1,1}> random_ArrayAccess_72(o1, iconst_0, env, static) :|: -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && iconst_0 <= static && 0 < o1
random_ArrayAccess_72(a6, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, i5, env, static) :|: i5 < a6 && iconst_0 = 0 && 0 < a6 && 0 <= i5
random_ArrayAccess_73(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_75(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_73(a6, iconst_0, i6, env, static) -{0,0}> random_ArrayAccess_76(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_76(a6, iconst_0, i6, env, static) -{1,1}> random_Store_81(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && o8 < a6 && iconst_0 = 0 && 0 < a6
random_Store_81(o8, a6, iconst_0, i6, env, static) -{1,1}> random_FieldAccess_83(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_0 = 0 && 0 < a6
random_FieldAccess_83(o8, a6, iconst_0, i6, env, static) -{1,1}> random_ConstantStackPush_87(iconst_0, o8, a6, i6, env, static) :|: 1 <= i6 && 0 <= o8 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && 0 < a6 && iconst_0 <= static
random_ConstantStackPush_87(iconst_0, o8, a6, i6, env, static) -{1,1}> random_IntArithmetic_90(iconst_0, iconst_1, o8, a6, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_IntArithmetic_90(iconst_0, iconst_1, o8, a6, i6, env, static) -{1,1}> random_FieldAccess_92(iconst_1, o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_FieldAccess_92(iconst_1, o8, a6, iconst_0, i6, env, static) -{1,1}> random_Load_96(o8, a6, iconst_1, i6, env, static') :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 <= static && 0 < a6 && static' <= static + iconst_1
random_Load_96(o8, a6, iconst_1, i6, env, static) -{1,1}> random_InvokeMethod_100(o8, a6, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_100(o12, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_102(o12, a6, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= o12 && 0 < o12 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_InvokeMethod_102(o12, a6, iconst_1, i6, env, static) -{1,1}> random_Return_106(i8, a6, iconst_1, i6, env, static) :|: 1 <= i6 && i8 <= o12 && 0 < o12 && iconst_1 = 1 && 0 < a6 && 0 <= i8
random_Return_106(i8, a6, iconst_1, i6, env, static) -{1,1}> main_Store_112(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Store_112(a6, i8, iconst_1, i6, env, static) -{1,1}> main_Load_115(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_115(a6, i8, iconst_1, i6, env, static) -{0,0}> main_Load_332(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_332(a63, i50, iconst_1, i6, env, static) -{0,0}> main_Load_416(a63, i50, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a63 && iconst_1 = 1 && 0 <= i50
main_Load_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
main_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0
main_LE_417(a103, i83, iconst_1, i6, env, static) -{0,0}> main_LE_419(a103, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1
main_LE_419(a103, i83, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_422(a103, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && 0 < i83
main_ConstantStackPush_422(a103, i83, iconst_1, i6, env, static) -{1,1}> main_Store_425(a103, iconst_0, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && iconst_0 = 0
main_Store_425(a103, iconst_0, i83, iconst_1, i6, env, static) -{1,1}> main_Load_427(a103, i83, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && iconst_0 = 0
main_Load_427(a103, i83, iconst_0, iconst_1, i6, env, static) -{0,0}> main_Load_472(a103, i83, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && 0 < a103 && 1 <= i83 && iconst_0 <= 2 && iconst_1 = 1 && iconst_0 = 0
main_Load_472(a125, i83, i92, iconst_1, i6, env, static) -{0,0}> main_Load_502(a125, i83, i92, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && i92 <= 2 && 0 < a125 && iconst_1 = 1 && 0 <= i92
main_Load_502(a135, i83, i97, iconst_1, i6, env, static) -{1,1}> main_Load_504(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_Load_504(a135, i97, i83, iconst_1, i6, env, static) -{1,1}> main_GE_509(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_GE_509(a135, i97, i83, iconst_1, i6, env, static) -{0,0}> main_GE_510(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && i83 <= i97 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_GE_509(a135, i97, i83, iconst_1, i6, env, static) -{0,0}> main_GE_511(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1 && i97 < i83
main_GE_510(a135, i97, i83, iconst_1, i6, env, static) -{1,1}> main_Inc_513(a135, i83, iconst_1, i6, env, static) :|: 1 <= i6 && i83 <= i97 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_GE_511(a135, i97, i83, iconst_1, i6, env, static) -{1,1}> main_Inc_518(a135, i83, i97, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1 && i97 < i83
main_Inc_513(a135, i83, iconst_1, i6, env, static) -{1,1}> main_JMP_521(a135, i99, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 < a135 && i83 + -1 = i99 && iconst_1 = 1 && 0 <= i99
main_Inc_518(a135, i83, i97, iconst_1, i6, env, static) -{1,1}> main_JMP_524(a135, i83, i100, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1 && 1 <= i100 && i97 + 1 = i100
main_JMP_521(a135, i99, iconst_1, i6, env, static) -{1,1}> main_Load_530(a135, i99, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a135 && iconst_1 = 1 && 0 <= i99
main_JMP_524(a135, i83, i100, iconst_1, i6, env, static) -{1,1}> main_Load_535(a135, i83, i100, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 < a135 && iconst_1 = 1 && 1 <= i100
main_Load_530(a135, i99, iconst_1, i6, env, static) -{0,0}> main_Load_416(a135, i99, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a135 && iconst_1 = 1 && 0 <= i99
main_Load_535(a135, i83, i100, iconst_1, i6, env, static) -{0,0}> main_Load_502(a135, i83, i100, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 < a135 && iconst_1 = 1 && 0 <= i100 && 1 <= i100

(7) StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

obtained
main_Load_1(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 <= 2 && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= 1 && 0 < 1
by chaining
main_Load_1(o1, env, static) -{0,0}> main_Load_3(o1, env, static) :|: 0 < o1
main_Load_3(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(o1, env, static) :|: 0 < o1
langle_clinit_rangle_ConstantStackPush_6(o1, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_9(iconst_0, o1, env, static) :|: iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ArrayCreate_9(iconst_0, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_11(a2, o1, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2 && 0 < o1
langle_clinit_rangle_FieldAccess_11(a2, o1, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_14(o1, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2 && 0 < o1
langle_clinit_rangle_New_14(o1, env, static) -{0,0}> langle_clinit_rangle_New_15(o1, env, static) :|: 0 < o1
langle_clinit_rangle_New_15(o1, env, static) -{0,0}> langle_clinit_rangle_New_16(o1, env, static) :|: 0 <= static && 0 < o1
langle_clinit_rangle_New_16(o1, env, static) -{1,1}> langle_clinit_rangle_Duplicate_18(o4, o1, env, static) :|: o4 = 1 && 0 < o4 && 0 < o1
langle_clinit_rangle_Duplicate_18(o4, o1, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_20(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_ConstantStackPush_20(o4, o1, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_22(o4, NULL, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_clinit_rangle_InvokeMethod_22(o4, NULL, o1, env, static) -{1,1}> langle_init_rangle_Load_24(o4, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_init_rangle_Load_24(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_26(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_26(o4, o1, env, static) -{1,1}> langle_init_rangle_Load_28(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Load_28(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_30(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_30(o4, o1, env, static) -{1,1}> langle_init_rangle_Return_33(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_33(o4, o1, env, static) -{1,1}> langle_init_rangle_Return_36(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_36(o4, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_38(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_FieldAccess_38(o4, o1, env, static) -{1,1}> langle_clinit_rangle_Return_43(o1, env, static') :|: 0 <= o4 && 0 < o4 && 0 <= static && 0 < o1 && static' <= static + o4
langle_clinit_rangle_Return_43(o1, env, static) -{1,1}> main_Load_54(o1, env, static) :|: 0 < o1
main_Load_54(o1, env, static) -{0,0}> main_Load_55(o1, env, static) :|: 0 < o1
main_Load_55(o1, env, static) -{0,0}> main_Load_56(o1, env, static) :|: 0 <= static && 0 < o1
main_Load_56(o1, env, static) -{0,0}> main_Load_57(o1, env, static) :|: 0 < o1
main_Load_57(o1, env, static) -{0,0}> main_Load_58(o1, env, static) :|: 0 < o1
main_Load_58(o1, env, static) -{1,1}> main_FieldAccess_59(o1, env, static) :|: 0 < o1
main_FieldAccess_59(o1, env, static) -{0,0}> main_FieldAccess_60(o1, env, static) :|: 0 < o1
main_FieldAccess_60(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_61(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ConstantStackPush_61(o1, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_63(iconst_0, o1, NULL, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_FieldAccess_63(iconst_0, o1, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_64(o1, NULL, iconst_0, env, static') :|: NULL = 0 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0 && 0 < o1
langle_clinit_rangle_Return_64(o1, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_65(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
main_FieldAccess_65(o1, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_66(o1, iconst_0, env, static') :|: static' <= static + o1 && NULL = 0 && 0 <= o1 && iconst_0 = 0 && 0 <= static && 0 < o1
main_InvokeMethod_66(o1, iconst_0, env, static) -{1,1}> random_FieldAccess_69(o1, iconst_0, env, static) :|: iconst_0 = 0 && 0 < o1
random_FieldAccess_69(o1, iconst_0, env, static) -{1,1}> random_FieldAccess_70(o1, iconst_0, env, static) :|: 0 <= o1 && o1 <= static && iconst_0 = 0 && 0 <= static && 0 < o1
random_FieldAccess_70(o1, iconst_0, env, static) -{1,1}> random_ArrayAccess_72(o1, iconst_0, env, static) :|: -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && iconst_0 <= static && 0 < o1
random_ArrayAccess_72(a6, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, i5, env, static) :|: i5 < a6 && iconst_0 = 0 && 0 < a6 && 0 <= i5

obtained
random_ArrayAccess_73(a6, 0, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1
by chaining
random_ArrayAccess_73(a6, iconst_0, i6, env, static) -{0,0}> random_ArrayAccess_76(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_76(a6, iconst_0, i6, env, static) -{1,1}> random_Store_81(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && o8 < a6 && iconst_0 = 0 && 0 < a6
random_Store_81(o8, a6, iconst_0, i6, env, static) -{1,1}> random_FieldAccess_83(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_0 = 0 && 0 < a6
random_FieldAccess_83(o8, a6, iconst_0, i6, env, static) -{1,1}> random_ConstantStackPush_87(iconst_0, o8, a6, i6, env, static) :|: 1 <= i6 && 0 <= o8 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && 0 < a6 && iconst_0 <= static
random_ConstantStackPush_87(iconst_0, o8, a6, i6, env, static) -{1,1}> random_IntArithmetic_90(iconst_0, iconst_1, o8, a6, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_IntArithmetic_90(iconst_0, iconst_1, o8, a6, i6, env, static) -{1,1}> random_FieldAccess_92(iconst_1, o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_FieldAccess_92(iconst_1, o8, a6, iconst_0, i6, env, static) -{1,1}> random_Load_96(o8, a6, iconst_1, i6, env, static') :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 <= static && 0 < a6 && static' <= static + iconst_1
random_Load_96(o8, a6, iconst_1, i6, env, static) -{1,1}> random_InvokeMethod_100(o8, a6, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && 0 < a6

obtained
random_InvokeMethod_100(o12, a6, 1, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12
by chaining
random_InvokeMethod_100(o12, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_102(o12, a6, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= o12 && 0 < o12 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_102(o12, a6, iconst_1, i6, env, static) -{1,1}> random_Return_106(i8, a6, iconst_1, i6, env, static) :|: 1 <= i6 && i8 <= o12 && 0 < o12 && iconst_1 = 1 && 0 < a6 && 0 <= i8
random_Return_106(i8, a6, iconst_1, i6, env, static) -{1,1}> main_Store_112(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Store_112(a6, i8, iconst_1, i6, env, static) -{1,1}> main_Load_115(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_115(a6, i8, iconst_1, i6, env, static) -{0,0}> main_Load_332(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_332(a63, i50, iconst_1, i6, env, static) -{0,0}> main_Load_416(a63, i50, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a63 && iconst_1 = 1 && 0 <= i50

obtained
main_LE_417(a103, i83, 1, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6
by chaining
main_LE_417(a103, i83, iconst_1, i6, env, static) -{0,0}> main_LE_419(a103, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1
main_LE_419(a103, i83, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_422(a103, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && 0 < i83
main_ConstantStackPush_422(a103, i83, iconst_1, i6, env, static) -{1,1}> main_Store_425(a103, iconst_0, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && iconst_0 = 0
main_Store_425(a103, iconst_0, i83, iconst_1, i6, env, static) -{1,1}> main_Load_427(a103, i83, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && iconst_0 = 0
main_Load_427(a103, i83, iconst_0, iconst_1, i6, env, static) -{0,0}> main_Load_472(a103, i83, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && 0 < a103 && 1 <= i83 && iconst_0 <= 2 && iconst_1 = 1 && iconst_0 = 0
main_Load_472(a125, i83, i92, iconst_1, i6, env, static) -{0,0}> main_Load_502(a125, i83, i92, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && i92 <= 2 && 0 < a125 && iconst_1 = 1 && 0 <= i92

obtained
main_Load_502(a135, i83, i97, 1, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83
by chaining
main_Load_502(a135, i83, i97, iconst_1, i6, env, static) -{1,1}> main_Load_504(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_Load_504(a135, i97, i83, iconst_1, i6, env, static) -{1,1}> main_GE_509(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1

obtained
main_GE_509(a135, i97, i83, 1, i6, env, static) -{3,3}> main_Load_502(a135, i83, i100', 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83
by chaining
main_GE_509(a135, i97, i83, iconst_1, i6, env, static) -{0,0}> main_GE_511(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1 && i97 < i83
main_GE_511(a135, i97, i83, iconst_1, i6, env, static) -{1,1}> main_Inc_518(a135, i83, i97, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1 && i97 < i83
main_Inc_518(a135, i83, i97, iconst_1, i6, env, static) -{1,1}> main_JMP_524(a135, i83, i100, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1 && 1 <= i100 && i97 + 1 = i100
main_JMP_524(a135, i83, i100, iconst_1, i6, env, static) -{1,1}> main_Load_535(a135, i83, i100, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 < a135 && iconst_1 = 1 && 1 <= i100
main_Load_535(a135, i83, i100, iconst_1, i6, env, static) -{0,0}> main_Load_502(a135, i83, i100, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 < a135 && iconst_1 = 1 && 0 <= i100 && 1 <= i100

obtained
main_GE_509(a135, i97, i83, 1, i6, env, static) -{3,3}> main_Load_416(a135, i99', 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97
by chaining
main_GE_509(a135, i97, i83, iconst_1, i6, env, static) -{0,0}> main_GE_510(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && i83 <= i97 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_GE_510(a135, i97, i83, iconst_1, i6, env, static) -{1,1}> main_Inc_513(a135, i83, iconst_1, i6, env, static) :|: 1 <= i6 && i83 <= i97 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_Inc_513(a135, i83, iconst_1, i6, env, static) -{1,1}> main_JMP_521(a135, i99, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 < a135 && i83 + -1 = i99 && iconst_1 = 1 && 0 <= i99
main_JMP_521(a135, i99, iconst_1, i6, env, static) -{1,1}> main_Load_530(a135, i99, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a135 && iconst_1 = 1 && 0 <= i99
main_Load_530(a135, i99, iconst_1, i6, env, static) -{0,0}> main_Load_416(a135, i99, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a135 && iconst_1 = 1 && 0 <= i99

(8) 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(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 <= 2 && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= 1 && 0 < 1
random_ArrayAccess_73(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_75(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_73(a6, 0, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1
random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
random_InvokeMethod_100(o12, a6, 1, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12
main_Load_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
main_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0
main_LE_417(a103, i83, 1, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6
main_Load_502(a135, i83, i97, 1, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83
main_GE_509(a135, i97, i83, 1, i6, env, static) -{3,3}> main_Load_502(a135, i83, i100', 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83
main_GE_509(a135, i97, i83, 1, i6, env, static) -{3,3}> main_Load_416(a135, i99', 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97

(9) MovedArithmeticToConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Moved arithmethic from lhss to constraints.

main_LE_417(a103, i83, 1, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6
was transformed to
main_LE_417(a103, i83, x, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6 && x = 1

random_InvokeMethod_100(o12, a6, 1, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12
was transformed to
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12 && x = 1

main_Load_502(a135, i83, i97, 1, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83
was transformed to
main_Load_502(a135, i83, i97, x, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83 && x = 1

main_GE_509(a135, i97, i83, 1, i6, env, static) -{3,3}> main_Load_502(a135, i83, i100', 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83
was transformed to
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_502(a135, i83, i100', 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83 && x = 1

random_ArrayAccess_73(a6, 0, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1
was transformed to
random_ArrayAccess_73(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0

main_GE_509(a135, i97, i83, 1, i6, env, static) -{3,3}> main_Load_416(a135, i99', 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97
was transformed to
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i99', 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97 && x = 1

(10) 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_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
random_ArrayAccess_73(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_75(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
main_LE_417(a103, i83, x, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6 && x = 1
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12 && x = 1
main_Load_502(a135, i83, i97, x, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83 && x = 1
main_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0
random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_Load_1(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 <= 2 && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= 1 && 0 < 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_502(a135, i83, i100', 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83 && x = 1
random_ArrayAccess_73(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i99', 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97 && x = 1

(11) LinearizedLhssProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Linearized lhss.

random_ArrayAccess_73(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_75(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
was transformed to
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_75(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0

(12) 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_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i99', 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97 && x = 1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_75(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_LE_417(a103, i83, x, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6 && x = 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_502(a135, i83, i100', 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83 && x = 1
main_Load_1(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 <= 2 && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= 1 && 0 < 1
random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0
random_ArrayAccess_73(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_Load_502(a135, i83, i97, x, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83 && x = 1
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12 && x = 1

(13) MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Moved arithmethic from constraints to rhss.

main_Load_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
was transformed to
main_Load_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, 1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1

main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i99', 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97 && x = 1
was transformed to
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i83 + -1, 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97 && x = 1

random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_75(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
was transformed to
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_75(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0

main_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0
was transformed to
main_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, 1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0

random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
was transformed to
random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6

main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_502(a135, i83, i100', 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83 && x = 1
was transformed to
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_502(a135, i83, i97 + 1, 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83 && 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_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, 1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i83 + -1, 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97 && x = 1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_75(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_LE_417(a103, i83, x, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6 && x = 1
main_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, 1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0
random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_Load_1(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 <= 2 && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= 1 && 0 < 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_502(a135, i83, i97 + 1, 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83 && x = 1
random_ArrayAccess_73(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_Load_502(a135, i83, i97, x, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83 && x = 1
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12 && x = 1

(15) ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Simplified expressions.

main_LE_417(a103, i83, x, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6 && x = 1
was transformed to
main_LE_417(a103, i83, x, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6 && x = 1

main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i83 + -1, 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97 && x = 1
was transformed to
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i83 - 1, 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 - 1 = i99' && 0 <= i97 && x = 1

main_Load_1(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 <= 2 && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= 1 && 0 < 1
was transformed to
main_Load_1(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 <= static'3

random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12 && x = 1
was transformed to
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && i8' <= o12 && x = 1

(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_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, 1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0
main_LE_417(a103, i83, x, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6 && x = 1
main_Load_1(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 <= static'3
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && i8' <= o12 && x = 1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_75(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i83 - 1, 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 - 1 = i99' && 0 <= i97 && x = 1
random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_Load_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, 1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_502(a135, i83, i97 + 1, 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83 && x = 1
random_ArrayAccess_73(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_Load_502(a135, i83, i97, x, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83 && x = 1

(17) JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID) transformation)

Transformed 70 jbc graph edges to a weighted ITS with 70 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.

(18) Obligation:

(19) StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(20) Obligation:

(21) MovedArithmeticToConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Moved arithmethic from lhss to constraints.

(22) Obligation:

(23) LinearizedLhssProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Linearized lhss.

(24) 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_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i99', 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97 && x = 1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_75(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_LE_417(a103, i83, x, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6 && x = 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_502(a135, i83, i100', 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83 && x = 1
main_Load_1(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 <= 2 && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= 1 && 0 < 1
random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(NULL, a6, iconst_1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0
random_ArrayAccess_73(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_Load_502(a135, i83, i97, x, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83 && x = 1
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12 && x = 1

(25) MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Moved arithmethic from constraints to rhss.

(26) 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_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, 1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_416(a135, i83 + -1, 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97 && x = 1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_75(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_LE_417(a103, i83, x, i6, env, static) -{3,3}> main_Load_502(a103, i83, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 0 < i83 && 0 < a103 && 1 <= i83 && 1 <= i6 && x = 1
main_LE_417(a103, i82, iconst_1, i6, env, static) -{0,0}> main_LE_418(a103, i82, 1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1 && i82 <= 0
random_InvokeMethod_100(NULL, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_103(0, a6, 1, i6, env, static) :|: NULL = 0 && 1 <= i6 && iconst_1 = 1 && 0 <= NULL && 0 < a6
main_Load_1(o1, env, static) -{23,23}> random_ArrayAccess_73(o1, 0, i5', env, static'3) :|: static'1 <= static''' + 1 && 0 <= i5' && 0 <= 2 && 0 < o1 && 0 <= static'2 && i5' < o1 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && -1 * static'3 <= 0 && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= 1 && 0 < 1
main_GE_509(a135, i97, i83, x, i6, env, static) -{3,3}> main_Load_502(a135, i83, i97 + 1, 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83 && x = 1
random_ArrayAccess_73(a6, x, i6, env, static) -{7,7}> random_InvokeMethod_100(o8', a6, 1, i6, env, static'4) :|: 0 <= i6 && 0 < a6 && 1 <= i6 && 0 <= static && 0 <= o8' && o8' < a6 && -1 * static <= 0 && static'4 <= static + 1 && x = 0
main_Load_502(a135, i83, i97, x, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83 && x = 1
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_416(a6, i8', 1, i6, env, static) :|: 0 < o12 && 0 <= i8' && 1 <= i6 && 0 < a6 && 0 <= o12 && i8' <= o12 && x = 1

(27) ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Simplified expressions.

(28) Obligation:

(29) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(47)) transformation)

Extracted set of 67 edges for the analysis of TIME complexity. Dropped leaves.

(30) Obligation:

Set of 67 edges based on JBC Program.
Performed SCC analyses:

Used field analysis yielded the following read fields:

Considered paths: all paths from start

(31) JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID) transformation)

Transformed 67 jbc graph edges to a weighted ITS with 67 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.

(32) Obligation:

IntTrs with 67 rules
Start term: main_Load_1(args, env, static)
Considered paths: all paths from start
Rules:
main_Load_1(o1, env, static) -{0,0}> main_Load_3(o1, env, static) :|: 0 < o1
main_Load_3(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(o1, env, static) :|: 0 < o1
langle_clinit_rangle_ConstantStackPush_6(o1, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_9(iconst_0, o1, env, static) :|: iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ArrayCreate_9(iconst_0, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_11(a2, o1, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2 && 0 < o1
langle_clinit_rangle_FieldAccess_11(a2, o1, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_14(o1, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2 && 0 < o1
langle_clinit_rangle_New_14(o1, env, static) -{0,0}> langle_clinit_rangle_New_15(o1, env, static) :|: 0 < o1
langle_clinit_rangle_New_15(o1, env, static) -{0,0}> langle_clinit_rangle_New_16(o1, env, static) :|: 0 <= static && 0 < o1
langle_clinit_rangle_New_16(o1, env, static) -{1,1}> langle_clinit_rangle_Duplicate_18(o4, o1, env, static) :|: o4 = 1 && 0 < o4 && 0 < o1
langle_clinit_rangle_Duplicate_18(o4, o1, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_20(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_ConstantStackPush_20(o4, o1, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_22(o4, NULL, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_clinit_rangle_InvokeMethod_22(o4, NULL, o1, env, static) -{1,1}> langle_init_rangle_Load_24(o4, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_init_rangle_Load_24(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_26(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_26(o4, o1, env, static) -{1,1}> langle_init_rangle_Load_28(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Load_28(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_30(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_30(o4, o1, env, static) -{1,1}> langle_init_rangle_Return_33(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_33(o4, o1, env, static) -{1,1}> langle_init_rangle_Return_36(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_36(o4, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_38(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_FieldAccess_38(o4, o1, env, static) -{1,1}> langle_clinit_rangle_Return_43(o1, env, static') :|: 0 <= o4 && 0 < o4 && 0 <= static && 0 < o1 && static' <= static + o4
langle_clinit_rangle_Return_43(o1, env, static) -{1,1}> main_Load_54(o1, env, static) :|: 0 < o1
main_Load_54(o1, env, static) -{0,0}> main_Load_55(o1, env, static) :|: 0 < o1
main_Load_55(o1, env, static) -{0,0}> main_Load_56(o1, env, static) :|: 0 <= static && 0 < o1
main_Load_56(o1, env, static) -{0,0}> main_Load_57(o1, env, static) :|: 0 < o1
main_Load_57(o1, env, static) -{0,0}> main_Load_58(o1, env, static) :|: 0 < o1
main_Load_58(o1, env, static) -{1,1}> main_FieldAccess_59(o1, env, static) :|: 0 < o1
main_FieldAccess_59(o1, env, static) -{0,0}> main_FieldAccess_60(o1, env, static) :|: 0 < o1
main_FieldAccess_60(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_61(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ConstantStackPush_61(o1, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_63(iconst_0, o1, NULL, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_FieldAccess_63(iconst_0, o1, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_64(o1, NULL, iconst_0, env, static') :|: NULL = 0 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0 && 0 < o1
langle_clinit_rangle_Return_64(o1, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_65(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
main_FieldAccess_65(o1, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_66(o1, iconst_0, env, static') :|: static' <= static + o1 && NULL = 0 && 0 <= o1 && iconst_0 = 0 && 0 <= static && 0 < o1
main_InvokeMethod_66(o1, iconst_0, env, static) -{1,1}> random_FieldAccess_69(o1, iconst_0, env, static) :|: iconst_0 = 0 && 0 < o1
random_FieldAccess_69(o1, iconst_0, env, static) -{1,1}> random_FieldAccess_70(o1, iconst_0, env, static) :|: 0 <= o1 && o1 <= static && iconst_0 = 0 && 0 <= static && 0 < o1
random_FieldAccess_70(o1, iconst_0, env, static) -{1,1}> random_ArrayAccess_72(o1, iconst_0, env, static) :|: -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && iconst_0 <= static && 0 < o1
random_ArrayAccess_72(a6, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, i5, env, static) :|: i5 < a6 && iconst_0 = 0 && 0 < a6 && 0 <= i5
random_ArrayAccess_73(a6, iconst_0, i6, env, static) -{0,0}> random_ArrayAccess_76(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_76(a6, iconst_0, i6, env, static) -{1,1}> random_Store_81(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && o8 < a6 && iconst_0 = 0 && 0 < a6
random_Store_81(o8, a6, iconst_0, i6, env, static) -{1,1}> random_FieldAccess_83(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_0 = 0 && 0 < a6
random_FieldAccess_83(o8, a6, iconst_0, i6, env, static) -{1,1}> random_ConstantStackPush_87(iconst_0, o8, a6, i6, env, static) :|: 1 <= i6 && 0 <= o8 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && 0 < a6 && iconst_0 <= static
random_ConstantStackPush_87(iconst_0, o8, a6, i6, env, static) -{1,1}> random_IntArithmetic_90(iconst_0, iconst_1, o8, a6, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_IntArithmetic_90(iconst_0, iconst_1, o8, a6, i6, env, static) -{1,1}> random_FieldAccess_92(iconst_1, o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_FieldAccess_92(iconst_1, o8, a6, iconst_0, i6, env, static) -{1,1}> random_Load_96(o8, a6, iconst_1, i6, env, static') :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 <= static && 0 < a6 && static' <= static + iconst_1
random_Load_96(o8, a6, iconst_1, i6, env, static) -{1,1}> random_InvokeMethod_100(o8, a6, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_100(o12, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_102(o12, a6, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= o12 && 0 < o12 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_102(o12, a6, iconst_1, i6, env, static) -{1,1}> random_Return_106(i8, a6, iconst_1, i6, env, static) :|: 1 <= i6 && i8 <= o12 && 0 < o12 && iconst_1 = 1 && 0 < a6 && 0 <= i8
random_Return_106(i8, a6, iconst_1, i6, env, static) -{1,1}> main_Store_112(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Store_112(a6, i8, iconst_1, i6, env, static) -{1,1}> main_Load_115(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_115(a6, i8, iconst_1, i6, env, static) -{0,0}> main_Load_332(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_332(a63, i50, iconst_1, i6, env, static) -{0,0}> main_Load_416(a63, i50, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a63 && iconst_1 = 1 && 0 <= i50
main_Load_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
main_LE_417(a103, i83, iconst_1, i6, env, static) -{0,0}> main_LE_419(a103, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1
main_LE_419(a103, i83, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_422(a103, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && 0 < i83
main_ConstantStackPush_422(a103, i83, iconst_1, i6, env, static) -{1,1}> main_Store_425(a103, iconst_0, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && iconst_0 = 0
main_Store_425(a103, iconst_0, i83, iconst_1, i6, env, static) -{1,1}> main_Load_427(a103, i83, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && iconst_0 = 0
main_Load_427(a103, i83, iconst_0, iconst_1, i6, env, static) -{0,0}> main_Load_472(a103, i83, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && 0 < a103 && 1 <= i83 && iconst_0 <= 2 && iconst_1 = 1 && iconst_0 = 0
main_Load_472(a125, i83, i92, iconst_1, i6, env, static) -{0,0}> main_Load_502(a125, i83, i92, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && i92 <= 2 && 0 < a125 && iconst_1 = 1 && 0 <= i92
main_Load_502(a135, i83, i97, iconst_1, i6, env, static) -{1,1}> main_Load_504(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_Load_504(a135, i97, i83, iconst_1, i6, env, static) -{1,1}> main_GE_509(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_GE_509(a135, i97, i83, iconst_1, i6, env, static) -{0,0}> main_GE_510(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && i83 <= i97 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_GE_509(a135, i97, i83, iconst_1, i6, env, static) -{0,0}> main_GE_511(a135, i97, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1 && i97 < i83
main_GE_510(a135, i97, i83, iconst_1, i6, env, static) -{1,1}> main_Inc_513(a135, i83, iconst_1, i6, env, static) :|: 1 <= i6 && i83 <= i97 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1
main_GE_511(a135, i97, i83, iconst_1, i6, env, static) -{1,1}> main_Inc_518(a135, i83, i97, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1 && i97 < i83
main_Inc_513(a135, i83, iconst_1, i6, env, static) -{1,1}> main_JMP_521(a135, i99, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 < a135 && i83 + -1 = i99 && iconst_1 = 1 && 0 <= i99
main_Inc_518(a135, i83, i97, iconst_1, i6, env, static) -{1,1}> main_JMP_524(a135, i83, i100, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 <= i97 && 0 < a135 && iconst_1 = 1 && 1 <= i100 && i97 + 1 = i100
main_JMP_521(a135, i99, iconst_1, i6, env, static) -{1,1}> main_Load_530(a135, i99, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a135 && iconst_1 = 1 && 0 <= i99
main_JMP_524(a135, i83, i100, iconst_1, i6, env, static) -{1,1}> main_Load_535(a135, i83, i100, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 < a135 && iconst_1 = 1 && 1 <= i100
main_Load_530(a135, i99, iconst_1, i6, env, static) -{0,0}> main_Load_416(a135, i99, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a135 && iconst_1 = 1 && 0 <= i99
main_Load_535(a135, i83, i100, iconst_1, i6, env, static) -{0,0}> main_Load_502(a135, i83, i100, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && 0 < a135 && iconst_1 = 1 && 0 <= i100 && 1 <= i100

(33) StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

obtained
main_Load_1(o1, env, static) -{33,33}> main_Load_416(o1, i8', 1, i5', env, static'4) :|: static'1 <= static''' + 1 && 0 <= i8' && 0 <= 2 && 0 <= static'2 && 1 <= i5' && 0 < o1 && o8' < o1 && 0 < o8' && i5' < o1 && i8' <= o8' && -1 * static'3 <= 0 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= o8' && 0 <= i5' && 0 <= 1 && 0 < 1 && static'4 <= static'3 + 1
by chaining
main_Load_1(o1, env, static) -{0,0}> main_Load_3(o1, env, static) :|: 0 < o1
main_Load_3(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(o1, env, static) :|: 0 < o1
langle_clinit_rangle_ConstantStackPush_6(o1, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_9(iconst_0, o1, env, static) :|: iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ArrayCreate_9(iconst_0, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_11(a2, o1, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2 && 0 < o1
langle_clinit_rangle_FieldAccess_11(a2, o1, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_14(o1, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2 && 0 < o1
langle_clinit_rangle_New_14(o1, env, static) -{0,0}> langle_clinit_rangle_New_15(o1, env, static) :|: 0 < o1
langle_clinit_rangle_New_15(o1, env, static) -{0,0}> langle_clinit_rangle_New_16(o1, env, static) :|: 0 <= static && 0 < o1
langle_clinit_rangle_New_16(o1, env, static) -{1,1}> langle_clinit_rangle_Duplicate_18(o4, o1, env, static) :|: o4 = 1 && 0 < o4 && 0 < o1
langle_clinit_rangle_Duplicate_18(o4, o1, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_20(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_ConstantStackPush_20(o4, o1, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_22(o4, NULL, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_clinit_rangle_InvokeMethod_22(o4, NULL, o1, env, static) -{1,1}> langle_init_rangle_Load_24(o4, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_init_rangle_Load_24(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_26(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_26(o4, o1, env, static) -{1,1}> langle_init_rangle_Load_28(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Load_28(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_30(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_30(o4, o1, env, static) -{1,1}> langle_init_rangle_Return_33(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_33(o4, o1, env, static) -{1,1}> langle_init_rangle_Return_36(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_36(o4, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_38(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_FieldAccess_38(o4, o1, env, static) -{1,1}> langle_clinit_rangle_Return_43(o1, env, static') :|: 0 <= o4 && 0 < o4 && 0 <= static && 0 < o1 && static' <= static + o4
langle_clinit_rangle_Return_43(o1, env, static) -{1,1}> main_Load_54(o1, env, static) :|: 0 < o1
main_Load_54(o1, env, static) -{0,0}> main_Load_55(o1, env, static) :|: 0 < o1
main_Load_55(o1, env, static) -{0,0}> main_Load_56(o1, env, static) :|: 0 <= static && 0 < o1
main_Load_56(o1, env, static) -{0,0}> main_Load_57(o1, env, static) :|: 0 < o1
main_Load_57(o1, env, static) -{0,0}> main_Load_58(o1, env, static) :|: 0 < o1
main_Load_58(o1, env, static) -{1,1}> main_FieldAccess_59(o1, env, static) :|: 0 < o1
main_FieldAccess_59(o1, env, static) -{0,0}> main_FieldAccess_60(o1, env, static) :|: 0 < o1
main_FieldAccess_60(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_61(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ConstantStackPush_61(o1, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_63(iconst_0, o1, NULL, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_FieldAccess_63(iconst_0, o1, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_64(o1, NULL, iconst_0, env, static') :|: NULL = 0 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0 && 0 < o1
langle_clinit_rangle_Return_64(o1, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_65(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
main_FieldAccess_65(o1, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_66(o1, iconst_0, env, static') :|: static' <= static + o1 && NULL = 0 && 0 <= o1 && iconst_0 = 0 && 0 <= static && 0 < o1
main_InvokeMethod_66(o1, iconst_0, env, static) -{1,1}> random_FieldAccess_69(o1, iconst_0, env, static) :|: iconst_0 = 0 && 0 < o1
random_FieldAccess_69(o1, iconst_0, env, static) -{1,1}> random_FieldAccess_70(o1, iconst_0, env, static) :|: 0 <= o1 && o1 <= static && iconst_0 = 0 && 0 <= static && 0 < o1
random_FieldAccess_70(o1, iconst_0, env, static) -{1,1}> random_ArrayAccess_72(o1, iconst_0, env, static) :|: -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && iconst_0 <= static && 0 < o1
random_ArrayAccess_72(a6, iconst_0, env, static) -{0,0}> random_ArrayAccess_73(a6, iconst_0, i5, env, static) :|: i5 < a6 && iconst_0 = 0 && 0 < a6 && 0 <= i5
random_ArrayAccess_73(a6, iconst_0, i6, env, static) -{0,0}> random_ArrayAccess_76(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_76(a6, iconst_0, i6, env, static) -{1,1}> random_Store_81(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && o8 < a6 && iconst_0 = 0 && 0 < a6
random_Store_81(o8, a6, iconst_0, i6, env, static) -{1,1}> random_FieldAccess_83(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_0 = 0 && 0 < a6
random_FieldAccess_83(o8, a6, iconst_0, i6, env, static) -{1,1}> random_ConstantStackPush_87(iconst_0, o8, a6, i6, env, static) :|: 1 <= i6 && 0 <= o8 && -1 * static <= iconst_0 && iconst_0 = 0 && 0 <= static && 0 < a6 && iconst_0 <= static
random_ConstantStackPush_87(iconst_0, o8, a6, i6, env, static) -{1,1}> random_IntArithmetic_90(iconst_0, iconst_1, o8, a6, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_IntArithmetic_90(iconst_0, iconst_1, o8, a6, i6, env, static) -{1,1}> random_FieldAccess_92(iconst_1, o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 < a6
random_FieldAccess_92(iconst_1, o8, a6, iconst_0, i6, env, static) -{1,1}> random_Load_96(o8, a6, iconst_1, i6, env, static') :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && iconst_0 = 0 && 0 <= static && 0 < a6 && static' <= static + iconst_1
random_Load_96(o8, a6, iconst_1, i6, env, static) -{1,1}> random_InvokeMethod_100(o8, a6, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_100(o12, a6, iconst_1, i6, env, static) -{0,0}> random_InvokeMethod_102(o12, a6, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= o12 && 0 < o12 && iconst_1 = 1 && 0 < a6
random_InvokeMethod_102(o12, a6, iconst_1, i6, env, static) -{1,1}> random_Return_106(i8, a6, iconst_1, i6, env, static) :|: 1 <= i6 && i8 <= o12 && 0 < o12 && iconst_1 = 1 && 0 < a6 && 0 <= i8
random_Return_106(i8, a6, iconst_1, i6, env, static) -{1,1}> main_Store_112(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Store_112(a6, i8, iconst_1, i6, env, static) -{1,1}> main_Load_115(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_115(a6, i8, iconst_1, i6, env, static) -{0,0}> main_Load_332(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_332(a63, i50, iconst_1, i6, env, static) -{0,0}> main_Load_416(a63, i50, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a63 && iconst_1 = 1 && 0 <= i50

obtained
main_Load_416(a103, i76, 1, i6, env, static) -{4,4}> main_Load_502(a103, i76, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 1 <= i76 && 0 < a103 && 0 < i76 && 1 <= i6
by chaining
main_Load_416(a103, i76, iconst_1, i6, env, static) -{1,1}> main_LE_417(a103, i76, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && iconst_1 = 1
main_LE_417(a103, i83, iconst_1, i6, env, static) -{0,0}> main_LE_419(a103, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1
main_LE_419(a103, i83, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_422(a103, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && 0 < i83
main_ConstantStackPush_422(a103, i83, iconst_1, i6, env, static) -{1,1}> main_Store_425(a103, iconst_0, i83, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && iconst_0 = 0
main_Store_425(a103, iconst_0, i83, iconst_1, i6, env, static) -{1,1}> main_Load_427(a103, i83, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a103 && 1 <= i83 && iconst_1 = 1 && iconst_0 = 0
main_Load_427(a103, i83, iconst_0, iconst_1, i6, env, static) -{0,0}> main_Load_472(a103, i83, iconst_0, iconst_1, i6, env, static) :|: 1 <= i6 && 0 <= iconst_0 && 0 < a103 && 1 <= i83 && iconst_0 <= 2 && iconst_1 = 1 && iconst_0 = 0
main_Load_472(a125, i83, i92, iconst_1, i6, env, static) -{0,0}> main_Load_502(a125, i83, i92, iconst_1, i6, env, static) :|: 1 <= i6 && 1 <= i83 && i92 <= 2 && 0 < a125 && iconst_1 = 1 && 0 <= i92

(34) Obligation:

IntTrs with 5 rules
Start term: main_Load_1(args, env, static)
Considered paths: all paths from start
Rules:
main_Load_1(o1, env, static) -{33,33}> main_Load_416(o1, i8', 1, i5', env, static'4) :|: static'1 <= static''' + 1 && 0 <= i8' && 0 <= 2 && 0 <= static'2 && 1 <= i5' && 0 < o1 && o8' < o1 && 0 < o8' && i5' < o1 && i8' <= o8' && -1 * static'3 <= 0 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= o8' && 0 <= i5' && 0 <= 1 && 0 < 1 && static'4 <= static'3 + 1
main_Load_416(a103, i76, 1, i6, env, static) -{4,4}> main_Load_502(a103, i76, 0, 1, i6, env, static) :|: 0 <= 0 && 0 <= 2 && 1 <= i76 && 0 < a103 && 0 < i76 && 1 <= i6
main_Load_502(a135, i83, i97, 1, i6, env, static) -{2,2}> main_GE_509(a135, i97, i83, 1, i6, env, static) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83
main_GE_509(a135, i97, i83, 1, i6, env, static) -{3,3}> main_Load_502(a135, i83, i100', 1, i6, env, static) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83
main_GE_509(a135, i97, i83, 1, i6, env, static) -{3,3}> main_Load_416(a135, i99', 1, i6, env, static) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97

(35) 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_416(x1, x2, x3, x4, x5, x6) → main_Load_416(x1, x2, x4)
main_Load_502(x1, x2, x3, x4, x5, x6, x7) → main_Load_502(x1, x2, x3, x5)
main_GE_509(x1, x2, x3, x4, x5, x6, x7) → main_GE_509(x1, x2, x3, x5)

(36) Obligation:

IntTrs with 5 rules
Start term: main_Load_1(args, static)
Considered paths: all paths from start
Rules:
main_Load_1(o1, static) -{33,33}> main_Load_416(o1, i8', i5') :|: static'1 <= static''' + 1 && 0 <= i8' && 0 <= 2 && 0 <= static'2 && 1 <= i5' && 0 < o1 && o8' < o1 && 0 < o8' && i5' < o1 && i8' <= o8' && -1 * static'3 <= 0 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= o8' && 0 <= i5' && 0 <= 1 && 0 < 1 && static'4 <= static'3 + 1
main_Load_416(a103, i76, i6) -{4,4}> main_Load_502(a103, i76, 0, i6) :|: 0 <= 0 && 0 <= 2 && 1 <= i76 && 0 < a103 && 0 < i76 && 1 <= i6
main_Load_502(a135, i83, i97, i6) -{2,2}> main_GE_509(a135, i97, i83, i6) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83
main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_502(a135, i83, i100', i6) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83
main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_416(a135, i99', i6) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97

(37) MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Moved arithmethic from constraints to rhss.

main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_416(a135, i99', i6) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97
was transformed to
main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_416(a135, i83 + -1, i6) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97

main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_502(a135, i83, i100', i6) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83
was transformed to
main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_502(a135, i83, i97 + 1, i6) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83

(38) Obligation:

IntTrs with 5 rules
Start term: main_Load_1(args, static)
Considered paths: all paths from start
Rules:
main_Load_416(a103, i76, i6) -{4,4}> main_Load_502(a103, i76, 0, i6) :|: 0 <= 0 && 0 <= 2 && 1 <= i76 && 0 < a103 && 0 < i76 && 1 <= i6
main_Load_502(a135, i83, i97, i6) -{2,2}> main_GE_509(a135, i97, i83, i6) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83
main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_416(a135, i83 + -1, i6) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97
main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_502(a135, i83, i97 + 1, i6) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83
main_Load_1(o1, static) -{33,33}> main_Load_416(o1, i8', i5') :|: static'1 <= static''' + 1 && 0 <= i8' && 0 <= 2 && 0 <= static'2 && 1 <= i5' && 0 < o1 && o8' < o1 && 0 < o8' && i5' < o1 && i8' <= o8' && -1 * static'3 <= 0 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= o8' && 0 <= i5' && 0 <= 1 && 0 < 1 && static'4 <= static'3 + 1

(39) ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

Simplified expressions.

main_Load_416(a103, i76, i6) -{4,4}> main_Load_502(a103, i76, 0, i6) :|: 0 <= 0 && 0 <= 2 && 1 <= i76 && 0 < a103 && 0 < i76 && 1 <= i6
was transformed to
main_Load_416(a103, i76, i6) -{4,4}> main_Load_502(a103, i76, 0, i6) :|: 1 <= i76 && 0 < a103 && 0 < i76 && 1 <= i6

main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_416(a135, i83 + -1, i6) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 + -1 = i99' && 0 <= i97
was transformed to
main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_416(a135, i83 - 1, i6) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 - 1 = i99' && 0 <= i97

main_Load_1(o1, static) -{33,33}> main_Load_416(o1, i8', i5') :|: static'1 <= static''' + 1 && 0 <= i8' && 0 <= 2 && 0 <= static'2 && 1 <= i5' && 0 < o1 && o8' < o1 && 0 < o8' && i5' < o1 && i8' <= o8' && -1 * static'3 <= 0 && static'2 <= static'1 + 0 && 0 <= o1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && 0 <= static''' && 0 < 2 && 0 <= static'3 && 0 <= o8' && 0 <= i5' && 0 <= 1 && 0 < 1 && static'4 <= static'3 + 1
was transformed to
main_Load_1(o1, static) -{33,33}> main_Load_416(o1, i8', i5') :|: static'1 <= static''' + 1 && 0 <= i8' && 0 <= static'2 && 1 <= i5' && 0 < o1 && o8' < o1 && 0 < o8' && i5' < o1 && i8' <= o8' && -1 * static'3 <= 0 && static'2 <= static'1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && 0 <= static''' && 0 <= static'3 && 0 <= i5' && static'4 <= static'3 + 1

(40) Obligation:

IntTrs with 5 rules
Start term: main_Load_1(args, static)
Considered paths: all paths from start
Rules:
main_Load_416(a103, i76, i6) -{4,4}> main_Load_502(a103, i76, 0, i6) :|: 1 <= i76 && 0 < a103 && 0 < i76 && 1 <= i6
main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_502(a135, i83, i97 + 1, i6) :|: i97 + 1 = i100' && 1 <= i100' && 1 <= i83 && 0 <= i100' && 1 <= i6 && 0 <= i97 && 0 < a135 && i97 < i83
main_Load_502(a135, i83, i97, i6) -{2,2}> main_GE_509(a135, i97, i83, i6) :|: 0 < a135 && 0 <= i97 && 1 <= i6 && 1 <= i83
main_Load_1(o1, static) -{33,33}> main_Load_416(o1, i8', i5') :|: static'1 <= static''' + 1 && 0 <= i8' && 0 <= static'2 && 1 <= i5' && 0 < o1 && o8' < o1 && 0 < o8' && i5' < o1 && i8' <= o8' && -1 * static'3 <= 0 && static'2 <= static'1 && o1 <= static'3 && static''' <= static + 2 && 0 <= static'1 && static'3 <= static'2 + o1 && 0 <= static && 0 <= static''' && 0 <= static'3 && 0 <= i5' && static'4 <= static'3 + 1
main_GE_509(a135, i97, i83, i6) -{3,3}> main_Load_416(a135, i83 - 1, i6) :|: i83 <= i97 && 0 <= i99' && 1 <= i83 && 1 <= i6 && 0 < a135 && i83 - 1 = i99' && 0 <= i97

(41) koat Proof (EQUIVALENT transformation)

YES(?, 18*ar_0 + 10*ar_0^2 + 33)

Initial complexity problem:
1: T:
(Comp: ?, Cost: 4) main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\ 0 < ar_0 /\ 0 < ar_1 /\ 1 <= ar_2 ]
(Comp: ?, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\ 1 <= i100' /\ 1 <= ar_2 /\ 0 <= i100' /\ 1 <= ar_3 /\ 0 <= ar_1 /\ 0 < ar_0 /\ ar_1 < ar_2 ]
(Comp: ?, Cost: 2) main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\ 0 <= ar_2 /\ 1 <= ar_3 /\ 1 <= ar_1 ]
(Comp: ?, Cost: 33) main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, i8', i5', arityPad)) [ static'1 <= static''' + 1 /\ 0 <= i8' /\ 0 <= static'2 /\ 1 <= i5' /\ 0 < ar_0 /\ o8' < ar_0 /\ 0 < o8' /\ i5' < ar_0 /\ i8' <= o8' /\ -static'3 <= 0 /\ static'2 <= static'1 /\ ar_0 <= static'3 /\ static''' <= ar_1 + 2 /\ 0 <= static'1 /\ static'3 <= static'2 + ar_0 /\ 0 <= ar_1 /\ 0 <= static''' /\ 0 <= static'3 /\ 0 <= i5' /\ static'4 <= static'3 + 1 ]
(Comp: ?, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\ 0 <= i99' /\ 1 <= ar_2 /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_2 - 1 = i99' /\ 0 <= ar_1 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2: T:
(Comp: ?, Cost: 4) main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\ 0 < ar_0 /\ 0 < ar_1 /\ 1 <= ar_2 ]
(Comp: ?, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\ 1 <= i100' /\ 1 <= ar_2 /\ 0 <= i100' /\ 1 <= ar_3 /\ 0 <= ar_1 /\ 0 < ar_0 /\ ar_1 < ar_2 ]
(Comp: ?, Cost: 2) main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\ 0 <= ar_2 /\ 1 <= ar_3 /\ 1 <= ar_1 ]
(Comp: 1, Cost: 33) main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, i8', i5', arityPad)) [ static'1 <= static''' + 1 /\ 0 <= i8' /\ 0 <= static'2 /\ 1 <= i5' /\ 0 < ar_0 /\ o8' < ar_0 /\ 0 < o8' /\ i5' < ar_0 /\ i8' <= o8' /\ -static'3 <= 0 /\ static'2 <= static'1 /\ ar_0 <= static'3 /\ static''' <= ar_1 + 2 /\ 0 <= static'1 /\ static'3 <= static'2 + ar_0 /\ 0 <= ar_1 /\ 0 <= static''' /\ 0 <= static'3 /\ 0 <= i5' /\ static'4 <= static'3 + 1 ]
(Comp: ?, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\ 0 <= i99' /\ 1 <= ar_2 /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_2 - 1 = i99' /\ 0 <= ar_1 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

A polynomial rank function with
Pol(main_Load_416) = 2*V_2 + 1
Pol(main_Load_502) = 2*V_2
Pol(main_GE_509) = 2*V_3
Pol(main_Load_1) = 2*V_1
Pol(koat_start) = 2*V_1
orients all transitions weakly and the transitions
main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\ 0 < ar_0 /\ 0 < ar_1 /\ 1 <= ar_2 ]
main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\ 0 <= i99' /\ 1 <= ar_2 /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_2 - 1 = i99' /\ 0 <= ar_1 ]
strictly and produces the following problem:
3: T:
(Comp: 2*ar_0, Cost: 4) main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\ 0 < ar_0 /\ 0 < ar_1 /\ 1 <= ar_2 ]
(Comp: ?, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\ 1 <= i100' /\ 1 <= ar_2 /\ 0 <= i100' /\ 1 <= ar_3 /\ 0 <= ar_1 /\ 0 < ar_0 /\ ar_1 < ar_2 ]
(Comp: ?, Cost: 2) main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\ 0 <= ar_2 /\ 1 <= ar_3 /\ 1 <= ar_1 ]
(Comp: 1, Cost: 33) main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, i8', i5', arityPad)) [ static'1 <= static''' + 1 /\ 0 <= i8' /\ 0 <= static'2 /\ 1 <= i5' /\ 0 < ar_0 /\ o8' < ar_0 /\ 0 < o8' /\ i5' < ar_0 /\ i8' <= o8' /\ -static'3 <= 0 /\ static'2 <= static'1 /\ ar_0 <= static'3 /\ static''' <= ar_1 + 2 /\ 0 <= static'1 /\ static'3 <= static'2 + ar_0 /\ 0 <= ar_1 /\ 0 <= static''' /\ 0 <= static'3 /\ 0 <= i5' /\ static'4 <= static'3 + 1 ]
(Comp: 2*ar_0, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\ 0 <= i99' /\ 1 <= ar_2 /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_2 - 1 = i99' /\ 0 <= ar_1 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

A polynomial rank function with
Pol(main_Load_502) = V_2 - V_3
Pol(main_GE_509) = -V_2 + V_3
and size complexities
S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
S("main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\\ 0 <= i99' /\\ 1 <= ar_2 /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ ar_2 - 1 = i99' /\\ 0 <= ar_1 ]", 0-0) = ar_0
S("main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\\ 0 <= i99' /\\ 1 <= ar_2 /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ ar_2 - 1 = i99' /\\ 0 <= ar_1 ]", 0-1) = ar_0
S("main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\\ 0 <= i99' /\\ 1 <= ar_2 /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ ar_2 - 1 = i99' /\\ 0 <= ar_1 ]", 0-2) = ar_0
S("main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\\ 0 <= i99' /\\ 1 <= ar_2 /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ ar_2 - 1 = i99' /\\ 0 <= ar_1 ]", 0-3) = ?
S("main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, i8', i5', arityPad)) [ static'1 <= static''' + 1 /\\ 0 <= i8' /\\ 0 <= static'2 /\\ 1 <= i5' /\\ 0 < ar_0 /\\ o8' < ar_0 /\\ 0 < o8' /\\ i5' < ar_0 /\\ i8' <= o8' /\\ -static'3 <= 0 /\\ static'2 <= static'1 /\\ ar_0 <= static'3 /\\ static''' <= ar_1 + 2 /\\ 0 <= static'1 /\\ static'3 <= static'2 + ar_0 /\\ 0 <= ar_1 /\\ 0 <= static''' /\\ 0 <= static'3 /\\ 0 <= i5' /\\ static'4 <= static'3 + 1 ]", 0-0) = ar_0
S("main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, i8', i5', arityPad)) [ static'1 <= static''' + 1 /\\ 0 <= i8' /\\ 0 <= static'2 /\\ 1 <= i5' /\\ 0 < ar_0 /\\ o8' < ar_0 /\\ 0 < o8' /\\ i5' < ar_0 /\\ i8' <= o8' /\\ -static'3 <= 0 /\\ static'2 <= static'1 /\\ ar_0 <= static'3 /\\ static''' <= ar_1 + 2 /\\ 0 <= static'1 /\\ static'3 <= static'2 + ar_0 /\\ 0 <= ar_1 /\\ 0 <= static''' /\\ 0 <= static'3 /\\ 0 <= i5' /\\ static'4 <= static'3 + 1 ]", 0-1) = ar_0
S("main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, i8', i5', arityPad)) [ static'1 <= static''' + 1 /\\ 0 <= i8' /\\ 0 <= static'2 /\\ 1 <= i5' /\\ 0 < ar_0 /\\ o8' < ar_0 /\\ 0 < o8' /\\ i5' < ar_0 /\\ i8' <= o8' /\\ -static'3 <= 0 /\\ static'2 <= static'1 /\\ ar_0 <= static'3 /\\ static''' <= ar_1 + 2 /\\ 0 <= static'1 /\\ static'3 <= static'2 + ar_0 /\\ 0 <= ar_1 /\\ 0 <= static''' /\\ 0 <= static'3 /\\ 0 <= i5' /\\ static'4 <= static'3 + 1 ]", 0-2) = ar_0
S("main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, i8', i5', arityPad)) [ static'1 <= static''' + 1 /\\ 0 <= i8' /\\ 0 <= static'2 /\\ 1 <= i5' /\\ 0 < ar_0 /\\ o8' < ar_0 /\\ 0 < o8' /\\ i5' < ar_0 /\\ i8' <= o8' /\\ -static'3 <= 0 /\\ static'2 <= static'1 /\\ ar_0 <= static'3 /\\ static''' <= ar_1 + 2 /\\ 0 <= static'1 /\\ static'3 <= static'2 + ar_0 /\\ 0 <= ar_1 /\\ 0 <= static''' /\\ 0 <= static'3 /\\ 0 <= i5' /\\ static'4 <= static'3 + 1 ]", 0-3) = ?
S("main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\\ 0 <= ar_2 /\\ 1 <= ar_3 /\\ 1 <= ar_1 ]", 0-0) = ar_0
S("main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\\ 0 <= ar_2 /\\ 1 <= ar_3 /\\ 1 <= ar_1 ]", 0-1) = ar_0
S("main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\\ 0 <= ar_2 /\\ 1 <= ar_3 /\\ 1 <= ar_1 ]", 0-2) = ar_0
S("main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\\ 0 <= ar_2 /\\ 1 <= ar_3 /\\ 1 <= ar_1 ]", 0-3) = ar_0
S("main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\\ 1 <= i100' /\\ 1 <= ar_2 /\\ 0 <= i100' /\\ 1 <= ar_3 /\\ 0 <= ar_1 /\\ 0 < ar_0 /\\ ar_1 < ar_2 ]", 0-0) = ar_0
S("main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\\ 1 <= i100' /\\ 1 <= ar_2 /\\ 0 <= i100' /\\ 1 <= ar_3 /\\ 0 <= ar_1 /\\ 0 < ar_0 /\\ ar_1 < ar_2 ]", 0-1) = ar_0
S("main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\\ 1 <= i100' /\\ 1 <= ar_2 /\\ 0 <= i100' /\\ 1 <= ar_3 /\\ 0 <= ar_1 /\\ 0 < ar_0 /\\ ar_1 < ar_2 ]", 0-2) = ar_0
S("main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\\ 1 <= i100' /\\ 1 <= ar_2 /\\ 0 <= i100' /\\ 1 <= ar_3 /\\ 0 <= ar_1 /\\ 0 < ar_0 /\\ ar_1 < ar_2 ]", 0-3) = ar_0
S("main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\\ 0 < ar_0 /\\ 0 < ar_1 /\\ 1 <= ar_2 ]", 0-0) = ar_0
S("main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\\ 0 < ar_0 /\\ 0 < ar_1 /\\ 1 <= ar_2 ]", 0-1) = ar_0
S("main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\\ 0 < ar_0 /\\ 0 < ar_1 /\\ 1 <= ar_2 ]", 0-2) = 0
S("main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\\ 0 < ar_0 /\\ 0 < ar_1 /\\ 1 <= ar_2 ]", 0-3) = ar_0
orients the transitions
main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\ 0 <= ar_2 /\ 1 <= ar_3 /\ 1 <= ar_1 ]
main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\ 1 <= i100' /\ 1 <= ar_2 /\ 0 <= i100' /\ 1 <= ar_3 /\ 0 <= ar_1 /\ 0 < ar_0 /\ ar_1 < ar_2 ]
weakly and the transition
main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\ 1 <= i100' /\ 1 <= ar_2 /\ 0 <= i100' /\ 1 <= ar_3 /\ 0 <= ar_1 /\ 0 < ar_0 /\ ar_1 < ar_2 ]
strictly and produces the following problem:
4: T:
(Comp: 2*ar_0, Cost: 4) main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\ 0 < ar_0 /\ 0 < ar_1 /\ 1 <= ar_2 ]
(Comp: 2*ar_0^2, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\ 1 <= i100' /\ 1 <= ar_2 /\ 0 <= i100' /\ 1 <= ar_3 /\ 0 <= ar_1 /\ 0 < ar_0 /\ ar_1 < ar_2 ]
(Comp: ?, Cost: 2) main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\ 0 <= ar_2 /\ 1 <= ar_3 /\ 1 <= ar_1 ]
(Comp: 1, Cost: 33) main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, i8', i5', arityPad)) [ static'1 <= static''' + 1 /\ 0 <= i8' /\ 0 <= static'2 /\ 1 <= i5' /\ 0 < ar_0 /\ o8' < ar_0 /\ 0 < o8' /\ i5' < ar_0 /\ i8' <= o8' /\ -static'3 <= 0 /\ static'2 <= static'1 /\ ar_0 <= static'3 /\ static''' <= ar_1 + 2 /\ 0 <= static'1 /\ static'3 <= static'2 + ar_0 /\ 0 <= ar_1 /\ 0 <= static''' /\ 0 <= static'3 /\ 0 <= i5' /\ static'4 <= static'3 + 1 ]
(Comp: 2*ar_0, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\ 0 <= i99' /\ 1 <= ar_2 /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_2 - 1 = i99' /\ 0 <= ar_1 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Repeatedly propagating knowledge in problem 4 produces the following problem:
5: T:
(Comp: 2*ar_0, Cost: 4) main_Load_416(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_1, 0, ar_2)) [ 1 <= ar_1 /\ 0 < ar_0 /\ 0 < ar_1 /\ 1 <= ar_2 ]
(Comp: 2*ar_0^2, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_502(ar_0, ar_2, ar_1 + 1, ar_3)) [ ar_1 + 1 = i100' /\ 1 <= i100' /\ 1 <= ar_2 /\ 0 <= i100' /\ 1 <= ar_3 /\ 0 <= ar_1 /\ 0 < ar_0 /\ ar_1 < ar_2 ]
(Comp: 2*ar_0^2 + 2*ar_0, Cost: 2) main_Load_502(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_GE_509(ar_0, ar_2, ar_1, ar_3)) [ 0 < ar_0 /\ 0 <= ar_2 /\ 1 <= ar_3 /\ 1 <= ar_1 ]
(Comp: 1, Cost: 33) main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, i8', i5', arityPad)) [ static'1 <= static''' + 1 /\ 0 <= i8' /\ 0 <= static'2 /\ 1 <= i5' /\ 0 < ar_0 /\ o8' < ar_0 /\ 0 < o8' /\ i5' < ar_0 /\ i8' <= o8' /\ -static'3 <= 0 /\ static'2 <= static'1 /\ ar_0 <= static'3 /\ static''' <= ar_1 + 2 /\ 0 <= static'1 /\ static'3 <= static'2 + ar_0 /\ 0 <= ar_1 /\ 0 <= static''' /\ 0 <= static'3 /\ 0 <= i5' /\ static'4 <= static'3 + 1 ]
(Comp: 2*ar_0, Cost: 3) main_GE_509(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_416(ar_0, ar_2 - 1, ar_3, arityPad)) [ ar_2 <= ar_1 /\ 0 <= i99' /\ 1 <= ar_2 /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_2 - 1 = i99' /\ 0 <= ar_1 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Complexity upper bound 18*ar_0 + 10*ar_0^2 + 33

Time: 0.223 sec (SMT: 0.202 sec)

(0) Obligation:

(1) JBCToGraph (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(2) Obligation:

(3) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(47)) transformation)

(4) Obligation:

(5) JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID) transformation)

(6) Obligation:

(7) StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(8) Obligation:

(9) MovedArithmeticToConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(10) Obligation:

(11) LinearizedLhssProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(12) Obligation:

(13) MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(14) Obligation:

(15) ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(16) Obligation:

(17) JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID) transformation)

(18) Obligation:

(19) StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(20) Obligation:

(21) MovedArithmeticToConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(22) Obligation:

(23) LinearizedLhssProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(24) Obligation:

(25) MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(26) Obligation:

(27) ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(28) Obligation:

(29) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(47)) transformation)

(30) Obligation:

(31) JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID) transformation)

(32) Obligation:

(33) StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(34) Obligation:

(35) WeightedIntTrsUnneededArgumentFilterProof (CONCRETE UPPER BOUND(ID) transformation)

(36) Obligation:

(37) MovedArithmeticFromConstraintsProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(38) Obligation:

(39) ExpressionSimplificationProof (BOTH CONCRETE BOUNDS(ID, ID) transformation)

(40) Obligation:

(41) koat Proof (EQUIVALENT transformation)

(42) BOUNDS(CONSTANT, 33 + 18 * |args| + 10 * |args|^2)