time complexity proof of /tmp/tmp0tLetH/PastaC2.jar

The time complexity of the given JBC problem could be proven to be BOUNDS(CONSTANT, 80 + 52 * |args| + 30 * |args|^2).

0 JBC problem

↳1 JBCToGraph (BOTH CONCRETE BOUNDS(ID, ID), 465 ms)

↳2 JBCTerminationGraph

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

↳4 JBCComplexityEdges

    ↳5 JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID), 96 ms)

    ↳6 WeightedIntTrs

        ↳7 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 46 ms)

        ↳8 WeightedIntTrs

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

        ↳10 WeightedIntTrs

        ↳11 LinearizedLhssProof (BOTH CONCRETE BOUNDS(ID, ID), 1 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), 114 ms)

    ↳18 WeightedIntTrs

        ↳19 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 20 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), 103 ms)

    ↳32 WeightedIntTrs

    ↳33 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 25 ms)

    ↳34 WeightedIntTrs

    ↳35 WeightedIntTrsUnneededArgumentFilterProof (CONCRETE UPPER BOUND(ID), 10 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 (⇔, 139 ms)

    ↳42 BOUNDS(CONSTANT, 33 + 52 * |args| + 30 * |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 PastaC2 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();

        while (x >= 0) {
            x = x+1;
            int y = 1;
            while (x >= y) {
                y++;
            }
            x = x-2;
        }
    }
}


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:
PastaC2.main([Ljava/lang/String;)V: Graph of 124 nodes with 1 SCC.

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

Extracted set of 77 edges for the analysis of TIME complexity. Kept leaves.

(4) Obligation:

Set of 77 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 77 jbc graph edges to a weighted ITS with 77 rules.
Filtered conditions with variables that do not depend on the variables on the lhs or rhs without taking transitive dependencies into account.
Did no encode lower bounds for putfield and astore.

(6) Obligation:

IntTrs with 77 rules
Start term: main_Load_2(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_2(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_12(iconst_0, o1, env, static) :|: iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ArrayCreate_12(iconst_0, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_14(a2, o1, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2 && 0 < o1
langle_clinit_rangle_FieldAccess_14(a2, o1, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_16(o1, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2 && 0 < o1
langle_clinit_rangle_New_16(o1, env, static) -{0,0}> langle_clinit_rangle_New_18(o1, env, static) :|: 0 < o1
langle_clinit_rangle_New_18(o1, env, static) -{0,0}> langle_clinit_rangle_New_19(o1, env, static) :|: 0 <= static && 0 < o1
langle_clinit_rangle_New_19(o1, env, static) -{1,1}> langle_clinit_rangle_Duplicate_20(o4, o1, env, static) :|: o4 = 1 && 0 < o4 && 0 < o1
langle_clinit_rangle_Duplicate_20(o4, o1, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_22(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_ConstantStackPush_22(o4, o1, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_23(o4, NULL, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_clinit_rangle_InvokeMethod_23(o4, NULL, o1, env, static) -{1,1}> langle_init_rangle_Load_25(o4, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_init_rangle_Load_25(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_27(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_27(o4, o1, env, static) -{1,1}> langle_init_rangle_Load_29(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Load_29(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_35(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_35(o4, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_37(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_FieldAccess_37(o4, o1, env, static) -{1,1}> langle_clinit_rangle_Return_39(o1, env, static') :|: 0 <= o4 && 0 < o4 && 0 <= static && 0 < o1 && static' <= static + o4
langle_clinit_rangle_Return_39(o1, env, static) -{1,1}> main_Load_41(o1, env, static) :|: 0 < o1
main_Load_41(o1, env, static) -{0,0}> main_Load_42(o1, env, static) :|: 0 < o1
main_Load_42(o1, env, static) -{0,0}> main_Load_49(o1, env, static) :|: 0 <= static && 0 < o1
main_Load_49(o1, env, static) -{0,0}> main_Load_50(o1, env, static) :|: 0 < o1
main_Load_50(o1, env, static) -{0,0}> main_Load_52(o1, env, static) :|: 0 < o1
main_Load_52(o1, env, static) -{1,1}> main_FieldAccess_55(o1, env, static) :|: 0 < o1
main_FieldAccess_55(o1, env, static) -{0,0}> main_FieldAccess_57(o1, env, static) :|: 0 < o1
main_FieldAccess_57(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_59(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ConstantStackPush_59(o1, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_60(iconst_0, o1, NULL, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_FieldAccess_60(iconst_0, o1, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_61(o1, NULL, iconst_0, env, static') :|: NULL = 0 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0 && 0 < o1
langle_clinit_rangle_Return_61(o1, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_62(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
main_FieldAccess_62(o1, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_68(o1, iconst_0, env, static') :|: static' <= static + o1 && NULL = 0 && 0 <= o1 && iconst_0 = 0 && 0 <= static && 0 < o1
main_InvokeMethod_68(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_74(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_75(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_75(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_84(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_0 = 0 && 0 < a6
random_FieldAccess_84(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_116(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_116(a6, i8, iconst_1, i6, env, static) -{0,0}> main_Load_365(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && -1 <= i8 && 0 < a6 && 0 <= i8
main_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28
main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, iconst_NEG1, iconst_1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -1
main_LT_367(a51, i32, iconst_1, i6, env, static) -{0,0}> main_LT_369(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && -1 <= i32 && iconst_1 = 1 && 0 <= i32
main_LT_369(a51, i32, iconst_1, i6, env, static) -{1,1}> main_Load_371(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_Load_371(a51, i32, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_373(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_ConstantStackPush_373(a51, i32, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_375(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_IntArithmetic_375(a51, i32, iconst_1, i6, env, static) -{1,1}> main_Store_377(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33 && i32 + iconst_1 = i33 && 0 <= i32
main_Store_377(a51, i33, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_379(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_ConstantStackPush_379(a51, i33, iconst_1, i6, env, static) -{1,1}> main_Store_381(a51, iconst_1, i33, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_Store_381(a51, iconst_1, i33, i6, env, static) -{1,1}> main_Load_382(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_Load_382(a51, i33, iconst_1, i6, env, static) -{0,0}> main_Load_405(a51, i33, iconst_1, iconst_1, i6, env, static) :|: iconst_1 <= 2 && 1 <= i6 && 0 < a51 && 1 <= iconst_1 && iconst_1 = 1 && 1 <= i33
main_Load_405(a59, i33, i34, iconst_1, i6, env, static) -{0,0}> main_Load_440(a59, i33, i34, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a59 && iconst_1 = 1 && i34 <= 2 && 1 <= i34 && 1 <= i33 && i34 <= 3
main_Load_440(a67, i33, i38, iconst_1, i6, env, static) -{0,0}> main_Load_480(a67, i33, i38, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && i38 <= 3 && 1 <= i33 && 1 <= i38 && 0 < a67
main_Load_480(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_Load_482(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && 1 <= i33
main_Load_482(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_LT_483(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && 1 <= i33
main_LT_483(a75, i33, i42, iconst_1, i6, env, static) -{0,0}> main_LT_485(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && i33 < i42 && 1 <= i33
main_LT_483(a75, i33, i42, iconst_1, i6, env, static) -{0,0}> main_LT_486(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && i42 <= i33 && iconst_1 = 1 && 1 <= i33
main_LT_485(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_Load_490(a75, i33, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && i33 < i42 && 1 <= i33
main_LT_486(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_Inc_495(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && i42 <= i33 && iconst_1 = 1 && 1 <= i33
main_Load_490(a75, i33, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_497(a75, i33, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && iconst_1 = 1 && 1 <= i33
main_Inc_495(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_JMP_498(a75, i33, i44, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && 2 <= i44 && iconst_1 = 1 && 1 <= i33 && i42 + 1 = i44
main_ConstantStackPush_497(a75, i33, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_499(a75, i33, iconst_2, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && iconst_1 = 1 && 1 <= i33 && iconst_2 = 2
main_JMP_498(a75, i33, i44, iconst_1, i6, env, static) -{1,1}> main_Load_502(a75, i33, i44, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && 2 <= i44 && iconst_1 = 1 && 1 <= i33
main_IntArithmetic_499(a75, i33, iconst_2, iconst_1, i6, env, static) -{1,1}> main_Store_505(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && i33 - iconst_2 = i46 && iconst_1 = 1 && 1 <= i33 && iconst_2 = 2
main_Load_502(a75, i33, i44, iconst_1, i6, env, static) -{0,0}> main_Load_480(a75, i33, i44, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && 2 <= i44 && iconst_1 = 1 && 1 <= i44 && 1 <= i33
main_Store_505(a75, i46, iconst_1, i6, env, static) -{1,1}> main_JMP_507(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && iconst_1 = 1
main_JMP_507(a75, i46, iconst_1, i6, env, static) -{1,1}> main_Load_511(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && iconst_1 = 1
main_Load_511(a75, i46, iconst_1, i6, env, static) -{0,0}> main_Load_365(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && iconst_1 = 1

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

obtained
main_Load_2(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_2(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_12(iconst_0, o1, env, static) :|: iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ArrayCreate_12(iconst_0, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_14(a2, o1, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2 && 0 < o1
langle_clinit_rangle_FieldAccess_14(a2, o1, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_16(o1, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2 && 0 < o1
langle_clinit_rangle_New_16(o1, env, static) -{0,0}> langle_clinit_rangle_New_18(o1, env, static) :|: 0 < o1
langle_clinit_rangle_New_18(o1, env, static) -{0,0}> langle_clinit_rangle_New_19(o1, env, static) :|: 0 <= static && 0 < o1
langle_clinit_rangle_New_19(o1, env, static) -{1,1}> langle_clinit_rangle_Duplicate_20(o4, o1, env, static) :|: o4 = 1 && 0 < o4 && 0 < o1
langle_clinit_rangle_Duplicate_20(o4, o1, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_22(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_ConstantStackPush_22(o4, o1, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_23(o4, NULL, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_clinit_rangle_InvokeMethod_23(o4, NULL, o1, env, static) -{1,1}> langle_init_rangle_Load_25(o4, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_init_rangle_Load_25(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_27(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_27(o4, o1, env, static) -{1,1}> langle_init_rangle_Load_29(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Load_29(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_35(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_35(o4, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_37(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_FieldAccess_37(o4, o1, env, static) -{1,1}> langle_clinit_rangle_Return_39(o1, env, static') :|: 0 <= o4 && 0 < o4 && 0 <= static && 0 < o1 && static' <= static + o4
langle_clinit_rangle_Return_39(o1, env, static) -{1,1}> main_Load_41(o1, env, static) :|: 0 < o1
main_Load_41(o1, env, static) -{0,0}> main_Load_42(o1, env, static) :|: 0 < o1
main_Load_42(o1, env, static) -{0,0}> main_Load_49(o1, env, static) :|: 0 <= static && 0 < o1
main_Load_49(o1, env, static) -{0,0}> main_Load_50(o1, env, static) :|: 0 < o1
main_Load_50(o1, env, static) -{0,0}> main_Load_52(o1, env, static) :|: 0 < o1
main_Load_52(o1, env, static) -{1,1}> main_FieldAccess_55(o1, env, static) :|: 0 < o1
main_FieldAccess_55(o1, env, static) -{0,0}> main_FieldAccess_57(o1, env, static) :|: 0 < o1
main_FieldAccess_57(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_59(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ConstantStackPush_59(o1, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_60(iconst_0, o1, NULL, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_FieldAccess_60(iconst_0, o1, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_61(o1, NULL, iconst_0, env, static') :|: NULL = 0 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0 && 0 < o1
langle_clinit_rangle_Return_61(o1, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_62(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
main_FieldAccess_62(o1, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_68(o1, iconst_0, env, static') :|: static' <= static + o1 && NULL = 0 && 0 <= o1 && iconst_0 = 0 && 0 <= static && 0 < o1
main_InvokeMethod_68(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_75(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_75(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_84(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_0 = 0 && 0 < a6
random_FieldAccess_84(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_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < 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_116(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_116(a6, i8, iconst_1, i6, env, static) -{0,0}> main_Load_365(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && -1 <= i8 && 0 < a6 && 0 <= i8

obtained
main_LT_367(a51, i32, 1, i6, env, static) -{7,7}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2
by chaining
main_LT_367(a51, i32, iconst_1, i6, env, static) -{0,0}> main_LT_369(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && -1 <= i32 && iconst_1 = 1 && 0 <= i32
main_LT_369(a51, i32, iconst_1, i6, env, static) -{1,1}> main_Load_371(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_Load_371(a51, i32, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_373(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_ConstantStackPush_373(a51, i32, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_375(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_IntArithmetic_375(a51, i32, iconst_1, i6, env, static) -{1,1}> main_Store_377(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33 && i32 + iconst_1 = i33 && 0 <= i32
main_Store_377(a51, i33, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_379(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_ConstantStackPush_379(a51, i33, iconst_1, i6, env, static) -{1,1}> main_Store_381(a51, iconst_1, i33, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_Store_381(a51, iconst_1, i33, i6, env, static) -{1,1}> main_Load_382(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_Load_382(a51, i33, iconst_1, i6, env, static) -{0,0}> main_Load_405(a51, i33, iconst_1, iconst_1, i6, env, static) :|: iconst_1 <= 2 && 1 <= i6 && 0 < a51 && 1 <= iconst_1 && iconst_1 = 1 && 1 <= i33
main_Load_405(a59, i33, i34, iconst_1, i6, env, static) -{0,0}> main_Load_440(a59, i33, i34, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a59 && iconst_1 = 1 && i34 <= 2 && 1 <= i34 && 1 <= i33 && i34 <= 3
main_Load_440(a67, i33, i38, iconst_1, i6, env, static) -{0,0}> main_Load_480(a67, i33, i38, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && i38 <= 3 && 1 <= i33 && 1 <= i38 && 0 < a67

obtained
main_Load_480(a75, i33, i42, 1, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42
by chaining
main_Load_480(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_Load_482(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && 1 <= i33
main_Load_482(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_LT_483(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && 1 <= i33

obtained
main_LT_483(a75, i33, i42, 1, i6, env, static) -{3,3}> main_Load_480(a75, i33, i44', 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33
by chaining
main_LT_483(a75, i33, i42, iconst_1, i6, env, static) -{0,0}> main_LT_486(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && i42 <= i33 && iconst_1 = 1 && 1 <= i33
main_LT_486(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_Inc_495(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && i42 <= i33 && iconst_1 = 1 && 1 <= i33
main_Inc_495(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_JMP_498(a75, i33, i44, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && 2 <= i44 && iconst_1 = 1 && 1 <= i33 && i42 + 1 = i44
main_JMP_498(a75, i33, i44, iconst_1, i6, env, static) -{1,1}> main_Load_502(a75, i33, i44, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && 2 <= i44 && iconst_1 = 1 && 1 <= i33
main_Load_502(a75, i33, i44, iconst_1, i6, env, static) -{0,0}> main_Load_480(a75, i33, i44, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && 2 <= i44 && iconst_1 = 1 && 1 <= i44 && 1 <= i33

obtained
main_LT_483(a75, i33, i42, 1, i6, env, static) -{6,6}> main_Load_365(a75, i46', 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33
by chaining
main_LT_483(a75, i33, i42, iconst_1, i6, env, static) -{0,0}> main_LT_485(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && i33 < i42 && 1 <= i33
main_LT_485(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_Load_490(a75, i33, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && i33 < i42 && 1 <= i33
main_Load_490(a75, i33, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_497(a75, i33, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && iconst_1 = 1 && 1 <= i33
main_ConstantStackPush_497(a75, i33, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_499(a75, i33, iconst_2, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && iconst_1 = 1 && 1 <= i33 && iconst_2 = 2
main_IntArithmetic_499(a75, i33, iconst_2, iconst_1, i6, env, static) -{1,1}> main_Store_505(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && i33 - iconst_2 = i46 && iconst_1 = 1 && 1 <= i33 && iconst_2 = 2
main_Store_505(a75, i46, iconst_1, i6, env, static) -{1,1}> main_JMP_507(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && iconst_1 = 1
main_JMP_507(a75, i46, iconst_1, i6, env, static) -{1,1}> main_Load_511(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && iconst_1 = 1
main_Load_511(a75, i46, iconst_1, i6, env, static) -{0,0}> main_Load_365(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && iconst_1 = 1

(8) Obligation:

IntTrs with 11 rules
Start term: main_Load_2(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_2(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_74(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_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12
main_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28
main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, iconst_NEG1, iconst_1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -1
main_LT_367(a51, i32, 1, i6, env, static) -{7,7}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2
main_Load_480(a75, i33, i42, 1, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42
main_LT_483(a75, i33, i42, 1, i6, env, static) -{3,3}> main_Load_480(a75, i33, i44', 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33
main_LT_483(a75, i33, i42, 1, i6, env, static) -{6,6}> main_Load_365(a75, i46', 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33

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

Moved arithmethic from lhss to constraints.

main_Load_480(a75, i33, i42, 1, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42
was transformed to
main_Load_480(a75, i33, i42, x, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42 && x = 1

main_LT_367(a51, i32, 1, i6, env, static) -{7,7}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2
was transformed to
main_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2 && x = 1

random_InvokeMethod_100(o12, a6, 1, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12
was transformed to
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12 && x = 1

main_LT_483(a75, i33, i42, 1, i6, env, static) -{6,6}> main_Load_365(a75, i46', 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33
was transformed to
main_LT_483(a75, i33, i42, x, i6, env, static) -{6,6}> main_Load_365(a75, i46', 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33 && x = 1

main_LT_483(a75, i33, i42, 1, i6, env, static) -{3,3}> main_Load_480(a75, i33, i44', 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33
was transformed to
main_LT_483(a75, i33, i42, x, i6, env, static) -{3,3}> main_Load_480(a75, i33, i44', 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33 && 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

(10) Obligation:

IntTrs with 11 rules
Start term: main_Load_2(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, iconst_NEG1, iconst_1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -1
main_Load_480(a75, i33, i42, x, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42 && x = 1
random_ArrayAccess_73(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_74(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6
main_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2 && x = 1
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12 && x = 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_LT_483(a75, i33, i42, x, i6, env, static) -{6,6}> main_Load_365(a75, i46', 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33 && x = 1
main_LT_483(a75, i33, i42, x, i6, env, static) -{3,3}> main_Load_480(a75, i33, i44', 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33 && 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_2(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_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28

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

Linearized lhss.

random_ArrayAccess_73(a6, iconst_0, iconst_0, env, static) -{0,0}> random_ArrayAccess_74(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_74(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_2(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, iconst_NEG1, iconst_1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_74(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12 && x = 1
main_Load_480(a75, i33, i42, x, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42 && x = 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_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_LT_483(a75, i33, i42, x, i6, env, static) -{6,6}> main_Load_365(a75, i46', 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33 && x = 1
main_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2 && x = 1
main_Load_2(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_LT_483(a75, i33, i42, x, i6, env, static) -{3,3}> main_Load_480(a75, i33, i44', 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33 && x = 1
main_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28

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

Moved arithmethic from constraints to rhss.

main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, iconst_NEG1, iconst_1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -1
was transformed to
main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, -1, 1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -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
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_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2 && x = 1
was transformed to
main_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i32 + 1, 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2 && x = 1

main_LT_483(a75, i33, i42, x, i6, env, static) -{6,6}> main_Load_365(a75, i46', 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33 && x = 1
was transformed to
main_LT_483(a75, i33, i42, x, i6, env, static) -{6,6}> main_Load_365(a75, i33 - 2, 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33 && x = 1

random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_74(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_74(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0

main_LT_483(a75, i33, i42, x, i6, env, static) -{3,3}> main_Load_480(a75, i33, i44', 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33 && x = 1
was transformed to
main_LT_483(a75, i33, i42, x, i6, env, static) -{3,3}> main_Load_480(a75, i33, i42 + 1, 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33 && x = 1

main_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28
was transformed to
main_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, 1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28

(14) Obligation:

IntTrs with 11 rules
Start term: main_Load_2(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, -1, 1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -1
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12 && x = 1
main_Load_480(a75, i33, i42, x, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42 && 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
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_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i32 + 1, 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2 && x = 1
main_LT_483(a75, i33, i42, x, i6, env, static) -{6,6}> main_Load_365(a75, i33 - 2, 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33 && x = 1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_74(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_LT_483(a75, i33, i42, x, i6, env, static) -{3,3}> main_Load_480(a75, i33, i42 + 1, 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33 && x = 1
main_Load_2(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_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, 1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28

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

Simplified expressions.

random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12 && x = 1
was transformed to
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12 && x = 1

main_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i32 + 1, 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2 && x = 1
was transformed to
main_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i32 + 1, 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= i6 && 1 <= i33' && i32 + 1 = i33' && -1 <= i32 && x = 1

main_Load_2(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_2(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

(16) Obligation:

IntTrs with 11 rules
Start term: main_Load_2(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, 1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12 && x = 1
main_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i32 + 1, 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= i6 && 1 <= i33' && i32 + 1 = i33' && -1 <= i32 && x = 1
main_LT_483(a75, i33, i42, x, i6, env, static) -{6,6}> main_Load_365(a75, i33 - 2, 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33 && 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_480(a75, i33, i42, x, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42 && x = 1
main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, -1, 1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -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_LT_483(a75, i33, i42, x, i6, env, static) -{3,3}> main_Load_480(a75, i33, i42 + 1, 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33 && x = 1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_74(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_Load_2(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

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

Transformed 77 jbc graph edges to a weighted ITS with 77 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.

(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_2(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, iconst_NEG1, iconst_1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_74(a6, iconst_0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12 && x = 1
main_Load_480(a75, i33, i42, x, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42 && x = 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_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_LT_483(a75, i33, i42, x, i6, env, static) -{6,6}> main_Load_365(a75, i46', 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33 && x = 1
main_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2 && x = 1
main_Load_2(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_LT_483(a75, i33, i42, x, i6, env, static) -{3,3}> main_Load_480(a75, i33, i44', 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33 && x = 1
main_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28

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

Moved arithmethic from constraints to rhss.

(26) Obligation:

IntTrs with 11 rules
Start term: main_Load_2(args, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LT_367(a51, iconst_NEG1, iconst_1, i6, env, static) -{0,0}> main_LT_368(a51, -1, 1, i6, env, static) :|: 1 <= i6 && -1 <= iconst_NEG1 && 0 < a51 && iconst_1 = 1 && iconst_NEG1 = -1
random_InvokeMethod_100(o12, a6, x, i6, env, static) -{3,3}> main_Load_365(a6, i8', 1, i6, env, static) :|: i8' <= o12 && 0 <= i8' && 0 <= o12 && 0 < a6 && -1 <= i8' && 1 <= i6 && 0 < o12 && x = 1
main_Load_480(a75, i33, i42, x, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42 && 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
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_LT_367(a51, i32, x, i6, env, static) -{7,7}> main_Load_480(a51, i32 + 1, 1, 1, i6, env, static) :|: 0 <= i32 && 0 < a51 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i32 + 1 = i33' && -1 <= i32 && 1 <= 2 && x = 1
main_LT_483(a75, i33, i42, x, i6, env, static) -{6,6}> main_Load_365(a75, i33 - 2, 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33 && x = 1
random_ArrayAccess_73(a6, iconst_0, x, env, static) -{0,0}> random_ArrayAccess_74(a6, 0, env, static) :|: 0 <= iconst_0 && iconst_0 = 0 && 0 < a6 && x = iconst_0
main_LT_483(a75, i33, i42, x, i6, env, static) -{3,3}> main_Load_480(a75, i33, i42 + 1, 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33 && x = 1
main_Load_2(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_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, 1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28

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

Simplified expressions.

(28) Obligation:

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

Extracted set of 74 edges for the analysis of TIME complexity. Dropped leaves.

(30) Obligation:

Set of 74 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 74 jbc graph edges to a weighted ITS with 74 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 74 rules
Start term: main_Load_2(args, env, static)
Considered paths: all paths from start
Rules:
main_Load_2(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_12(iconst_0, o1, env, static) :|: iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ArrayCreate_12(iconst_0, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_14(a2, o1, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2 && 0 < o1
langle_clinit_rangle_FieldAccess_14(a2, o1, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_16(o1, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2 && 0 < o1
langle_clinit_rangle_New_16(o1, env, static) -{0,0}> langle_clinit_rangle_New_18(o1, env, static) :|: 0 < o1
langle_clinit_rangle_New_18(o1, env, static) -{0,0}> langle_clinit_rangle_New_19(o1, env, static) :|: 0 <= static && 0 < o1
langle_clinit_rangle_New_19(o1, env, static) -{1,1}> langle_clinit_rangle_Duplicate_20(o4, o1, env, static) :|: o4 = 1 && 0 < o4 && 0 < o1
langle_clinit_rangle_Duplicate_20(o4, o1, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_22(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_ConstantStackPush_22(o4, o1, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_23(o4, NULL, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_clinit_rangle_InvokeMethod_23(o4, NULL, o1, env, static) -{1,1}> langle_init_rangle_Load_25(o4, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_init_rangle_Load_25(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_27(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_27(o4, o1, env, static) -{1,1}> langle_init_rangle_Load_29(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Load_29(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_35(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_35(o4, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_37(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_FieldAccess_37(o4, o1, env, static) -{1,1}> langle_clinit_rangle_Return_39(o1, env, static') :|: 0 <= o4 && 0 < o4 && 0 <= static && 0 < o1 && static' <= static + o4
langle_clinit_rangle_Return_39(o1, env, static) -{1,1}> main_Load_41(o1, env, static) :|: 0 < o1
main_Load_41(o1, env, static) -{0,0}> main_Load_42(o1, env, static) :|: 0 < o1
main_Load_42(o1, env, static) -{0,0}> main_Load_49(o1, env, static) :|: 0 <= static && 0 < o1
main_Load_49(o1, env, static) -{0,0}> main_Load_50(o1, env, static) :|: 0 < o1
main_Load_50(o1, env, static) -{0,0}> main_Load_52(o1, env, static) :|: 0 < o1
main_Load_52(o1, env, static) -{1,1}> main_FieldAccess_55(o1, env, static) :|: 0 < o1
main_FieldAccess_55(o1, env, static) -{0,0}> main_FieldAccess_57(o1, env, static) :|: 0 < o1
main_FieldAccess_57(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_59(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ConstantStackPush_59(o1, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_60(iconst_0, o1, NULL, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_FieldAccess_60(iconst_0, o1, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_61(o1, NULL, iconst_0, env, static') :|: NULL = 0 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0 && 0 < o1
langle_clinit_rangle_Return_61(o1, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_62(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
main_FieldAccess_62(o1, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_68(o1, iconst_0, env, static') :|: static' <= static + o1 && NULL = 0 && 0 <= o1 && iconst_0 = 0 && 0 <= static && 0 < o1
main_InvokeMethod_68(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_75(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_75(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_84(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_0 = 0 && 0 < a6
random_FieldAccess_84(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_116(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_116(a6, i8, iconst_1, i6, env, static) -{0,0}> main_Load_365(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && -1 <= i8 && 0 < a6 && 0 <= i8
main_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28
main_LT_367(a51, i32, iconst_1, i6, env, static) -{0,0}> main_LT_369(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && -1 <= i32 && iconst_1 = 1 && 0 <= i32
main_LT_369(a51, i32, iconst_1, i6, env, static) -{1,1}> main_Load_371(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_Load_371(a51, i32, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_373(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_ConstantStackPush_373(a51, i32, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_375(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_IntArithmetic_375(a51, i32, iconst_1, i6, env, static) -{1,1}> main_Store_377(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33 && i32 + iconst_1 = i33 && 0 <= i32
main_Store_377(a51, i33, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_379(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_ConstantStackPush_379(a51, i33, iconst_1, i6, env, static) -{1,1}> main_Store_381(a51, iconst_1, i33, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_Store_381(a51, iconst_1, i33, i6, env, static) -{1,1}> main_Load_382(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_Load_382(a51, i33, iconst_1, i6, env, static) -{0,0}> main_Load_405(a51, i33, iconst_1, iconst_1, i6, env, static) :|: iconst_1 <= 2 && 1 <= i6 && 0 < a51 && 1 <= iconst_1 && iconst_1 = 1 && 1 <= i33
main_Load_405(a59, i33, i34, iconst_1, i6, env, static) -{0,0}> main_Load_440(a59, i33, i34, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a59 && iconst_1 = 1 && i34 <= 2 && 1 <= i34 && 1 <= i33 && i34 <= 3
main_Load_440(a67, i33, i38, iconst_1, i6, env, static) -{0,0}> main_Load_480(a67, i33, i38, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && i38 <= 3 && 1 <= i33 && 1 <= i38 && 0 < a67
main_Load_480(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_Load_482(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && 1 <= i33
main_Load_482(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_LT_483(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && 1 <= i33
main_LT_483(a75, i33, i42, iconst_1, i6, env, static) -{0,0}> main_LT_485(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && i33 < i42 && 1 <= i33
main_LT_483(a75, i33, i42, iconst_1, i6, env, static) -{0,0}> main_LT_486(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && i42 <= i33 && iconst_1 = 1 && 1 <= i33
main_LT_485(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_Load_490(a75, i33, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && iconst_1 = 1 && i33 < i42 && 1 <= i33
main_LT_486(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_Inc_495(a75, i33, i42, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && i42 <= i33 && iconst_1 = 1 && 1 <= i33
main_Load_490(a75, i33, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_497(a75, i33, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && iconst_1 = 1 && 1 <= i33
main_Inc_495(a75, i33, i42, iconst_1, i6, env, static) -{1,1}> main_JMP_498(a75, i33, i44, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i42 && 1 <= i6 && 2 <= i44 && iconst_1 = 1 && 1 <= i33 && i42 + 1 = i44
main_ConstantStackPush_497(a75, i33, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_499(a75, i33, iconst_2, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && iconst_1 = 1 && 1 <= i33 && iconst_2 = 2
main_JMP_498(a75, i33, i44, iconst_1, i6, env, static) -{1,1}> main_Load_502(a75, i33, i44, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && 2 <= i44 && iconst_1 = 1 && 1 <= i33
main_IntArithmetic_499(a75, i33, iconst_2, iconst_1, i6, env, static) -{1,1}> main_Store_505(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && i33 - iconst_2 = i46 && iconst_1 = 1 && 1 <= i33 && iconst_2 = 2
main_Load_502(a75, i33, i44, iconst_1, i6, env, static) -{0,0}> main_Load_480(a75, i33, i44, iconst_1, i6, env, static) :|: 0 < a75 && 1 <= i6 && 2 <= i44 && iconst_1 = 1 && 1 <= i44 && 1 <= i33
main_Store_505(a75, i46, iconst_1, i6, env, static) -{1,1}> main_JMP_507(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && iconst_1 = 1
main_JMP_507(a75, i46, iconst_1, i6, env, static) -{1,1}> main_Load_511(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && iconst_1 = 1
main_Load_511(a75, i46, iconst_1, i6, env, static) -{0,0}> main_Load_365(a75, i46, iconst_1, i6, env, static) :|: 0 < a75 && -1 <= i46 && 1 <= i6 && iconst_1 = 1

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

obtained
main_Load_2(o1, env, static) -{33,33}> main_Load_365(o1, i8', 1, i5', env, static'4) :|: static'4 <= static'3 + 1 && 0 <= i8' && 0 < 1 && 0 < o1 && 0 <= 1 && -1 <= i8' && 0 <= i5' && 1 <= i5' && 0 <= o8' && 0 <= static'3 && 0 < 2 && 0 <= static''' && 0 <= static && static'3 <= static'2 + o1 && 0 <= static'1 && static''' <= static + 2 && o1 <= static'3 && 0 <= o1 && static'2 <= static'1 + 0 && -1 * static'3 <= 0 && i8' <= o8' && i5' < o1 && 0 < o8' && o8' < o1 && 0 <= static'2 && 0 <= 2 && static'1 <= static''' + 1
by chaining
main_Load_2(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_12(iconst_0, o1, env, static) :|: iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ArrayCreate_12(iconst_0, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_14(a2, o1, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2 && 0 < o1
langle_clinit_rangle_FieldAccess_14(a2, o1, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_16(o1, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2 && 0 < o1
langle_clinit_rangle_New_16(o1, env, static) -{0,0}> langle_clinit_rangle_New_18(o1, env, static) :|: 0 < o1
langle_clinit_rangle_New_18(o1, env, static) -{0,0}> langle_clinit_rangle_New_19(o1, env, static) :|: 0 <= static && 0 < o1
langle_clinit_rangle_New_19(o1, env, static) -{1,1}> langle_clinit_rangle_Duplicate_20(o4, o1, env, static) :|: o4 = 1 && 0 < o4 && 0 < o1
langle_clinit_rangle_Duplicate_20(o4, o1, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_22(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_ConstantStackPush_22(o4, o1, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_23(o4, NULL, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_clinit_rangle_InvokeMethod_23(o4, NULL, o1, env, static) -{1,1}> langle_init_rangle_Load_25(o4, o1, env, static) :|: NULL = 0 && 0 < o4 && 0 < o1
langle_init_rangle_Load_25(o4, o1, env, static) -{1,1}> langle_init_rangle_InvokeMethod_27(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_InvokeMethod_27(o4, o1, env, static) -{1,1}> langle_init_rangle_Load_29(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Load_29(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_35(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_init_rangle_Return_35(o4, o1, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_37(o4, o1, env, static) :|: 0 < o4 && 0 < o1
langle_clinit_rangle_FieldAccess_37(o4, o1, env, static) -{1,1}> langle_clinit_rangle_Return_39(o1, env, static') :|: 0 <= o4 && 0 < o4 && 0 <= static && 0 < o1 && static' <= static + o4
langle_clinit_rangle_Return_39(o1, env, static) -{1,1}> main_Load_41(o1, env, static) :|: 0 < o1
main_Load_41(o1, env, static) -{0,0}> main_Load_42(o1, env, static) :|: 0 < o1
main_Load_42(o1, env, static) -{0,0}> main_Load_49(o1, env, static) :|: 0 <= static && 0 < o1
main_Load_49(o1, env, static) -{0,0}> main_Load_50(o1, env, static) :|: 0 < o1
main_Load_50(o1, env, static) -{0,0}> main_Load_52(o1, env, static) :|: 0 < o1
main_Load_52(o1, env, static) -{1,1}> main_FieldAccess_55(o1, env, static) :|: 0 < o1
main_FieldAccess_55(o1, env, static) -{0,0}> main_FieldAccess_57(o1, env, static) :|: 0 < o1
main_FieldAccess_57(o1, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_59(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_ConstantStackPush_59(o1, NULL, iconst_0, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_60(iconst_0, o1, NULL, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
langle_clinit_rangle_FieldAccess_60(iconst_0, o1, NULL, env, static) -{1,1}> langle_clinit_rangle_Return_61(o1, NULL, iconst_0, env, static') :|: NULL = 0 && iconst_0 = 0 && 0 <= static && static' <= static + iconst_0 && 0 < o1
langle_clinit_rangle_Return_61(o1, NULL, iconst_0, env, static) -{1,1}> main_FieldAccess_62(o1, NULL, iconst_0, env, static) :|: NULL = 0 && iconst_0 = 0 && 0 < o1
main_FieldAccess_62(o1, NULL, iconst_0, env, static) -{1,1}> main_InvokeMethod_68(o1, iconst_0, env, static') :|: static' <= static + o1 && NULL = 0 && 0 <= o1 && iconst_0 = 0 && 0 <= static && 0 < o1
main_InvokeMethod_68(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_75(a6, iconst_0, i6, env, static) :|: 0 <= i6 && 1 <= i6 && iconst_0 = 0 && 0 < a6
random_ArrayAccess_75(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_84(o8, a6, iconst_0, i6, env, static) :|: 1 <= i6 && 0 <= o8 && iconst_0 = 0 && 0 < a6
random_FieldAccess_84(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_116(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && 0 < a6 && 0 <= i8
main_Load_116(a6, i8, iconst_1, i6, env, static) -{0,0}> main_Load_365(a6, i8, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && -1 <= i8 && 0 < a6 && 0 <= i8

obtained
main_Load_365(a51, i28, 1, i6, env, static) -{8,8}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i28 && 0 < a51 && -1 <= i28 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i28 + 1 = i33' && 1 <= 2
by chaining
main_Load_365(a51, i28, iconst_1, i6, env, static) -{1,1}> main_LT_367(a51, i28, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && -1 <= i28
main_LT_367(a51, i32, iconst_1, i6, env, static) -{0,0}> main_LT_369(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && -1 <= i32 && iconst_1 = 1 && 0 <= i32
main_LT_369(a51, i32, iconst_1, i6, env, static) -{1,1}> main_Load_371(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_Load_371(a51, i32, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_373(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_ConstantStackPush_373(a51, i32, iconst_1, i6, env, static) -{1,1}> main_IntArithmetic_375(a51, i32, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 0 <= i32
main_IntArithmetic_375(a51, i32, iconst_1, i6, env, static) -{1,1}> main_Store_377(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33 && i32 + iconst_1 = i33 && 0 <= i32
main_Store_377(a51, i33, iconst_1, i6, env, static) -{1,1}> main_ConstantStackPush_379(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_ConstantStackPush_379(a51, i33, iconst_1, i6, env, static) -{1,1}> main_Store_381(a51, iconst_1, i33, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_Store_381(a51, iconst_1, i33, i6, env, static) -{1,1}> main_Load_382(a51, i33, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a51 && iconst_1 = 1 && 1 <= i33
main_Load_382(a51, i33, iconst_1, i6, env, static) -{0,0}> main_Load_405(a51, i33, iconst_1, iconst_1, i6, env, static) :|: iconst_1 <= 2 && 1 <= i6 && 0 < a51 && 1 <= iconst_1 && iconst_1 = 1 && 1 <= i33
main_Load_405(a59, i33, i34, iconst_1, i6, env, static) -{0,0}> main_Load_440(a59, i33, i34, iconst_1, i6, env, static) :|: 1 <= i6 && 0 < a59 && iconst_1 = 1 && i34 <= 2 && 1 <= i34 && 1 <= i33 && i34 <= 3
main_Load_440(a67, i33, i38, iconst_1, i6, env, static) -{0,0}> main_Load_480(a67, i33, i38, iconst_1, i6, env, static) :|: 1 <= i6 && iconst_1 = 1 && i38 <= 3 && 1 <= i33 && 1 <= i38 && 0 < a67

(34) Obligation:

IntTrs with 5 rules
Start term: main_Load_2(args, env, static)
Considered paths: all paths from start
Rules:
main_Load_2(o1, env, static) -{33,33}> main_Load_365(o1, i8', 1, i5', env, static'4) :|: static'4 <= static'3 + 1 && 0 <= i8' && 0 < 1 && 0 < o1 && 0 <= 1 && -1 <= i8' && 0 <= i5' && 1 <= i5' && 0 <= o8' && 0 <= static'3 && 0 < 2 && 0 <= static''' && 0 <= static && static'3 <= static'2 + o1 && 0 <= static'1 && static''' <= static + 2 && o1 <= static'3 && 0 <= o1 && static'2 <= static'1 + 0 && -1 * static'3 <= 0 && i8' <= o8' && i5' < o1 && 0 < o8' && o8' < o1 && 0 <= static'2 && 0 <= 2 && static'1 <= static''' + 1
main_Load_365(a51, i28, 1, i6, env, static) -{8,8}> main_Load_480(a51, i33', 1, 1, i6, env, static) :|: 0 <= i28 && 0 < a51 && -1 <= i28 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i28 + 1 = i33' && 1 <= 2
main_Load_480(a75, i33, i42, 1, i6, env, static) -{2,2}> main_LT_483(a75, i33, i42, 1, i6, env, static) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42
main_LT_483(a75, i33, i42, 1, i6, env, static) -{3,3}> main_Load_480(a75, i33, i44', 1, i6, env, static) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33
main_LT_483(a75, i33, i42, 1, i6, env, static) -{6,6}> main_Load_365(a75, i46', 1, i6, env, static) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33

(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_2(x1, x2, x3) → main_Load_2(x1, x3)
main_Load_365(x1, x2, x3, x4, x5, x6) → main_Load_365(x1, x2, x4)
main_Load_480(x1, x2, x3, x4, x5, x6, x7) → main_Load_480(x1, x2, x3, x5)
main_LT_483(x1, x2, x3, x4, x5, x6, x7) → main_LT_483(x1, x2, x3, x5)

(36) Obligation:

IntTrs with 5 rules
Start term: main_Load_2(args, static)
Considered paths: all paths from start
Rules:
main_Load_2(o1, static) -{33,33}> main_Load_365(o1, i8', i5') :|: static'4 <= static'3 + 1 && 0 <= i8' && 0 < 1 && 0 < o1 && 0 <= 1 && -1 <= i8' && 0 <= i5' && 1 <= i5' && 0 <= o8' && 0 <= static'3 && 0 < 2 && 0 <= static''' && 0 <= static && static'3 <= static'2 + o1 && 0 <= static'1 && static''' <= static + 2 && o1 <= static'3 && 0 <= o1 && static'2 <= static'1 + 0 && -1 * static'3 <= 0 && i8' <= o8' && i5' < o1 && 0 < o8' && o8' < o1 && 0 <= static'2 && 0 <= 2 && static'1 <= static''' + 1
main_Load_365(a51, i28, i6) -{8,8}> main_Load_480(a51, i33', 1, i6) :|: 0 <= i28 && 0 < a51 && -1 <= i28 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i28 + 1 = i33' && 1 <= 2
main_Load_480(a75, i33, i42, i6) -{2,2}> main_LT_483(a75, i33, i42, i6) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42
main_LT_483(a75, i33, i42, i6) -{3,3}> main_Load_480(a75, i33, i44', i6) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33
main_LT_483(a75, i33, i42, i6) -{6,6}> main_Load_365(a75, i46', i6) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33

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

Moved arithmethic from constraints to rhss.

main_LT_483(a75, i33, i42, i6) -{6,6}> main_Load_365(a75, i46', i6) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33
was transformed to
main_LT_483(a75, i33, i42, i6) -{6,6}> main_Load_365(a75, i33 - 2, i6) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33

main_Load_365(a51, i28, i6) -{8,8}> main_Load_480(a51, i33', 1, i6) :|: 0 <= i28 && 0 < a51 && -1 <= i28 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i28 + 1 = i33' && 1 <= 2
was transformed to
main_Load_365(a51, i28, i6) -{8,8}> main_Load_480(a51, i28 + 1, 1, i6) :|: 0 <= i28 && 0 < a51 && -1 <= i28 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i28 + 1 = i33' && 1 <= 2

main_LT_483(a75, i33, i42, i6) -{3,3}> main_Load_480(a75, i33, i44', i6) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33
was transformed to
main_LT_483(a75, i33, i42, i6) -{3,3}> main_Load_480(a75, i33, i42 + 1, i6) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33

(38) Obligation:

IntTrs with 5 rules
Start term: main_Load_2(args, static)
Considered paths: all paths from start
Rules:
main_LT_483(a75, i33, i42, i6) -{6,6}> main_Load_365(a75, i33 - 2, i6) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33
main_Load_480(a75, i33, i42, i6) -{2,2}> main_LT_483(a75, i33, i42, i6) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42
main_Load_2(o1, static) -{33,33}> main_Load_365(o1, i8', i5') :|: static'4 <= static'3 + 1 && 0 <= i8' && 0 < 1 && 0 < o1 && 0 <= 1 && -1 <= i8' && 0 <= i5' && 1 <= i5' && 0 <= o8' && 0 <= static'3 && 0 < 2 && 0 <= static''' && 0 <= static && static'3 <= static'2 + o1 && 0 <= static'1 && static''' <= static + 2 && o1 <= static'3 && 0 <= o1 && static'2 <= static'1 + 0 && -1 * static'3 <= 0 && i8' <= o8' && i5' < o1 && 0 < o8' && o8' < o1 && 0 <= static'2 && 0 <= 2 && static'1 <= static''' + 1
main_Load_365(a51, i28, i6) -{8,8}> main_Load_480(a51, i28 + 1, 1, i6) :|: 0 <= i28 && 0 < a51 && -1 <= i28 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i28 + 1 = i33' && 1 <= 2
main_LT_483(a75, i33, i42, i6) -{3,3}> main_Load_480(a75, i33, i42 + 1, i6) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33

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

Simplified expressions.

main_Load_2(o1, static) -{33,33}> main_Load_365(o1, i8', i5') :|: static'4 <= static'3 + 1 && 0 <= i8' && 0 < 1 && 0 < o1 && 0 <= 1 && -1 <= i8' && 0 <= i5' && 1 <= i5' && 0 <= o8' && 0 <= static'3 && 0 < 2 && 0 <= static''' && 0 <= static && static'3 <= static'2 + o1 && 0 <= static'1 && static''' <= static + 2 && o1 <= static'3 && 0 <= o1 && static'2 <= static'1 + 0 && -1 * static'3 <= 0 && i8' <= o8' && i5' < o1 && 0 < o8' && o8' < o1 && 0 <= static'2 && 0 <= 2 && static'1 <= static''' + 1
was transformed to
main_Load_2(o1, static) -{33,33}> main_Load_365(o1, i8', i5') :|: static'4 <= static'3 + 1 && 0 <= i8' && 0 < o1 && -1 <= i8' && 0 <= i5' && 1 <= i5' && 0 <= static'3 && 0 <= static''' && 0 <= static && static'3 <= static'2 + o1 && 0 <= static'1 && static''' <= static + 2 && o1 <= static'3 && static'2 <= static'1 && -1 * static'3 <= 0 && i8' <= o8' && i5' < o1 && 0 < o8' && o8' < o1 && 0 <= static'2 && static'1 <= static''' + 1

main_Load_365(a51, i28, i6) -{8,8}> main_Load_480(a51, i28 + 1, 1, i6) :|: 0 <= i28 && 0 < a51 && -1 <= i28 && 1 <= 1 && 1 <= i6 && 1 <= i33' && 1 <= 3 && i28 + 1 = i33' && 1 <= 2
was transformed to
main_Load_365(a51, i28, i6) -{8,8}> main_Load_480(a51, i28 + 1, 1, i6) :|: 0 <= i28 && 0 < a51 && -1 <= i28 && 1 <= i6 && 1 <= i33' && i28 + 1 = i33'

(40) Obligation:

IntTrs with 5 rules
Start term: main_Load_2(args, static)
Considered paths: all paths from start
Rules:
main_LT_483(a75, i33, i42, i6) -{6,6}> main_Load_365(a75, i33 - 2, i6) :|: i33 - 2 = i46' && -1 <= i46' && 1 <= i6 && 0 < a75 && i33 < i42 && 1 <= i42 && 1 <= i33
main_Load_480(a75, i33, i42, i6) -{2,2}> main_LT_483(a75, i33, i42, i6) :|: 1 <= i33 && 1 <= i6 && 0 < a75 && 1 <= i42
main_LT_483(a75, i33, i42, i6) -{3,3}> main_Load_480(a75, i33, i42 + 1, i6) :|: i42 + 1 = i44' && 1 <= i33 && 1 <= i42 && 1 <= i44' && 0 < a75 && 1 <= i6 && 2 <= i44' && i42 <= i33
main_Load_2(o1, static) -{33,33}> main_Load_365(o1, i8', i5') :|: static'4 <= static'3 + 1 && 0 <= i8' && 0 < o1 && -1 <= i8' && 0 <= i5' && 1 <= i5' && 0 <= static'3 && 0 <= static''' && 0 <= static && static'3 <= static'2 + o1 && 0 <= static'1 && static''' <= static + 2 && o1 <= static'3 && static'2 <= static'1 && -1 * static'3 <= 0 && i8' <= o8' && i5' < o1 && 0 < o8' && o8' < o1 && 0 <= static'2 && static'1 <= static''' + 1
main_Load_365(a51, i28, i6) -{8,8}> main_Load_480(a51, i28 + 1, 1, i6) :|: 0 <= i28 && 0 < a51 && -1 <= i28 && 1 <= i6 && 1 <= i33' && i28 + 1 = i33'

(41) koat Proof (EQUIVALENT transformation)

YES(?, 52*ar_0 + 30*ar_0^2 + 33)

Initial complexity problem:
1: T:
(Comp: ?, Cost: 6) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\ -1 <= i46' /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_1 < ar_2 /\ 1 <= ar_2 /\ 1 <= ar_1 ]
(Comp: ?, Cost: 2) main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\ 1 <= ar_3 /\ 0 < ar_0 /\ 1 <= ar_2 ]
(Comp: ?, Cost: 3) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\ 1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i44' /\ 0 < ar_0 /\ 1 <= ar_3 /\ 2 <= i44' /\ ar_2 <= ar_1 ]
(Comp: ?, Cost: 33) main_Load_2(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, i8', i5', arityPad)) [ static'4 <= static'3 + 1 /\ 0 <= i8' /\ 0 < ar_0 /\ -1 <= i8' /\ 0 <= i5' /\ 1 <= i5' /\ 0 <= static'3 /\ 0 <= static''' /\ 0 <= ar_1 /\ static'3 <= static'2 + ar_0 /\ 0 <= static'1 /\ static''' <= ar_1 + 2 /\ ar_0 <= static'3 /\ static'2 <= static'1 /\ -static'3 <= 0 /\ i8' <= o8' /\ i5' < ar_0 /\ 0 < o8' /\ o8' < ar_0 /\ 0 <= static'2 /\ static'1 <= static''' + 1 ]
(Comp: ?, Cost: 8) main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\ 0 < ar_0 /\ -1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i33' /\ ar_1 + 1 = i33' ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_2(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: 6) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\ -1 <= i46' /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_1 < ar_2 /\ 1 <= ar_2 /\ 1 <= ar_1 ]
(Comp: ?, Cost: 2) main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\ 1 <= ar_3 /\ 0 < ar_0 /\ 1 <= ar_2 ]
(Comp: ?, Cost: 3) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\ 1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i44' /\ 0 < ar_0 /\ 1 <= ar_3 /\ 2 <= i44' /\ ar_2 <= ar_1 ]
(Comp: 1, Cost: 33) main_Load_2(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, i8', i5', arityPad)) [ static'4 <= static'3 + 1 /\ 0 <= i8' /\ 0 < ar_0 /\ -1 <= i8' /\ 0 <= i5' /\ 1 <= i5' /\ 0 <= static'3 /\ 0 <= static''' /\ 0 <= ar_1 /\ static'3 <= static'2 + ar_0 /\ 0 <= static'1 /\ static''' <= ar_1 + 2 /\ ar_0 <= static'3 /\ static'2 <= static'1 /\ -static'3 <= 0 /\ i8' <= o8' /\ i5' < ar_0 /\ 0 < o8' /\ o8' < ar_0 /\ 0 <= static'2 /\ static'1 <= static''' + 1 ]
(Comp: ?, Cost: 8) main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\ 0 < ar_0 /\ -1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i33' /\ ar_1 + 1 = i33' ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_2(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

A polynomial rank function with
Pol(main_LT_483) = 2*V_2 - 1
Pol(main_Load_365) = 2*V_2 + 2
Pol(main_Load_480) = 2*V_2 - 1
Pol(main_Load_2) = 2*V_1
Pol(koat_start) = 2*V_1
orients all transitions weakly and the transitions
main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\ 0 < ar_0 /\ -1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i33' /\ ar_1 + 1 = i33' ]
main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\ -1 <= i46' /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_1 < ar_2 /\ 1 <= ar_2 /\ 1 <= ar_1 ]
strictly and produces the following problem:
3: T:
(Comp: 2*ar_0, Cost: 6) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\ -1 <= i46' /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_1 < ar_2 /\ 1 <= ar_2 /\ 1 <= ar_1 ]
(Comp: ?, Cost: 2) main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\ 1 <= ar_3 /\ 0 < ar_0 /\ 1 <= ar_2 ]
(Comp: ?, Cost: 3) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\ 1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i44' /\ 0 < ar_0 /\ 1 <= ar_3 /\ 2 <= i44' /\ ar_2 <= ar_1 ]
(Comp: 1, Cost: 33) main_Load_2(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, i8', i5', arityPad)) [ static'4 <= static'3 + 1 /\ 0 <= i8' /\ 0 < ar_0 /\ -1 <= i8' /\ 0 <= i5' /\ 1 <= i5' /\ 0 <= static'3 /\ 0 <= static''' /\ 0 <= ar_1 /\ static'3 <= static'2 + ar_0 /\ 0 <= static'1 /\ static''' <= ar_1 + 2 /\ ar_0 <= static'3 /\ static'2 <= static'1 /\ -static'3 <= 0 /\ i8' <= o8' /\ i5' < ar_0 /\ 0 < o8' /\ o8' < ar_0 /\ 0 <= static'2 /\ static'1 <= static''' + 1 ]
(Comp: 2*ar_0, Cost: 8) main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\ 0 < ar_0 /\ -1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i33' /\ ar_1 + 1 = i33' ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_2(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_480) = V_2 - V_3 + 1
Pol(main_LT_483) = V_2 - V_3 + 1
and size complexities
S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_2(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_2(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_2(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_2(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
S("main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\\ 0 < ar_0 /\\ -1 <= ar_1 /\\ 1 <= ar_2 /\\ 1 <= i33' /\\ ar_1 + 1 = i33' ]", 0-0) = ar_0
S("main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\\ 0 < ar_0 /\\ -1 <= ar_1 /\\ 1 <= ar_2 /\\ 1 <= i33' /\\ ar_1 + 1 = i33' ]", 0-1) = 3*ar_0
S("main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\\ 0 < ar_0 /\\ -1 <= ar_1 /\\ 1 <= ar_2 /\\ 1 <= i33' /\\ ar_1 + 1 = i33' ]", 0-2) = 1
S("main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\\ 0 < ar_0 /\\ -1 <= ar_1 /\\ 1 <= ar_2 /\\ 1 <= i33' /\\ ar_1 + 1 = i33' ]", 0-3) = ar_0
S("main_Load_2(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, i8', i5', arityPad)) [ static'4 <= static'3 + 1 /\\ 0 <= i8' /\\ 0 < ar_0 /\\ -1 <= i8' /\\ 0 <= i5' /\\ 1 <= i5' /\\ 0 <= static'3 /\\ 0 <= static''' /\\ 0 <= ar_1 /\\ static'3 <= static'2 + ar_0 /\\ 0 <= static'1 /\\ static''' <= ar_1 + 2 /\\ ar_0 <= static'3 /\\ static'2 <= static'1 /\\ -static'3 <= 0 /\\ i8' <= o8' /\\ i5' < ar_0 /\\ 0 < o8' /\\ o8' < ar_0 /\\ 0 <= static'2 /\\ static'1 <= static''' + 1 ]", 0-0) = ar_0
S("main_Load_2(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, i8', i5', arityPad)) [ static'4 <= static'3 + 1 /\\ 0 <= i8' /\\ 0 < ar_0 /\\ -1 <= i8' /\\ 0 <= i5' /\\ 1 <= i5' /\\ 0 <= static'3 /\\ 0 <= static''' /\\ 0 <= ar_1 /\\ static'3 <= static'2 + ar_0 /\\ 0 <= static'1 /\\ static''' <= ar_1 + 2 /\\ ar_0 <= static'3 /\\ static'2 <= static'1 /\\ -static'3 <= 0 /\\ i8' <= o8' /\\ i5' < ar_0 /\\ 0 < o8' /\\ o8' < ar_0 /\\ 0 <= static'2 /\\ static'1 <= static''' + 1 ]", 0-1) = ar_0
S("main_Load_2(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, i8', i5', arityPad)) [ static'4 <= static'3 + 1 /\\ 0 <= i8' /\\ 0 < ar_0 /\\ -1 <= i8' /\\ 0 <= i5' /\\ 1 <= i5' /\\ 0 <= static'3 /\\ 0 <= static''' /\\ 0 <= ar_1 /\\ static'3 <= static'2 + ar_0 /\\ 0 <= static'1 /\\ static''' <= ar_1 + 2 /\\ ar_0 <= static'3 /\\ static'2 <= static'1 /\\ -static'3 <= 0 /\\ i8' <= o8' /\\ i5' < ar_0 /\\ 0 < o8' /\\ o8' < ar_0 /\\ 0 <= static'2 /\\ static'1 <= static''' + 1 ]", 0-2) = ar_0
S("main_Load_2(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, i8', i5', arityPad)) [ static'4 <= static'3 + 1 /\\ 0 <= i8' /\\ 0 < ar_0 /\\ -1 <= i8' /\\ 0 <= i5' /\\ 1 <= i5' /\\ 0 <= static'3 /\\ 0 <= static''' /\\ 0 <= ar_1 /\\ static'3 <= static'2 + ar_0 /\\ 0 <= static'1 /\\ static''' <= ar_1 + 2 /\\ ar_0 <= static'3 /\\ static'2 <= static'1 /\\ -static'3 <= 0 /\\ i8' <= o8' /\\ i5' < ar_0 /\\ 0 < o8' /\\ o8' < ar_0 /\\ 0 <= static'2 /\\ static'1 <= static''' + 1 ]", 0-3) = ?
S("main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\\ 1 <= ar_1 /\\ 1 <= ar_2 /\\ 1 <= i44' /\\ 0 < ar_0 /\\ 1 <= ar_3 /\\ 2 <= i44' /\\ ar_2 <= ar_1 ]", 0-0) = ar_0
S("main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\\ 1 <= ar_1 /\\ 1 <= ar_2 /\\ 1 <= i44' /\\ 0 < ar_0 /\\ 1 <= ar_3 /\\ 2 <= i44' /\\ ar_2 <= ar_1 ]", 0-1) = 3*ar_0
S("main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\\ 1 <= ar_1 /\\ 1 <= ar_2 /\\ 1 <= i44' /\\ 0 < ar_0 /\\ 1 <= ar_3 /\\ 2 <= i44' /\\ ar_2 <= ar_1 ]", 0-2) = ?
S("main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\\ 1 <= ar_1 /\\ 1 <= ar_2 /\\ 1 <= i44' /\\ 0 < ar_0 /\\ 1 <= ar_3 /\\ 2 <= i44' /\\ ar_2 <= ar_1 ]", 0-3) = ar_0
S("main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ 1 <= ar_2 ]", 0-0) = ar_0
S("main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ 1 <= ar_2 ]", 0-1) = 3*ar_0
S("main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ 1 <= ar_2 ]", 0-2) = ?
S("main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ 1 <= ar_2 ]", 0-3) = ar_0
S("main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\\ -1 <= i46' /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ ar_1 < ar_2 /\\ 1 <= ar_2 /\\ 1 <= ar_1 ]", 0-0) = ar_0
S("main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\\ -1 <= i46' /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ ar_1 < ar_2 /\\ 1 <= ar_2 /\\ 1 <= ar_1 ]", 0-1) = 3*ar_0
S("main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\\ -1 <= i46' /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ ar_1 < ar_2 /\\ 1 <= ar_2 /\\ 1 <= ar_1 ]", 0-2) = ar_0
S("main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\\ -1 <= i46' /\\ 1 <= ar_3 /\\ 0 < ar_0 /\\ ar_1 < ar_2 /\\ 1 <= ar_2 /\\ 1 <= ar_1 ]", 0-3) = ?
orients the transitions
main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\ 1 <= ar_3 /\ 0 < ar_0 /\ 1 <= ar_2 ]
main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\ 1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i44' /\ 0 < ar_0 /\ 1 <= ar_3 /\ 2 <= i44' /\ ar_2 <= ar_1 ]
weakly and the transition
main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\ 1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i44' /\ 0 < ar_0 /\ 1 <= ar_3 /\ 2 <= i44' /\ ar_2 <= ar_1 ]
strictly and produces the following problem:
4: T:
(Comp: 2*ar_0, Cost: 6) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\ -1 <= i46' /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_1 < ar_2 /\ 1 <= ar_2 /\ 1 <= ar_1 ]
(Comp: ?, Cost: 2) main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\ 1 <= ar_3 /\ 0 < ar_0 /\ 1 <= ar_2 ]
(Comp: 6*ar_0^2 + 4*ar_0, Cost: 3) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\ 1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i44' /\ 0 < ar_0 /\ 1 <= ar_3 /\ 2 <= i44' /\ ar_2 <= ar_1 ]
(Comp: 1, Cost: 33) main_Load_2(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, i8', i5', arityPad)) [ static'4 <= static'3 + 1 /\ 0 <= i8' /\ 0 < ar_0 /\ -1 <= i8' /\ 0 <= i5' /\ 1 <= i5' /\ 0 <= static'3 /\ 0 <= static''' /\ 0 <= ar_1 /\ static'3 <= static'2 + ar_0 /\ 0 <= static'1 /\ static''' <= ar_1 + 2 /\ ar_0 <= static'3 /\ static'2 <= static'1 /\ -static'3 <= 0 /\ i8' <= o8' /\ i5' < ar_0 /\ 0 < o8' /\ o8' < ar_0 /\ 0 <= static'2 /\ static'1 <= static''' + 1 ]
(Comp: 2*ar_0, Cost: 8) main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\ 0 < ar_0 /\ -1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i33' /\ ar_1 + 1 = i33' ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_2(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: 6) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, ar_1 - 2, ar_3, arityPad)) [ ar_1 - 2 = i46' /\ -1 <= i46' /\ 1 <= ar_3 /\ 0 < ar_0 /\ ar_1 < ar_2 /\ 1 <= ar_2 /\ 1 <= ar_1 ]
(Comp: 6*ar_0 + 6*ar_0^2, Cost: 2) main_Load_480(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_LT_483(ar_0, ar_1, ar_2, ar_3)) [ 1 <= ar_1 /\ 1 <= ar_3 /\ 0 < ar_0 /\ 1 <= ar_2 ]
(Comp: 6*ar_0^2 + 4*ar_0, Cost: 3) main_LT_483(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_2 + 1 = i44' /\ 1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i44' /\ 0 < ar_0 /\ 1 <= ar_3 /\ 2 <= i44' /\ ar_2 <= ar_1 ]
(Comp: 1, Cost: 33) main_Load_2(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_365(ar_0, i8', i5', arityPad)) [ static'4 <= static'3 + 1 /\ 0 <= i8' /\ 0 < ar_0 /\ -1 <= i8' /\ 0 <= i5' /\ 1 <= i5' /\ 0 <= static'3 /\ 0 <= static''' /\ 0 <= ar_1 /\ static'3 <= static'2 + ar_0 /\ 0 <= static'1 /\ static''' <= ar_1 + 2 /\ ar_0 <= static'3 /\ static'2 <= static'1 /\ -static'3 <= 0 /\ i8' <= o8' /\ i5' < ar_0 /\ 0 < o8' /\ o8' < ar_0 /\ 0 <= static'2 /\ static'1 <= static''' + 1 ]
(Comp: 2*ar_0, Cost: 8) main_Load_365(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_480(ar_0, ar_1 + 1, 1, ar_2)) [ 0 <= ar_1 /\ 0 < ar_0 /\ -1 <= ar_1 /\ 1 <= ar_2 /\ 1 <= i33' /\ ar_1 + 1 = i33' ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_2(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Complexity upper bound 52*ar_0 + 30*ar_0^2 + 33

Time: 0.218 sec (SMT: 0.197 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 + 52 * |args| + 30 * |args|^2)