time complexity proof of /tmp/tmpzO2IXf/PastaA7.jar

The time complexity of the given JBC problem could be proven to be BOUNDS(CONSTANT, 30 + 9 * |#0| + 9 * |#1|).

0 JBC problem

↳1 JBCToGraph (BOTH CONCRETE BOUNDS(ID, ID), 594 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(7)), 2 ms)

↳4 JBCComplexityEdges

    ↳5 JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID), 113 ms)

    ↳6 WeightedIntTrs

        ↳7 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 45 ms)

        ↳8 WeightedIntTrs

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

        ↳10 WeightedIntTrs

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

        ↳12 WeightedIntTrs

    ↳13 JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID), 85 ms)

    ↳14 WeightedIntTrs

        ↳15 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 41 ms)

        ↳16 WeightedIntTrs

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

        ↳18 WeightedIntTrs

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

        ↳20 WeightedIntTrs

↳21 TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(7)), 7 ms)

↳22 JBCComplexityEdges

    ↳23 JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID), 87 ms)

    ↳24 WeightedIntTrs

    ↳25 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 29 ms)

    ↳26 WeightedIntTrs

    ↳27 WeightedIntTrsUnneededArgumentFilterProof (CONCRETE UPPER BOUND(ID), 37 ms)

    ↳28 WeightedIntTrs

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

    ↳30 WeightedIntTrs

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

    ↳32 WeightedIntTrs

    ↳33 koat Proof (⇔, 82 ms)

    ↳34 BOUNDS(CONSTANT, 23 + 9 * |#0| + 9 * |#1|)

(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 PastaA7 {
    public static void main(int x, int y, int z) {
        while (x > y && x > z) {
            y++;
            z++;
        }
    }
}

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

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
PastaA7.main(III)V: Graph of 57 nodes with 1 SCC.

(3) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(7)) transformation)

Extracted set of 50 edges for the analysis of TIME complexity. Kept leaves.

(4) Obligation:

Set of 50 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 50 jbc graph edges to a weighted ITS with 50 rules.
Used simplified encoding of division and modulo.
Filtered conditions with variables that do not depend on the variables on the lhs or rhs without taking transitive dependencies into account.
Did no encode lower bounds for putfield and astore.

(6) Obligation:

IntTrs with 50 rules
Start term: main_Load_1(#0, #1, #2, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(i2, i3, i5, env, static) -{0,0}> main_Load_5(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_5(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i3, i5, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_12(iconst_0, i2, i3, i5, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_12(iconst_0, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_14(a2, i2, i3, i5, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_14(a2, i2, i3, i5, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_17(i2, i3, i5, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_17(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_New_18(i2, i3, i5, env, static) :|: 0 >= 0
langle_clinit_rangle_New_18(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_New_19(i2, i3, i5, env, static) :|: 0 <= static
langle_clinit_rangle_New_19(i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_Duplicate_21(o2, i2, i3, i5, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_21(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_22(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_22(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_24(o2, NULL, i2, i3, i5, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_24(o2, NULL, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Load_26(o2, i2, i3, i5, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_26(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_InvokeMethod_28(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_28(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Load_30(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Load_30(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_InvokeMethod_32(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_32(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Return_35(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Return_35(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Return_38(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Return_38(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_39(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_39(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_Return_40(i2, i3, i5, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_40(i2, i3, i5, env, static) -{1,1}> main_Load_46(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_46(i2, i3, i5, env, static) -{0,0}> main_Load_47(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_47(i2, i3, i5, env, static) -{0,0}> main_Load_48(i2, i3, i5, env, static) :|: 0 <= static
main_Load_48(i2, i3, i5, env, static) -{0,0}> main_Load_49(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_49(i2, i3, i5, env, static) -{0,0}> main_Load_50(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_50(i2, i3, i5, env, static) -{1,1}> main_Load_51(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_51(i2, i3, i5, env, static) -{1,1}> main_LE_55(i2, i3, i5, env, static) :|: 0 >= 0
main_LE_55(i2, i3, i5, env, static) -{0,0}> main_LE_56(i2, i3, i5, env, static) :|: i2 <= i3
main_LE_55(i2, i3, i5, env, static) -{0,0}> main_LE_57(i2, i3, i5, env, static) :|: i3 < i2
main_LE_57(i2, i3, i5, env, static) -{1,1}> main_Load_63(i2, i3, i5, env, static) :|: i3 < i2
main_Load_63(i2, i3, i5, env, static) -{1,1}> main_Load_65(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_65(i2, i3, i5, env, static) -{1,1}> main_LE_72(i2, i3, i5, env, static) :|: 0 >= 0
main_LE_72(i2, i3, i5, env, static) -{0,0}> main_LE_77(i2, i3, i5, env, static) :|: i2 <= i5
main_LE_72(i2, i3, i5, env, static) -{0,0}> main_LE_78(i2, i3, i5, env, static) :|: i5 < i2
main_LE_78(i2, i3, i5, env, static) -{1,1}> main_Inc_83(i2, i3, i5, env, static) :|: i5 < i2
main_Inc_83(i2, i3, i5, env, static) -{1,1}> main_Inc_85(i2, i3, i5, i9, env, static) :|: i3 + 1 = i9
main_Inc_85(i2, i3, i5, i9, env, static) -{1,1}> main_JMP_86(i2, i3, i5, i9, i10, env, static) :|: i5 + 1 = i10
main_JMP_86(i2, i3, i5, i9, i10, env, static) -{0,0}> main_JMP_183(i2, i3, i5, i9, i10, env, static) :|: 0 >= 0
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_186(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_186(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_187(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_187(i2, i3, i5, i41, i44, env, static) -{1,1}> main_LE_195(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_LE_195(i2, i3, i5, i41, i44, env, static) -{0,0}> main_LE_198(i2, i3, i5, i41, i44, env, static) :|: i2 <= i41
main_LE_195(i2, i3, i5, i41, i44, env, static) -{0,0}> main_LE_199(i2, i3, i5, i41, i44, env, static) :|: i41 < i2
main_LE_199(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_209(i2, i3, i5, i41, i44, env, static) :|: i41 < i2
main_Load_209(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_230(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_230(i2, i3, i5, i41, i44, env, static) -{1,1}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: 0 >= 0
main_LE_240(i2, i3, i5, i44, i41, env, static) -{0,0}> main_LE_254(i2, i3, i5, i44, i41, env, static) :|: i2 <= i44
main_LE_240(i2, i3, i5, i44, i41, env, static) -{0,0}> main_LE_255(i2, i3, i5, i44, i41, env, static) :|: i44 < i2
main_LE_255(i2, i3, i5, i44, i41, env, static) -{1,1}> main_Inc_277(i2, i3, i5, i41, i44, env, static) :|: i44 < i2
main_Inc_277(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Inc_286(i2, i3, i5, i79, i44, env, static) :|: i41 + 1 = i79
main_Inc_286(i2, i3, i5, i79, i44, env, static) -{1,1}> main_JMP_291(i2, i3, i5, i79, i84, env, static) :|: i44 + 1 = i84
main_JMP_291(i2, i3, i5, i79, i84, env, static) -{0,0}> main_JMP_183(i2, i3, i5, i79, i84, env, static) :|: 0 >= 0

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

obtained
main_Load_1(i2, i3, i5, env, static) -{17,17}> main_LE_55(i2, i3, i5, env, static'1) :|: 0 >= 0 && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && static'1 <= static''' + 1
by chaining
main_Load_1(i2, i3, i5, env, static) -{0,0}> main_Load_5(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_5(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i3, i5, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_12(iconst_0, i2, i3, i5, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_12(iconst_0, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_14(a2, i2, i3, i5, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_14(a2, i2, i3, i5, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_17(i2, i3, i5, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_17(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_New_18(i2, i3, i5, env, static) :|: 0 >= 0
langle_clinit_rangle_New_18(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_New_19(i2, i3, i5, env, static) :|: 0 <= static
langle_clinit_rangle_New_19(i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_Duplicate_21(o2, i2, i3, i5, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_21(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_22(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_22(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_24(o2, NULL, i2, i3, i5, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_24(o2, NULL, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Load_26(o2, i2, i3, i5, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_26(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_InvokeMethod_28(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_28(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Load_30(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Load_30(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_InvokeMethod_32(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_32(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Return_35(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Return_35(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Return_38(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Return_38(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_39(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_39(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_Return_40(i2, i3, i5, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_40(i2, i3, i5, env, static) -{1,1}> main_Load_46(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_46(i2, i3, i5, env, static) -{0,0}> main_Load_47(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_47(i2, i3, i5, env, static) -{0,0}> main_Load_48(i2, i3, i5, env, static) :|: 0 <= static
main_Load_48(i2, i3, i5, env, static) -{0,0}> main_Load_49(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_49(i2, i3, i5, env, static) -{0,0}> main_Load_50(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_50(i2, i3, i5, env, static) -{1,1}> main_Load_51(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_51(i2, i3, i5, env, static) -{1,1}> main_LE_55(i2, i3, i5, env, static) :|: 0 >= 0

obtained
main_LE_55(i2, i3, i5, env, static) -{3,3}> main_LE_72(i2, i3, i5, env, static) :|: 0 >= 0 && i3 < i2
by chaining
main_LE_55(i2, i3, i5, env, static) -{0,0}> main_LE_57(i2, i3, i5, env, static) :|: i3 < i2
main_LE_57(i2, i3, i5, env, static) -{1,1}> main_Load_63(i2, i3, i5, env, static) :|: i3 < i2
main_Load_63(i2, i3, i5, env, static) -{1,1}> main_Load_65(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_65(i2, i3, i5, env, static) -{1,1}> main_LE_72(i2, i3, i5, env, static) :|: 0 >= 0

obtained
main_LE_72(i2, i3, i5, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i9', i10', env, static) :|: 0 >= 0 && i3 + 1 = i9' && i5 + 1 = i10' && i5 < i2
by chaining
main_LE_72(i2, i3, i5, env, static) -{0,0}> main_LE_78(i2, i3, i5, env, static) :|: i5 < i2
main_LE_78(i2, i3, i5, env, static) -{1,1}> main_Inc_83(i2, i3, i5, env, static) :|: i5 < i2
main_Inc_83(i2, i3, i5, env, static) -{1,1}> main_Inc_85(i2, i3, i5, i9, env, static) :|: i3 + 1 = i9
main_Inc_85(i2, i3, i5, i9, env, static) -{1,1}> main_JMP_86(i2, i3, i5, i9, i10, env, static) :|: i5 + 1 = i10
main_JMP_86(i2, i3, i5, i9, i10, env, static) -{0,0}> main_JMP_183(i2, i3, i5, i9, i10, env, static) :|: 0 >= 0

obtained
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_195(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
by chaining
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_186(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_186(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_187(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_187(i2, i3, i5, i41, i44, env, static) -{1,1}> main_LE_195(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0

obtained
main_LE_195(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: 0 >= 0 && i41 < i2
by chaining
main_LE_195(i2, i3, i5, i41, i44, env, static) -{0,0}> main_LE_199(i2, i3, i5, i41, i44, env, static) :|: i41 < i2
main_LE_199(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_209(i2, i3, i5, i41, i44, env, static) :|: i41 < i2
main_Load_209(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_230(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_230(i2, i3, i5, i41, i44, env, static) -{1,1}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: 0 >= 0

obtained
main_LE_240(i2, i3, i5, i44, i41, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i79', i84', env, static) :|: 0 >= 0 && i41 + 1 = i79' && i44 + 1 = i84' && i44 < i2
by chaining
main_LE_240(i2, i3, i5, i44, i41, env, static) -{0,0}> main_LE_255(i2, i3, i5, i44, i41, env, static) :|: i44 < i2
main_LE_255(i2, i3, i5, i44, i41, env, static) -{1,1}> main_Inc_277(i2, i3, i5, i41, i44, env, static) :|: i44 < i2
main_Inc_277(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Inc_286(i2, i3, i5, i79, i44, env, static) :|: i41 + 1 = i79
main_Inc_286(i2, i3, i5, i79, i44, env, static) -{1,1}> main_JMP_291(i2, i3, i5, i79, i84, env, static) :|: i44 + 1 = i84
main_JMP_291(i2, i3, i5, i79, i84, env, static) -{0,0}> main_JMP_183(i2, i3, i5, i79, i84, env, static) :|: 0 >= 0

(8) Obligation:

IntTrs with 10 rules
Start term: main_Load_1(#0, #1, #2, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_1(i2, i3, i5, env, static) -{17,17}> main_LE_55(i2, i3, i5, env, static'1) :|: 0 >= 0 && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && static'1 <= static''' + 1
main_LE_55(i2, i3, i5, env, static) -{0,0}> main_LE_56(i2, i3, i5, env, static) :|: i2 <= i3
main_LE_55(i2, i3, i5, env, static) -{3,3}> main_LE_72(i2, i3, i5, env, static) :|: 0 >= 0 && i3 < i2
main_LE_72(i2, i3, i5, env, static) -{0,0}> main_LE_77(i2, i3, i5, env, static) :|: i2 <= i5
main_LE_72(i2, i3, i5, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i9', i10', env, static) :|: 0 >= 0 && i3 + 1 = i9' && i5 + 1 = i10' && i5 < i2
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_195(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_LE_195(i2, i3, i5, i41, i44, env, static) -{0,0}> main_LE_198(i2, i3, i5, i41, i44, env, static) :|: i2 <= i41
main_LE_195(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: 0 >= 0 && i41 < i2
main_LE_240(i2, i3, i5, i44, i41, env, static) -{0,0}> main_LE_254(i2, i3, i5, i44, i41, env, static) :|: i2 <= i44
main_LE_240(i2, i3, i5, i44, i41, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i79', i84', env, static) :|: 0 >= 0 && i41 + 1 = i79' && i44 + 1 = i84' && i44 < i2

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

Moved arithmethic from constraints to rhss.

main_LE_72(i2, i3, i5, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i9', i10', env, static) :|: 0 >= 0 && i3 + 1 = i9' && i5 + 1 = i10' && i5 < i2
was transformed to
main_LE_72(i2, i3, i5, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i3 + 1, i5 + 1, env, static) :|: 0 >= 0 && i3 + 1 = i9' && i5 + 1 = i10' && i5 < i2

main_LE_240(i2, i3, i5, i44, i41, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i79', i84', env, static) :|: 0 >= 0 && i41 + 1 = i79' && i44 + 1 = i84' && i44 < i2
was transformed to
main_LE_240(i2, i3, i5, i44, i41, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i41 + 1, i44 + 1, env, static) :|: 0 >= 0 && i41 + 1 = i79' && i44 + 1 = i84' && i44 < i2

(10) Obligation:

IntTrs with 10 rules
Start term: main_Load_1(#0, #1, #2, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_240(i2, i3, i5, i44, i41, env, static) -{0,0}> main_LE_254(i2, i3, i5, i44, i41, env, static) :|: i2 <= i44
main_Load_1(i2, i3, i5, env, static) -{17,17}> main_LE_55(i2, i3, i5, env, static'1) :|: 0 >= 0 && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && static'1 <= static''' + 1
main_LE_72(i2, i3, i5, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i3 + 1, i5 + 1, env, static) :|: 0 >= 0 && i3 + 1 = i9' && i5 + 1 = i10' && i5 < i2
main_LE_55(i2, i3, i5, env, static) -{0,0}> main_LE_56(i2, i3, i5, env, static) :|: i2 <= i3
main_LE_72(i2, i3, i5, env, static) -{0,0}> main_LE_77(i2, i3, i5, env, static) :|: i2 <= i5
main_LE_55(i2, i3, i5, env, static) -{3,3}> main_LE_72(i2, i3, i5, env, static) :|: 0 >= 0 && i3 < i2
main_LE_195(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: 0 >= 0 && i41 < i2
main_LE_240(i2, i3, i5, i44, i41, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i41 + 1, i44 + 1, env, static) :|: 0 >= 0 && i41 + 1 = i79' && i44 + 1 = i84' && i44 < i2
main_LE_195(i2, i3, i5, i41, i44, env, static) -{0,0}> main_LE_198(i2, i3, i5, i41, i44, env, static) :|: i2 <= i41
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_195(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0

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

Simplified expressions.

main_Load_1(i2, i3, i5, env, static) -{17,17}> main_LE_55(i2, i3, i5, env, static'1) :|: 0 >= 0 && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && static'1 <= static''' + 1
was transformed to
main_Load_1(i2, i3, i5, env, static) -{17,17}> main_LE_55(i2, i3, i5, env, static'1) :|: 0 <= static'1 && 0 <= static && static''' <= static + 2 && 0 <= static''' && static'1 <= static''' + 1

main_LE_72(i2, i3, i5, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i3 + 1, i5 + 1, env, static) :|: 0 >= 0 && i3 + 1 = i9' && i5 + 1 = i10' && i5 < i2
was transformed to
main_LE_72(i2, i3, i5, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i3 + 1, i5 + 1, env, static) :|: i3 + 1 = i9' && i5 + 1 = i10' && i5 < i2

main_LE_240(i2, i3, i5, i44, i41, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i41 + 1, i44 + 1, env, static) :|: 0 >= 0 && i41 + 1 = i79' && i44 + 1 = i84' && i44 < i2
was transformed to
main_LE_240(i2, i3, i5, i44, i41, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i41 + 1, i44 + 1, env, static) :|: i41 + 1 = i79' && i44 + 1 = i84' && i44 < i2

main_LE_55(i2, i3, i5, env, static) -{3,3}> main_LE_72(i2, i3, i5, env, static) :|: 0 >= 0 && i3 < i2
was transformed to
main_LE_55(i2, i3, i5, env, static) -{3,3}> main_LE_72(i2, i3, i5, env, static) :|: i3 < i2

main_LE_195(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: 0 >= 0 && i41 < i2
was transformed to
main_LE_195(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: i41 < i2

(12) Obligation:

IntTrs with 10 rules
Start term: main_Load_1(#0, #1, #2, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_240(i2, i3, i5, i44, i41, env, static) -{0,0}> main_LE_254(i2, i3, i5, i44, i41, env, static) :|: i2 <= i44
main_LE_240(i2, i3, i5, i44, i41, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i41 + 1, i44 + 1, env, static) :|: i41 + 1 = i79' && i44 + 1 = i84' && i44 < i2
main_LE_55(i2, i3, i5, env, static) -{0,0}> main_LE_56(i2, i3, i5, env, static) :|: i2 <= i3
main_Load_1(i2, i3, i5, env, static) -{17,17}> main_LE_55(i2, i3, i5, env, static'1) :|: 0 <= static'1 && 0 <= static && static''' <= static + 2 && 0 <= static''' && static'1 <= static''' + 1
main_LE_72(i2, i3, i5, env, static) -{0,0}> main_LE_77(i2, i3, i5, env, static) :|: i2 <= i5
main_LE_55(i2, i3, i5, env, static) -{3,3}> main_LE_72(i2, i3, i5, env, static) :|: i3 < i2
main_LE_72(i2, i3, i5, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i3 + 1, i5 + 1, env, static) :|: i3 + 1 = i9' && i5 + 1 = i10' && i5 < i2
main_LE_195(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: i41 < i2
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_195(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_LE_195(i2, i3, i5, i41, i44, env, static) -{0,0}> main_LE_198(i2, i3, i5, i41, i44, env, static) :|: i2 <= i41

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

Transformed 50 jbc graph edges to a weighted ITS with 50 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.

(14) Obligation:

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

(16) Obligation:

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

Moved arithmethic from constraints to rhss.

(18) Obligation:

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

Simplified expressions.

(20) Obligation:

IntTrs with 10 rules
Start term: main_Load_1(#0, #1, #2, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_240(i2, i3, i5, i44, i41, env, static) -{0,0}> main_LE_254(i2, i3, i5, i44, i41, env, static) :|: i2 <= i44
main_LE_240(i2, i3, i5, i44, i41, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i41 + 1, i44 + 1, env, static) :|: i41 + 1 = i79' && i44 + 1 = i84' && i44 < i2
main_LE_55(i2, i3, i5, env, static) -{0,0}> main_LE_56(i2, i3, i5, env, static) :|: i2 <= i3
main_Load_1(i2, i3, i5, env, static) -{17,17}> main_LE_55(i2, i3, i5, env, static'1) :|: 0 <= static'1 && 0 <= static && static''' <= static + 2 && 0 <= static''' && static'1 <= static''' + 1
main_LE_72(i2, i3, i5, env, static) -{0,0}> main_LE_77(i2, i3, i5, env, static) :|: i2 <= i5
main_LE_55(i2, i3, i5, env, static) -{3,3}> main_LE_72(i2, i3, i5, env, static) :|: i3 < i2
main_LE_72(i2, i3, i5, env, static) -{3,3}> main_JMP_183(i2, i3, i5, i3 + 1, i5 + 1, env, static) :|: i3 + 1 = i9' && i5 + 1 = i10' && i5 < i2
main_LE_195(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: i41 < i2
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{3,3}> main_LE_195(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_LE_195(i2, i3, i5, i41, i44, env, static) -{0,0}> main_LE_198(i2, i3, i5, i41, i44, env, static) :|: i2 <= i41

(21) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(7)) transformation)

Extracted set of 46 edges for the analysis of TIME complexity. Dropped leaves.

(22) Obligation:

Set of 46 edges based on JBC Program.
Performed SCC analyses:

Used field analysis yielded the following read fields:

Considered paths: all paths from start

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

Transformed 46 jbc graph edges to a weighted ITS with 46 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.

(24) Obligation:

IntTrs with 46 rules
Start term: main_Load_1(#0, #1, #2, env, static)
Considered paths: all paths from start
Rules:
main_Load_1(i2, i3, i5, env, static) -{0,0}> main_Load_5(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_5(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i3, i5, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_12(iconst_0, i2, i3, i5, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_12(iconst_0, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_14(a2, i2, i3, i5, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_14(a2, i2, i3, i5, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_17(i2, i3, i5, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_17(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_New_18(i2, i3, i5, env, static) :|: 0 >= 0
langle_clinit_rangle_New_18(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_New_19(i2, i3, i5, env, static) :|: 0 <= static
langle_clinit_rangle_New_19(i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_Duplicate_21(o2, i2, i3, i5, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_21(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_22(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_22(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_24(o2, NULL, i2, i3, i5, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_24(o2, NULL, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Load_26(o2, i2, i3, i5, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_26(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_InvokeMethod_28(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_28(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Load_30(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Load_30(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_InvokeMethod_32(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_32(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Return_35(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Return_35(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Return_38(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Return_38(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_39(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_39(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_Return_40(i2, i3, i5, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_40(i2, i3, i5, env, static) -{1,1}> main_Load_46(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_46(i2, i3, i5, env, static) -{0,0}> main_Load_47(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_47(i2, i3, i5, env, static) -{0,0}> main_Load_48(i2, i3, i5, env, static) :|: 0 <= static
main_Load_48(i2, i3, i5, env, static) -{0,0}> main_Load_49(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_49(i2, i3, i5, env, static) -{0,0}> main_Load_50(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_50(i2, i3, i5, env, static) -{1,1}> main_Load_51(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_51(i2, i3, i5, env, static) -{1,1}> main_LE_55(i2, i3, i5, env, static) :|: 0 >= 0
main_LE_55(i2, i3, i5, env, static) -{0,0}> main_LE_57(i2, i3, i5, env, static) :|: i3 < i2
main_LE_57(i2, i3, i5, env, static) -{1,1}> main_Load_63(i2, i3, i5, env, static) :|: i3 < i2
main_Load_63(i2, i3, i5, env, static) -{1,1}> main_Load_65(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_65(i2, i3, i5, env, static) -{1,1}> main_LE_72(i2, i3, i5, env, static) :|: 0 >= 0
main_LE_72(i2, i3, i5, env, static) -{0,0}> main_LE_78(i2, i3, i5, env, static) :|: i5 < i2
main_LE_78(i2, i3, i5, env, static) -{1,1}> main_Inc_83(i2, i3, i5, env, static) :|: i5 < i2
main_Inc_83(i2, i3, i5, env, static) -{1,1}> main_Inc_85(i2, i3, i5, i9, env, static) :|: i3 + 1 = i9
main_Inc_85(i2, i3, i5, i9, env, static) -{1,1}> main_JMP_86(i2, i3, i5, i9, i10, env, static) :|: i5 + 1 = i10
main_JMP_86(i2, i3, i5, i9, i10, env, static) -{0,0}> main_JMP_183(i2, i3, i5, i9, i10, env, static) :|: 0 >= 0
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_186(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_186(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_187(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_187(i2, i3, i5, i41, i44, env, static) -{1,1}> main_LE_195(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_LE_195(i2, i3, i5, i41, i44, env, static) -{0,0}> main_LE_199(i2, i3, i5, i41, i44, env, static) :|: i41 < i2
main_LE_199(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_209(i2, i3, i5, i41, i44, env, static) :|: i41 < i2
main_Load_209(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_230(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_230(i2, i3, i5, i41, i44, env, static) -{1,1}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: 0 >= 0
main_LE_240(i2, i3, i5, i44, i41, env, static) -{0,0}> main_LE_255(i2, i3, i5, i44, i41, env, static) :|: i44 < i2
main_LE_255(i2, i3, i5, i44, i41, env, static) -{1,1}> main_Inc_277(i2, i3, i5, i41, i44, env, static) :|: i44 < i2
main_Inc_277(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Inc_286(i2, i3, i5, i79, i44, env, static) :|: i41 + 1 = i79
main_Inc_286(i2, i3, i5, i79, i44, env, static) -{1,1}> main_JMP_291(i2, i3, i5, i79, i84, env, static) :|: i44 + 1 = i84
main_JMP_291(i2, i3, i5, i79, i84, env, static) -{0,0}> main_JMP_183(i2, i3, i5, i79, i84, env, static) :|: 0 >= 0

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

obtained
main_Load_1(i2, i3, i5, env, static) -{23,23}> main_JMP_183(i2, i3, i5, i9', i10', env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && i3 + 1 = i9' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i3 < i2 && i5 < i2 && i5 + 1 = i10' && 0 < 2
by chaining
main_Load_1(i2, i3, i5, env, static) -{0,0}> main_Load_5(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_5(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i3, i5, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_12(iconst_0, i2, i3, i5, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_12(iconst_0, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_14(a2, i2, i3, i5, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_14(a2, i2, i3, i5, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_17(i2, i3, i5, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_17(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_New_18(i2, i3, i5, env, static) :|: 0 >= 0
langle_clinit_rangle_New_18(i2, i3, i5, env, static) -{0,0}> langle_clinit_rangle_New_19(i2, i3, i5, env, static) :|: 0 <= static
langle_clinit_rangle_New_19(i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_Duplicate_21(o2, i2, i3, i5, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_21(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_22(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_22(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_24(o2, NULL, i2, i3, i5, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_24(o2, NULL, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Load_26(o2, i2, i3, i5, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_26(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_InvokeMethod_28(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_28(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Load_30(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Load_30(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_InvokeMethod_32(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_32(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Return_35(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Return_35(o2, i2, i3, i5, env, static) -{1,1}> langle_init_rangle_Return_38(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_init_rangle_Return_38(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_39(o2, i2, i3, i5, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_39(o2, i2, i3, i5, env, static) -{1,1}> langle_clinit_rangle_Return_40(i2, i3, i5, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_40(i2, i3, i5, env, static) -{1,1}> main_Load_46(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_46(i2, i3, i5, env, static) -{0,0}> main_Load_47(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_47(i2, i3, i5, env, static) -{0,0}> main_Load_48(i2, i3, i5, env, static) :|: 0 <= static
main_Load_48(i2, i3, i5, env, static) -{0,0}> main_Load_49(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_49(i2, i3, i5, env, static) -{0,0}> main_Load_50(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_50(i2, i3, i5, env, static) -{1,1}> main_Load_51(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_51(i2, i3, i5, env, static) -{1,1}> main_LE_55(i2, i3, i5, env, static) :|: 0 >= 0
main_LE_55(i2, i3, i5, env, static) -{0,0}> main_LE_57(i2, i3, i5, env, static) :|: i3 < i2
main_LE_57(i2, i3, i5, env, static) -{1,1}> main_Load_63(i2, i3, i5, env, static) :|: i3 < i2
main_Load_63(i2, i3, i5, env, static) -{1,1}> main_Load_65(i2, i3, i5, env, static) :|: 0 >= 0
main_Load_65(i2, i3, i5, env, static) -{1,1}> main_LE_72(i2, i3, i5, env, static) :|: 0 >= 0
main_LE_72(i2, i3, i5, env, static) -{0,0}> main_LE_78(i2, i3, i5, env, static) :|: i5 < i2
main_LE_78(i2, i3, i5, env, static) -{1,1}> main_Inc_83(i2, i3, i5, env, static) :|: i5 < i2
main_Inc_83(i2, i3, i5, env, static) -{1,1}> main_Inc_85(i2, i3, i5, i9, env, static) :|: i3 + 1 = i9
main_Inc_85(i2, i3, i5, i9, env, static) -{1,1}> main_JMP_86(i2, i3, i5, i9, i10, env, static) :|: i5 + 1 = i10
main_JMP_86(i2, i3, i5, i9, i10, env, static) -{0,0}> main_JMP_183(i2, i3, i5, i9, i10, env, static) :|: 0 >= 0

obtained
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{9,9}> main_JMP_183(i2, i3, i5, i79', i84', env, static) :|: 0 >= 0 && i41 + 1 = i79' && i44 < i2 && i44 + 1 = i84' && i41 < i2
by chaining
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_186(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_186(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_187(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_187(i2, i3, i5, i41, i44, env, static) -{1,1}> main_LE_195(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_LE_195(i2, i3, i5, i41, i44, env, static) -{0,0}> main_LE_199(i2, i3, i5, i41, i44, env, static) :|: i41 < i2
main_LE_199(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_209(i2, i3, i5, i41, i44, env, static) :|: i41 < i2
main_Load_209(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Load_230(i2, i3, i5, i41, i44, env, static) :|: 0 >= 0
main_Load_230(i2, i3, i5, i41, i44, env, static) -{1,1}> main_LE_240(i2, i3, i5, i44, i41, env, static) :|: 0 >= 0
main_LE_240(i2, i3, i5, i44, i41, env, static) -{0,0}> main_LE_255(i2, i3, i5, i44, i41, env, static) :|: i44 < i2
main_LE_255(i2, i3, i5, i44, i41, env, static) -{1,1}> main_Inc_277(i2, i3, i5, i41, i44, env, static) :|: i44 < i2
main_Inc_277(i2, i3, i5, i41, i44, env, static) -{1,1}> main_Inc_286(i2, i3, i5, i79, i44, env, static) :|: i41 + 1 = i79
main_Inc_286(i2, i3, i5, i79, i44, env, static) -{1,1}> main_JMP_291(i2, i3, i5, i79, i84, env, static) :|: i44 + 1 = i84
main_JMP_291(i2, i3, i5, i79, i84, env, static) -{0,0}> main_JMP_183(i2, i3, i5, i79, i84, env, static) :|: 0 >= 0

(26) Obligation:

IntTrs with 2 rules
Start term: main_Load_1(#0, #1, #2, env, static)
Considered paths: all paths from start
Rules:
main_Load_1(i2, i3, i5, env, static) -{23,23}> main_JMP_183(i2, i3, i5, i9', i10', env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && i3 + 1 = i9' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i3 < i2 && i5 < i2 && i5 + 1 = i10' && 0 < 2
main_JMP_183(i2, i3, i5, i41, i44, env, static) -{9,9}> main_JMP_183(i2, i3, i5, i79', i84', env, static) :|: 0 >= 0 && i41 + 1 = i79' && i44 < i2 && i44 + 1 = i84' && i41 < i2

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

Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

main_Load_1(x1, x2, x3, x4, x5) → main_Load_1(x1, x2, x3, x5)
main_JMP_183(x1, x2, x3, x4, x5, x6, x7) → main_JMP_183(x1, x4, x5)

(28) Obligation:

IntTrs with 2 rules
Start term: main_Load_1(#0, #1, #2, static)
Considered paths: all paths from start
Rules:
main_Load_1(i2, i3, i5, static) -{23,23}> main_JMP_183(i2, i9', i10') :|: 0 >= 0 && static'1 <= static''' + 1 && i3 + 1 = i9' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i3 < i2 && i5 < i2 && i5 + 1 = i10' && 0 < 2
main_JMP_183(i2, i41, i44) -{9,9}> main_JMP_183(i2, i79', i84') :|: 0 >= 0 && i41 + 1 = i79' && i44 < i2 && i44 + 1 = i84' && i41 < i2

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

Moved arithmethic from constraints to rhss.

main_Load_1(i2, i3, i5, static) -{23,23}> main_JMP_183(i2, i9', i10') :|: 0 >= 0 && static'1 <= static''' + 1 && i3 + 1 = i9' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i3 < i2 && i5 < i2 && i5 + 1 = i10' && 0 < 2
was transformed to
main_Load_1(i2, i3, i5, static) -{23,23}> main_JMP_183(i2, i3 + 1, i5 + 1) :|: 0 >= 0 && static'1 <= static''' + 1 && i3 + 1 = i9' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i3 < i2 && i5 < i2 && i5 + 1 = i10' && 0 < 2

main_JMP_183(i2, i41, i44) -{9,9}> main_JMP_183(i2, i79', i84') :|: 0 >= 0 && i41 + 1 = i79' && i44 < i2 && i44 + 1 = i84' && i41 < i2
was transformed to
main_JMP_183(i2, i41, i44) -{9,9}> main_JMP_183(i2, i41 + 1, i44 + 1) :|: 0 >= 0 && i41 + 1 = i79' && i44 < i2 && i44 + 1 = i84' && i41 < i2

(30) Obligation:

IntTrs with 2 rules
Start term: main_Load_1(#0, #1, #2, static)
Considered paths: all paths from start
Rules:
main_Load_1(i2, i3, i5, static) -{23,23}> main_JMP_183(i2, i3 + 1, i5 + 1) :|: 0 >= 0 && static'1 <= static''' + 1 && i3 + 1 = i9' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i3 < i2 && i5 < i2 && i5 + 1 = i10' && 0 < 2
main_JMP_183(i2, i41, i44) -{9,9}> main_JMP_183(i2, i41 + 1, i44 + 1) :|: 0 >= 0 && i41 + 1 = i79' && i44 < i2 && i44 + 1 = i84' && i41 < i2

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

Simplified expressions.

main_Load_1(i2, i3, i5, static) -{23,23}> main_JMP_183(i2, i3 + 1, i5 + 1) :|: 0 >= 0 && static'1 <= static''' + 1 && i3 + 1 = i9' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i3 < i2 && i5 < i2 && i5 + 1 = i10' && 0 < 2
was transformed to
main_Load_1(i2, i3, i5, static) -{23,23}> main_JMP_183(i2, i3 + 1, i5 + 1) :|: static'1 <= static''' + 1 && i3 + 1 = i9' && 0 <= static''' && static''' <= static + 2 && 0 <= static && 0 <= static'1 && i3 < i2 && i5 < i2 && i5 + 1 = i10'

main_JMP_183(i2, i41, i44) -{9,9}> main_JMP_183(i2, i41 + 1, i44 + 1) :|: 0 >= 0 && i41 + 1 = i79' && i44 < i2 && i44 + 1 = i84' && i41 < i2
was transformed to
main_JMP_183(i2, i41, i44) -{9,9}> main_JMP_183(i2, i41 + 1, i44 + 1) :|: i41 + 1 = i79' && i44 < i2 && i44 + 1 = i84' && i41 < i2

(32) Obligation:

IntTrs with 2 rules
Start term: main_Load_1(#0, #1, #2, static)
Considered paths: all paths from start
Rules:
main_Load_1(i2, i3, i5, static) -{23,23}> main_JMP_183(i2, i3 + 1, i5 + 1) :|: static'1 <= static''' + 1 && i3 + 1 = i9' && 0 <= static''' && static''' <= static + 2 && 0 <= static && 0 <= static'1 && i3 < i2 && i5 < i2 && i5 + 1 = i10'
main_JMP_183(i2, i41, i44) -{9,9}> main_JMP_183(i2, i41 + 1, i44 + 1) :|: i41 + 1 = i79' && i44 < i2 && i44 + 1 = i84' && i41 < i2

(33) koat Proof (EQUIVALENT transformation)

YES(?, 9*ar_0 + 9*ar_1 + 23)

Initial complexity problem:
1: T:
(Comp: ?, Cost: 23) main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_JMP_183(ar_0, ar_1 + 1, ar_2 + 1, arityPad)) [ static'1 <= static''' + 1 /\ ar_1 + 1 = i9' /\ 0 <= static''' /\ static''' <= ar_3 + 2 /\ 0 <= ar_3 /\ 0 <= static'1 /\ ar_1 < ar_0 /\ ar_2 < ar_0 /\ ar_2 + 1 = i10' ]
(Comp: ?, Cost: 9) main_JMP_183(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_JMP_183(ar_0, ar_1 + 1, ar_2 + 1, arityPad)) [ ar_1 + 1 = i79' /\ ar_2 < ar_0 /\ ar_2 + 1 = i84' /\ ar_1 < ar_0 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2: T:
(Comp: 1, Cost: 23) main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_JMP_183(ar_0, ar_1 + 1, ar_2 + 1, arityPad)) [ static'1 <= static''' + 1 /\ ar_1 + 1 = i9' /\ 0 <= static''' /\ static''' <= ar_3 + 2 /\ 0 <= ar_3 /\ 0 <= static'1 /\ ar_1 < ar_0 /\ ar_2 < ar_0 /\ ar_2 + 1 = i10' ]
(Comp: ?, Cost: 9) main_JMP_183(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_JMP_183(ar_0, ar_1 + 1, ar_2 + 1, arityPad)) [ ar_1 + 1 = i79' /\ ar_2 < ar_0 /\ ar_2 + 1 = i84' /\ ar_1 < ar_0 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

A polynomial rank function with
Pol(main_Load_1) = V_1 - V_2
Pol(main_JMP_183) = V_1 - V_2
Pol(koat_start) = V_1 - V_2
orients all transitions weakly and the transition
main_JMP_183(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_JMP_183(ar_0, ar_1 + 1, ar_2 + 1, arityPad)) [ ar_1 + 1 = i79' /\ ar_2 < ar_0 /\ ar_2 + 1 = i84' /\ ar_1 < ar_0 ]
strictly and produces the following problem:
3: T:
(Comp: 1, Cost: 23) main_Load_1(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_JMP_183(ar_0, ar_1 + 1, ar_2 + 1, arityPad)) [ static'1 <= static''' + 1 /\ ar_1 + 1 = i9' /\ 0 <= static''' /\ static''' <= ar_3 + 2 /\ 0 <= ar_3 /\ 0 <= static'1 /\ ar_1 < ar_0 /\ ar_2 < ar_0 /\ ar_2 + 1 = i10' ]
(Comp: ar_0 + ar_1, Cost: 9) main_JMP_183(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_JMP_183(ar_0, ar_1 + 1, ar_2 + 1, arityPad)) [ ar_1 + 1 = i79' /\ ar_2 < ar_0 /\ ar_2 + 1 = i84' /\ ar_1 < ar_0 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(main_Load_1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Complexity upper bound 9*ar_0 + 9*ar_1 + 23

Time: 0.145 sec (SMT: 0.135 sec)

(0) Obligation:

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

(2) Obligation:

(3) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(7)) transformation)

(4) Obligation:

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

(6) Obligation:

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

(8) Obligation:

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

(10) Obligation:

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

(12) Obligation:

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

(14) Obligation:

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

(16) Obligation:

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

(18) Obligation:

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

(20) Obligation:

(21) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(7)) transformation)

(22) Obligation:

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

(24) Obligation:

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

(26) Obligation:

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

(28) Obligation:

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

(30) Obligation:

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

(32) Obligation:

(33) koat Proof (EQUIVALENT transformation)

(34) BOUNDS(CONSTANT, 23 + 9 * |#0| + 9 * |#1|)