time complexity proof of /tmp/tmpGoXiFD/PastaA6.jar

The time complexity of the given JBC problem could be proven to be BOUNDS(CONSTANT, 25 + 8 * |#0| + 8 * |#1| + 8 * |#2|).

0 JBC problem

↳1 JBCToGraph (BOTH CONCRETE BOUNDS(ID, ID), 369 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(3)), 16 ms)

↳4 JBCComplexityEdges

    ↳5 JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID), 85 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), 88 ms)

    ↳14 WeightedIntTrs

        ↳15 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 46 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(3)), 15 ms)

↳22 JBCComplexityEdges

    ↳23 JBCGraphEdgesToCpxIntTrsProof (CONCRETE UPPER BOUND(ID), 109 ms)

    ↳24 WeightedIntTrs

    ↳25 StraightLineCodeCompressionProof (BOTH CONCRETE BOUNDS(ID, ID), 48 ms)

    ↳26 WeightedIntTrs

    ↳27 WeightedIntTrsUnneededArgumentFilterProof (CONCRETE UPPER BOUND(ID), 0 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 (⇔, 93 ms)

    ↳34 BOUNDS(CONSTANT, 22 + 8 * |#0| + 8 * |#1| + 8 * |#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 PastaA6 {
    public static void main(int x, int y, int z) {
        while (x > y + z) {
            y++;
            z++;
        }
    }
}

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

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
PastaA6.main(III)V: Graph of 48 nodes with 1 SCC.

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

Extracted set of 44 edges for the analysis of TIME complexity. Kept leaves.

(4) Obligation:

Set of 44 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 44 jbc graph edges to a weighted ITS with 44 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 44 rules
Start term: main_Load_2(#0, #1, #2, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_2(i1, i4, i6, env, static) -{0,0}> main_Load_3(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_3(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i1, i4, i6, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_12(iconst_0, i1, i4, i6, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_12(iconst_0, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_13(a2, i1, i4, i6, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_13(a2, i1, i4, i6, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_14(i1, i4, i6, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_14(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_New_16(i1, i4, i6, env, static) :|: 0 >= 0
langle_clinit_rangle_New_16(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_New_17(i1, i4, i6, env, static) :|: 0 <= static
langle_clinit_rangle_New_17(i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_Duplicate_19(o2, i1, i4, i6, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_19(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_21(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_21(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_22(o2, NULL, i1, i4, i6, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_22(o2, NULL, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Load_23(o2, i1, i4, i6, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_23(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_InvokeMethod_26(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_26(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Load_27(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Load_27(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_InvokeMethod_30(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_30(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Return_32(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Return_32(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Return_34(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Return_34(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_36(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_36(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_Return_38(i1, i4, i6, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_38(i1, i4, i6, env, static) -{1,1}> main_Load_41(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_41(i1, i4, i6, env, static) -{0,0}> main_Load_42(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_42(i1, i4, i6, env, static) -{0,0}> main_Load_43(i1, i4, i6, env, static) :|: 0 <= static
main_Load_43(i1, i4, i6, env, static) -{0,0}> main_Load_48(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_48(i1, i4, i6, env, static) -{0,0}> main_Load_49(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_49(i1, i4, i6, env, static) -{1,1}> main_Load_51(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_51(i1, i4, i6, env, static) -{1,1}> main_Load_53(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_53(i1, i4, i6, env, static) -{1,1}> main_IntArithmetic_54(i1, i4, i6, env, static) :|: 0 >= 0
main_IntArithmetic_54(i1, i4, i6, env, static) -{1,1}> main_LE_59(i1, i4, i6, i8, env, static) :|: i4 + i6 = i8
main_LE_59(i1, i4, i6, i8, env, static) -{0,0}> main_LE_60(i1, i4, i6, i8, env, static) :|: i1 <= i8
main_LE_59(i1, i4, i6, i8, env, static) -{0,0}> main_LE_61(i1, i4, i6, i8, env, static) :|: i8 < i1
main_LE_61(i1, i4, i6, i8, env, static) -{1,1}> main_Inc_72(i1, i4, i6, env, static) :|: i8 < i1
main_Inc_72(i1, i4, i6, env, static) -{1,1}> main_Inc_74(i1, i4, i6, i12, env, static) :|: i4 + 1 = i12
main_Inc_74(i1, i4, i6, i12, env, static) -{1,1}> main_JMP_75(i1, i4, i6, i12, i13, env, static) :|: i6 + 1 = i13
main_JMP_75(i1, i4, i6, i12, i13, env, static) -{0,0}> main_JMP_135(i1, i4, i6, i12, i13, env, static) :|: 0 >= 0
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_139(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_139(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_142(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_142(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_149(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_149(i1, i4, i6, i43, i48, env, static) -{1,1}> main_IntArithmetic_151(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_IntArithmetic_151(i1, i4, i6, i43, i48, env, static) -{1,1}> main_LE_166(i1, i4, i6, i63, i43, i48, env, static) :|: i43 + i48 = i63
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{0,0}> main_LE_171(i1, i4, i6, i63, i43, i48, env, static) :|: i1 <= i63
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{0,0}> main_LE_172(i1, i4, i6, i63, i43, i48, env, static) :|: i63 < i1
main_LE_172(i1, i4, i6, i63, i43, i48, env, static) -{1,1}> main_Inc_182(i1, i4, i6, i43, i48, env, static) :|: i63 < i1
main_Inc_182(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Inc_189(i1, i4, i6, i81, i48, env, static) :|: i43 + 1 = i81
main_Inc_189(i1, i4, i6, i81, i48, env, static) -{1,1}> main_JMP_195(i1, i4, i6, i81, i86, env, static) :|: i48 + 1 = i86
main_JMP_195(i1, i4, i6, i81, i86, env, static) -{0,0}> main_JMP_135(i1, i4, i6, i81, i86, env, static) :|: 0 >= 0

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

obtained
main_Load_2(i1, i4, i6, env, static) -{19,19}> main_LE_59(i1, i4, i6, i8', env, static'1) :|: i4 + i6 = i8' && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1
by chaining
main_Load_2(i1, i4, i6, env, static) -{0,0}> main_Load_3(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_3(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i1, i4, i6, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_12(iconst_0, i1, i4, i6, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_12(iconst_0, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_13(a2, i1, i4, i6, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_13(a2, i1, i4, i6, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_14(i1, i4, i6, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_14(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_New_16(i1, i4, i6, env, static) :|: 0 >= 0
langle_clinit_rangle_New_16(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_New_17(i1, i4, i6, env, static) :|: 0 <= static
langle_clinit_rangle_New_17(i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_Duplicate_19(o2, i1, i4, i6, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_19(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_21(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_21(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_22(o2, NULL, i1, i4, i6, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_22(o2, NULL, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Load_23(o2, i1, i4, i6, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_23(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_InvokeMethod_26(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_26(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Load_27(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Load_27(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_InvokeMethod_30(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_30(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Return_32(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Return_32(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Return_34(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Return_34(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_36(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_36(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_Return_38(i1, i4, i6, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_38(i1, i4, i6, env, static) -{1,1}> main_Load_41(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_41(i1, i4, i6, env, static) -{0,0}> main_Load_42(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_42(i1, i4, i6, env, static) -{0,0}> main_Load_43(i1, i4, i6, env, static) :|: 0 <= static
main_Load_43(i1, i4, i6, env, static) -{0,0}> main_Load_48(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_48(i1, i4, i6, env, static) -{0,0}> main_Load_49(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_49(i1, i4, i6, env, static) -{1,1}> main_Load_51(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_51(i1, i4, i6, env, static) -{1,1}> main_Load_53(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_53(i1, i4, i6, env, static) -{1,1}> main_IntArithmetic_54(i1, i4, i6, env, static) :|: 0 >= 0
main_IntArithmetic_54(i1, i4, i6, env, static) -{1,1}> main_LE_59(i1, i4, i6, i8, env, static) :|: i4 + i6 = i8

obtained
main_LE_59(i1, i4, i6, i8, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i12', i13', env, static) :|: 0 >= 0 && i4 + 1 = i12' && i6 + 1 = i13' && i8 < i1
by chaining
main_LE_59(i1, i4, i6, i8, env, static) -{0,0}> main_LE_61(i1, i4, i6, i8, env, static) :|: i8 < i1
main_LE_61(i1, i4, i6, i8, env, static) -{1,1}> main_Inc_72(i1, i4, i6, env, static) :|: i8 < i1
main_Inc_72(i1, i4, i6, env, static) -{1,1}> main_Inc_74(i1, i4, i6, i12, env, static) :|: i4 + 1 = i12
main_Inc_74(i1, i4, i6, i12, env, static) -{1,1}> main_JMP_75(i1, i4, i6, i12, i13, env, static) :|: i6 + 1 = i13
main_JMP_75(i1, i4, i6, i12, i13, env, static) -{0,0}> main_JMP_135(i1, i4, i6, i12, i13, env, static) :|: 0 >= 0

obtained
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{5,5}> main_LE_166(i1, i4, i6, i63', i43, i48, env, static) :|: 0 >= 0 && i43 + i48 = i63'
by chaining
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_139(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_139(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_142(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_142(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_149(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_149(i1, i4, i6, i43, i48, env, static) -{1,1}> main_IntArithmetic_151(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_IntArithmetic_151(i1, i4, i6, i43, i48, env, static) -{1,1}> main_LE_166(i1, i4, i6, i63, i43, i48, env, static) :|: i43 + i48 = i63

obtained
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i81', i86', env, static) :|: 0 >= 0 && i43 + 1 = i81' && i48 + 1 = i86' && i63 < i1
by chaining
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{0,0}> main_LE_172(i1, i4, i6, i63, i43, i48, env, static) :|: i63 < i1
main_LE_172(i1, i4, i6, i63, i43, i48, env, static) -{1,1}> main_Inc_182(i1, i4, i6, i43, i48, env, static) :|: i63 < i1
main_Inc_182(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Inc_189(i1, i4, i6, i81, i48, env, static) :|: i43 + 1 = i81
main_Inc_189(i1, i4, i6, i81, i48, env, static) -{1,1}> main_JMP_195(i1, i4, i6, i81, i86, env, static) :|: i48 + 1 = i86
main_JMP_195(i1, i4, i6, i81, i86, env, static) -{0,0}> main_JMP_135(i1, i4, i6, i81, i86, env, static) :|: 0 >= 0

(8) Obligation:

IntTrs with 6 rules
Start term: main_Load_2(#0, #1, #2, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_2(i1, i4, i6, env, static) -{19,19}> main_LE_59(i1, i4, i6, i8', env, static'1) :|: i4 + i6 = i8' && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1
main_LE_59(i1, i4, i6, i8, env, static) -{0,0}> main_LE_60(i1, i4, i6, i8, env, static) :|: i1 <= i8
main_LE_59(i1, i4, i6, i8, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i12', i13', env, static) :|: 0 >= 0 && i4 + 1 = i12' && i6 + 1 = i13' && i8 < i1
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{5,5}> main_LE_166(i1, i4, i6, i63', i43, i48, env, static) :|: 0 >= 0 && i43 + i48 = i63'
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{0,0}> main_LE_171(i1, i4, i6, i63, i43, i48, env, static) :|: i1 <= i63
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i81', i86', env, static) :|: 0 >= 0 && i43 + 1 = i81' && i48 + 1 = i86' && i63 < i1

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

Moved arithmethic from constraints to rhss.

main_LE_59(i1, i4, i6, i8, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i12', i13', env, static) :|: 0 >= 0 && i4 + 1 = i12' && i6 + 1 = i13' && i8 < i1
was transformed to
main_LE_59(i1, i4, i6, i8, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1, env, static) :|: 0 >= 0 && i4 + 1 = i12' && i6 + 1 = i13' && i8 < i1

main_JMP_135(i1, i4, i6, i43, i48, env, static) -{5,5}> main_LE_166(i1, i4, i6, i63', i43, i48, env, static) :|: 0 >= 0 && i43 + i48 = i63'
was transformed to
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{5,5}> main_LE_166(i1, i4, i6, i43 + i48, i43, i48, env, static) :|: 0 >= 0 && i43 + i48 = i63'

main_Load_2(i1, i4, i6, env, static) -{19,19}> main_LE_59(i1, i4, i6, i8', env, static'1) :|: i4 + i6 = i8' && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1
was transformed to
main_Load_2(i1, i4, i6, env, static) -{19,19}> main_LE_59(i1, i4, i6, i4 + i6, env, static'1) :|: i4 + i6 = i8' && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1

main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i81', i86', env, static) :|: 0 >= 0 && i43 + 1 = i81' && i48 + 1 = i86' && i63 < i1
was transformed to
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1, env, static) :|: 0 >= 0 && i43 + 1 = i81' && i48 + 1 = i86' && i63 < i1

(10) Obligation:

IntTrs with 6 rules
Start term: main_Load_2(#0, #1, #2, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_59(i1, i4, i6, i8, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1, env, static) :|: 0 >= 0 && i4 + 1 = i12' && i6 + 1 = i13' && i8 < i1
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{5,5}> main_LE_166(i1, i4, i6, i43 + i48, i43, i48, env, static) :|: 0 >= 0 && i43 + i48 = i63'
main_LE_59(i1, i4, i6, i8, env, static) -{0,0}> main_LE_60(i1, i4, i6, i8, env, static) :|: i1 <= i8
main_Load_2(i1, i4, i6, env, static) -{19,19}> main_LE_59(i1, i4, i6, i4 + i6, env, static'1) :|: i4 + i6 = i8' && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1, env, static) :|: 0 >= 0 && i43 + 1 = i81' && i48 + 1 = i86' && i63 < i1
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{0,0}> main_LE_171(i1, i4, i6, i63, i43, i48, env, static) :|: i1 <= i63

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

Simplified expressions.

main_Load_2(i1, i4, i6, env, static) -{19,19}> main_LE_59(i1, i4, i6, i4 + i6, env, static'1) :|: i4 + i6 = i8' && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1
was transformed to
main_Load_2(i1, i4, i6, env, static) -{19,19}> main_LE_59(i1, i4, i6, i4 + i6, env, static'1) :|: i4 + i6 = i8' && 0 <= static'1 && 0 <= static && static''' <= static + 2 && 0 <= static''' && static'1 <= static''' + 1

main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1, env, static) :|: 0 >= 0 && i43 + 1 = i81' && i48 + 1 = i86' && i63 < i1
was transformed to
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1, env, static) :|: i43 + 1 = i81' && i48 + 1 = i86' && i63 < i1

main_JMP_135(i1, i4, i6, i43, i48, env, static) -{5,5}> main_LE_166(i1, i4, i6, i43 + i48, i43, i48, env, static) :|: 0 >= 0 && i43 + i48 = i63'
was transformed to
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{5,5}> main_LE_166(i1, i4, i6, i43 + i48, i43, i48, env, static) :|: i43 + i48 = i63'

main_LE_59(i1, i4, i6, i8, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1, env, static) :|: 0 >= 0 && i4 + 1 = i12' && i6 + 1 = i13' && i8 < i1
was transformed to
main_LE_59(i1, i4, i6, i8, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1, env, static) :|: i4 + 1 = i12' && i6 + 1 = i13' && i8 < i1

(12) Obligation:

IntTrs with 6 rules
Start term: main_Load_2(#0, #1, #2, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{5,5}> main_LE_166(i1, i4, i6, i43 + i48, i43, i48, env, static) :|: i43 + i48 = i63'
main_LE_59(i1, i4, i6, i8, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1, env, static) :|: i4 + 1 = i12' && i6 + 1 = i13' && i8 < i1
main_LE_59(i1, i4, i6, i8, env, static) -{0,0}> main_LE_60(i1, i4, i6, i8, env, static) :|: i1 <= i8
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{3,3}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1, env, static) :|: i43 + 1 = i81' && i48 + 1 = i86' && i63 < i1
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{0,0}> main_LE_171(i1, i4, i6, i63, i43, i48, env, static) :|: i1 <= i63
main_Load_2(i1, i4, i6, env, static) -{19,19}> main_LE_59(i1, i4, i6, i4 + i6, env, static'1) :|: i4 + i6 = i8' && 0 <= static'1 && 0 <= static && static''' <= static + 2 && 0 <= static''' && static'1 <= static''' + 1

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

Transformed 44 jbc graph edges to a weighted ITS with 44 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.

(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:

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

Extracted set of 42 edges for the analysis of TIME complexity. Dropped leaves.

(22) Obligation:

Set of 42 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 42 jbc graph edges to a weighted ITS with 42 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 42 rules
Start term: main_Load_2(#0, #1, #2, env, static)
Considered paths: all paths from start
Rules:
main_Load_2(i1, i4, i6, env, static) -{0,0}> main_Load_3(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_3(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i1, i4, i6, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_12(iconst_0, i1, i4, i6, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_12(iconst_0, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_13(a2, i1, i4, i6, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_13(a2, i1, i4, i6, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_14(i1, i4, i6, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_14(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_New_16(i1, i4, i6, env, static) :|: 0 >= 0
langle_clinit_rangle_New_16(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_New_17(i1, i4, i6, env, static) :|: 0 <= static
langle_clinit_rangle_New_17(i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_Duplicate_19(o2, i1, i4, i6, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_19(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_21(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_21(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_22(o2, NULL, i1, i4, i6, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_22(o2, NULL, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Load_23(o2, i1, i4, i6, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_23(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_InvokeMethod_26(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_26(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Load_27(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Load_27(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_InvokeMethod_30(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_30(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Return_32(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Return_32(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Return_34(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Return_34(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_36(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_36(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_Return_38(i1, i4, i6, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_38(i1, i4, i6, env, static) -{1,1}> main_Load_41(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_41(i1, i4, i6, env, static) -{0,0}> main_Load_42(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_42(i1, i4, i6, env, static) -{0,0}> main_Load_43(i1, i4, i6, env, static) :|: 0 <= static
main_Load_43(i1, i4, i6, env, static) -{0,0}> main_Load_48(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_48(i1, i4, i6, env, static) -{0,0}> main_Load_49(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_49(i1, i4, i6, env, static) -{1,1}> main_Load_51(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_51(i1, i4, i6, env, static) -{1,1}> main_Load_53(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_53(i1, i4, i6, env, static) -{1,1}> main_IntArithmetic_54(i1, i4, i6, env, static) :|: 0 >= 0
main_IntArithmetic_54(i1, i4, i6, env, static) -{1,1}> main_LE_59(i1, i4, i6, i8, env, static) :|: i4 + i6 = i8
main_LE_59(i1, i4, i6, i8, env, static) -{0,0}> main_LE_61(i1, i4, i6, i8, env, static) :|: i8 < i1
main_LE_61(i1, i4, i6, i8, env, static) -{1,1}> main_Inc_72(i1, i4, i6, env, static) :|: i8 < i1
main_Inc_72(i1, i4, i6, env, static) -{1,1}> main_Inc_74(i1, i4, i6, i12, env, static) :|: i4 + 1 = i12
main_Inc_74(i1, i4, i6, i12, env, static) -{1,1}> main_JMP_75(i1, i4, i6, i12, i13, env, static) :|: i6 + 1 = i13
main_JMP_75(i1, i4, i6, i12, i13, env, static) -{0,0}> main_JMP_135(i1, i4, i6, i12, i13, env, static) :|: 0 >= 0
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_139(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_139(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_142(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_142(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_149(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_149(i1, i4, i6, i43, i48, env, static) -{1,1}> main_IntArithmetic_151(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_IntArithmetic_151(i1, i4, i6, i43, i48, env, static) -{1,1}> main_LE_166(i1, i4, i6, i63, i43, i48, env, static) :|: i43 + i48 = i63
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{0,0}> main_LE_172(i1, i4, i6, i63, i43, i48, env, static) :|: i63 < i1
main_LE_172(i1, i4, i6, i63, i43, i48, env, static) -{1,1}> main_Inc_182(i1, i4, i6, i43, i48, env, static) :|: i63 < i1
main_Inc_182(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Inc_189(i1, i4, i6, i81, i48, env, static) :|: i43 + 1 = i81
main_Inc_189(i1, i4, i6, i81, i48, env, static) -{1,1}> main_JMP_195(i1, i4, i6, i81, i86, env, static) :|: i48 + 1 = i86
main_JMP_195(i1, i4, i6, i81, i86, env, static) -{0,0}> main_JMP_135(i1, i4, i6, i81, i86, env, static) :|: 0 >= 0

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

obtained
main_Load_2(i1, i4, i6, env, static) -{22,22}> main_JMP_135(i1, i4, i6, i12', i13', env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && i4 + 1 = i12' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i4 + i6 = i8' && i8' < i1 && i6 + 1 = i13' && 0 < 2
by chaining
main_Load_2(i1, i4, i6, env, static) -{0,0}> main_Load_3(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_3(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i1, i4, i6, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_12(iconst_0, i1, i4, i6, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_12(iconst_0, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_13(a2, i1, i4, i6, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_13(a2, i1, i4, i6, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_14(i1, i4, i6, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_14(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_New_16(i1, i4, i6, env, static) :|: 0 >= 0
langle_clinit_rangle_New_16(i1, i4, i6, env, static) -{0,0}> langle_clinit_rangle_New_17(i1, i4, i6, env, static) :|: 0 <= static
langle_clinit_rangle_New_17(i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_Duplicate_19(o2, i1, i4, i6, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_19(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_21(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_21(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_22(o2, NULL, i1, i4, i6, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_22(o2, NULL, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Load_23(o2, i1, i4, i6, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_23(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_InvokeMethod_26(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_26(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Load_27(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Load_27(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_InvokeMethod_30(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_30(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Return_32(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Return_32(o2, i1, i4, i6, env, static) -{1,1}> langle_init_rangle_Return_34(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_init_rangle_Return_34(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_36(o2, i1, i4, i6, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_36(o2, i1, i4, i6, env, static) -{1,1}> langle_clinit_rangle_Return_38(i1, i4, i6, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_38(i1, i4, i6, env, static) -{1,1}> main_Load_41(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_41(i1, i4, i6, env, static) -{0,0}> main_Load_42(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_42(i1, i4, i6, env, static) -{0,0}> main_Load_43(i1, i4, i6, env, static) :|: 0 <= static
main_Load_43(i1, i4, i6, env, static) -{0,0}> main_Load_48(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_48(i1, i4, i6, env, static) -{0,0}> main_Load_49(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_49(i1, i4, i6, env, static) -{1,1}> main_Load_51(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_51(i1, i4, i6, env, static) -{1,1}> main_Load_53(i1, i4, i6, env, static) :|: 0 >= 0
main_Load_53(i1, i4, i6, env, static) -{1,1}> main_IntArithmetic_54(i1, i4, i6, env, static) :|: 0 >= 0
main_IntArithmetic_54(i1, i4, i6, env, static) -{1,1}> main_LE_59(i1, i4, i6, i8, env, static) :|: i4 + i6 = i8
main_LE_59(i1, i4, i6, i8, env, static) -{0,0}> main_LE_61(i1, i4, i6, i8, env, static) :|: i8 < i1
main_LE_61(i1, i4, i6, i8, env, static) -{1,1}> main_Inc_72(i1, i4, i6, env, static) :|: i8 < i1
main_Inc_72(i1, i4, i6, env, static) -{1,1}> main_Inc_74(i1, i4, i6, i12, env, static) :|: i4 + 1 = i12
main_Inc_74(i1, i4, i6, i12, env, static) -{1,1}> main_JMP_75(i1, i4, i6, i12, i13, env, static) :|: i6 + 1 = i13
main_JMP_75(i1, i4, i6, i12, i13, env, static) -{0,0}> main_JMP_135(i1, i4, i6, i12, i13, env, static) :|: 0 >= 0

obtained
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{8,8}> main_JMP_135(i1, i4, i6, i81', i86', env, static) :|: 0 >= 0 && i43 + 1 = i81' && i63' < i1 && i48 + 1 = i86' && i43 + i48 = i63'
by chaining
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_139(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_139(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_142(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_142(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Load_149(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_Load_149(i1, i4, i6, i43, i48, env, static) -{1,1}> main_IntArithmetic_151(i1, i4, i6, i43, i48, env, static) :|: 0 >= 0
main_IntArithmetic_151(i1, i4, i6, i43, i48, env, static) -{1,1}> main_LE_166(i1, i4, i6, i63, i43, i48, env, static) :|: i43 + i48 = i63
main_LE_166(i1, i4, i6, i63, i43, i48, env, static) -{0,0}> main_LE_172(i1, i4, i6, i63, i43, i48, env, static) :|: i63 < i1
main_LE_172(i1, i4, i6, i63, i43, i48, env, static) -{1,1}> main_Inc_182(i1, i4, i6, i43, i48, env, static) :|: i63 < i1
main_Inc_182(i1, i4, i6, i43, i48, env, static) -{1,1}> main_Inc_189(i1, i4, i6, i81, i48, env, static) :|: i43 + 1 = i81
main_Inc_189(i1, i4, i6, i81, i48, env, static) -{1,1}> main_JMP_195(i1, i4, i6, i81, i86, env, static) :|: i48 + 1 = i86
main_JMP_195(i1, i4, i6, i81, i86, env, static) -{0,0}> main_JMP_135(i1, i4, i6, i81, i86, env, static) :|: 0 >= 0

(26) Obligation:

IntTrs with 2 rules
Start term: main_Load_2(#0, #1, #2, env, static)
Considered paths: all paths from start
Rules:
main_Load_2(i1, i4, i6, env, static) -{22,22}> main_JMP_135(i1, i4, i6, i12', i13', env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && i4 + 1 = i12' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i4 + i6 = i8' && i8' < i1 && i6 + 1 = i13' && 0 < 2
main_JMP_135(i1, i4, i6, i43, i48, env, static) -{8,8}> main_JMP_135(i1, i4, i6, i81', i86', env, static) :|: 0 >= 0 && i43 + 1 = i81' && i63' < i1 && i48 + 1 = i86' && i43 + i48 = i63'

(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_2(x1, x2, x3, x4, x5) → main_Load_2(x1, x2, x3, x5)
main_JMP_135(x1, x2, x3, x4, x5, x6, x7) → main_JMP_135(x1, x2, x3, x4, x5)

(28) Obligation:

IntTrs with 2 rules
Start term: main_Load_2(#0, #1, #2, static)
Considered paths: all paths from start
Rules:
main_Load_2(i1, i4, i6, static) -{22,22}> main_JMP_135(i1, i4, i6, i12', i13') :|: 0 >= 0 && static'1 <= static''' + 1 && i4 + 1 = i12' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i4 + i6 = i8' && i8' < i1 && i6 + 1 = i13' && 0 < 2
main_JMP_135(i1, i4, i6, i43, i48) -{8,8}> main_JMP_135(i1, i4, i6, i81', i86') :|: 0 >= 0 && i43 + 1 = i81' && i63' < i1 && i48 + 1 = i86' && i43 + i48 = i63'

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

Moved arithmethic from constraints to rhss.

main_Load_2(i1, i4, i6, static) -{22,22}> main_JMP_135(i1, i4, i6, i12', i13') :|: 0 >= 0 && static'1 <= static''' + 1 && i4 + 1 = i12' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i4 + i6 = i8' && i8' < i1 && i6 + 1 = i13' && 0 < 2
was transformed to
main_Load_2(i1, i4, i6, static) -{22,22}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1) :|: 0 >= 0 && static'1 <= static''' + 1 && i4 + 1 = i12' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i4 + i6 = i8' && i8' < i1 && i6 + 1 = i13' && 0 < 2

main_JMP_135(i1, i4, i6, i43, i48) -{8,8}> main_JMP_135(i1, i4, i6, i81', i86') :|: 0 >= 0 && i43 + 1 = i81' && i63' < i1 && i48 + 1 = i86' && i43 + i48 = i63'
was transformed to
main_JMP_135(i1, i4, i6, i43, i48) -{8,8}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1) :|: 0 >= 0 && i43 + 1 = i81' && i63' < i1 && i48 + 1 = i86' && i43 + i48 = i63'

(30) Obligation:

IntTrs with 2 rules
Start term: main_Load_2(#0, #1, #2, static)
Considered paths: all paths from start
Rules:
main_Load_2(i1, i4, i6, static) -{22,22}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1) :|: 0 >= 0 && static'1 <= static''' + 1 && i4 + 1 = i12' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i4 + i6 = i8' && i8' < i1 && i6 + 1 = i13' && 0 < 2
main_JMP_135(i1, i4, i6, i43, i48) -{8,8}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1) :|: 0 >= 0 && i43 + 1 = i81' && i63' < i1 && i48 + 1 = i86' && i43 + i48 = i63'

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

Simplified expressions.

main_Load_2(i1, i4, i6, static) -{22,22}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1) :|: 0 >= 0 && static'1 <= static''' + 1 && i4 + 1 = i12' && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && i4 + i6 = i8' && i8' < i1 && i6 + 1 = i13' && 0 < 2
was transformed to
main_Load_2(i1, i4, i6, static) -{22,22}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1) :|: static'1 <= static''' + 1 && i4 + 1 = i12' && 0 <= static''' && static''' <= static + 2 && 0 <= static && 0 <= static'1 && i4 + i6 = i8' && i8' < i1 && i6 + 1 = i13'

main_JMP_135(i1, i4, i6, i43, i48) -{8,8}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1) :|: 0 >= 0 && i43 + 1 = i81' && i63' < i1 && i48 + 1 = i86' && i43 + i48 = i63'
was transformed to
main_JMP_135(i1, i4, i6, i43, i48) -{8,8}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1) :|: i43 + 1 = i81' && i63' < i1 && i48 + 1 = i86' && i43 + i48 = i63'

(32) Obligation:

IntTrs with 2 rules
Start term: main_Load_2(#0, #1, #2, static)
Considered paths: all paths from start
Rules:
main_JMP_135(i1, i4, i6, i43, i48) -{8,8}> main_JMP_135(i1, i4, i6, i43 + 1, i48 + 1) :|: i43 + 1 = i81' && i63' < i1 && i48 + 1 = i86' && i43 + i48 = i63'
main_Load_2(i1, i4, i6, static) -{22,22}> main_JMP_135(i1, i4, i6, i4 + 1, i6 + 1) :|: static'1 <= static''' + 1 && i4 + 1 = i12' && 0 <= static''' && static''' <= static + 2 && 0 <= static && 0 <= static'1 && i4 + i6 = i8' && i8' < i1 && i6 + 1 = i13'

(33) koat Proof (EQUIVALENT transformation)

YES(?, 8*ar_0 + 8*ar_1 + 8*ar_2 + 22)

Initial complexity problem:
1: T:
(Comp: ?, Cost: 8) main_JMP_135(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_JMP_135(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) [ ar_3 + 1 = i81' /\ i63' < ar_0 /\ ar_4 + 1 = i86' /\ ar_3 + ar_4 = i63' ]
(Comp: ?, Cost: 22) main_Load_2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_JMP_135(ar_0, ar_1, ar_2, ar_1 + 1, ar_2 + 1)) [ static'1 <= static''' + 1 /\ ar_1 + 1 = i12' /\ 0 <= static''' /\ static''' <= ar_3 + 2 /\ 0 <= ar_3 /\ 0 <= static'1 /\ ar_1 + ar_2 = i8' /\ i8' < ar_0 /\ ar_2 + 1 = i13' ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_Load_2(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2: T:
(Comp: ?, Cost: 8) main_JMP_135(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_JMP_135(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) [ ar_3 + 1 = i81' /\ i63' < ar_0 /\ ar_4 + 1 = i86' /\ ar_3 + ar_4 = i63' ]
(Comp: 1, Cost: 22) main_Load_2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_JMP_135(ar_0, ar_1, ar_2, ar_1 + 1, ar_2 + 1)) [ static'1 <= static''' + 1 /\ ar_1 + 1 = i12' /\ 0 <= static''' /\ static''' <= ar_3 + 2 /\ 0 <= ar_3 /\ 0 <= static'1 /\ ar_1 + ar_2 = i8' /\ i8' < ar_0 /\ ar_2 + 1 = i13' ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_Load_2(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

A polynomial rank function with
Pol(main_JMP_135) = V_1 - V_4 - V_5
Pol(main_Load_2) = V_1 - V_2 - V_3
Pol(koat_start) = V_1 - V_2 - V_3
orients all transitions weakly and the transition
main_JMP_135(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_JMP_135(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) [ ar_3 + 1 = i81' /\ i63' < ar_0 /\ ar_4 + 1 = i86' /\ ar_3 + ar_4 = i63' ]
strictly and produces the following problem:
3: T:
(Comp: ar_0 + ar_1 + ar_2, Cost: 8) main_JMP_135(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_JMP_135(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) [ ar_3 + 1 = i81' /\ i63' < ar_0 /\ ar_4 + 1 = i86' /\ ar_3 + ar_4 = i63' ]
(Comp: 1, Cost: 22) main_Load_2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_JMP_135(ar_0, ar_1, ar_2, ar_1 + 1, ar_2 + 1)) [ static'1 <= static''' + 1 /\ ar_1 + 1 = i12' /\ 0 <= static''' /\ static''' <= ar_3 + 2 /\ 0 <= ar_3 /\ 0 <= static'1 /\ ar_1 + ar_2 = i8' /\ i8' < ar_0 /\ ar_2 + 1 = i13' ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(main_Load_2(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Complexity upper bound 8*ar_0 + 8*ar_1 + 8*ar_2 + 22

Time: 0.225 sec (SMT: 0.189 sec)

(0) Obligation:

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

(2) Obligation:

(3) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(3)) 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(3)) 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, 22 + 8 * |#0| + 8 * |#1| + 8 * |#2|)