The time complexity of the given JBC problem could be proven to be BOUNDS(CONSTANT, 26 + 8 * |#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 PastaB3 {
    public static void main(int x, int y) {
        if (x > 0) {
            while (x > y) {
                y = x+y;
            }
        }
    }
}

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

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
PastaB3.main(II)V: Graph of 50 nodes with 1 SCC.

(3) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(6)) 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, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_2(i2, i4, env, static) -{0,0}> main_Load_3(i2, i4, env, static) :|: 0 >= 0
main_Load_3(i2, i4, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_25(i2, i4, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_25(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_28(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_New_28(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_29(i2, i4, env, static) :|: 0 <= static
langle_clinit_rangle_New_29(i2, i4, env, static) -{1,1}> langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_44(o2, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_44(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_46(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Load_46(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_48(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_48(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_49(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_49(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_Return_51(i2, i4, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_51(i2, i4, env, static) -{1,1}> main_Load_52(i2, i4, env, static) :|: 0 >= 0
main_Load_52(i2, i4, env, static) -{0,0}> main_Load_53(i2, i4, env, static) :|: 0 >= 0
main_Load_53(i2, i4, env, static) -{0,0}> main_Load_54(i2, i4, env, static) :|: 0 <= static
main_Load_54(i2, i4, env, static) -{0,0}> main_Load_55(i2, i4, env, static) :|: 0 >= 0
main_Load_55(i2, i4, env, static) -{0,0}> main_Load_56(i2, i4, env, static) :|: 0 >= 0
main_Load_56(i2, i4, env, static) -{1,1}> main_LE_57(i2, i4, env, static) :|: 0 >= 0
main_LE_57(i11, i4, env, static) -{0,0}> main_LE_58(i11, i4, env, static) :|: i11 <= 0
main_LE_57(i12, i4, env, static) -{0,0}> main_LE_59(i12, i4, env, static) :|: 1 <= i12
main_LE_59(i12, i4, env, static) -{1,1}> main_Load_61(i12, i4, env, static) :|: 0 < i12 && 1 <= i12
main_Load_61(i12, i4, env, static) -{1,1}> main_Load_63(i12, i4, env, static) :|: 1 <= i12
main_Load_63(i12, i4, env, static) -{1,1}> main_LE_88(i12, i4, env, static) :|: 1 <= i12
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_91(i12, i4, env, static) :|: i12 <= i4 && 1 <= i12
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_92(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_LE_92(i12, i4, env, static) -{1,1}> main_Load_116(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_Load_116(i12, i4, env, static) -{0,0}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12
main_Load_191(i12, i4, i17, env, static) -{1,1}> main_Load_201(i12, i4, i17, env, static) :|: 1 <= i12
main_Load_201(i12, i4, i17, env, static) -{1,1}> main_IntArithmetic_205(i12, i4, i17, env, static) :|: 1 <= i12
main_IntArithmetic_205(i12, i4, i17, env, static) -{1,1}> main_Store_206(i12, i4, i31, env, static) :|: i12 + i17 = i31 && 1 <= i12
main_Store_206(i12, i4, i31, env, static) -{1,1}> main_JMP_208(i12, i4, i31, env, static) :|: 1 <= i12
main_JMP_208(i12, i4, i31, env, static) -{1,1}> main_Load_215(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_215(i12, i4, i31, env, static) -{1,1}> main_Load_218(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_218(i12, i4, i31, env, static) -{1,1}> main_LE_234(i12, i4, i31, env, static) :|: 1 <= i12
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_243(i12, i4, i31, env, static) :|: i12 <= i31 && 1 <= i12
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_245(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_LE_245(i12, i4, i31, env, static) -{1,1}> main_Load_261(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_Load_261(i12, i4, i31, env, static) -{0,0}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12

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

obtained
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && 0 < 2
by chaining
main_Load_2(i2, i4, env, static) -{0,0}> main_Load_3(i2, i4, env, static) :|: 0 >= 0
main_Load_3(i2, i4, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_25(i2, i4, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_25(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_28(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_New_28(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_29(i2, i4, env, static) :|: 0 <= static
langle_clinit_rangle_New_29(i2, i4, env, static) -{1,1}> langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_44(o2, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_44(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_46(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Load_46(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_48(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_48(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_49(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_49(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_Return_51(i2, i4, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_51(i2, i4, env, static) -{1,1}> main_Load_52(i2, i4, env, static) :|: 0 >= 0
main_Load_52(i2, i4, env, static) -{0,0}> main_Load_53(i2, i4, env, static) :|: 0 >= 0
main_Load_53(i2, i4, env, static) -{0,0}> main_Load_54(i2, i4, env, static) :|: 0 <= static
main_Load_54(i2, i4, env, static) -{0,0}> main_Load_55(i2, i4, env, static) :|: 0 >= 0
main_Load_55(i2, i4, env, static) -{0,0}> main_Load_56(i2, i4, env, static) :|: 0 >= 0
main_Load_56(i2, i4, env, static) -{1,1}> main_LE_57(i2, i4, env, static) :|: 0 >= 0

obtained
main_LE_57(i12, i4, env, static) -{3,3}> main_LE_88(i12, i4, env, static) :|: 1 <= i12 && 0 < i12
by chaining
main_LE_57(i12, i4, env, static) -{0,0}> main_LE_59(i12, i4, env, static) :|: 1 <= i12
main_LE_59(i12, i4, env, static) -{1,1}> main_Load_61(i12, i4, env, static) :|: 0 < i12 && 1 <= i12
main_Load_61(i12, i4, env, static) -{1,1}> main_Load_63(i12, i4, env, static) :|: 1 <= i12
main_Load_63(i12, i4, env, static) -{1,1}> main_LE_88(i12, i4, env, static) :|: 1 <= i12

obtained
main_LE_88(i12, i4, env, static) -{1,1}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12 && i4 < i12
by chaining
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_92(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_LE_92(i12, i4, env, static) -{1,1}> main_Load_116(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_Load_116(i12, i4, env, static) -{0,0}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12

obtained
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i31', env, static) :|: 1 <= i12 && i12 + i17 = i31'
by chaining
main_Load_191(i12, i4, i17, env, static) -{1,1}> main_Load_201(i12, i4, i17, env, static) :|: 1 <= i12
main_Load_201(i12, i4, i17, env, static) -{1,1}> main_IntArithmetic_205(i12, i4, i17, env, static) :|: 1 <= i12
main_IntArithmetic_205(i12, i4, i17, env, static) -{1,1}> main_Store_206(i12, i4, i31, env, static) :|: i12 + i17 = i31 && 1 <= i12
main_Store_206(i12, i4, i31, env, static) -{1,1}> main_JMP_208(i12, i4, i31, env, static) :|: 1 <= i12
main_JMP_208(i12, i4, i31, env, static) -{1,1}> main_Load_215(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_215(i12, i4, i31, env, static) -{1,1}> main_Load_218(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_218(i12, i4, i31, env, static) -{1,1}> main_LE_234(i12, i4, i31, env, static) :|: 1 <= i12

obtained
main_LE_234(i12, i4, i31, env, static) -{1,1}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12 && i31 < i12
by chaining
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_245(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_LE_245(i12, i4, i31, env, static) -{1,1}> main_Load_261(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_Load_261(i12, i4, i31, env, static) -{0,0}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12

(8) Obligation:

IntTrs with 8 rules
Start term: main_Load_2(#0, #1, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && 0 < 2
main_LE_57(i11, i4, env, static) -{0,0}> main_LE_58(i11, i4, env, static) :|: i11 <= 0
main_LE_57(i12, i4, env, static) -{3,3}> main_LE_88(i12, i4, env, static) :|: 1 <= i12 && 0 < i12
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_91(i12, i4, env, static) :|: i12 <= i4 && 1 <= i12
main_LE_88(i12, i4, env, static) -{1,1}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12 && i4 < i12
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i31', env, static) :|: 1 <= i12 && i12 + i17 = i31'
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_243(i12, i4, i31, env, static) :|: i12 <= i31 && 1 <= i12
main_LE_234(i12, i4, i31, env, static) -{1,1}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12 && i31 < i12

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

Moved arithmethic from constraints to rhss.

main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i31', env, static) :|: 1 <= i12 && i12 + i17 = i31'
was transformed to
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i12 + i17, env, static) :|: 1 <= i12 && i12 + i17 = i31'

(10) Obligation:

IntTrs with 8 rules
Start term: main_Load_2(#0, #1, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_91(i12, i4, env, static) :|: i12 <= i4 && 1 <= i12
main_LE_57(i11, i4, env, static) -{0,0}> main_LE_58(i11, i4, env, static) :|: i11 <= 0
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_243(i12, i4, i31, env, static) :|: i12 <= i31 && 1 <= i12
main_LE_88(i12, i4, env, static) -{1,1}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12 && i4 < i12
main_LE_57(i12, i4, env, static) -{3,3}> main_LE_88(i12, i4, env, static) :|: 1 <= i12 && 0 < i12
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && 0 < 2
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i12 + i17, env, static) :|: 1 <= i12 && i12 + i17 = i31'
main_LE_234(i12, i4, i31, env, static) -{1,1}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12 && i31 < i12

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

Simplified expressions.

main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && 0 < 2
was transformed to
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: static'1 <= static''' + 1 && 0 <= static''' && static''' <= static + 2 && 0 <= static && 0 <= static'1

(12) Obligation:

IntTrs with 8 rules
Start term: main_Load_2(#0, #1, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_57(i11, i4, env, static) -{0,0}> main_LE_58(i11, i4, env, static) :|: i11 <= 0
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_91(i12, i4, env, static) :|: i12 <= i4 && 1 <= i12
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i12 + i17, env, static) :|: 1 <= i12 && i12 + i17 = i31'
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_243(i12, i4, i31, env, static) :|: i12 <= i31 && 1 <= i12
main_LE_57(i12, i4, env, static) -{3,3}> main_LE_88(i12, i4, env, static) :|: 1 <= i12 && 0 < i12
main_LE_88(i12, i4, env, static) -{1,1}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12 && i4 < i12
main_LE_234(i12, i4, i31, env, static) -{1,1}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12 && i31 < i12
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: static'1 <= static''' + 1 && 0 <= static''' && static''' <= static + 2 && 0 <= static && 0 <= 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:

IntTrs with 44 rules
Start term: main_Load_2(#0, #1, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_2(i2, i4, env, static) -{0,0}> main_Load_3(i2, i4, env, static) :|: 0 >= 0
main_Load_3(i2, i4, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_25(i2, i4, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_25(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_28(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_New_28(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_29(i2, i4, env, static) :|: 0 <= static
langle_clinit_rangle_New_29(i2, i4, env, static) -{1,1}> langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_44(o2, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_44(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_46(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Load_46(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_48(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_48(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_49(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_49(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_Return_51(i2, i4, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_51(i2, i4, env, static) -{1,1}> main_Load_52(i2, i4, env, static) :|: 0 >= 0
main_Load_52(i2, i4, env, static) -{0,0}> main_Load_53(i2, i4, env, static) :|: 0 >= 0
main_Load_53(i2, i4, env, static) -{0,0}> main_Load_54(i2, i4, env, static) :|: 0 <= static
main_Load_54(i2, i4, env, static) -{0,0}> main_Load_55(i2, i4, env, static) :|: 0 >= 0
main_Load_55(i2, i4, env, static) -{0,0}> main_Load_56(i2, i4, env, static) :|: 0 >= 0
main_Load_56(i2, i4, env, static) -{1,1}> main_LE_57(i2, i4, env, static) :|: 0 >= 0
main_LE_57(i11, i4, env, static) -{0,0}> main_LE_58(i11, i4, env, static) :|: i11 <= 0
main_LE_57(i12, i4, env, static) -{0,0}> main_LE_59(i12, i4, env, static) :|: 1 <= i12
main_LE_59(i12, i4, env, static) -{1,1}> main_Load_61(i12, i4, env, static) :|: 0 < i12 && 1 <= i12
main_Load_61(i12, i4, env, static) -{1,1}> main_Load_63(i12, i4, env, static) :|: 1 <= i12
main_Load_63(i12, i4, env, static) -{1,1}> main_LE_88(i12, i4, env, static) :|: 1 <= i12
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_91(i12, i4, env, static) :|: i12 <= i4 && 1 <= i12
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_92(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_LE_92(i12, i4, env, static) -{1,1}> main_Load_116(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_Load_116(i12, i4, env, static) -{0,0}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12
main_Load_191(i12, i4, i17, env, static) -{1,1}> main_Load_201(i12, i4, i17, env, static) :|: 1 <= i12
main_Load_201(i12, i4, i17, env, static) -{1,1}> main_IntArithmetic_205(i12, i4, i17, env, static) :|: 1 <= i12
main_IntArithmetic_205(i12, i4, i17, env, static) -{1,1}> main_Store_206(i12, i4, i31, env, static) :|: i12 + i17 = i31 && 1 <= i12
main_Store_206(i12, i4, i31, env, static) -{1,1}> main_JMP_208(i12, i4, i31, env, static) :|: 1 <= i12
main_JMP_208(i12, i4, i31, env, static) -{1,1}> main_Load_215(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_215(i12, i4, i31, env, static) -{1,1}> main_Load_218(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_218(i12, i4, i31, env, static) -{1,1}> main_LE_234(i12, i4, i31, env, static) :|: 1 <= i12
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_243(i12, i4, i31, env, static) :|: i12 <= i31 && 1 <= i12
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_245(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_LE_245(i12, i4, i31, env, static) -{1,1}> main_Load_261(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_Load_261(i12, i4, i31, env, static) -{0,0}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12

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

obtained
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && 0 < 2
by chaining
main_Load_2(i2, i4, env, static) -{0,0}> main_Load_3(i2, i4, env, static) :|: 0 >= 0
main_Load_3(i2, i4, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_25(i2, i4, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_25(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_28(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_New_28(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_29(i2, i4, env, static) :|: 0 <= static
langle_clinit_rangle_New_29(i2, i4, env, static) -{1,1}> langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_44(o2, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_44(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_46(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Load_46(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_48(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_48(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_49(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_49(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_Return_51(i2, i4, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_51(i2, i4, env, static) -{1,1}> main_Load_52(i2, i4, env, static) :|: 0 >= 0
main_Load_52(i2, i4, env, static) -{0,0}> main_Load_53(i2, i4, env, static) :|: 0 >= 0
main_Load_53(i2, i4, env, static) -{0,0}> main_Load_54(i2, i4, env, static) :|: 0 <= static
main_Load_54(i2, i4, env, static) -{0,0}> main_Load_55(i2, i4, env, static) :|: 0 >= 0
main_Load_55(i2, i4, env, static) -{0,0}> main_Load_56(i2, i4, env, static) :|: 0 >= 0
main_Load_56(i2, i4, env, static) -{1,1}> main_LE_57(i2, i4, env, static) :|: 0 >= 0

obtained
main_LE_57(i12, i4, env, static) -{3,3}> main_LE_88(i12, i4, env, static) :|: 1 <= i12 && 0 < i12
by chaining
main_LE_57(i12, i4, env, static) -{0,0}> main_LE_59(i12, i4, env, static) :|: 1 <= i12
main_LE_59(i12, i4, env, static) -{1,1}> main_Load_61(i12, i4, env, static) :|: 0 < i12 && 1 <= i12
main_Load_61(i12, i4, env, static) -{1,1}> main_Load_63(i12, i4, env, static) :|: 1 <= i12
main_Load_63(i12, i4, env, static) -{1,1}> main_LE_88(i12, i4, env, static) :|: 1 <= i12

obtained
main_LE_88(i12, i4, env, static) -{1,1}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12 && i4 < i12
by chaining
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_92(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_LE_92(i12, i4, env, static) -{1,1}> main_Load_116(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_Load_116(i12, i4, env, static) -{0,0}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12

obtained
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i31', env, static) :|: 1 <= i12 && i12 + i17 = i31'
by chaining
main_Load_191(i12, i4, i17, env, static) -{1,1}> main_Load_201(i12, i4, i17, env, static) :|: 1 <= i12
main_Load_201(i12, i4, i17, env, static) -{1,1}> main_IntArithmetic_205(i12, i4, i17, env, static) :|: 1 <= i12
main_IntArithmetic_205(i12, i4, i17, env, static) -{1,1}> main_Store_206(i12, i4, i31, env, static) :|: i12 + i17 = i31 && 1 <= i12
main_Store_206(i12, i4, i31, env, static) -{1,1}> main_JMP_208(i12, i4, i31, env, static) :|: 1 <= i12
main_JMP_208(i12, i4, i31, env, static) -{1,1}> main_Load_215(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_215(i12, i4, i31, env, static) -{1,1}> main_Load_218(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_218(i12, i4, i31, env, static) -{1,1}> main_LE_234(i12, i4, i31, env, static) :|: 1 <= i12

obtained
main_LE_234(i12, i4, i31, env, static) -{1,1}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12 && i31 < i12
by chaining
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_245(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_LE_245(i12, i4, i31, env, static) -{1,1}> main_Load_261(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_Load_261(i12, i4, i31, env, static) -{0,0}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12

(16) Obligation:

IntTrs with 8 rules
Start term: main_Load_2(#0, #1, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && 0 < 2
main_LE_57(i11, i4, env, static) -{0,0}> main_LE_58(i11, i4, env, static) :|: i11 <= 0
main_LE_57(i12, i4, env, static) -{3,3}> main_LE_88(i12, i4, env, static) :|: 1 <= i12 && 0 < i12
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_91(i12, i4, env, static) :|: i12 <= i4 && 1 <= i12
main_LE_88(i12, i4, env, static) -{1,1}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12 && i4 < i12
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i31', env, static) :|: 1 <= i12 && i12 + i17 = i31'
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_243(i12, i4, i31, env, static) :|: i12 <= i31 && 1 <= i12
main_LE_234(i12, i4, i31, env, static) -{1,1}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12 && i31 < i12

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

Moved arithmethic from constraints to rhss.

main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i31', env, static) :|: 1 <= i12 && i12 + i17 = i31'
was transformed to
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i12 + i17, env, static) :|: 1 <= i12 && i12 + i17 = i31'

(18) Obligation:

IntTrs with 8 rules
Start term: main_Load_2(#0, #1, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_91(i12, i4, env, static) :|: i12 <= i4 && 1 <= i12
main_LE_57(i11, i4, env, static) -{0,0}> main_LE_58(i11, i4, env, static) :|: i11 <= 0
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_243(i12, i4, i31, env, static) :|: i12 <= i31 && 1 <= i12
main_LE_88(i12, i4, env, static) -{1,1}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12 && i4 < i12
main_LE_57(i12, i4, env, static) -{3,3}> main_LE_88(i12, i4, env, static) :|: 1 <= i12 && 0 < i12
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && 0 < 2
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i12 + i17, env, static) :|: 1 <= i12 && i12 + i17 = i31'
main_LE_234(i12, i4, i31, env, static) -{1,1}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12 && i31 < i12

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

Simplified expressions.

main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: 0 >= 0 && static'1 <= static''' + 1 && 0 <= 2 && 0 <= static''' && static''' <= static + 2 && 0 < 1 && 0 <= 1 && 0 <= static && 0 <= static'1 && 0 < 2
was transformed to
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: static'1 <= static''' + 1 && 0 <= static''' && static''' <= static + 2 && 0 <= static && 0 <= static'1

(20) Obligation:

IntTrs with 8 rules
Start term: main_Load_2(#0, #1, env, static)
Considered paths: nonterm paths and paths from start to sinks
Rules:
main_LE_57(i11, i4, env, static) -{0,0}> main_LE_58(i11, i4, env, static) :|: i11 <= 0
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_91(i12, i4, env, static) :|: i12 <= i4 && 1 <= i12
main_Load_191(i12, i4, i17, env, static) -{7,7}> main_LE_234(i12, i4, i12 + i17, env, static) :|: 1 <= i12 && i12 + i17 = i31'
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_243(i12, i4, i31, env, static) :|: i12 <= i31 && 1 <= i12
main_LE_57(i12, i4, env, static) -{3,3}> main_LE_88(i12, i4, env, static) :|: 1 <= i12 && 0 < i12
main_LE_88(i12, i4, env, static) -{1,1}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12 && i4 < i12
main_LE_234(i12, i4, i31, env, static) -{1,1}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12 && i31 < i12
main_Load_2(i2, i4, env, static) -{16,16}> main_LE_57(i2, i4, env, static'1) :|: static'1 <= static''' + 1 && 0 <= static''' && static''' <= static + 2 && 0 <= static && 0 <= static'1

(21) TerminationGraphToComplexityProof (BOTH CONCRETE BOUNDS(ID, ADD(6)) transformation)

Extracted set of 41 edges for the analysis of TIME complexity. Dropped leaves.

(22) Obligation:

Set of 41 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 41 jbc graph edges to a weighted ITS with 41 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 41 rules
Start term: main_Load_2(#0, #1, env, static)
Considered paths: all paths from start
Rules:
main_Load_2(i2, i4, env, static) -{0,0}> main_Load_3(i2, i4, env, static) :|: 0 >= 0
main_Load_3(i2, i4, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_25(i2, i4, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_25(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_28(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_New_28(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_29(i2, i4, env, static) :|: 0 <= static
langle_clinit_rangle_New_29(i2, i4, env, static) -{1,1}> langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_44(o2, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_44(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_46(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Load_46(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_48(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_48(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_49(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_49(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_Return_51(i2, i4, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_51(i2, i4, env, static) -{1,1}> main_Load_52(i2, i4, env, static) :|: 0 >= 0
main_Load_52(i2, i4, env, static) -{0,0}> main_Load_53(i2, i4, env, static) :|: 0 >= 0
main_Load_53(i2, i4, env, static) -{0,0}> main_Load_54(i2, i4, env, static) :|: 0 <= static
main_Load_54(i2, i4, env, static) -{0,0}> main_Load_55(i2, i4, env, static) :|: 0 >= 0
main_Load_55(i2, i4, env, static) -{0,0}> main_Load_56(i2, i4, env, static) :|: 0 >= 0
main_Load_56(i2, i4, env, static) -{1,1}> main_LE_57(i2, i4, env, static) :|: 0 >= 0
main_LE_57(i12, i4, env, static) -{0,0}> main_LE_59(i12, i4, env, static) :|: 1 <= i12
main_LE_59(i12, i4, env, static) -{1,1}> main_Load_61(i12, i4, env, static) :|: 0 < i12 && 1 <= i12
main_Load_61(i12, i4, env, static) -{1,1}> main_Load_63(i12, i4, env, static) :|: 1 <= i12
main_Load_63(i12, i4, env, static) -{1,1}> main_LE_88(i12, i4, env, static) :|: 1 <= i12
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_92(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_LE_92(i12, i4, env, static) -{1,1}> main_Load_116(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_Load_116(i12, i4, env, static) -{0,0}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12
main_Load_191(i12, i4, i17, env, static) -{1,1}> main_Load_201(i12, i4, i17, env, static) :|: 1 <= i12
main_Load_201(i12, i4, i17, env, static) -{1,1}> main_IntArithmetic_205(i12, i4, i17, env, static) :|: 1 <= i12
main_IntArithmetic_205(i12, i4, i17, env, static) -{1,1}> main_Store_206(i12, i4, i31, env, static) :|: i12 + i17 = i31 && 1 <= i12
main_Store_206(i12, i4, i31, env, static) -{1,1}> main_JMP_208(i12, i4, i31, env, static) :|: 1 <= i12
main_JMP_208(i12, i4, i31, env, static) -{1,1}> main_Load_215(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_215(i12, i4, i31, env, static) -{1,1}> main_Load_218(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_218(i12, i4, i31, env, static) -{1,1}> main_LE_234(i12, i4, i31, env, static) :|: 1 <= i12
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_245(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_LE_245(i12, i4, i31, env, static) -{1,1}> main_Load_261(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_Load_261(i12, i4, i31, env, static) -{0,0}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12

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

obtained
main_Load_2(i2, i4, env, static) -{20,20}> main_Load_191(i2, i4, i4, env, static'1) :|: 1 <= i2 && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1 && 0 < i2 && i4 < i2
by chaining
main_Load_2(i2, i4, env, static) -{0,0}> main_Load_3(i2, i4, env, static) :|: 0 >= 0
main_Load_3(i2, i4, env, static) -{0,0}> langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_ConstantStackPush_6(i2, i4, env, static) -{1,1}> langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) :|: iconst_0 = 0
langle_clinit_rangle_ArrayCreate_20(iconst_0, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) :|: a2 = 2 && iconst_0 = 0 && 0 < a2
langle_clinit_rangle_FieldAccess_23(a2, i2, i4, iconst_0, env, static) -{1,1}> langle_clinit_rangle_New_25(i2, i4, env, static') :|: 0 <= a2 && iconst_0 = 0 && static' <= static + a2 && 0 <= static && 0 < a2
langle_clinit_rangle_New_25(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_28(i2, i4, env, static) :|: 0 >= 0
langle_clinit_rangle_New_28(i2, i4, env, static) -{0,0}> langle_clinit_rangle_New_29(i2, i4, env, static) :|: 0 <= static
langle_clinit_rangle_New_29(i2, i4, env, static) -{1,1}> langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) :|: 0 < o2 && o2 = 1
langle_clinit_rangle_Duplicate_31(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_ConstantStackPush_37(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_clinit_rangle_InvokeMethod_43(o2, NULL, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_44(o2, i2, i4, env, static) :|: NULL = 0 && 0 < o2
langle_init_rangle_Load_44(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_45(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Load_46(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Load_46(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_InvokeMethod_47(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_48(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_48(o2, i2, i4, env, static) -{1,1}> langle_init_rangle_Return_49(o2, i2, i4, env, static) :|: 0 < o2
langle_init_rangle_Return_49(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) :|: 0 < o2
langle_clinit_rangle_FieldAccess_50(o2, i2, i4, env, static) -{1,1}> langle_clinit_rangle_Return_51(i2, i4, env, static') :|: 0 < o2 && 0 <= o2 && 0 <= static && static' <= static + o2
langle_clinit_rangle_Return_51(i2, i4, env, static) -{1,1}> main_Load_52(i2, i4, env, static) :|: 0 >= 0
main_Load_52(i2, i4, env, static) -{0,0}> main_Load_53(i2, i4, env, static) :|: 0 >= 0
main_Load_53(i2, i4, env, static) -{0,0}> main_Load_54(i2, i4, env, static) :|: 0 <= static
main_Load_54(i2, i4, env, static) -{0,0}> main_Load_55(i2, i4, env, static) :|: 0 >= 0
main_Load_55(i2, i4, env, static) -{0,0}> main_Load_56(i2, i4, env, static) :|: 0 >= 0
main_Load_56(i2, i4, env, static) -{1,1}> main_LE_57(i2, i4, env, static) :|: 0 >= 0
main_LE_57(i12, i4, env, static) -{0,0}> main_LE_59(i12, i4, env, static) :|: 1 <= i12
main_LE_59(i12, i4, env, static) -{1,1}> main_Load_61(i12, i4, env, static) :|: 0 < i12 && 1 <= i12
main_Load_61(i12, i4, env, static) -{1,1}> main_Load_63(i12, i4, env, static) :|: 1 <= i12
main_Load_63(i12, i4, env, static) -{1,1}> main_LE_88(i12, i4, env, static) :|: 1 <= i12
main_LE_88(i12, i4, env, static) -{0,0}> main_LE_92(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_LE_92(i12, i4, env, static) -{1,1}> main_Load_116(i12, i4, env, static) :|: i4 < i12 && 1 <= i12
main_Load_116(i12, i4, env, static) -{0,0}> main_Load_191(i12, i4, i4, env, static) :|: 1 <= i12

obtained
main_Load_191(i12, i4, i17, env, static) -{8,8}> main_Load_191(i12, i4, i31', env, static) :|: 1 <= i12 && i12 + i17 = i31' && i31' < i12
by chaining
main_Load_191(i12, i4, i17, env, static) -{1,1}> main_Load_201(i12, i4, i17, env, static) :|: 1 <= i12
main_Load_201(i12, i4, i17, env, static) -{1,1}> main_IntArithmetic_205(i12, i4, i17, env, static) :|: 1 <= i12
main_IntArithmetic_205(i12, i4, i17, env, static) -{1,1}> main_Store_206(i12, i4, i31, env, static) :|: i12 + i17 = i31 && 1 <= i12
main_Store_206(i12, i4, i31, env, static) -{1,1}> main_JMP_208(i12, i4, i31, env, static) :|: 1 <= i12
main_JMP_208(i12, i4, i31, env, static) -{1,1}> main_Load_215(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_215(i12, i4, i31, env, static) -{1,1}> main_Load_218(i12, i4, i31, env, static) :|: 1 <= i12
main_Load_218(i12, i4, i31, env, static) -{1,1}> main_LE_234(i12, i4, i31, env, static) :|: 1 <= i12
main_LE_234(i12, i4, i31, env, static) -{0,0}> main_LE_245(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_LE_245(i12, i4, i31, env, static) -{1,1}> main_Load_261(i12, i4, i31, env, static) :|: i31 < i12 && 1 <= i12
main_Load_261(i12, i4, i31, env, static) -{0,0}> main_Load_191(i12, i4, i31, env, static) :|: 1 <= i12

(26) Obligation:

IntTrs with 2 rules
Start term: main_Load_2(#0, #1, env, static)
Considered paths: all paths from start
Rules:
main_Load_2(i2, i4, env, static) -{20,20}> main_Load_191(i2, i4, i4, env, static'1) :|: 1 <= i2 && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1 && 0 < i2 && i4 < i2
main_Load_191(i12, i4, i17, env, static) -{8,8}> main_Load_191(i12, i4, i31', env, static) :|: 1 <= i12 && i12 + i17 = i31' && i31' < i12

(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) → main_Load_2(x1, x2, x4)
main_Load_191(x1, x2, x3, x4, x5) → main_Load_191(x1, x3)

(28) Obligation:

IntTrs with 2 rules
Start term: main_Load_2(#0, #1, static)
Considered paths: all paths from start
Rules:
main_Load_2(i2, i4, static) -{20,20}> main_Load_191(i2, i4) :|: 1 <= i2 && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1 && 0 < i2 && i4 < i2
main_Load_191(i12, i17) -{8,8}> main_Load_191(i12, i31') :|: 1 <= i12 && i12 + i17 = i31' && i31' < i12

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

Moved arithmethic from constraints to rhss.

main_Load_191(i12, i17) -{8,8}> main_Load_191(i12, i31') :|: 1 <= i12 && i12 + i17 = i31' && i31' < i12
was transformed to
main_Load_191(i12, i17) -{8,8}> main_Load_191(i12, i12 + i17) :|: 1 <= i12 && i12 + i17 = i31' && i31' < i12

(30) Obligation:

IntTrs with 2 rules
Start term: main_Load_2(#0, #1, static)
Considered paths: all paths from start
Rules:
main_Load_2(i2, i4, static) -{20,20}> main_Load_191(i2, i4) :|: 1 <= i2 && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1 && 0 < i2 && i4 < i2
main_Load_191(i12, i17) -{8,8}> main_Load_191(i12, i12 + i17) :|: 1 <= i12 && i12 + i17 = i31' && i31' < i12

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

Simplified expressions.

main_Load_2(i2, i4, static) -{20,20}> main_Load_191(i2, i4) :|: 1 <= i2 && 0 < 2 && 0 <= static'1 && 0 <= static && 0 <= 1 && 0 < 1 && static''' <= static + 2 && 0 <= static''' && 0 <= 2 && 0 >= 0 && static'1 <= static''' + 1 && 0 < i2 && i4 < i2
was transformed to
main_Load_2(i2, i4, static) -{20,20}> main_Load_191(i2, i4) :|: 1 <= i2 && 0 <= static'1 && 0 <= static && static''' <= static + 2 && 0 <= static''' && static'1 <= static''' + 1 && 0 < i2 && i4 < i2

(32) Obligation:

IntTrs with 2 rules
Start term: main_Load_2(#0, #1, static)
Considered paths: all paths from start
Rules:
main_Load_191(i12, i17) -{8,8}> main_Load_191(i12, i12 + i17) :|: 1 <= i12 && i12 + i17 = i31' && i31' < i12
main_Load_2(i2, i4, static) -{20,20}> main_Load_191(i2, i4) :|: 1 <= i2 && 0 <= static'1 && 0 <= static && static''' <= static + 2 && 0 <= static''' && static'1 <= static''' + 1 && 0 < i2 && i4 < i2

(33) koat Proof (EQUIVALENT transformation)

YES(?, 8*ar_1 + 20)

Initial complexity problem:
1: T:
(Comp: ?, Cost: 8) main_Load_191(ar_0, ar_1, ar_2) -> Com_1(main_Load_191(ar_0, ar_0 + ar_1, arityPad)) [ 1 <= ar_0 /\ ar_0 + ar_1 = i31' /\ i31' < ar_0 ]
(Comp: ?, Cost: 20) main_Load_2(ar_0, ar_1, ar_2) -> Com_1(main_Load_191(ar_0, ar_1, arityPad)) [ 1 <= ar_0 /\ 0 <= static'1 /\ 0 <= ar_2 /\ static''' <= ar_2 + 2 /\ 0 <= static''' /\ static'1 <= static''' + 1 /\ 0 < ar_0 /\ ar_1 < ar_0 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(main_Load_2(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2: T:
(Comp: ?, Cost: 8) main_Load_191(ar_0, ar_1, ar_2) -> Com_1(main_Load_191(ar_0, ar_0 + ar_1, arityPad)) [ 1 <= ar_0 /\ ar_0 + ar_1 = i31' /\ i31' < ar_0 ]
(Comp: 1, Cost: 20) main_Load_2(ar_0, ar_1, ar_2) -> Com_1(main_Load_191(ar_0, ar_1, arityPad)) [ 1 <= ar_0 /\ 0 <= static'1 /\ 0 <= ar_2 /\ static''' <= ar_2 + 2 /\ 0 <= static''' /\ static'1 <= static''' + 1 /\ 0 < ar_0 /\ ar_1 < ar_0 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(main_Load_2(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

A polynomial rank function with
Pol(main_Load_191) = -V_2
Pol(main_Load_2) = -V_2
Pol(koat_start) = -V_2
orients all transitions weakly and the transition
main_Load_191(ar_0, ar_1, ar_2) -> Com_1(main_Load_191(ar_0, ar_0 + ar_1, arityPad)) [ 1 <= ar_0 /\ ar_0 + ar_1 = i31' /\ i31' < ar_0 ]
strictly and produces the following problem:
3: T:
(Comp: ar_1, Cost: 8) main_Load_191(ar_0, ar_1, ar_2) -> Com_1(main_Load_191(ar_0, ar_0 + ar_1, arityPad)) [ 1 <= ar_0 /\ ar_0 + ar_1 = i31' /\ i31' < ar_0 ]
(Comp: 1, Cost: 20) main_Load_2(ar_0, ar_1, ar_2) -> Com_1(main_Load_191(ar_0, ar_1, arityPad)) [ 1 <= ar_0 /\ 0 <= static'1 /\ 0 <= ar_2 /\ static''' <= ar_2 + 2 /\ 0 <= static''' /\ static'1 <= static''' + 1 /\ 0 < ar_0 /\ ar_1 < ar_0 ]
(Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(main_Load_2(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
start location: koat_start
leaf cost: 0

Complexity upper bound 8*ar_1 + 20

Time: 0.108 sec (SMT: 0.090 sec)

(34) BOUNDS(CONSTANT, 20 + 8 * |#1|)