Termination proof of /tmp/tmp2pjg7M/Take.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 IDP

↳5 IDPNonInfProof (⇒)

↳6 AND

    ↳7 IDP

        ↳8 IDependencyGraphProof (⇔)

        ↳9 TRUE

    ↳10 IDP

        ↳11 IDependencyGraphProof (⇔)

        ↳12 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: Take

/**
 * Java can do infinite data objects, too.
 * Here we take the first n elements from an
 * ascending infinite list of integer numbers.
 *
 * @author Carsten Fuhs
 */
public class Take {

    public static int[] take(int n, MyIterator f) {
        int[] result = new int[n];
        for (int i = 0; i < n; ++i) {
            if (f.hasNext()) {
                result[i] = f.next();
            }
            else {
                break;
            }
        }
        return result;
    }

    public static void main(String args[]) {
        int start = args[0].length();
        int howMany = args[1].length();
        From f = new From(start);
        int[] firstHowMany = take(howMany, f);
    }
}

interface MyIterator {
    boolean hasNext();
    int next();
}

class From implements MyIterator {

    private int current;

    public From(int start) {
        this.current = start;
    }

    public boolean hasNext() {
        return true;
    }

    public int next() {
        return current++;
    }
}

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Take.main([Ljava/lang/String;)V: Graph of 196 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 26 rules for P and 29 rules for R.

Combined rules. Obtained 1 rules for P and 0 rules for R.

Filtered ground terms:

From(x1, x2) → From(x2)
1005_0_take_Load(x1, x2, x3, x4, x5, x6) → 1005_0_take_Load(x2, x3, x4, x5, x6)

Filtered duplicate args:

1005_0_take_Load(x1, x2, x3, x4, x5) → 1005_0_take_Load(x1, x2, x3, x5)

Combined rules. Obtained 1 rules for P and 0 rules for R.

Finished conversion. Obtained 1 rules for P and 0 rules for R. System has predefined symbols.

(4) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0]))) → COND_1005_1_MAIN_INVOKEMETHOD(x3[0] >= 0 && x3[0] < x0[0], 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))
(1): COND_1005_1_MAIN_INVOKEMETHOD(TRUE, 1005_0_take_Load(x0[1], java.lang.Object(From(x1[1])), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1]), x0[1], java.lang.Object(From(x1[1]))) → 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(x1[1] + 1)), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1] + 1), x0[1], java.lang.Object(From(x1[1] + 1)))

(0) -> (1), if ((x3[0] >= 0 && x3[0] < x0[0] →^* TRUE)∧(1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]) →^* 1005_0_take_Load(x0[1], java.lang.Object(From(x1[1])), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1]))∧(x0[0] →^* x0[1])∧(java.lang.Object(From(x1[0])) →^* java.lang.Object(From(x1[1]))))

(1) -> (0), if ((1005_0_take_Load(x0[1], java.lang.Object(From(x1[1] + 1)), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1] + 1) →^* 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]))∧(x0[1] →^* x0[0])∧(java.lang.Object(From(x1[1] + 1)) →^* java.lang.Object(From(x1[0]))))

The set Q is empty.

(5) IDPNonInfProof (SOUND transformation)

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.

For Pair 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3), x0, java.lang.Object(From(x1))) → COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3, 0), <(x3, x0)), 1005_0_take_Load(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3), x0, java.lang.Object(From(x1))) the following chains were created:

We consider the chain 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0]))) → COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0]))), COND_1005_1_MAIN_INVOKEMETHOD(TRUE, 1005_0_take_Load(x0[1], java.lang.Object(From(x1[1])), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1]), x0[1], java.lang.Object(From(x1[1]))) → 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1)))) which results in the following constraint:
(1)    (&&(>=(x3[0], 0), <(x3[0], x0[0]))=TRUE∧1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0])=1005_0_take_Load(x0[1], java.lang.Object(From(x1[1])), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1])∧x0[0]=x0[1]∧java.lang.Object(From(x1[0]))=java.lang.Object(From(x1[1])) ⇒ 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))≥NonInfC∧1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))≥COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))∧(U^Increasing(COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>=(x3[0], 0)=TRUE∧<(x3[0], x0[0])=TRUE ⇒ 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))≥NonInfC∧1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))≥COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))∧(U^Increasing(COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x3[0] ≥ 0∧x0[0] + [-1] + [-1]x3[0] ≥ 0 ⇒ (U^Increasing(COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))), ≥)∧[bni_19 + (-1)Bound*bni_19] + [(4)bni_19]x0[0] + [(-2)bni_19]x3[0] ≥ 0∧[(-1)bso_20] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x3[0] ≥ 0∧x0[0] + [-1] + [-1]x3[0] ≥ 0 ⇒ (U^Increasing(COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))), ≥)∧[bni_19 + (-1)Bound*bni_19] + [(4)bni_19]x0[0] + [(-2)bni_19]x3[0] ≥ 0∧[(-1)bso_20] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x3[0] ≥ 0∧x0[0] + [-1] + [-1]x3[0] ≥ 0 ⇒ (U^Increasing(COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))), ≥)∧[bni_19 + (-1)Bound*bni_19] + [(4)bni_19]x0[0] + [(-2)bni_19]x3[0] ≥ 0∧[(-1)bso_20] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (x3[0] ≥ 0∧x0[0] + [-1] + [-1]x3[0] ≥ 0 ⇒ (U^Increasing(COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))), ≥)∧0 = 0∧0 = 0∧[bni_19 + (-1)Bound*bni_19] + [(4)bni_19]x0[0] + [(-2)bni_19]x3[0] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_20] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x3[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))), ≥)∧0 = 0∧0 = 0∧[(5)bni_19 + (-1)Bound*bni_19] + [(2)bni_19]x3[0] + [(4)bni_19]x0[0] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_20] ≥ 0)

For Pair COND_1005_1_MAIN_INVOKEMETHOD(TRUE, 1005_0_take_Load(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3), x0, java.lang.Object(From(x1))) → 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0, java.lang.Object(From(+(x1, 1))), java.lang.Object(ARRAY(x0, x2)), +(x3, 1)), x0, java.lang.Object(From(+(x1, 1)))) the following chains were created:

We consider the chain COND_1005_1_MAIN_INVOKEMETHOD(TRUE, 1005_0_take_Load(x0[1], java.lang.Object(From(x1[1])), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1]), x0[1], java.lang.Object(From(x1[1]))) → 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1)))) which results in the following constraint:
(8)    (COND_1005_1_MAIN_INVOKEMETHOD(TRUE, 1005_0_take_Load(x0[1], java.lang.Object(From(x1[1])), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1]), x0[1], java.lang.Object(From(x1[1])))≥NonInfC∧COND_1005_1_MAIN_INVOKEMETHOD(TRUE, 1005_0_take_Load(x0[1], java.lang.Object(From(x1[1])), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1]), x0[1], java.lang.Object(From(x1[1])))≥1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1))))∧(U^Increasing(1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1))))), ≥))

We simplified constraint (8) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(9)    ((U^Increasing(1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1))))), ≥)∧[2 + (-1)bso_22] ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(10)    ((U^Increasing(1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1))))), ≥)∧[2 + (-1)bso_22] ≥ 0)

We simplified constraint (10) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(11)    ((U^Increasing(1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1))))), ≥)∧[2 + (-1)bso_22] ≥ 0)

We simplified constraint (11) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(12)    ((U^Increasing(1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1))))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_22] ≥ 0)

To summarize, we get the following constraints P_≥ for the following pairs.

1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3), x0, java.lang.Object(From(x1))) → COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3, 0), <(x3, x0)), 1005_0_take_Load(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3), x0, java.lang.Object(From(x1)))
- (x3[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))), ≥)∧0 = 0∧0 = 0∧[(5)bni_19 + (-1)Bound*bni_19] + [(2)bni_19]x3[0] + [(4)bni_19]x0[0] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_20] ≥ 0)
COND_1005_1_MAIN_INVOKEMETHOD(TRUE, 1005_0_take_Load(x0, java.lang.Object(From(x1)), java.lang.Object(ARRAY(x0, x2)), x3), x0, java.lang.Object(From(x1))) → 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0, java.lang.Object(From(+(x1, 1))), java.lang.Object(ARRAY(x0, x2)), +(x3, 1)), x0, java.lang.Object(From(+(x1, 1))))
- ((U^Increasing(1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1))))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_22] ≥ 0)

The constraints for P_> respective P_bound are constructed from P_≥ where we just replace every occurence of "t ≥ s" in P_≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for P_bound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0
POL(FALSE) = 0
POL(1005_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃)) = [1] + [2]x₃ + [2]x₂ + [2]x₁
POL(1005_0_take_Load(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂
POL(java.lang.Object(x₁)) = x₁
POL(From(x₁)) = x₁
POL(ARRAY(x₁, x₂)) = [-1] + [-1]x₁
POL(COND_1005_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [1] + [2]x₄ + [2]x₃ + [2]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(0) = 0
POL(<(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]

The following pairs are in P_>:

COND_1005_1_MAIN_INVOKEMETHOD(TRUE, 1005_0_take_Load(x0[1], java.lang.Object(From(x1[1])), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1]), x0[1], java.lang.Object(From(x1[1]))) → 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(+(x1[1], 1))), java.lang.Object(ARRAY(x0[1], x2[1])), +(x3[1], 1)), x0[1], java.lang.Object(From(+(x1[1], 1))))

The following pairs are in P_bound:

1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0]))) → COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))

The following pairs are in P_≥:

1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0]))) → COND_1005_1_MAIN_INVOKEMETHOD(&&(>=(x3[0], 0), <(x3[0], x0[0])), 1005_0_take_Load(x0[0], java.lang.Object(From(x1[0])), java.lang.Object(ARRAY(x0[0], x2[0])), x3[0]), x0[0], java.lang.Object(From(x1[0])))

There are no usable rules.

(6) Complex Obligation (AND)

(7) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

(8) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(9) TRUE

(10) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_1005_1_MAIN_INVOKEMETHOD(TRUE, 1005_0_take_Load(x0[1], java.lang.Object(From(x1[1])), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1]), x0[1], java.lang.Object(From(x1[1]))) → 1005_1_MAIN_INVOKEMETHOD(1005_0_take_Load(x0[1], java.lang.Object(From(x1[1] + 1)), java.lang.Object(ARRAY(x0[1], x2[1])), x3[1] + 1), x0[1], java.lang.Object(From(x1[1] + 1)))

The set Q is empty.

(11) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Obligation:

(5) IDPNonInfProof (SOUND transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) IDependencyGraphProof (EQUIVALENT transformation)

(9) TRUE

(10) Obligation:

(11) IDependencyGraphProof (EQUIVALENT transformation)

(12) TRUE