### (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:

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]))=TRUE1005_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])))∧(UIncreasing(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])=TRUE1005_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])))∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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))))∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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 ⇒ (UIncreasing(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))))
• ((UIncreasing(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 Pbound 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 Pbound.
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 Pbound:

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.

### (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

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])))

The set Q is empty.

### (8) IDependencyGraphProof (EQUIVALENT transformation)

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

### (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.