Termination proof of /tmp/tmpZTM7Uc/LogAG.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: LogAG

public class LogAG{

  // adapted from Arts&Giesl, 2001

  public static int half(int x) {

    int res = 0;

    while (x > 1) {

      x = x-2;
      res++;

    }

    return res;

  }


  public static int log(int x) {

    int res = 0;

    while (x > 1) {

      x = half(x-2)+1;
      res++;

    }

    return res;

  }


  public static void main(String[] args) {
    Random.args = args;
    int x  = Random.random();
    log(x);
  }
}



public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
LogAG.main([Ljava/lang/String;)V: Graph of 122 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 34 rules for P and 5 rules for R.

Combined rules. Obtained 2 rules for P and 0 rules for R.

Filtered ground terms:

983_0_half_LE(x1, x2, x3, x4, x5) → 983_0_half_LE(x2, x3, x4)

Filtered duplicate args:

983_0_half_LE(x1, x2, x3) → 983_0_half_LE(x2, x3)

Combined rules. Obtained 2 rules for P and 0 rules for R.

Finished conversion. Obtained 2 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): 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(x1[0] >= 0 && x0[0] <= 1 && 1 < x1[0] + 1, 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))
(1): COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, x1[1] + 1 - 2)))
(2): 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(x1[2] >= 0 && x0[2] > 1, 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))
(3): COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[3] + 1, x0[3] - 2)))

(0) -> (1), if ((x1[0] >= 0 && x0[0] <= 1 && 1 < x1[0] + 1 →^* TRUE)∧(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])) →^* 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))))

(1) -> (0), if ((983_1_log_InvokeMethod(983_0_half_LE(0, x1[1] + 1 - 2)) →^* 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))))

(1) -> (2), if ((983_1_log_InvokeMethod(983_0_half_LE(0, x1[1] + 1 - 2)) →^* 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))))

(2) -> (3), if ((x1[2] >= 0 && x0[2] > 1 →^* TRUE)∧(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])) →^* 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))))

(3) -> (0), if ((983_1_log_InvokeMethod(983_0_half_LE(x1[3] + 1, x0[3] - 2)) →^* 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))))

(3) -> (2), if ((983_1_log_InvokeMethod(983_0_half_LE(x1[3] + 1, x0[3] - 2)) →^* 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))))

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 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1, 0), <=(x0, 1)), <(1, +(x1, 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) the following chains were created:

We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))) which results in the following constraint:
(1)    (&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))=983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1])) ⇒ 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))≥NonInfC∧983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))≥COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))∧(U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (<(1, +(x1[0], 1))=TRUE∧>=(x1[0], 0)=TRUE∧<=(x0[0], 1)=TRUE ⇒ 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))≥NonInfC∧983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))≥COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))∧(U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x1[0] + [-1] ≥ 0∧x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥)∧[(3)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[0] + [bni_21]x1[0] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x1[0] + [-1] ≥ 0∧x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥)∧[(3)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[0] + [bni_21]x1[0] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x1[0] + [-1] ≥ 0∧x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥)∧[(3)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[0] + [bni_21]x1[0] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x1[0] ≥ 0∧[1] + x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥)∧[(4)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[0] + [bni_21]x1[0] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(7)    (x1[0] ≥ 0∧[1] + x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥)∧[(4)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[0] + [bni_21]x1[0] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

(8)    (x1[0] ≥ 0∧[1] + x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥)∧[(4)bni_21 + (-1)Bound*bni_21] + [(-1)bni_21]x0[0] + [bni_21]x1[0] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

For Pair COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1, 1), 2)))) the following chains were created:

We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))) which results in the following constraint:
(9) (&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))=983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))∧983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[0]1, x0[0]1))∧&&(&&(>=(x1[0]1, 0), <=(x0[0]1, 1)), <(1, +(x1[0]1, 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0]1, x0[0]1))=983_1_log_InvokeMethod(983_0_half_LE(x1[1]1, x0[1]1))∧983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1]1, 1), 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[0]2, x0[0]2))∧&&(&&(>=(x1[0]2, 0), <=(x0[0]2, 1)), <(1, +(x1[0]2, 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0]2, x0[0]2))=983_1_log_InvokeMethod(983_0_half_LE(x1[1]2, x0[1]2)) ⇒ COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1]1, x0[1]1)))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1]1, x0[1]1)))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1]1, 1), 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1]1, 1), 2))))), ≥))

We solved constraint (9) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN).
We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))) which results in the following constraint:
(10) (&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))=983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))∧983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[0]1, x0[0]1))∧&&(&&(>=(x1[0]1, 0), <=(x0[0]1, 1)), <(1, +(x1[0]1, 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0]1, x0[0]1))=983_1_log_InvokeMethod(983_0_half_LE(x1[1]1, x0[1]1))∧983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1]1, 1), 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))∧&&(>=(x1[2], 0), >(x0[2], 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))=983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3])) ⇒ COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1]1, x0[1]1)))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1]1, x0[1]1)))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1]1, 1), 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1]1, 1), 2))))), ≥))

We solved constraint (10) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN).
We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))) which results in the following constraint:
(11) (&&(>=(x1[2], 0), >(x0[2], 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))=983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))∧983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))∧&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))=983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))∧983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[0]1, x0[0]1))∧&&(&&(>=(x1[0]1, 0), <=(x0[0]1, 1)), <(1, +(x1[0]1, 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0]1, x0[0]1))=983_1_log_InvokeMethod(983_0_half_LE(x1[1]1, x0[1]1)) ⇒ COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1])))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1])))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))), ≥))

We solved constraint (11) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN).
We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))) which results in the following constraint:
(12)    (&&(>=(x1[2], 0), >(x0[2], 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))=983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))∧983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))∧&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))=983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))∧983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[2]1, x0[2]1))∧&&(>=(x1[2]1, 0), >(x0[2]1, 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2]1, x0[2]1))=983_1_log_InvokeMethod(983_0_half_LE(x1[3]1, x0[3]1)) ⇒ COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1])))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1])))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))), ≥))

We simplified constraint (12) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:
(13)    (>=(x1[2], 0)=TRUE∧>(x0[2], 1)=TRUE∧<(1, +(+(x1[2], 1), 1))=TRUE∧>(-(+(+(x1[2], 1), 1), 2), 1)=TRUE∧>=(+(x1[2], 1), 0)=TRUE∧<=(-(x0[2], 2), 1)=TRUE ⇒ COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(+(x1[2], 1), -(x0[2], 2))))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(+(x1[2], 1), -(x0[2], 2))))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(+(x1[2], 1), 1), 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))), ≥))

We simplified constraint (13) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(14)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧x1[2] ≥ 0∧x1[2] + [-2] ≥ 0∧x1[2] + [1] ≥ 0∧[3] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))), ≥)∧[bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] + [bni_23]x1[2] ≥ 0∧[-2 + (-1)bso_24] + x0[2] ≥ 0)

We simplified constraint (14) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(15)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧x1[2] ≥ 0∧x1[2] + [-2] ≥ 0∧x1[2] + [1] ≥ 0∧[3] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))), ≥)∧[bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] + [bni_23]x1[2] ≥ 0∧[-2 + (-1)bso_24] + x0[2] ≥ 0)

We simplified constraint (15) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(16)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧x1[2] ≥ 0∧x1[2] + [-2] ≥ 0∧x1[2] + [1] ≥ 0∧[3] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))), ≥)∧[bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] + [bni_23]x1[2] ≥ 0∧[-2 + (-1)bso_24] + x0[2] ≥ 0)

We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(17)    ([2] + x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧[2] + x1[2] ≥ 0∧x1[2] ≥ 0∧[3] + x1[2] ≥ 0∧[3] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))), ≥)∧[(3)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] + [bni_23]x1[2] ≥ 0∧[-2 + (-1)bso_24] + x0[2] ≥ 0)

We simplified constraint (17) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(18)    ([2] + x1[2] ≥ 0∧x0[2] ≥ 0∧[2] + x1[2] ≥ 0∧x1[2] ≥ 0∧[3] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))), ≥)∧[(5)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] + [bni_23]x1[2] ≥ 0∧[(-1)bso_24] + x0[2] ≥ 0)

For Pair 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1, 0), >(x0, 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) the following chains were created:

We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))) which results in the following constraint:
(19)    (&&(>=(x1[2], 0), >(x0[2], 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))=983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3])) ⇒ 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))≥NonInfC∧983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))≥COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))∧(U^Increasing(COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))), ≥))

We simplified constraint (19) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(20)    (>=(x1[2], 0)=TRUE∧>(x0[2], 1)=TRUE ⇒ 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))≥NonInfC∧983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))≥COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))∧(U^Increasing(COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))), ≥))

We simplified constraint (20) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(21)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))), ≥)∧[(3)bni_25 + (-1)Bound*bni_25] + [bni_25]x0[2] + [bni_25]x1[2] ≥ 0∧[1 + (-1)bso_26] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))), ≥)∧[(3)bni_25 + (-1)Bound*bni_25] + [bni_25]x0[2] + [bni_25]x1[2] ≥ 0∧[1 + (-1)bso_26] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))), ≥)∧[(3)bni_25 + (-1)Bound*bni_25] + [bni_25]x0[2] + [bni_25]x1[2] ≥ 0∧[1 + (-1)bso_26] ≥ 0)

We simplified constraint (23) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(24)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))), ≥)∧[(5)bni_25 + (-1)Bound*bni_25] + [bni_25]x0[2] + [bni_25]x1[2] ≥ 0∧[1 + (-1)bso_26] ≥ 0)

For Pair COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1, 1), -(x0, 2)))) the following chains were created:

We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))) which results in the following constraint:
(25)    (&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))=983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))∧983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))∧&&(>=(x1[2], 0), >(x0[2], 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))=983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))∧983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[0]1, x0[0]1))∧&&(&&(>=(x1[0]1, 0), <=(x0[0]1, 1)), <(1, +(x1[0]1, 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0]1, x0[0]1))=983_1_log_InvokeMethod(983_0_half_LE(x1[1]1, x0[1]1)) ⇒ COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3])))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3])))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥))

We simplified constraint (25) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:
(26)    (<(1, +(x1[0], 1))=TRUE∧>(-(+(x1[0], 1), 2), 1)=TRUE∧>=(x1[0], 0)=TRUE∧<=(x0[0], 1)=TRUE∧<=(-(-(+(x1[0], 1), 2), 2), 1)=TRUE ⇒ COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[0], 1), 2))))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[0], 1), 2))))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(0, 1), -(-(+(x1[0], 1), 2), 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥))

We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(27)    (x1[0] + [-1] ≥ 0∧x1[0] + [-3] ≥ 0∧x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (27) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(28)    (x1[0] + [-1] ≥ 0∧x1[0] + [-3] ≥ 0∧x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (28) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(29)    (x1[0] + [-1] ≥ 0∧x1[0] + [-3] ≥ 0∧x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (29) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(30)    (x1[0] ≥ 0∧[-2] + x1[0] ≥ 0∧[1] + x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[3] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[(2)bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (30) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(31)    ([2] + x1[0] ≥ 0∧x1[0] ≥ 0∧[3] + x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[(4)bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (31) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(32)    ([2] + x1[0] ≥ 0∧x1[0] ≥ 0∧[3] + x1[0] ≥ 0∧[1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[(4)bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)
We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))) which results in the following constraint:
(33)    (&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))=983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))∧983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))∧&&(>=(x1[2], 0), >(x0[2], 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))=983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))∧983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[2]1, x0[2]1))∧&&(>=(x1[2]1, 0), >(x0[2]1, 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2]1, x0[2]1))=983_1_log_InvokeMethod(983_0_half_LE(x1[3]1, x0[3]1)) ⇒ COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3])))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3])))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥))

We simplified constraint (33) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:
(34)    (<(1, +(x1[0], 1))=TRUE∧>(-(+(x1[0], 1), 2), 1)=TRUE∧>(-(-(+(x1[0], 1), 2), 2), 1)=TRUE∧>=(x1[0], 0)=TRUE∧<=(x0[0], 1)=TRUE ⇒ COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[0], 1), 2))))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[0], 1), 2))))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(0, 1), -(-(+(x1[0], 1), 2), 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥))

We simplified constraint (34) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(35)    (x1[0] + [-1] ≥ 0∧x1[0] + [-3] ≥ 0∧x1[0] + [-5] ≥ 0∧x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (35) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(36)    (x1[0] + [-1] ≥ 0∧x1[0] + [-3] ≥ 0∧x1[0] + [-5] ≥ 0∧x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (36) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(37)    (x1[0] + [-1] ≥ 0∧x1[0] + [-3] ≥ 0∧x1[0] + [-5] ≥ 0∧x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(38)    (x1[0] ≥ 0∧[-2] + x1[0] ≥ 0∧[-4] + x1[0] ≥ 0∧[1] + x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[(2)bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (38) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(39)    ([2] + x1[0] ≥ 0∧x1[0] ≥ 0∧[-2] + x1[0] ≥ 0∧[3] + x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[(4)bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (39) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(40)    ([4] + x1[0] ≥ 0∧[2] + x1[0] ≥ 0∧x1[0] ≥ 0∧[5] + x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[(6)bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (40) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(41)    ([4] + x1[0] ≥ 0∧[2] + x1[0] ≥ 0∧x1[0] ≥ 0∧[5] + x1[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[(6)bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)
We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))), COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2)))) which results in the following constraint:
(42)    (&&(>=(x1[2], 0), >(x0[2], 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))=983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))∧983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[2]1, x0[2]1))∧&&(>=(x1[2]1, 0), >(x0[2]1, 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2]1, x0[2]1))=983_1_log_InvokeMethod(983_0_half_LE(x1[3]1, x0[3]1))∧983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))∧&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1)))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))=983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1])) ⇒ COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3]1, x0[3]1)))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3]1, x0[3]1)))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥))

We simplified constraint (42) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(43)    (>=(x1[2], 0)=TRUE∧>(x0[2], 1)=TRUE∧>=(+(x1[2], 1), 0)=TRUE∧>(-(x0[2], 2), 1)=TRUE∧<(1, +(+(+(x1[2], 1), 1), 1))=TRUE∧>=(+(+(x1[2], 1), 1), 0)=TRUE∧<=(-(-(x0[2], 2), 2), 1)=TRUE ⇒ COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(+(x1[2], 1), -(x0[2], 2))))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(+(x1[2], 1), -(x0[2], 2))))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(+(x1[2], 1), 1), -(-(x0[2], 2), 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥))

We simplified constraint (43) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(44)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] + [-4] ≥ 0∧x1[2] + [1] ≥ 0∧x1[2] + [2] ≥ 0∧[5] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (44) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(45)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] + [-4] ≥ 0∧x1[2] + [1] ≥ 0∧x1[2] + [2] ≥ 0∧[5] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (45) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(46)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] + [-4] ≥ 0∧x1[2] + [1] ≥ 0∧x1[2] + [2] ≥ 0∧[5] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (46) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(47)    (x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧[-2] + x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧x1[2] + [2] ≥ 0∧[3] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[(3)bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (47) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(48)    (x1[2] ≥ 0∧[2] + x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧x1[2] + [2] ≥ 0∧[1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[(5)bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (48) using rule (IDP_POLY_GCD) which results in the following new constraint:
(49)    (x1[2] ≥ 0∧[2] + x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[1] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[(5)bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)
We consider the chain 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))), 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))), COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))) which results in the following constraint:
(50)    (&&(>=(x1[2], 0), >(x0[2], 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))=983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))∧983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[2]1, x0[2]1))∧&&(>=(x1[2]1, 0), >(x0[2]1, 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2]1, x0[2]1))=983_1_log_InvokeMethod(983_0_half_LE(x1[3]1, x0[3]1))∧983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2)))=983_1_log_InvokeMethod(983_0_half_LE(x1[2]2, x0[2]2))∧&&(>=(x1[2]2, 0), >(x0[2]2, 1))=TRUE∧983_1_log_InvokeMethod(983_0_half_LE(x1[2]2, x0[2]2))=983_1_log_InvokeMethod(983_0_half_LE(x1[3]2, x0[3]2)) ⇒ COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3]1, x0[3]1)))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3]1, x0[3]1)))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥))

We simplified constraint (50) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(51)    (>=(x1[2], 0)=TRUE∧>(x0[2], 1)=TRUE∧>=(+(x1[2], 1), 0)=TRUE∧>(-(x0[2], 2), 1)=TRUE∧>=(+(+(x1[2], 1), 1), 0)=TRUE∧>(-(-(x0[2], 2), 2), 1)=TRUE ⇒ COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(+(x1[2], 1), -(x0[2], 2))))≥NonInfC∧COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(+(x1[2], 1), -(x0[2], 2))))≥983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(+(x1[2], 1), 1), -(-(x0[2], 2), 2))))∧(U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥))

We simplified constraint (51) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(52)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] + [-4] ≥ 0∧x1[2] + [2] ≥ 0∧x0[2] + [-6] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (52) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(53)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] + [-4] ≥ 0∧x1[2] + [2] ≥ 0∧x0[2] + [-6] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (53) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(54)    (x1[2] ≥ 0∧x0[2] + [-2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] + [-4] ≥ 0∧x1[2] + [2] ≥ 0∧x0[2] + [-6] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (54) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(55)    (x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧[-2] + x0[2] ≥ 0∧x1[2] + [2] ≥ 0∧[-4] + x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[(3)bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(56)    (x1[2] ≥ 0∧[2] + x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] ≥ 0∧x1[2] + [2] ≥ 0∧[-2] + x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[(5)bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (56) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(57)    (x1[2] ≥ 0∧[4] + x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧[2] + x0[2] ≥ 0∧x1[2] + [2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[(7)bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

We simplified constraint (57) using rule (IDP_POLY_GCD) which results in the following new constraint:
(58)    (x1[2] ≥ 0∧[4] + x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧[2] + x0[2] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[(7)bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)

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

983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1, 0), <=(x0, 1)), <(1, +(x1, 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1, x0)))
- (x1[0] ≥ 0∧[1] + x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥)∧[(4)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[0] + [bni_21]x1[0] ≥ 0∧[1 + (-1)bso_22] ≥ 0)
- (x1[0] ≥ 0∧[1] + x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))), ≥)∧[(4)bni_21 + (-1)Bound*bni_21] + [(-1)bni_21]x0[0] + [bni_21]x1[0] ≥ 0∧[1 + (-1)bso_22] ≥ 0)
COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1, 1), 2))))
- ([2] + x1[2] ≥ 0∧x0[2] ≥ 0∧[2] + x1[2] ≥ 0∧x1[2] ≥ 0∧[3] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))), ≥)∧[(5)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] + [bni_23]x1[2] ≥ 0∧[(-1)bso_24] + x0[2] ≥ 0)
983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1, 0), >(x0, 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1, x0)))
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))), ≥)∧[(5)bni_25 + (-1)Bound*bni_25] + [bni_25]x0[2] + [bni_25]x1[2] ≥ 0∧[1 + (-1)bso_26] ≥ 0)
COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1, x0))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1, 1), -(x0, 2))))
- ([2] + x1[0] ≥ 0∧x1[0] ≥ 0∧[3] + x1[0] ≥ 0∧[1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[(4)bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)
- ([4] + x1[0] ≥ 0∧[2] + x1[0] ≥ 0∧x1[0] ≥ 0∧[5] + x1[0] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))), ≥)∧[(6)bni_27 + (-1)Bound*bni_27] + [bni_27]x1[0] ≥ 0∧[(-1)bso_28] ≥ 0)
- (x1[2] ≥ 0∧[2] + x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[1] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[(5)bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 0)
- (x1[2] ≥ 0∧[4] + x0[2] ≥ 0∧x1[2] + [1] ≥ 0∧[2] + x0[2] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0 ⇒ (U^Increasing(983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3]1, 1), -(x0[3]1, 2))))), ≥)∧[(7)bni_27 + (-1)Bound*bni_27] + [bni_27]x0[2] + [bni_27]x1[2] ≥ 0∧[(-1)bso_28] ≥ 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) = [1]
POL(FALSE) = [1]
POL(983_2_MAIN_INVOKEMETHOD(x₁)) = [1] + [-1]x₁
POL(983_1_log_InvokeMethod(x₁)) = [-1] + x₁
POL(983_0_half_LE(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(COND_983_2_MAIN_INVOKEMETHOD(x₁, x₂)) = [1] + [-1]x₂ + [-1]x₁
POL(&&(x₁, x₂)) = [1]
POL(>=(x₁, x₂)) = [-1]
POL(0) = 0
POL(<=(x₁, x₂)) = [-1]
POL(1) = [1]
POL(<(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(2) = [2]
POL(COND_983_2_MAIN_INVOKEMETHOD1(x₁, x₂)) = [-1]x₂
POL(>(x₁, x₂)) = [-1]

The following pairs are in P_>:

983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0]))) → COND_983_2_MAIN_INVOKEMETHOD(&&(&&(>=(x1[0], 0), <=(x0[0], 1)), <(1, +(x1[0], 1))), 983_1_log_InvokeMethod(983_0_half_LE(x1[0], x0[0])))
983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))

The following pairs are in P_bound:

COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))
983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2]))) → COND_983_2_MAIN_INVOKEMETHOD1(&&(>=(x1[2], 0), >(x0[2], 1)), 983_1_log_InvokeMethod(983_0_half_LE(x1[2], x0[2])))
COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))

The following pairs are in P_≥:

COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, -(+(x1[1], 1), 2))))
COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(+(x1[3], 1), -(x0[3], 2))))

At least the following rules have been oriented under context sensitive arithmetic replacement:

&&(TRUE, TRUE)¹ ↔ TRUE¹
&&(TRUE, FALSE)¹ ↔ FALSE¹
&&(FALSE, TRUE)¹ ↔ FALSE¹
&&(FALSE, FALSE)¹ ↔ FALSE¹

(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:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_983_2_MAIN_INVOKEMETHOD(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[1], x0[1]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(0, x1[1] + 1 - 2)))
(3): COND_983_2_MAIN_INVOKEMETHOD1(TRUE, 983_1_log_InvokeMethod(983_0_half_LE(x1[3], x0[3]))) → 983_2_MAIN_INVOKEMETHOD(983_1_log_InvokeMethod(983_0_half_LE(x1[3] + 1, x0[3] - 2)))

The set Q is empty.

(8) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.

(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:

Boolean, Integer

(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