### (0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_14 (Sun Microsystems Inc.) Main-Class: AProVEMathRecursive
`public class AProVEMathRecursive {  public static void main(String[] args) {    Random.args = args;    int x = Random.random();    int y = Random.random();    power(x, y);  }  public static int power(int base, int exponent) {               if (exponent <= 0) {      return 1;    } else if (exponent == 1) {      return base;    } else if (base == 2) {      return base << (exponent-1);    } else if (exponent % 2 == 1) {      return base * power(base, exponent-1);    } else {      int halfPower = power(base, exponent/2);      return halfPower * halfPower;    }  }}public class Random {  static String[] args;  static int index = 0;  public static int random() {    if (args.length <= index) {      return 0;    }    String string = args[index];    index++;    if (string == null) {      return 0;    }    return string.length();  }}`

### (1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

### (2) Obligation:

FIGraph based on JBC Program:
AProVEMathRecursive.main([Ljava/lang/String;)V: Graph of 138 nodes with 0 SCCs.

AProVEMathRecursive.power(II)I: Graph of 139 nodes with 0 SCCs.

### (3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 65 rules for P and 80 rules for R.

Combined rules. Obtained 6 rules for P and 13 rules for R.

Filtered ground terms:

574_0_power_GT(x1, x2, x3, x4) → 574_0_power_GT(x2, x3, x4)
Cond_574_0_power_GT5(x1, x2, x3, x4, x5) → Cond_574_0_power_GT5(x1, x3, x4, x5)
Cond_574_0_power_GT4(x1, x2, x3, x4, x5) → Cond_574_0_power_GT4(x1, x3, x4, x5)
Cond_574_0_power_GT3(x1, x2, x3, x4, x5) → Cond_574_0_power_GT3(x1, x3, x4, x5)
Cond_574_0_power_GT2(x1, x2, x3, x4, x5) → Cond_574_0_power_GT2(x1, x3, x4, x5)
Cond_574_0_power_GT1(x1, x2, x3, x4, x5) → Cond_574_0_power_GT1(x1, x3, x4, x5)
Cond_574_0_power_GT(x1, x2, x3, x4, x5) → Cond_574_0_power_GT(x1, x3, x4, x5)
895_0_power_Return(x1, x2, x3) → 895_0_power_Return(x2, x3)
Cond_868_1_power_InvokeMethod2(x1, x2, x3, x4, x5, x6, x7) → Cond_868_1_power_InvokeMethod2(x1, x3, x4, x5, x6, x7)
951_0_power_Return(x1) → 951_0_power_Return
Cond_868_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → Cond_868_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6)
644_0_power_Return(x1, x2, x3, x4) → 644_0_power_Return(x2, x4)
Cond_840_1_power_InvokeMethod(x1, x2, x3, x4) → Cond_840_1_power_InvokeMethod(x1, x2, x3)
969_0_power_Return(x1, x2, x3) → 969_0_power_Return(x2, x3)
Cond_855_1_power_InvokeMethod2(x1, x2, x3, x4, x5, x6, x7) → Cond_855_1_power_InvokeMethod2(x1, x3, x4, x5, x6, x7)
1056_0_power_Return(x1) → 1056_0_power_Return
Cond_855_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → Cond_855_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6)
587_0_power_Return(x1, x2, x3) → 587_0_power_Return(x2)

Filtered duplicate args:

574_0_power_GT(x1, x2, x3) → 574_0_power_GT(x1, x3)
Cond_574_0_power_GT5(x1, x2, x3, x4) → Cond_574_0_power_GT5(x1, x2, x4)
868_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6) → 868_1_power_InvokeMethod(x1, x3, x5, x6)
Cond_574_0_power_GT4(x1, x2, x3, x4) → Cond_574_0_power_GT4(x1, x2, x4)
Cond_574_0_power_GT3(x1, x2, x3, x4) → Cond_574_0_power_GT3(x1, x2, x4)
Cond_574_0_power_GT2(x1, x2, x3, x4) → Cond_574_0_power_GT2(x1, x2, x4)
855_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6) → 855_1_power_InvokeMethod(x1, x3, x5, x6)
Cond_574_0_power_GT1(x1, x2, x3, x4) → Cond_574_0_power_GT1(x1, x2, x4)
Cond_574_0_power_GT(x1, x2, x3, x4) → Cond_574_0_power_GT(x1, x2, x4)
Cond_868_1_power_InvokeMethod2(x1, x2, x3, x4, x5, x6) → Cond_868_1_power_InvokeMethod2(x1, x3, x5, x6)
Cond_868_1_power_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7) → Cond_868_1_power_InvokeMethod1(x1, x2, x4, x6, x7)
Cond_868_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_868_1_power_InvokeMethod(x1, x2, x4, x6)
644_0_power_Return(x1, x2) → 644_0_power_Return(x2)
Cond_855_1_power_InvokeMethod2(x1, x2, x3, x4, x5, x6) → Cond_855_1_power_InvokeMethod2(x1, x3, x5, x6)
Cond_855_1_power_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7) → Cond_855_1_power_InvokeMethod1(x1, x2, x4, x6, x7)
Cond_855_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_855_1_power_InvokeMethod(x1, x2, x4, x6)

Filtered unneeded arguments:

Cond_855_1_power_InvokeMethod2(x1, x2, x3, x4) → Cond_855_1_power_InvokeMethod2(x1, x2, x3)
Cond_868_1_power_InvokeMethod2(x1, x2, x3, x4) → Cond_868_1_power_InvokeMethod2(x1, x2, x3)

Combined rules. Obtained 6 rules for P and 13 rules for R.

Finished conversion. Obtained 6 rules for P and 13 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:

Integer, Boolean

The ITRS R consists of the following rules:
574_0_power_GT(x0, 0) → 587_0_power_Return(x0)
827_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1) → 1056_0_power_Return
827_1_power_InvokeMethod(969_0_power_Return(x0, x1), x0, x1) → 1056_0_power_Return
827_1_power_InvokeMethod(1056_0_power_Return, x0, x1) → 1056_0_power_Return
855_1_power_InvokeMethod(644_0_power_Return(x0), x2, x0, 1) → Cond_855_1_power_InvokeMethod(x0 <= 1, 644_0_power_Return(x0), x2, x0, 1)
Cond_855_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x2, x0, 1) → 969_0_power_Return(x0, x2)
855_1_power_InvokeMethod(969_0_power_Return(x0, x1), x2, x0, x1) → Cond_855_1_power_InvokeMethod1(x0 <= 1, 969_0_power_Return(x0, x1), x2, x0, x1)
Cond_855_1_power_InvokeMethod1(TRUE, 969_0_power_Return(x0, x1), x2, x0, x1) → 969_0_power_Return(x0, x2)
855_1_power_InvokeMethod(1056_0_power_Return, x1, x0, x2) → Cond_855_1_power_InvokeMethod2(x0 <= 1, 1056_0_power_Return, x1, x0, x2)
Cond_855_1_power_InvokeMethod2(TRUE, 1056_0_power_Return, x1, x0, x2) → 969_0_power_Return(x0, x1)
840_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1) → Cond_840_1_power_InvokeMethod(x0 > 1, 644_0_power_Return(x0), x0, 1)
Cond_840_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x0, 1) → 951_0_power_Return
840_1_power_InvokeMethod(895_0_power_Return(x0, x1), x0, x1) → 951_0_power_Return
840_1_power_InvokeMethod(951_0_power_Return, x0, x1) → 951_0_power_Return
868_1_power_InvokeMethod(644_0_power_Return(x0), x2, x0, 1) → Cond_868_1_power_InvokeMethod(x0 > 1, 644_0_power_Return(x0), x2, x0, 1)
Cond_868_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x2, x0, 1) → 895_0_power_Return(x0, x2)
868_1_power_InvokeMethod(895_0_power_Return(x0, x1), x2, x0, x1) → Cond_868_1_power_InvokeMethod1(x0 > 1, 895_0_power_Return(x0, x1), x2, x0, x1)
Cond_868_1_power_InvokeMethod1(TRUE, 895_0_power_Return(x0, x1), x2, x0, x1) → 895_0_power_Return(x0, x2)
868_1_power_InvokeMethod(951_0_power_Return, x1, x0, x2) → Cond_868_1_power_InvokeMethod2(x0 > 1, 951_0_power_Return, x1, x0, x2)
Cond_868_1_power_InvokeMethod2(TRUE, 951_0_power_Return, x1, x0, x2) → 895_0_power_Return(x0, x1)

The integer pair graph contains the following rules and edges:
(0): 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(x1[0] > 1 && !(x0[0] = 2) && 0 = x1[0] % 2, x0[0], x1[0])
(1): COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], x1[1] / 2)
(2): 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) && 1 = x1[2] % 2, x0[2], x1[2])
(3): COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], x1[3] - 1)
(4): 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(x1[4] > 1 && !(x0[4] = 2) && !(x1[4] % 2 = 1), x0[4], x1[4])
(5): 574_0_POWER_GT(x0[5], x1[5]) → COND_574_0_POWER_GT3(x1[5] > 1 && !(x0[5] = 2) && 0 = x1[5] % 2, x0[5], x1[5])
(6): COND_574_0_POWER_GT3(TRUE, x0[6], x1[6]) → 574_0_POWER_GT(x0[6], x1[6] / 2)
(7): 574_0_POWER_GT(x0[7], x1[7]) → COND_574_0_POWER_GT4(x1[7] > 0 && !(x1[7] = 1) && !(x0[7] = 2) && 1 = x1[7] % 2, x0[7], x1[7])
(8): COND_574_0_POWER_GT4(TRUE, x0[8], x1[8]) → 574_0_POWER_GT(x0[8], x1[8] - 1)
(9): 574_0_POWER_GT(x0[9], x1[9]) → COND_574_0_POWER_GT3(x1[9] > 1 && !(x0[9] = 2) && !(x1[9] % 2 = 1), x0[9], x1[9])

(0) -> (1), if ((x1[0] > 1 && !(x0[0] = 2) && 0 = x1[0] % 2* TRUE)∧(x0[0]* x0[1])∧(x1[0]* x1[1]))

(1) -> (0), if ((x0[1]* x0[0])∧(x1[1] / 2* x1[0]))

(1) -> (2), if ((x0[1]* x0[2])∧(x1[1] / 2* x1[2]))

(1) -> (4), if ((x0[1]* x0[4])∧(x1[1] / 2* x1[4]))

(1) -> (5), if ((x0[1]* x0[5])∧(x1[1] / 2* x1[5]))

(1) -> (7), if ((x0[1]* x0[7])∧(x1[1] / 2* x1[7]))

(1) -> (9), if ((x0[1]* x0[9])∧(x1[1] / 2* x1[9]))

(2) -> (3), if ((x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) && 1 = x1[2] % 2* TRUE)∧(x0[2]* x0[3])∧(x1[2]* x1[3]))

(3) -> (0), if ((x0[3]* x0[0])∧(x1[3] - 1* x1[0]))

(3) -> (2), if ((x0[3]* x0[2])∧(x1[3] - 1* x1[2]))

(3) -> (4), if ((x0[3]* x0[4])∧(x1[3] - 1* x1[4]))

(3) -> (5), if ((x0[3]* x0[5])∧(x1[3] - 1* x1[5]))

(3) -> (7), if ((x0[3]* x0[7])∧(x1[3] - 1* x1[7]))

(3) -> (9), if ((x0[3]* x0[9])∧(x1[3] - 1* x1[9]))

(4) -> (1), if ((x1[4] > 1 && !(x0[4] = 2) && !(x1[4] % 2 = 1) →* TRUE)∧(x0[4]* x0[1])∧(x1[4]* x1[1]))

(5) -> (6), if ((x1[5] > 1 && !(x0[5] = 2) && 0 = x1[5] % 2* TRUE)∧(x0[5]* x0[6])∧(x1[5]* x1[6]))

(6) -> (0), if ((x0[6]* x0[0])∧(x1[6] / 2* x1[0]))

(6) -> (2), if ((x0[6]* x0[2])∧(x1[6] / 2* x1[2]))

(6) -> (4), if ((x0[6]* x0[4])∧(x1[6] / 2* x1[4]))

(6) -> (5), if ((x0[6]* x0[5])∧(x1[6] / 2* x1[5]))

(6) -> (7), if ((x0[6]* x0[7])∧(x1[6] / 2* x1[7]))

(6) -> (9), if ((x0[6]* x0[9])∧(x1[6] / 2* x1[9]))

(7) -> (8), if ((x1[7] > 0 && !(x1[7] = 1) && !(x0[7] = 2) && 1 = x1[7] % 2* TRUE)∧(x0[7]* x0[8])∧(x1[7]* x1[8]))

(8) -> (0), if ((x0[8]* x0[0])∧(x1[8] - 1* x1[0]))

(8) -> (2), if ((x0[8]* x0[2])∧(x1[8] - 1* x1[2]))

(8) -> (4), if ((x0[8]* x0[4])∧(x1[8] - 1* x1[4]))

(8) -> (5), if ((x0[8]* x0[5])∧(x1[8] - 1* x1[5]))

(8) -> (7), if ((x0[8]* x0[7])∧(x1[8] - 1* x1[7]))

(8) -> (9), if ((x0[8]* x0[9])∧(x1[8] - 1* x1[9]))

(9) -> (6), if ((x1[9] > 1 && !(x0[9] = 2) && !(x1[9] % 2 = 1) →* TRUE)∧(x0[9]* x0[6])∧(x1[9]* x1[6]))

The set Q consists of the following terms:
574_0_power_GT(x0, 0)
827_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
827_1_power_InvokeMethod(969_0_power_Return(x0, x1), x0, x1)
827_1_power_InvokeMethod(1056_0_power_Return, x0, x1)
855_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_855_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
855_1_power_InvokeMethod(969_0_power_Return(x0, x1), x2, x0, x1)
Cond_855_1_power_InvokeMethod1(TRUE, 969_0_power_Return(x0, x1), x2, x0, x1)
855_1_power_InvokeMethod(1056_0_power_Return, x0, x1, x2)
Cond_855_1_power_InvokeMethod2(TRUE, 1056_0_power_Return, x0, x1, x2)
840_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
Cond_840_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x0, 1)
840_1_power_InvokeMethod(895_0_power_Return(x0, x1), x0, x1)
840_1_power_InvokeMethod(951_0_power_Return, x0, x1)
868_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_868_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
868_1_power_InvokeMethod(895_0_power_Return(x0, x1), x2, x0, x1)
Cond_868_1_power_InvokeMethod1(TRUE, 895_0_power_Return(x0, x1), x2, x0, x1)
868_1_power_InvokeMethod(951_0_power_Return, x0, x1, x2)
Cond_868_1_power_InvokeMethod2(TRUE, 951_0_power_Return, x0, x1, x2)

### (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 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT(&&(&&(>(x1, 1), !(=(x0, 2))), =(0, %(x1, 2))), x0, x1) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0]), COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:

(1)    (&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2)))=TRUEx0[0]=x0[1]x1[0]=x1[1]574_0_POWER_GT(x0[0], x1[0])≥NonInfC∧574_0_POWER_GT(x0[0], x1[0])≥COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:

(2)    (>(x1[0], 1)=TRUE>=(0, %(x1[0], 2))=TRUE<=(0, %(x1[0], 2))=TRUE<(x0[0], 2)=TRUE574_0_POWER_GT(x0[0], x1[0])≥NonInfC∧574_0_POWER_GT(x0[0], x1[0])≥COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥))

(3)    (>(x1[0], 1)=TRUE>=(0, %(x1[0], 2))=TRUE<=(0, %(x1[0], 2))=TRUE>(x0[0], 2)=TRUE574_0_POWER_GT(x0[0], x1[0])≥NonInfC∧574_0_POWER_GT(x0[0], x1[0])≥COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(4)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (3) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(5)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (4) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(6)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (5) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(7)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (6) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(8)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (7) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(9)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(10)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (9) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(11)    (x1[0] ≥ 0∧x0[0] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (10) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(12)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

(13)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (12) using rule (IDP_POLY_GCD) which results in the following new constraint:

(14)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (13) using rule (IDP_POLY_GCD) which results in the following new constraint:

(15)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (11) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(16)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

We simplified constraint (16) using rule (IDP_POLY_GCD) which results in the following new constraint:

(17)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

For Pair COND_574_0_POWER_GT(TRUE, x0, x1) → 574_0_POWER_GT(x0, /(x1, 2)) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0]), COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:

(18)    (&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2)))=TRUEx0[0]=x0[1]x1[0]=x1[1]COND_574_0_POWER_GT(TRUE, x0[1], x1[1])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[1], x1[1])≥574_0_POWER_GT(x0[1], /(x1[1], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (18) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:

(19)    (>(x1[0], 1)=TRUE>=(0, %(x1[0], 2))=TRUE<=(0, %(x1[0], 2))=TRUE<(x0[0], 2)=TRUECOND_574_0_POWER_GT(TRUE, x0[0], x1[0])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[0], x1[0])≥574_0_POWER_GT(x0[0], /(x1[0], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

(20)    (>(x1[0], 1)=TRUE>=(0, %(x1[0], 2))=TRUE<=(0, %(x1[0], 2))=TRUE>(x0[0], 2)=TRUECOND_574_0_POWER_GT(TRUE, x0[0], x1[0])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[0], x1[0])≥574_0_POWER_GT(x0[0], /(x1[0], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (19) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(21)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (20) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(22)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(23)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (22) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(24)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (23) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(25)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (24) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(26)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(27)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (26) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(28)    (x1[0] ≥ 0∧x0[0] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (27) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(29)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

(30)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (29) using rule (IDP_POLY_GCD) which results in the following new constraint:

(31)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (30) using rule (IDP_POLY_GCD) which results in the following new constraint:

(32)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (28) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(33)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (33) using rule (IDP_POLY_GCD) which results in the following new constraint:

(34)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)

• We consider the chain 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4]), COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:

(35)    (&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1)))=TRUEx0[4]=x0[1]x1[4]=x1[1]COND_574_0_POWER_GT(TRUE, x0[1], x1[1])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[1], x1[1])≥574_0_POWER_GT(x0[1], /(x1[1], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (35) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:

(36)    (>(x1[4], 1)=TRUE<(%(x1[4], 2), 1)=TRUE<(x0[4], 2)=TRUECOND_574_0_POWER_GT(TRUE, x0[4], x1[4])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[4], x1[4])≥574_0_POWER_GT(x0[4], /(x1[4], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

(37)    (>(x1[4], 1)=TRUE<(%(x1[4], 2), 1)=TRUE>(x0[4], 2)=TRUECOND_574_0_POWER_GT(TRUE, x0[4], x1[4])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[4], x1[4])≥574_0_POWER_GT(x0[4], /(x1[4], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (36) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(38)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (37) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(39)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (38) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(40)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(41)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(43)    (x1[4] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (44) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(45)    (x1[4] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(46)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (41) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(47)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(48)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (45) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(49)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (46) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(50)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (47) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(51)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(52)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (49) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(53)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (50) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(54)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

(55)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (54) using rule (IDP_POLY_GCD) which results in the following new constraint:

(56)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (55) using rule (IDP_POLY_GCD) which results in the following new constraint:

(57)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (51) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(58)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (58) using rule (IDP_POLY_GCD) which results in the following new constraint:

(59)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (52) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(60)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

(61)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (60) using rule (IDP_POLY_GCD) which results in the following new constraint:

(62)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (61) using rule (IDP_POLY_GCD) which results in the following new constraint:

(63)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (53) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(64)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

We simplified constraint (64) using rule (IDP_POLY_GCD) which results in the following new constraint:

(65)    (x1[4] ≥ 0∧x0[4] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

For Pair 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), =(1, %(x1, 2))), x0, x1) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2]), COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1)) which results in the following constraint:

(66)    (&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2)))=TRUEx0[2]=x0[3]x1[2]=x1[3]574_0_POWER_GT(x0[2], x1[2])≥NonInfC∧574_0_POWER_GT(x0[2], x1[2])≥COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])∧(UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥))

We simplified constraint (66) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:

(67)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE<(x1[2], 1)=TRUE574_0_POWER_GT(x0[2], x1[2])≥NonInfC∧574_0_POWER_GT(x0[2], x1[2])≥COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])∧(UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥))

(68)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE>(x1[2], 1)=TRUE574_0_POWER_GT(x0[2], x1[2])≥NonInfC∧574_0_POWER_GT(x0[2], x1[2])≥COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])∧(UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥))

We simplified constraint (67) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(69)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (68) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(70)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (69) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(71)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (70) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(72)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (73) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(74)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (75) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(76)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We solved constraint (71) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (72) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(77)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We solved constraint (74) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (76) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(78)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (77) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(79)    (x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (78) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(80)    (x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (79) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(81)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (81) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(82)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

(83)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (82) using rule (IDP_POLY_GCD) which results in the following new constraint:

(84)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (83) using rule (IDP_POLY_GCD) which results in the following new constraint:

(85)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (80) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(86)    ([1] + x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (86) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(87)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

We simplified constraint (87) using rule (IDP_POLY_GCD) which results in the following new constraint:

(88)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

For Pair COND_574_0_POWER_GT1(TRUE, x0, x1) → 574_0_POWER_GT(x0, -(x1, 1)) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2]), COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1)) which results in the following constraint:

(89)    (&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2)))=TRUEx0[2]=x0[3]x1[2]=x1[3]COND_574_0_POWER_GT1(TRUE, x0[3], x1[3])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[3], x1[3])≥574_0_POWER_GT(x0[3], -(x1[3], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (89) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:

(90)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE<(x1[2], 1)=TRUECOND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥574_0_POWER_GT(x0[2], -(x1[2], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

(91)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE>(x1[2], 1)=TRUECOND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥574_0_POWER_GT(x0[2], -(x1[2], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (90) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(92)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (91) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(93)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (92) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(94)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (93) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(95)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (96) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(97)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (98) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(99)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We solved constraint (94) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (95) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(100)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We solved constraint (97) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (99) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(101)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (100) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(102)    (x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (101) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(103)    (x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (102) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(104)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (104) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(105)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

(106)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (105) using rule (IDP_POLY_GCD) which results in the following new constraint:

(107)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (106) using rule (IDP_POLY_GCD) which results in the following new constraint:

(108)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (103) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(109)    ([1] + x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (109) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(110)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

We simplified constraint (110) using rule (IDP_POLY_GCD) which results in the following new constraint:

(111)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

For Pair 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT(&&(&&(>(x1, 1), !(=(x0, 2))), !(=(%(x1, 2), 1))), x0, x1) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4]), COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:

(112)    (&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1)))=TRUEx0[4]=x0[1]x1[4]=x1[1]574_0_POWER_GT(x0[4], x1[4])≥NonInfC∧574_0_POWER_GT(x0[4], x1[4])≥COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥))

We simplified constraint (112) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:

(113)    (>(x1[4], 1)=TRUE<(%(x1[4], 2), 1)=TRUE<(x0[4], 2)=TRUE574_0_POWER_GT(x0[4], x1[4])≥NonInfC∧574_0_POWER_GT(x0[4], x1[4])≥COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥))

(114)    (>(x1[4], 1)=TRUE<(%(x1[4], 2), 1)=TRUE>(x0[4], 2)=TRUE574_0_POWER_GT(x0[4], x1[4])≥NonInfC∧574_0_POWER_GT(x0[4], x1[4])≥COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥))

We simplified constraint (113) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(115)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (114) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(116)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (115) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(117)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (116) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(118)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (119) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(120)    (x1[4] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (121) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(122)    (x1[4] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (117) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(123)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (118) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(124)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (120) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(125)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (122) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(126)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (123) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(127)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (124) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(128)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (125) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(129)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (126) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(130)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (127) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(131)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

(132)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (131) using rule (IDP_POLY_GCD) which results in the following new constraint:

(133)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (132) using rule (IDP_POLY_GCD) which results in the following new constraint:

(134)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (128) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(135)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (135) using rule (IDP_POLY_GCD) which results in the following new constraint:

(136)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (129) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(137)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

(138)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (137) using rule (IDP_POLY_GCD) which results in the following new constraint:

(139)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (138) using rule (IDP_POLY_GCD) which results in the following new constraint:

(140)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (130) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(141)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

We simplified constraint (141) using rule (IDP_POLY_GCD) which results in the following new constraint:

(142)    (x1[4] ≥ 0∧x0[4] ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

For Pair 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT3(&&(&&(>(x1, 1), !(=(x0, 2))), =(0, %(x1, 2))), x0, x1) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[5], x1[5]) → COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5]), COND_574_0_POWER_GT3(TRUE, x0[6], x1[6]) → 574_0_POWER_GT(x0[6], /(x1[6], 2)) which results in the following constraint:

(143)    (&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2)))=TRUEx0[5]=x0[6]x1[5]=x1[6]574_0_POWER_GT(x0[5], x1[5])≥NonInfC∧574_0_POWER_GT(x0[5], x1[5])≥COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])∧(UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥))

We simplified constraint (143) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:

(144)    (>(x1[5], 1)=TRUE>=(0, %(x1[5], 2))=TRUE<=(0, %(x1[5], 2))=TRUE<(x0[5], 2)=TRUE574_0_POWER_GT(x0[5], x1[5])≥NonInfC∧574_0_POWER_GT(x0[5], x1[5])≥COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])∧(UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥))

(145)    (>(x1[5], 1)=TRUE>=(0, %(x1[5], 2))=TRUE<=(0, %(x1[5], 2))=TRUE>(x0[5], 2)=TRUE574_0_POWER_GT(x0[5], x1[5])≥NonInfC∧574_0_POWER_GT(x0[5], x1[5])≥COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])∧(UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥))

We simplified constraint (144) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(146)    (x1[5] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[5] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (145) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(147)    (x1[5] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[5] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (146) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(148)    (x1[5] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[5] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (147) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(149)    (x1[5] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[5] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (148) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(150)    (x1[5] + [-2] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (149) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(151)    (x1[5] + [-2] ≥ 0∧x0[5] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (150) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(152)    (x1[5] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (151) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(153)    (x1[5] ≥ 0∧x0[5] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (152) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(154)    (x1[5] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧x0[5] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

(155)    (x1[5] ≥ 0∧[1] + x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧x0[5] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (154) using rule (IDP_POLY_GCD) which results in the following new constraint:

(156)    (x1[5] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (155) using rule (IDP_POLY_GCD) which results in the following new constraint:

(157)    (x1[5] ≥ 0∧[1] + x0[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (153) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(158)    (x1[5] ≥ 0∧x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

We simplified constraint (158) using rule (IDP_POLY_GCD) which results in the following new constraint:

(159)    (x1[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

For Pair COND_574_0_POWER_GT3(TRUE, x0, x1) → 574_0_POWER_GT(x0, /(x1, 2)) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[5], x1[5]) → COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5]), COND_574_0_POWER_GT3(TRUE, x0[6], x1[6]) → 574_0_POWER_GT(x0[6], /(x1[6], 2)) which results in the following constraint:

(160)    (&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2)))=TRUEx0[5]=x0[6]x1[5]=x1[6]COND_574_0_POWER_GT3(TRUE, x0[6], x1[6])≥NonInfC∧COND_574_0_POWER_GT3(TRUE, x0[6], x1[6])≥574_0_POWER_GT(x0[6], /(x1[6], 2))∧(UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥))

We simplified constraint (160) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:

(161)    (>(x1[5], 1)=TRUE>=(0, %(x1[5], 2))=TRUE<=(0, %(x1[5], 2))=TRUE<(x0[5], 2)=TRUECOND_574_0_POWER_GT3(TRUE, x0[5], x1[5])≥NonInfC∧COND_574_0_POWER_GT3(TRUE, x0[5], x1[5])≥574_0_POWER_GT(x0[5], /(x1[5], 2))∧(UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥))

(162)    (>(x1[5], 1)=TRUE>=(0, %(x1[5], 2))=TRUE<=(0, %(x1[5], 2))=TRUE>(x0[5], 2)=TRUECOND_574_0_POWER_GT3(TRUE, x0[5], x1[5])≥NonInfC∧COND_574_0_POWER_GT3(TRUE, x0[5], x1[5])≥574_0_POWER_GT(x0[5], /(x1[5], 2))∧(UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥))

We simplified constraint (161) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(163)    (x1[5] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] + x1[5] + [-1]max{x1[5], [-1]x1[5]} ≥ 0)

We simplified constraint (162) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(164)    (x1[5] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[5] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] + x1[5] + [-1]max{x1[5], [-1]x1[5]} ≥ 0)

We simplified constraint (163) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(165)    (x1[5] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] + x1[5] + [-1]max{x1[5], [-1]x1[5]} ≥ 0)

We simplified constraint (164) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(166)    (x1[5] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[5] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] + x1[5] + [-1]max{x1[5], [-1]x1[5]} ≥ 0)

We simplified constraint (165) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(167)    (x1[5] + [-2] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[2]x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (166) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(168)    (x1[5] + [-2] ≥ 0∧x0[5] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[2]x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (167) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(169)    (x1[5] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (168) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(170)    (x1[5] ≥ 0∧x0[5] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (169) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(171)    (x1[5] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

(172)    (x1[5] ≥ 0∧[1] + x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (171) using rule (IDP_POLY_GCD) which results in the following new constraint:

(173)    (x1[5] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (172) using rule (IDP_POLY_GCD) which results in the following new constraint:

(174)    (x1[5] ≥ 0∧[1] + x0[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (170) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(175)    (x1[5] ≥ 0∧x0[5] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (175) using rule (IDP_POLY_GCD) which results in the following new constraint:

(176)    (x1[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)

• We consider the chain 574_0_POWER_GT(x0[9], x1[9]) → COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9]), COND_574_0_POWER_GT3(TRUE, x0[6], x1[6]) → 574_0_POWER_GT(x0[6], /(x1[6], 2)) which results in the following constraint:

(177)    (&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1)))=TRUEx0[9]=x0[6]x1[9]=x1[6]COND_574_0_POWER_GT3(TRUE, x0[6], x1[6])≥NonInfC∧COND_574_0_POWER_GT3(TRUE, x0[6], x1[6])≥574_0_POWER_GT(x0[6], /(x1[6], 2))∧(UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥))

We simplified constraint (177) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:

(178)    (>(x1[9], 1)=TRUE<(%(x1[9], 2), 1)=TRUE<(x0[9], 2)=TRUECOND_574_0_POWER_GT3(TRUE, x0[9], x1[9])≥NonInfC∧COND_574_0_POWER_GT3(TRUE, x0[9], x1[9])≥574_0_POWER_GT(x0[9], /(x1[9], 2))∧(UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥))

(179)    (>(x1[9], 1)=TRUE<(%(x1[9], 2), 1)=TRUE>(x0[9], 2)=TRUECOND_574_0_POWER_GT3(TRUE, x0[9], x1[9])≥NonInfC∧COND_574_0_POWER_GT3(TRUE, x0[9], x1[9])≥574_0_POWER_GT(x0[9], /(x1[9], 2))∧(UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥))

We simplified constraint (178) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(180)    (x1[9] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] + x1[9] + [-1]max{x1[9], [-1]x1[9]} ≥ 0)

We simplified constraint (179) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(181)    (x1[9] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[9] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] + x1[9] + [-1]max{x1[9], [-1]x1[9]} ≥ 0)

We simplified constraint (180) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(182)    (x1[9] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] + x1[9] + [-1]max{x1[9], [-1]x1[9]} ≥ 0)

We simplified constraint (181) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(183)    (x1[9] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[9] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] + x1[9] + [-1]max{x1[9], [-1]x1[9]} ≥ 0)

We simplified constraint (184) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(185)    (x1[9] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧[1] + [-1]x0[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] + x1[9] + [-1]max{x1[9], [-1]x1[9]} ≥ 0)

We simplified constraint (186) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(187)    (x1[9] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧x0[9] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] + x1[9] + [-1]max{x1[9], [-1]x1[9]} ≥ 0)

We simplified constraint (182) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(188)    (x1[9] + [-2] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (183) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(189)    (x1[9] + [-2] ≥ 0∧x0[9] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (185) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(190)    (x1[9] + [-2] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (187) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(191)    (x1[9] + [-2] ≥ 0∧x0[9] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[(-1)bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (188) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(192)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (189) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(193)    (x1[9] ≥ 0∧x0[9] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (190) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(194)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (191) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(195)    (x1[9] ≥ 0∧x0[9] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (192) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(196)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[9] ≥ 0∧x0[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

(197)    (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[9] ≥ 0∧x0[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (196) using rule (IDP_POLY_GCD) which results in the following new constraint:

(198)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (197) using rule (IDP_POLY_GCD) which results in the following new constraint:

(199)    (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (193) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(200)    (x1[9] ≥ 0∧x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (200) using rule (IDP_POLY_GCD) which results in the following new constraint:

(201)    (x1[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (194) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(202)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[9] ≥ 0∧x0[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

(203)    (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[9] ≥ 0∧x0[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (202) using rule (IDP_POLY_GCD) which results in the following new constraint:

(204)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (203) using rule (IDP_POLY_GCD) which results in the following new constraint:

(205)    (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (195) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(206)    (x1[9] ≥ 0∧x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

We simplified constraint (206) using rule (IDP_POLY_GCD) which results in the following new constraint:

(207)    (x1[9] ≥ 0∧x0[9] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

For Pair 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT4(&&(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), =(1, %(x1, 2))), x0, x1) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[7], x1[7]) → COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7]), COND_574_0_POWER_GT4(TRUE, x0[8], x1[8]) → 574_0_POWER_GT(x0[8], -(x1[8], 1)) which results in the following constraint:

(208)    (&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2)))=TRUEx0[7]=x0[8]x1[7]=x1[8]574_0_POWER_GT(x0[7], x1[7])≥NonInfC∧574_0_POWER_GT(x0[7], x1[7])≥COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])∧(UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥))

We simplified constraint (208) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:

(209)    (>=(1, %(x1[7], 2))=TRUE<=(1, %(x1[7], 2))=TRUE>(x1[7], 0)=TRUE<(x0[7], 2)=TRUE<(x1[7], 1)=TRUE574_0_POWER_GT(x0[7], x1[7])≥NonInfC∧574_0_POWER_GT(x0[7], x1[7])≥COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])∧(UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥))

(210)    (>=(1, %(x1[7], 2))=TRUE<=(1, %(x1[7], 2))=TRUE>(x1[7], 0)=TRUE<(x0[7], 2)=TRUE>(x1[7], 1)=TRUE574_0_POWER_GT(x0[7], x1[7])≥NonInfC∧574_0_POWER_GT(x0[7], x1[7])≥COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])∧(UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥))

We simplified constraint (209) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(211)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧[-1]x1[7] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (210) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(212)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] + [-2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (211) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(213)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧[-1]x1[7] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (212) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(214)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] + [-2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (215) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(216)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧x0[7] + [-3] ≥ 0∧[-1]x1[7] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (217) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(218)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧x0[7] + [-3] ≥ 0∧x1[7] + [-2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We solved constraint (213) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (214) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(219)    (x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We solved constraint (216) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (218) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(220)    (x1[7] + [-1] ≥ 0∧x0[7] + [-3] ≥ 0∧x1[7] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (219) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(221)    (x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧[-1] + x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (220) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(222)    (x1[7] ≥ 0∧x0[7] + [-3] ≥ 0∧[-1] + x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (221) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(223)    ([1] + x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (223) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(224)    ([1] + x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

(225)    ([1] + x1[7] ≥ 0∧[1] + x0[7] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (224) using rule (IDP_POLY_GCD) which results in the following new constraint:

(226)    ([1] + x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (225) using rule (IDP_POLY_GCD) which results in the following new constraint:

(227)    ([1] + x1[7] ≥ 0∧[1] + x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (222) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(228)    ([1] + x1[7] ≥ 0∧x0[7] + [-3] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (228) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(229)    ([1] + x1[7] ≥ 0∧x0[7] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

We simplified constraint (229) using rule (IDP_POLY_GCD) which results in the following new constraint:

(230)    ([1] + x1[7] ≥ 0∧x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

For Pair COND_574_0_POWER_GT4(TRUE, x0, x1) → 574_0_POWER_GT(x0, -(x1, 1)) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[7], x1[7]) → COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7]), COND_574_0_POWER_GT4(TRUE, x0[8], x1[8]) → 574_0_POWER_GT(x0[8], -(x1[8], 1)) which results in the following constraint:

(231)    (&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2)))=TRUEx0[7]=x0[8]x1[7]=x1[8]COND_574_0_POWER_GT4(TRUE, x0[8], x1[8])≥NonInfC∧COND_574_0_POWER_GT4(TRUE, x0[8], x1[8])≥574_0_POWER_GT(x0[8], -(x1[8], 1))∧(UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥))

We simplified constraint (231) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:

(232)    (>=(1, %(x1[7], 2))=TRUE<=(1, %(x1[7], 2))=TRUE>(x1[7], 0)=TRUE<(x0[7], 2)=TRUE<(x1[7], 1)=TRUECOND_574_0_POWER_GT4(TRUE, x0[7], x1[7])≥NonInfC∧COND_574_0_POWER_GT4(TRUE, x0[7], x1[7])≥574_0_POWER_GT(x0[7], -(x1[7], 1))∧(UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥))

(233)    (>=(1, %(x1[7], 2))=TRUE<=(1, %(x1[7], 2))=TRUE>(x1[7], 0)=TRUE<(x0[7], 2)=TRUE>(x1[7], 1)=TRUECOND_574_0_POWER_GT4(TRUE, x0[7], x1[7])≥NonInfC∧COND_574_0_POWER_GT4(TRUE, x0[7], x1[7])≥574_0_POWER_GT(x0[7], -(x1[7], 1))∧(UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥))

We simplified constraint (232) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(234)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧[-1]x1[7] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (233) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(235)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (234) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(236)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧[-1]x1[7] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (235) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(237)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (238) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(239)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧x0[7] + [-3] ≥ 0∧[-1]x1[7] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (240) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(241)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[7] + [-1] ≥ 0∧x0[7] + [-3] ≥ 0∧x1[7] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We solved constraint (236) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (237) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(242)    (x1[7] + [-1] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We solved constraint (239) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (241) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(243)    (x1[7] + [-1] ≥ 0∧x0[7] + [-3] ≥ 0∧x1[7] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (242) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(244)    (x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧[-1] + x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (243) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(245)    (x1[7] ≥ 0∧x0[7] + [-3] ≥ 0∧[-1] + x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[(-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (244) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(246)    ([1] + x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (246) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(247)    ([1] + x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

(248)    ([1] + x1[7] ≥ 0∧[1] + x0[7] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (247) using rule (IDP_POLY_GCD) which results in the following new constraint:

(249)    ([1] + x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (248) using rule (IDP_POLY_GCD) which results in the following new constraint:

(250)    ([1] + x1[7] ≥ 0∧[1] + x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (245) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(251)    ([1] + x1[7] ≥ 0∧x0[7] + [-3] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (251) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(252)    ([1] + x1[7] ≥ 0∧x0[7] ≥ 0∧x1[7] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

We simplified constraint (252) using rule (IDP_POLY_GCD) which results in the following new constraint:

(253)    ([1] + x1[7] ≥ 0∧x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

For Pair 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT3(&&(&&(>(x1, 1), !(=(x0, 2))), !(=(%(x1, 2), 1))), x0, x1) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[9], x1[9]) → COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9]), COND_574_0_POWER_GT3(TRUE, x0[6], x1[6]) → 574_0_POWER_GT(x0[6], /(x1[6], 2)) which results in the following constraint:

(254)    (&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1)))=TRUEx0[9]=x0[6]x1[9]=x1[6]574_0_POWER_GT(x0[9], x1[9])≥NonInfC∧574_0_POWER_GT(x0[9], x1[9])≥COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])∧(UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥))

We simplified constraint (254) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:

(255)    (>(x1[9], 1)=TRUE<(%(x1[9], 2), 1)=TRUE<(x0[9], 2)=TRUE574_0_POWER_GT(x0[9], x1[9])≥NonInfC∧574_0_POWER_GT(x0[9], x1[9])≥COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])∧(UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥))

(256)    (>(x1[9], 1)=TRUE<(%(x1[9], 2), 1)=TRUE>(x0[9], 2)=TRUE574_0_POWER_GT(x0[9], x1[9])≥NonInfC∧574_0_POWER_GT(x0[9], x1[9])≥COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])∧(UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥))

We simplified constraint (255) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(257)    (x1[9] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[9] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (256) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(258)    (x1[9] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[9] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (257) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(259)    (x1[9] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[9] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (258) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(260)    (x1[9] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[9] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (261) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(262)    (x1[9] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧[1] + [-1]x0[9] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (263) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(264)    (x1[9] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧x0[9] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (259) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(265)    (x1[9] + [-2] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (260) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(266)    (x1[9] + [-2] ≥ 0∧x0[9] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (262) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(267)    (x1[9] + [-2] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (264) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(268)    (x1[9] + [-2] ≥ 0∧x0[9] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (265) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(269)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (266) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(270)    (x1[9] ≥ 0∧x0[9] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (267) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(271)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (268) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(272)    (x1[9] ≥ 0∧x0[9] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (269) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(273)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧x0[9] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

(274)    (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧x0[9] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (273) using rule (IDP_POLY_GCD) which results in the following new constraint:

(275)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (274) using rule (IDP_POLY_GCD) which results in the following new constraint:

(276)    (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (270) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(277)    (x1[9] ≥ 0∧x0[9] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (277) using rule (IDP_POLY_GCD) which results in the following new constraint:

(278)    (x1[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (271) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(279)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

(280)    (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (279) using rule (IDP_POLY_GCD) which results in the following new constraint:

(281)    (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (280) using rule (IDP_POLY_GCD) which results in the following new constraint:

(282)    (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (272) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(283)    (x1[9] ≥ 0∧x0[9] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

We simplified constraint (283) using rule (IDP_POLY_GCD) which results in the following new constraint:

(284)    (x1[9] ≥ 0∧x0[9] ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT(&&(&&(>(x1, 1), !(=(x0, 2))), =(0, %(x1, 2))), x0, x1)
• (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)
• (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)
• (x1[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_101 + (2)bni_101] + [bni_101]x1[0] ≥ 0∧[(-1)bso_102] ≥ 0)

• COND_574_0_POWER_GT(TRUE, x0, x1) → 574_0_POWER_GT(x0, /(x1, 2))
• (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)
• (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)
• (x1[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[0] ≥ 0∧[(-1)bso_107] ≥ 0)
• (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)
• (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)
• (x1[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)
• (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)
• (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)
• (x1[4] ≥ 0∧x0[4] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_103 + (-1)Bound*bni_103] + [bni_103]x1[4] ≥ 0∧[(-1)bso_107] ≥ 0)

• 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), =(1, %(x1, 2))), x0, x1)
• ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)
• ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)
• ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_108 + (2)bni_108] + [bni_108]x1[2] ≥ 0∧[(-1)bso_109] ≥ 0)

• COND_574_0_POWER_GT1(TRUE, x0, x1) → 574_0_POWER_GT(x0, -(x1, 1))
• ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)
• ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)
• ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_110 + (-1)Bound*bni_110] + [bni_110]x1[2] ≥ 0∧[(-1)bso_111] ≥ 0)

• 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT(&&(&&(>(x1, 1), !(=(x0, 2))), !(=(%(x1, 2), 1))), x0, x1)
• (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)
• (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)
• (x1[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)
• (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)
• (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)
• (x1[4] ≥ 0∧x0[4] ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)Bound*bni_112 + (2)bni_112] + [bni_112]x1[4] ≥ 0∧[(-1)bso_113] ≥ 0)

• 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT3(&&(&&(>(x1, 1), !(=(x0, 2))), =(0, %(x1, 2))), x0, x1)
• (x1[5] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)
• (x1[5] ≥ 0∧[1] + x0[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)
• (x1[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])), ≥)∧[(-1)Bound*bni_114 + (2)bni_114] + [bni_114]x1[5] ≥ 0∧[1 + (-1)bso_115] ≥ 0)

• COND_574_0_POWER_GT3(TRUE, x0, x1) → 574_0_POWER_GT(x0, /(x1, 2))
• (x1[5] ≥ 0∧[1] + [-1]x0[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)
• (x1[5] ≥ 0∧[1] + x0[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)
• (x1[5] ≥ 0∧x0[5] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[5] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[5] ≥ 0∧[(-1)bso_117] ≥ 0)
• (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)
• (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)
• (x1[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)
• (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)
• (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)
• (x1[9] ≥ 0∧x0[9] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧[2] + x1[9] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[6], /(x1[6], 2))), ≥)∧[bni_116 + (-1)Bound*bni_116] + [bni_116]x1[9] ≥ 0∧[(-1)bso_117] ≥ 0)

• 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT4(&&(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), =(1, %(x1, 2))), x0, x1)
• ([1] + x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)
• ([1] + x1[7] ≥ 0∧[1] + x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)
• ([1] + x1[7] ≥ 0∧x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])), ≥)∧[(-1)Bound*bni_118 + (2)bni_118] + [bni_118]x1[7] ≥ 0∧[1 + (-1)bso_119] ≥ 0)

• COND_574_0_POWER_GT4(TRUE, x0, x1) → 574_0_POWER_GT(x0, -(x1, 1))
• ([1] + x1[7] ≥ 0∧[1] + [-1]x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)
• ([1] + x1[7] ≥ 0∧[1] + x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧x0[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)
• ([1] + x1[7] ≥ 0∧x0[7] ≥ 0∧x1[7] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[8], -(x1[8], 1))), ≥)∧[bni_120 + (-1)Bound*bni_120] + [bni_120]x1[7] ≥ 0∧[(-1)bso_121] ≥ 0)

• 574_0_POWER_GT(x0, x1) → COND_574_0_POWER_GT3(&&(&&(>(x1, 1), !(=(x0, 2))), !(=(%(x1, 2), 1))), x0, x1)
• (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)
• (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)
• (x1[9] ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)
• (x1[9] ≥ 0∧[1] + [-1]x0[9] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)
• (x1[9] ≥ 0∧[1] + x0[9] ≥ 0∧0 ≥ 0∧x0[9] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 0)
• (x1[9] ≥ 0∧x0[9] ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])), ≥)∧[(-1)Bound*bni_122 + (2)bni_122] + [bni_122]x1[9] ≥ 0∧[1 + (-1)bso_123] ≥ 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) = [3]
POL(574_0_power_GT(x1, x2)) = [-1] + [-1]x2 + [-1]x1
POL(0) = 0
POL(587_0_power_Return(x1)) = [-1] + [-1]x1
POL(827_1_power_InvokeMethod(x1, x2, x3)) = [-1] + [-1]x3 + [-1]x2 + [-1]x1
POL(644_0_power_Return(x1)) = [-1] + [-1]x1
POL(1) = [1]
POL(1056_0_power_Return) = [-1]
POL(969_0_power_Return(x1, x2)) = [-1] + [-1]x2 + [-1]x1
POL(855_1_power_InvokeMethod(x1, x2, x3, x4)) = [-1] + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(Cond_855_1_power_InvokeMethod(x1, x2, x3, x4, x5)) = [-1] + [-1]x5 + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(<=(x1, x2)) = [-1]
POL(Cond_855_1_power_InvokeMethod1(x1, x2, x3, x4, x5)) = [-1] + [-1]x5 + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(Cond_855_1_power_InvokeMethod2(x1, x2, x3, x4, x5)) = [-1] + [-1]x5 + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(840_1_power_InvokeMethod(x1, x2, x3)) = [-1] + [-1]x3 + [-1]x2 + [-1]x1
POL(Cond_840_1_power_InvokeMethod(x1, x2, x3, x4)) = [-1] + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(>(x1, x2)) = [-1]
POL(951_0_power_Return) = [-1]
POL(895_0_power_Return(x1, x2)) = [-1] + [-1]x2 + [-1]x1
POL(868_1_power_InvokeMethod(x1, x2, x3, x4)) = [-1] + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(Cond_868_1_power_InvokeMethod(x1, x2, x3, x4, x5)) = [-1] + [-1]x5 + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(Cond_868_1_power_InvokeMethod1(x1, x2, x3, x4, x5)) = [-1] + [-1]x5 + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(Cond_868_1_power_InvokeMethod2(x1, x2, x3, x4, x5)) = [-1] + [-1]x5 + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1
POL(574_0_POWER_GT(x1, x2)) = x2
POL(COND_574_0_POWER_GT(x1, x2, x3)) = [-1] + x3 + [-1]x1
POL(&&(x1, x2)) = [-1]
POL(!(x1)) = [-1]
POL(=(x1, x2)) = [-1]
POL(2) = [2]
POL(COND_574_0_POWER_GT1(x1, x2, x3)) = [-1] + x3 + [-1]x1
POL(-(x1, x2)) = x1 + [-1]x2
POL(COND_574_0_POWER_GT3(x1, x2, x3)) = [-1] + x3
POL(COND_574_0_POWER_GT4(x1, x2, x3)) = [-1] + x3

Polynomial Interpretations with Context Sensitive Arithemetic Replacement
POL(TermCSAR-Mode @ Context)

POL(%(x1, 2)-1 @ {}) = min{x2, [-1]x2}
POL(%(x1, 2)1 @ {}) = max{x2, [-1]x2}
POL(/(x1, 2)1 @ {574_0_POWER_GT_2/1}) = max{x1, [-1]x1} + [-1]

The following pairs are in P>:

574_0_POWER_GT(x0[5], x1[5]) → COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])
574_0_POWER_GT(x0[7], x1[7]) → COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])
574_0_POWER_GT(x0[9], x1[9]) → COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])

The following pairs are in Pbound:

574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])
COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2))
574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])
COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1))
574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])
574_0_POWER_GT(x0[5], x1[5]) → COND_574_0_POWER_GT3(&&(&&(>(x1[5], 1), !(=(x0[5], 2))), =(0, %(x1[5], 2))), x0[5], x1[5])
COND_574_0_POWER_GT3(TRUE, x0[6], x1[6]) → 574_0_POWER_GT(x0[6], /(x1[6], 2))
574_0_POWER_GT(x0[7], x1[7]) → COND_574_0_POWER_GT4(&&(&&(&&(>(x1[7], 0), !(=(x1[7], 1))), !(=(x0[7], 2))), =(1, %(x1[7], 2))), x0[7], x1[7])
COND_574_0_POWER_GT4(TRUE, x0[8], x1[8]) → 574_0_POWER_GT(x0[8], -(x1[8], 1))
574_0_POWER_GT(x0[9], x1[9]) → COND_574_0_POWER_GT3(&&(&&(>(x1[9], 1), !(=(x0[9], 2))), !(=(%(x1[9], 2), 1))), x0[9], x1[9])

The following pairs are in P:

574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])
COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2))
574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])
COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1))
574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])
COND_574_0_POWER_GT3(TRUE, x0[6], x1[6]) → 574_0_POWER_GT(x0[6], /(x1[6], 2))
COND_574_0_POWER_GT4(TRUE, x0[8], x1[8]) → 574_0_POWER_GT(x0[8], -(x1[8], 1))

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

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

### (6) 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, Boolean

The ITRS R consists of the following rules:
574_0_power_GT(x0, 0) → 587_0_power_Return(x0)
827_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1) → 1056_0_power_Return
827_1_power_InvokeMethod(969_0_power_Return(x0, x1), x0, x1) → 1056_0_power_Return
827_1_power_InvokeMethod(1056_0_power_Return, x0, x1) → 1056_0_power_Return
855_1_power_InvokeMethod(644_0_power_Return(x0), x2, x0, 1) → Cond_855_1_power_InvokeMethod(x0 <= 1, 644_0_power_Return(x0), x2, x0, 1)
Cond_855_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x2, x0, 1) → 969_0_power_Return(x0, x2)
855_1_power_InvokeMethod(969_0_power_Return(x0, x1), x2, x0, x1) → Cond_855_1_power_InvokeMethod1(x0 <= 1, 969_0_power_Return(x0, x1), x2, x0, x1)
Cond_855_1_power_InvokeMethod1(TRUE, 969_0_power_Return(x0, x1), x2, x0, x1) → 969_0_power_Return(x0, x2)
855_1_power_InvokeMethod(1056_0_power_Return, x1, x0, x2) → Cond_855_1_power_InvokeMethod2(x0 <= 1, 1056_0_power_Return, x1, x0, x2)
Cond_855_1_power_InvokeMethod2(TRUE, 1056_0_power_Return, x1, x0, x2) → 969_0_power_Return(x0, x1)
840_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1) → Cond_840_1_power_InvokeMethod(x0 > 1, 644_0_power_Return(x0), x0, 1)
Cond_840_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x0, 1) → 951_0_power_Return
840_1_power_InvokeMethod(895_0_power_Return(x0, x1), x0, x1) → 951_0_power_Return
840_1_power_InvokeMethod(951_0_power_Return, x0, x1) → 951_0_power_Return
868_1_power_InvokeMethod(644_0_power_Return(x0), x2, x0, 1) → Cond_868_1_power_InvokeMethod(x0 > 1, 644_0_power_Return(x0), x2, x0, 1)
Cond_868_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x2, x0, 1) → 895_0_power_Return(x0, x2)
868_1_power_InvokeMethod(895_0_power_Return(x0, x1), x2, x0, x1) → Cond_868_1_power_InvokeMethod1(x0 > 1, 895_0_power_Return(x0, x1), x2, x0, x1)
Cond_868_1_power_InvokeMethod1(TRUE, 895_0_power_Return(x0, x1), x2, x0, x1) → 895_0_power_Return(x0, x2)
868_1_power_InvokeMethod(951_0_power_Return, x1, x0, x2) → Cond_868_1_power_InvokeMethod2(x0 > 1, 951_0_power_Return, x1, x0, x2)
Cond_868_1_power_InvokeMethod2(TRUE, 951_0_power_Return, x1, x0, x2) → 895_0_power_Return(x0, x1)

The integer pair graph contains the following rules and edges:
(0): 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(x1[0] > 1 && !(x0[0] = 2) && 0 = x1[0] % 2, x0[0], x1[0])
(1): COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], x1[1] / 2)
(2): 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) && 1 = x1[2] % 2, x0[2], x1[2])
(3): COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], x1[3] - 1)
(4): 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(x1[4] > 1 && !(x0[4] = 2) && !(x1[4] % 2 = 1), x0[4], x1[4])
(6): COND_574_0_POWER_GT3(TRUE, x0[6], x1[6]) → 574_0_POWER_GT(x0[6], x1[6] / 2)
(8): COND_574_0_POWER_GT4(TRUE, x0[8], x1[8]) → 574_0_POWER_GT(x0[8], x1[8] - 1)

(1) -> (0), if ((x0[1]* x0[0])∧(x1[1] / 2* x1[0]))

(3) -> (0), if ((x0[3]* x0[0])∧(x1[3] - 1* x1[0]))

(6) -> (0), if ((x0[6]* x0[0])∧(x1[6] / 2* x1[0]))

(8) -> (0), if ((x0[8]* x0[0])∧(x1[8] - 1* x1[0]))

(0) -> (1), if ((x1[0] > 1 && !(x0[0] = 2) && 0 = x1[0] % 2* TRUE)∧(x0[0]* x0[1])∧(x1[0]* x1[1]))

(4) -> (1), if ((x1[4] > 1 && !(x0[4] = 2) && !(x1[4] % 2 = 1) →* TRUE)∧(x0[4]* x0[1])∧(x1[4]* x1[1]))

(1) -> (2), if ((x0[1]* x0[2])∧(x1[1] / 2* x1[2]))

(3) -> (2), if ((x0[3]* x0[2])∧(x1[3] - 1* x1[2]))

(6) -> (2), if ((x0[6]* x0[2])∧(x1[6] / 2* x1[2]))

(8) -> (2), if ((x0[8]* x0[2])∧(x1[8] - 1* x1[2]))

(2) -> (3), if ((x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) && 1 = x1[2] % 2* TRUE)∧(x0[2]* x0[3])∧(x1[2]* x1[3]))

(1) -> (4), if ((x0[1]* x0[4])∧(x1[1] / 2* x1[4]))

(3) -> (4), if ((x0[3]* x0[4])∧(x1[3] - 1* x1[4]))

(6) -> (4), if ((x0[6]* x0[4])∧(x1[6] / 2* x1[4]))

(8) -> (4), if ((x0[8]* x0[4])∧(x1[8] - 1* x1[4]))

The set Q consists of the following terms:
574_0_power_GT(x0, 0)
827_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
827_1_power_InvokeMethod(969_0_power_Return(x0, x1), x0, x1)
827_1_power_InvokeMethod(1056_0_power_Return, x0, x1)
855_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_855_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
855_1_power_InvokeMethod(969_0_power_Return(x0, x1), x2, x0, x1)
Cond_855_1_power_InvokeMethod1(TRUE, 969_0_power_Return(x0, x1), x2, x0, x1)
855_1_power_InvokeMethod(1056_0_power_Return, x0, x1, x2)
Cond_855_1_power_InvokeMethod2(TRUE, 1056_0_power_Return, x0, x1, x2)
840_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
Cond_840_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x0, 1)
840_1_power_InvokeMethod(895_0_power_Return(x0, x1), x0, x1)
840_1_power_InvokeMethod(951_0_power_Return, x0, x1)
868_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_868_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
868_1_power_InvokeMethod(895_0_power_Return(x0, x1), x2, x0, x1)
Cond_868_1_power_InvokeMethod1(TRUE, 895_0_power_Return(x0, x1), x2, x0, x1)
868_1_power_InvokeMethod(951_0_power_Return, x0, x1, x2)
Cond_868_1_power_InvokeMethod2(TRUE, 951_0_power_Return, x0, x1, x2)

### (7) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

### (8) 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, Boolean

The ITRS R consists of the following rules:
574_0_power_GT(x0, 0) → 587_0_power_Return(x0)
827_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1) → 1056_0_power_Return
827_1_power_InvokeMethod(969_0_power_Return(x0, x1), x0, x1) → 1056_0_power_Return
827_1_power_InvokeMethod(1056_0_power_Return, x0, x1) → 1056_0_power_Return
855_1_power_InvokeMethod(644_0_power_Return(x0), x2, x0, 1) → Cond_855_1_power_InvokeMethod(x0 <= 1, 644_0_power_Return(x0), x2, x0, 1)
Cond_855_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x2, x0, 1) → 969_0_power_Return(x0, x2)
855_1_power_InvokeMethod(969_0_power_Return(x0, x1), x2, x0, x1) → Cond_855_1_power_InvokeMethod1(x0 <= 1, 969_0_power_Return(x0, x1), x2, x0, x1)
Cond_855_1_power_InvokeMethod1(TRUE, 969_0_power_Return(x0, x1), x2, x0, x1) → 969_0_power_Return(x0, x2)
855_1_power_InvokeMethod(1056_0_power_Return, x1, x0, x2) → Cond_855_1_power_InvokeMethod2(x0 <= 1, 1056_0_power_Return, x1, x0, x2)
Cond_855_1_power_InvokeMethod2(TRUE, 1056_0_power_Return, x1, x0, x2) → 969_0_power_Return(x0, x1)
840_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1) → Cond_840_1_power_InvokeMethod(x0 > 1, 644_0_power_Return(x0), x0, 1)
Cond_840_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x0, 1) → 951_0_power_Return
840_1_power_InvokeMethod(895_0_power_Return(x0, x1), x0, x1) → 951_0_power_Return
840_1_power_InvokeMethod(951_0_power_Return, x0, x1) → 951_0_power_Return
868_1_power_InvokeMethod(644_0_power_Return(x0), x2, x0, 1) → Cond_868_1_power_InvokeMethod(x0 > 1, 644_0_power_Return(x0), x2, x0, 1)
Cond_868_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x2, x0, 1) → 895_0_power_Return(x0, x2)
868_1_power_InvokeMethod(895_0_power_Return(x0, x1), x2, x0, x1) → Cond_868_1_power_InvokeMethod1(x0 > 1, 895_0_power_Return(x0, x1), x2, x0, x1)
Cond_868_1_power_InvokeMethod1(TRUE, 895_0_power_Return(x0, x1), x2, x0, x1) → 895_0_power_Return(x0, x2)
868_1_power_InvokeMethod(951_0_power_Return, x1, x0, x2) → Cond_868_1_power_InvokeMethod2(x0 > 1, 951_0_power_Return, x1, x0, x2)
Cond_868_1_power_InvokeMethod2(TRUE, 951_0_power_Return, x1, x0, x2) → 895_0_power_Return(x0, x1)

The integer pair graph contains the following rules and edges:
(4): 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(x1[4] > 1 && !(x0[4] = 2) && !(x1[4] % 2 = 1), x0[4], x1[4])
(3): COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], x1[3] - 1)
(2): 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) && 1 = x1[2] % 2, x0[2], x1[2])
(1): COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], x1[1] / 2)
(0): 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(x1[0] > 1 && !(x0[0] = 2) && 0 = x1[0] % 2, x0[0], x1[0])

(1) -> (0), if ((x0[1]* x0[0])∧(x1[1] / 2* x1[0]))

(3) -> (0), if ((x0[3]* x0[0])∧(x1[3] - 1* x1[0]))

(0) -> (1), if ((x1[0] > 1 && !(x0[0] = 2) && 0 = x1[0] % 2* TRUE)∧(x0[0]* x0[1])∧(x1[0]* x1[1]))

(4) -> (1), if ((x1[4] > 1 && !(x0[4] = 2) && !(x1[4] % 2 = 1) →* TRUE)∧(x0[4]* x0[1])∧(x1[4]* x1[1]))

(1) -> (2), if ((x0[1]* x0[2])∧(x1[1] / 2* x1[2]))

(3) -> (2), if ((x0[3]* x0[2])∧(x1[3] - 1* x1[2]))

(2) -> (3), if ((x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) && 1 = x1[2] % 2* TRUE)∧(x0[2]* x0[3])∧(x1[2]* x1[3]))

(1) -> (4), if ((x0[1]* x0[4])∧(x1[1] / 2* x1[4]))

(3) -> (4), if ((x0[3]* x0[4])∧(x1[3] - 1* x1[4]))

The set Q consists of the following terms:
574_0_power_GT(x0, 0)
827_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
827_1_power_InvokeMethod(969_0_power_Return(x0, x1), x0, x1)
827_1_power_InvokeMethod(1056_0_power_Return, x0, x1)
855_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_855_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
855_1_power_InvokeMethod(969_0_power_Return(x0, x1), x2, x0, x1)
Cond_855_1_power_InvokeMethod1(TRUE, 969_0_power_Return(x0, x1), x2, x0, x1)
855_1_power_InvokeMethod(1056_0_power_Return, x0, x1, x2)
Cond_855_1_power_InvokeMethod2(TRUE, 1056_0_power_Return, x0, x1, x2)
840_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
Cond_840_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x0, 1)
840_1_power_InvokeMethod(895_0_power_Return(x0, x1), x0, x1)
840_1_power_InvokeMethod(951_0_power_Return, x0, x1)
868_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_868_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
868_1_power_InvokeMethod(895_0_power_Return(x0, x1), x2, x0, x1)
Cond_868_1_power_InvokeMethod1(TRUE, 895_0_power_Return(x0, x1), x2, x0, x1)
868_1_power_InvokeMethod(951_0_power_Return, x0, x1, x2)
Cond_868_1_power_InvokeMethod2(TRUE, 951_0_power_Return, x0, x1, x2)

### (9) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

### (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

R is empty.

The integer pair graph contains the following rules and edges:
(4): 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(x1[4] > 1 && !(x0[4] = 2) && !(x1[4] % 2 = 1), x0[4], x1[4])
(3): COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], x1[3] - 1)
(2): 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) && 1 = x1[2] % 2, x0[2], x1[2])
(1): COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], x1[1] / 2)
(0): 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(x1[0] > 1 && !(x0[0] = 2) && 0 = x1[0] % 2, x0[0], x1[0])

(1) -> (0), if ((x0[1]* x0[0])∧(x1[1] / 2* x1[0]))

(3) -> (0), if ((x0[3]* x0[0])∧(x1[3] - 1* x1[0]))

(0) -> (1), if ((x1[0] > 1 && !(x0[0] = 2) && 0 = x1[0] % 2* TRUE)∧(x0[0]* x0[1])∧(x1[0]* x1[1]))

(4) -> (1), if ((x1[4] > 1 && !(x0[4] = 2) && !(x1[4] % 2 = 1) →* TRUE)∧(x0[4]* x0[1])∧(x1[4]* x1[1]))

(1) -> (2), if ((x0[1]* x0[2])∧(x1[1] / 2* x1[2]))

(3) -> (2), if ((x0[3]* x0[2])∧(x1[3] - 1* x1[2]))

(2) -> (3), if ((x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) && 1 = x1[2] % 2* TRUE)∧(x0[2]* x0[3])∧(x1[2]* x1[3]))

(1) -> (4), if ((x0[1]* x0[4])∧(x1[1] / 2* x1[4]))

(3) -> (4), if ((x0[3]* x0[4])∧(x1[3] - 1* x1[4]))

The set Q consists of the following terms:
574_0_power_GT(x0, 0)
827_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
827_1_power_InvokeMethod(969_0_power_Return(x0, x1), x0, x1)
827_1_power_InvokeMethod(1056_0_power_Return, x0, x1)
855_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_855_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
855_1_power_InvokeMethod(969_0_power_Return(x0, x1), x2, x0, x1)
Cond_855_1_power_InvokeMethod1(TRUE, 969_0_power_Return(x0, x1), x2, x0, x1)
855_1_power_InvokeMethod(1056_0_power_Return, x0, x1, x2)
Cond_855_1_power_InvokeMethod2(TRUE, 1056_0_power_Return, x0, x1, x2)
840_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
Cond_840_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x0, 1)
840_1_power_InvokeMethod(895_0_power_Return(x0, x1), x0, x1)
840_1_power_InvokeMethod(951_0_power_Return, x0, x1)
868_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_868_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
868_1_power_InvokeMethod(895_0_power_Return(x0, x1), x2, x0, x1)
Cond_868_1_power_InvokeMethod1(TRUE, 895_0_power_Return(x0, x1), x2, x0, x1)
868_1_power_InvokeMethod(951_0_power_Return, x0, x1, x2)
Cond_868_1_power_InvokeMethod2(TRUE, 951_0_power_Return, x0, x1, x2)

### (11) 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 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4]) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4]), COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:

(1)    (&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1)))=TRUEx0[4]=x0[1]x1[4]=x1[1]574_0_POWER_GT(x0[4], x1[4])≥NonInfC∧574_0_POWER_GT(x0[4], x1[4])≥COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:

(2)    (>(x1[4], 1)=TRUE<(%(x1[4], 2), 1)=TRUE<(x0[4], 2)=TRUE574_0_POWER_GT(x0[4], x1[4])≥NonInfC∧574_0_POWER_GT(x0[4], x1[4])≥COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥))

(3)    (>(x1[4], 1)=TRUE<(%(x1[4], 2), 1)=TRUE>(x0[4], 2)=TRUE574_0_POWER_GT(x0[4], x1[4])≥NonInfC∧574_0_POWER_GT(x0[4], x1[4])≥COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(4)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (3) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(5)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (4) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(6)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (5) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(7)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(9)    (x1[4] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(11)    (x1[4] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (6) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(12)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (7) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(13)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(14)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(15)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[(-1)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(16)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(17)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(18)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(19)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(20)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

(21)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (20) using rule (IDP_POLY_GCD) which results in the following new constraint:

(22)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_GCD) which results in the following new constraint:

(23)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (17) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(24)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (24) using rule (IDP_POLY_GCD) which results in the following new constraint:

(25)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (18) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(26)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

(27)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (26) using rule (IDP_POLY_GCD) which results in the following new constraint:

(28)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (27) using rule (IDP_POLY_GCD) which results in the following new constraint:

(29)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(30)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

We simplified constraint (30) using rule (IDP_POLY_GCD) which results in the following new constraint:

(31)    (x1[4] ≥ 0∧x0[4] ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

For Pair COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1)) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2]), COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1)), 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0]) which results in the following constraint:

(32)    (&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2)))=TRUEx0[2]=x0[3]x1[2]=x1[3]x0[3]=x0[0]-(x1[3], 1)=x1[0]COND_574_0_POWER_GT1(TRUE, x0[3], x1[3])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[3], x1[3])≥574_0_POWER_GT(x0[3], -(x1[3], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (32) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraints:

(33)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE<(x1[2], 1)=TRUECOND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥574_0_POWER_GT(x0[2], -(x1[2], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

(34)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE>(x1[2], 1)=TRUECOND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥574_0_POWER_GT(x0[2], -(x1[2], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (33) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(35)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (34) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(36)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (35) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(37)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (36) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(38)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(40)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (41) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(42)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We solved constraint (37) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (38) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(43)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We solved constraint (40) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (42) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(44)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (43) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(45)    (x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (44) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(46)    (x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (45) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(47)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (47) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(48)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

(49)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (48) using rule (IDP_POLY_GCD) which results in the following new constraint:

(50)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (49) using rule (IDP_POLY_GCD) which results in the following new constraint:

(51)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (46) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(52)    ([1] + x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (52) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(53)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (53) using rule (IDP_POLY_GCD) which results in the following new constraint:

(54)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

• We consider the chain 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2]), COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1)), 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2]) which results in the following constraint:

(55)    (&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2)))=TRUEx0[2]=x0[3]x1[2]=x1[3]x0[3]=x0[2]1-(x1[3], 1)=x1[2]1COND_574_0_POWER_GT1(TRUE, x0[3], x1[3])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[3], x1[3])≥574_0_POWER_GT(x0[3], -(x1[3], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (55) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraints:

(56)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE<(x1[2], 1)=TRUECOND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥574_0_POWER_GT(x0[2], -(x1[2], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

(57)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE>(x1[2], 1)=TRUECOND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥574_0_POWER_GT(x0[2], -(x1[2], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (56) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(58)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (57) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(59)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (58) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(60)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (59) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(61)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (62) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(63)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (64) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(65)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We solved constraint (60) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (61) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(66)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We solved constraint (63) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (65) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(67)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (66) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(68)    (x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (67) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(69)    (x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (68) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(70)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (70) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(71)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

(72)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (71) using rule (IDP_POLY_GCD) which results in the following new constraint:

(73)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (72) using rule (IDP_POLY_GCD) which results in the following new constraint:

(74)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (69) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(75)    ([1] + x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (75) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(76)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (76) using rule (IDP_POLY_GCD) which results in the following new constraint:

(77)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

• We consider the chain 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2]), COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1)), 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4]) which results in the following constraint:

(78)    (&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2)))=TRUEx0[2]=x0[3]x1[2]=x1[3]x0[3]=x0[4]-(x1[3], 1)=x1[4]COND_574_0_POWER_GT1(TRUE, x0[3], x1[3])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[3], x1[3])≥574_0_POWER_GT(x0[3], -(x1[3], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (78) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraints:

(79)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE<(x1[2], 1)=TRUECOND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥574_0_POWER_GT(x0[2], -(x1[2], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

(80)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE>(x1[2], 1)=TRUECOND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_574_0_POWER_GT1(TRUE, x0[2], x1[2])≥574_0_POWER_GT(x0[2], -(x1[2], 1))∧(UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (79) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(81)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (80) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(82)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (81) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(83)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (82) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(84)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (85) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(86)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (87) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(88)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We solved constraint (83) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (84) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(89)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We solved constraint (86) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (88) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(90)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (89) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(91)    (x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (90) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(92)    (x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (91) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(93)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (93) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(94)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

(95)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (94) using rule (IDP_POLY_GCD) which results in the following new constraint:

(96)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (95) using rule (IDP_POLY_GCD) which results in the following new constraint:

(97)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (92) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(98)    ([1] + x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (98) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(99)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

We simplified constraint (99) using rule (IDP_POLY_GCD) which results in the following new constraint:

(100)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

For Pair 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2]) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2]), COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1)) which results in the following constraint:

(101)    (&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2)))=TRUEx0[2]=x0[3]x1[2]=x1[3]574_0_POWER_GT(x0[2], x1[2])≥NonInfC∧574_0_POWER_GT(x0[2], x1[2])≥COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])∧(UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥))

We simplified constraint (101) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:

(102)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE<(x1[2], 1)=TRUE574_0_POWER_GT(x0[2], x1[2])≥NonInfC∧574_0_POWER_GT(x0[2], x1[2])≥COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])∧(UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥))

(103)    (>=(1, %(x1[2], 2))=TRUE<=(1, %(x1[2], 2))=TRUE>(x1[2], 0)=TRUE<(x0[2], 2)=TRUE>(x1[2], 1)=TRUE574_0_POWER_GT(x0[2], x1[2])≥NonInfC∧574_0_POWER_GT(x0[2], x1[2])≥COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])∧(UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥))

We simplified constraint (102) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(104)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (103) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(105)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (104) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(106)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (105) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(107)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (108) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(109)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (110) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(111)    ([1] + [-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} + [-1] ≥ 0∧x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We solved constraint (106) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (107) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(112)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We solved constraint (109) using rule (POLY_REMOVE_MIN_MAX).We simplified constraint (111) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(113)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (112) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(114)    (x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (113) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(115)    (x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1] + x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (114) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(116)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (116) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(117)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

(118)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (117) using rule (IDP_POLY_GCD) which results in the following new constraint:

(119)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (118) using rule (IDP_POLY_GCD) which results in the following new constraint:

(120)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (115) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(121)    ([1] + x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (121) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(122)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[4] ≥ 0∧[3] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

We simplified constraint (122) using rule (IDP_POLY_GCD) which results in the following new constraint:

(123)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

For Pair COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2)) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0]), COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:

(124)    (&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2)))=TRUEx0[0]=x0[1]x1[0]=x1[1]COND_574_0_POWER_GT(TRUE, x0[1], x1[1])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[1], x1[1])≥574_0_POWER_GT(x0[1], /(x1[1], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (124) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:

(125)    (>(x1[0], 1)=TRUE>=(0, %(x1[0], 2))=TRUE<=(0, %(x1[0], 2))=TRUE<(x0[0], 2)=TRUECOND_574_0_POWER_GT(TRUE, x0[0], x1[0])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[0], x1[0])≥574_0_POWER_GT(x0[0], /(x1[0], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

(126)    (>(x1[0], 1)=TRUE>=(0, %(x1[0], 2))=TRUE<=(0, %(x1[0], 2))=TRUE>(x0[0], 2)=TRUECOND_574_0_POWER_GT(TRUE, x0[0], x1[0])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[0], x1[0])≥574_0_POWER_GT(x0[0], /(x1[0], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (125) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(127)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (126) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(128)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (127) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(129)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (128) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(130)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (129) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(131)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (130) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(132)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (131) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(133)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (132) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(134)    (x1[0] ≥ 0∧x0[0] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (133) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(135)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

(136)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (135) using rule (IDP_POLY_GCD) which results in the following new constraint:

(137)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (136) using rule (IDP_POLY_GCD) which results in the following new constraint:

(138)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (134) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(139)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (139) using rule (IDP_POLY_GCD) which results in the following new constraint:

(140)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

• We consider the chain 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4]), COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:

(141)    (&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1)))=TRUEx0[4]=x0[1]x1[4]=x1[1]COND_574_0_POWER_GT(TRUE, x0[1], x1[1])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[1], x1[1])≥574_0_POWER_GT(x0[1], /(x1[1], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (141) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:

(142)    (>(x1[4], 1)=TRUE<(%(x1[4], 2), 1)=TRUE<(x0[4], 2)=TRUECOND_574_0_POWER_GT(TRUE, x0[4], x1[4])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[4], x1[4])≥574_0_POWER_GT(x0[4], /(x1[4], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

(143)    (>(x1[4], 1)=TRUE<(%(x1[4], 2), 1)=TRUE>(x0[4], 2)=TRUECOND_574_0_POWER_GT(TRUE, x0[4], x1[4])≥NonInfC∧COND_574_0_POWER_GT(TRUE, x0[4], x1[4])≥574_0_POWER_GT(x0[4], /(x1[4], 2))∧(UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (142) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(144)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (143) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(145)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (144) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(146)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (145) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(147)    (x1[4] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (148) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(149)    (x1[4] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (150) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(151)    (x1[4] + [-2] ≥ 0∧max{[2], [-2]} + [-2] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (146) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(152)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (147) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(153)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (149) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(154)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (151) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(155)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (152) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(156)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (153) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(157)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (154) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(158)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (155) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(159)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (156) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(160)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

(161)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (160) using rule (IDP_POLY_GCD) which results in the following new constraint:

(162)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (161) using rule (IDP_POLY_GCD) which results in the following new constraint:

(163)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (157) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(164)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (164) using rule (IDP_POLY_GCD) which results in the following new constraint:

(165)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (158) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(166)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

(167)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (166) using rule (IDP_POLY_GCD) which results in the following new constraint:

(168)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (167) using rule (IDP_POLY_GCD) which results in the following new constraint:

(169)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (159) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(170)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[4] ≥ 0∧0 ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

We simplified constraint (170) using rule (IDP_POLY_GCD) which results in the following new constraint:

(171)    (x1[4] ≥ 0∧x0[4] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

For Pair 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0]) the following chains were created:
• We consider the chain 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0]), COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:

(172)    (&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2)))=TRUEx0[0]=x0[1]x1[0]=x1[1]574_0_POWER_GT(x0[0], x1[0])≥NonInfC∧574_0_POWER_GT(x0[0], x1[0])≥COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥))

We simplified constraint (172) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:

(173)    (>(x1[0], 1)=TRUE>=(0, %(x1[0], 2))=TRUE<=(0, %(x1[0], 2))=TRUE<(x0[0], 2)=TRUE574_0_POWER_GT(x0[0], x1[0])≥NonInfC∧574_0_POWER_GT(x0[0], x1[0])≥COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥))

(174)    (>(x1[0], 1)=TRUE>=(0, %(x1[0], 2))=TRUE<=(0, %(x1[0], 2))=TRUE>(x0[0], 2)=TRUE574_0_POWER_GT(x0[0], x1[0])≥NonInfC∧574_0_POWER_GT(x0[0], x1[0])≥COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])∧(UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥))

We simplified constraint (173) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(175)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (174) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

(176)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (175) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(177)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (176) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

(178)    (x1[0] + [-2] ≥ 0∧[-1]min{[2], [-2]} ≥ 0∧max{[2], [-2]} ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (177) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(179)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (178) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

(180)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (179) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(181)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (180) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(182)    (x1[0] ≥ 0∧x0[0] + [-3] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (181) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

(183)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

(184)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0∧x0[0] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (183) using rule (IDP_POLY_GCD) which results in the following new constraint:

(185)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (184) using rule (IDP_POLY_GCD) which results in the following new constraint:

(186)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (182) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

(187)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[4] ≥ 0∧[2] ≥ 0∧[2] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

We simplified constraint (187) using rule (IDP_POLY_GCD) which results in the following new constraint:

(188)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)

To summarize, we get the following constraints P for the following pairs.
• 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])
• (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)
• (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)
• (x1[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)
• (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)
• (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)
• (x1[4] ≥ 0∧x0[4] ≥ 0∧0 ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[4] ≥ 0∧[(-1)bso_19] ≥ 0)

• COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1))
• ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)
• ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)
• ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)
• ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)
• ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)
• ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)
• ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)
• ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)
• ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[2] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

• 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])
• ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)
• ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧x0[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)
• ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])), ≥)∧[bni_22 + (-1)Bound*bni_22] + [bni_22]x1[2] ≥ 0∧[(-1)bso_23] ≥ 0)

• COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2))
• (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)
• (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)
• (x1[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[0] ≥ 0∧[1 + (-1)bso_28] ≥ 0)
• (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)
• (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)
• (x1[4] ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)
• (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)
• (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧0 ≥ 0∧x0[4] ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)
• (x1[4] ≥ 0∧x0[4] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (UIncreasing(574_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[4] ≥ 0∧[1 + (-1)bso_28] ≥ 0)

• 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])
• (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)
• (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 0)
• (x1[0] ≥ 0∧x0[0] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0 ⇒ (UIncreasing(COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])), ≥)∧[bni_29 + (-1)Bound*bni_29] + [bni_29]x1[0] ≥ 0∧[(-1)bso_30] ≥ 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) = [1]
POL(574_0_POWER_GT(x1, x2)) = [-1] + x2
POL(COND_574_0_POWER_GT(x1, x2, x3)) = [-1] + x3
POL(&&(x1, x2)) = [-1]
POL(>(x1, x2)) = [-1]
POL(1) = [1]
POL(!(x1)) = [-1]
POL(=(x1, x2)) = [-1]
POL(2) = [2]
POL(COND_574_0_POWER_GT1(x1, x2, x3)) = [-1] + x3
POL(-(x1, x2)) = x1 + [-1]x2
POL(0) = 0

Polynomial Interpretations with Context Sensitive Arithemetic Replacement
POL(TermCSAR-Mode @ Context)

POL(%(x1, 2)-1 @ {}) = min{x2, [-1]x2}
POL(%(x1, 2)1 @ {}) = max{x2, [-1]x2}
POL(/(x1, 2)1 @ {574_0_POWER_GT_2/1}) = max{x1, [-1]x1} + [-1]

The following pairs are in P>:

COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1))
COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2))

The following pairs are in Pbound:

574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])
COND_574_0_POWER_GT1(TRUE, x0[3], x1[3]) → 574_0_POWER_GT(x0[3], -(x1[3], 1))
574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])
COND_574_0_POWER_GT(TRUE, x0[1], x1[1]) → 574_0_POWER_GT(x0[1], /(x1[1], 2))
574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])

The following pairs are in P:

574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(&&(&&(>(x1[4], 1), !(=(x0[4], 2))), !(=(%(x1[4], 2), 1))), x0[4], x1[4])
574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(&&(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), =(1, %(x1[2], 2))), x0[2], x1[2])
574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(&&(&&(>(x1[0], 1), !(=(x0[0], 2))), =(0, %(x1[0], 2))), x0[0], x1[0])

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

FALSE1&&(FALSE, FALSE)1
/1

### (12) 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:
(4): 574_0_POWER_GT(x0[4], x1[4]) → COND_574_0_POWER_GT(x1[4] > 1 && !(x0[4] = 2) && !(x1[4] % 2 = 1), x0[4], x1[4])
(2): 574_0_POWER_GT(x0[2], x1[2]) → COND_574_0_POWER_GT1(x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) && 1 = x1[2] % 2, x0[2], x1[2])
(0): 574_0_POWER_GT(x0[0], x1[0]) → COND_574_0_POWER_GT(x1[0] > 1 && !(x0[0] = 2) && 0 = x1[0] % 2, x0[0], x1[0])

The set Q consists of the following terms:
574_0_power_GT(x0, 0)
827_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
827_1_power_InvokeMethod(969_0_power_Return(x0, x1), x0, x1)
827_1_power_InvokeMethod(1056_0_power_Return, x0, x1)
855_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_855_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
855_1_power_InvokeMethod(969_0_power_Return(x0, x1), x2, x0, x1)
Cond_855_1_power_InvokeMethod1(TRUE, 969_0_power_Return(x0, x1), x2, x0, x1)
855_1_power_InvokeMethod(1056_0_power_Return, x0, x1, x2)
Cond_855_1_power_InvokeMethod2(TRUE, 1056_0_power_Return, x0, x1, x2)
840_1_power_InvokeMethod(644_0_power_Return(x0), x0, 1)
Cond_840_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x0, 1)
840_1_power_InvokeMethod(895_0_power_Return(x0, x1), x0, x1)
840_1_power_InvokeMethod(951_0_power_Return, x0, x1)
868_1_power_InvokeMethod(644_0_power_Return(x0), x1, x0, 1)
Cond_868_1_power_InvokeMethod(TRUE, 644_0_power_Return(x0), x1, x0, 1)
868_1_power_InvokeMethod(895_0_power_Return(x0, x1), x2, x0, x1)
Cond_868_1_power_InvokeMethod1(TRUE, 895_0_power_Return(x0, x1), x2, x0, x1)
868_1_power_InvokeMethod(951_0_power_Return, x0, x1, x2)
Cond_868_1_power_InvokeMethod2(TRUE, 951_0_power_Return, x0, x1, x2)

### (13) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.