Termination proof of /tmp/tmpnocLdT/PastaC7.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 450 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 JBCTerminationSCC

↳5 SCCToIDPv1Proof (⇒, 20 ms)

↳6 IDP

↳7 IDPNonInfProof (⇒, 500 ms)

↳8 IDP

↳9 IDependencyGraphProof (⇔, 0 ms)

↳10 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC7

/**
 * Example taken from "A Term Rewriting Approach to the Automated Termination
 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
 * and converted to Java.
 */

public class PastaC7 {
    public static void main(String[] args) {
        Random.args = args;
        int i = Random.random();
        int j = Random.random();
        int k = Random.random();

        while (i <= 100 && j <= k) {
            int t = i;
            i = j;
            j = i + 1;
            k--;
        }
    }
}


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

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

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
PastaC7.main([Ljava/lang/String;)V: Graph of 260 nodes with 1 SCC.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 1 SCCs.

(4) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: PastaC7.main([Ljava/lang/String;)V
SCC calls the following helper methods:
Performed SCC analyses: UsedFieldsAnalysis

(5) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 19 rules for P and 0 rules for R.

P rules:
899_0_main_ConstantStackPush(EOS(STATIC_899), i198, i199, i200, i198) → 901_0_main_GT(EOS(STATIC_901), i198, i199, i200, i198, 100)
901_0_main_GT(EOS(STATIC_901), i208, i199, i200, i208, matching1) → 904_0_main_GT(EOS(STATIC_904), i208, i199, i200, i208, 100) | =(matching1, 100)
904_0_main_GT(EOS(STATIC_904), i208, i199, i200, i208, matching1) → 907_0_main_Load(EOS(STATIC_907), i208, i199, i200) | &&(<=(i208, 100), =(matching1, 100))
907_0_main_Load(EOS(STATIC_907), i208, i199, i200) → 910_0_main_Load(EOS(STATIC_910), i208, i199, i200, i199)
910_0_main_Load(EOS(STATIC_910), i208, i199, i200, i199) → 915_0_main_GT(EOS(STATIC_915), i208, i199, i200, i199, i200)
915_0_main_GT(EOS(STATIC_915), i208, i199, i200, i199, i200) → 918_0_main_GT(EOS(STATIC_918), i208, i199, i200, i199, i200)
918_0_main_GT(EOS(STATIC_918), i208, i199, i200, i199, i200) → 925_0_main_Load(EOS(STATIC_925), i208, i199, i200) | <=(i199, i200)
925_0_main_Load(EOS(STATIC_925), i208, i199, i200) → 928_0_main_Store(EOS(STATIC_928), i199, i200, i208)
928_0_main_Store(EOS(STATIC_928), i199, i200, i208) → 931_0_main_Load(EOS(STATIC_931), i199, i200)
931_0_main_Load(EOS(STATIC_931), i199, i200) → 932_0_main_Store(EOS(STATIC_932), i200, i199)
932_0_main_Store(EOS(STATIC_932), i200, i199) → 934_0_main_Load(EOS(STATIC_934), i199, i200)
934_0_main_Load(EOS(STATIC_934), i199, i200) → 936_0_main_ConstantStackPush(EOS(STATIC_936), i199, i200, i199)
936_0_main_ConstantStackPush(EOS(STATIC_936), i199, i200, i199) → 938_0_main_IntArithmetic(EOS(STATIC_938), i199, i200, i199, 1)
938_0_main_IntArithmetic(EOS(STATIC_938), i199, i200, i199, matching1) → 940_0_main_Store(EOS(STATIC_940), i199, i200, +(i199, 1)) | =(matching1, 1)
940_0_main_Store(EOS(STATIC_940), i199, i200, i212) → 942_0_main_Inc(EOS(STATIC_942), i199, i212, i200)
942_0_main_Inc(EOS(STATIC_942), i199, i212, i200) → 944_0_main_JMP(EOS(STATIC_944), i199, i212, +(i200, -1))
944_0_main_JMP(EOS(STATIC_944), i199, i212, i213) → 961_0_main_Load(EOS(STATIC_961), i199, i212, i213)
961_0_main_Load(EOS(STATIC_961), i199, i212, i213) → 896_0_main_Load(EOS(STATIC_896), i199, i212, i213)
896_0_main_Load(EOS(STATIC_896), i198, i199, i200) → 899_0_main_ConstantStackPush(EOS(STATIC_899), i198, i199, i200, i198)
R rules:

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

P rules:
899_0_main_ConstantStackPush(EOS(STATIC_899), x0, x1, x2, x0) → 899_0_main_ConstantStackPush(EOS(STATIC_899), x1, +(x1, 1), +(x2, -1), x1) | &&(>=(x2, x1), <=(x0, 100))
R rules:

Filtered ground terms:

899_0_main_ConstantStackPush(x1, x2, x3, x4, x5) → 899_0_main_ConstantStackPush(x2, x3, x4, x5)
EOS(x1) → EOS
Cond_899_0_main_ConstantStackPush(x1, x2, x3, x4, x5, x6) → Cond_899_0_main_ConstantStackPush(x1, x3, x4, x5, x6)

Filtered duplicate args:

899_0_main_ConstantStackPush(x1, x2, x3, x4) → 899_0_main_ConstantStackPush(x2, x3, x4)
Cond_899_0_main_ConstantStackPush(x1, x2, x3, x4, x5) → Cond_899_0_main_ConstantStackPush(x1, x3, x4, x5)

Filtered unneeded arguments:

Cond_899_0_main_ConstantStackPush(x1, x2, x3, x4) → Cond_899_0_main_ConstantStackPush(x1, x2, x3)

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

P rules:
899_0_main_ConstantStackPush(x1, x2, x0) → 899_0_main_ConstantStackPush(+(x1, 1), +(x2, -1), x1) | &&(>=(x2, x1), <=(x0, 100))
R rules:

Finished conversion. Obtained 2 rules for P and 0 rules for R. System has predefined symbols.

P rules:
899_0_MAIN_CONSTANTSTACKPUSH(x1, x2, x0) → COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2, x1), <=(x0, 100)), x1, x2, x0)
COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1, x2, x0) → 899_0_MAIN_CONSTANTSTACKPUSH(+(x1, 1), +(x2, -1), x1)
R rules:

(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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_899_0_MAIN_CONSTANTSTACKPUSH(x2[0] >= x1[0] && x0[0] <= 100, x1[0], x2[0], x0[0])
(1): COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 899_0_MAIN_CONSTANTSTACKPUSH(x1[1] + 1, x2[1] + -1, x1[1])

(0) -> (1), if (x2[0] >= x1[0] && x0[0] <= 100 ∧x1[0] →^* x1[1]∧x2[0] →^* x2[1]∧x0[0] →^* x0[1])

(1) -> (0), if (x1[1] + 1 →^* x1[0]∧x2[1] + -1 →^* x2[0]∧x1[1] →^* x0[0])

The set Q is empty.

(7) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@1fff293 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 1 Max Right Steps: 1

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 899_0_MAIN_CONSTANTSTACKPUSH(x1, x2, x0) → COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2, x1), <=(x0, 100)), x1, x2, x0) the following chains were created:

We consider the chain 899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0]), COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1]) which results in the following constraint:
(1)    (&&(>=(x2[0], x1[0]), <=(x0[0], 100))=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1] ⇒ 899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0])≥NonInfC∧899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0])≥COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])∧(U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>=(x2[0], x1[0])=TRUE∧<=(x0[0], 100)=TRUE ⇒ 899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0])≥NonInfC∧899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0])≥COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])∧(U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] + [(-1)bni_15]x1[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] + [(-1)bni_15]x1[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] + [(-1)bni_15]x1[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(7)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

(8)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(9)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

(10)    (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(11)    (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

(12)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

For Pair COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1, x2, x0) → 899_0_MAIN_CONSTANTSTACKPUSH(+(x1, 1), +(x2, -1), x1) the following chains were created:

We consider the chain 899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0]), COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1]), 899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0]) which results in the following constraint:
(13)    (&&(>=(x2[0], x1[0]), <=(x0[0], 100))=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧+(x1[1], 1)=x1[0]1∧+(x2[1], -1)=x2[0]1∧x1[1]=x0[0]1 ⇒ COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1])≥899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])∧(U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥))

We simplified constraint (13) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(14)    (>=(x2[0], x1[0])=TRUE∧<=(x0[0], 100)=TRUE ⇒ COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[0], x2[0], x0[0])≥NonInfC∧COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[0], x2[0], x0[0])≥899_0_MAIN_CONSTANTSTACKPUSH(+(x1[0], 1), +(x2[0], -1), x1[0])∧(U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥))

We simplified constraint (14) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(15)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] + [(-1)bni_17]x1[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] + [(-1)bni_17]x1[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] + [(-1)bni_17]x1[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (17) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(18)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (18) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(19)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

(20)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(21)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

(22)    (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(23)    (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

(24)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

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

899_0_MAIN_CONSTANTSTACKPUSH(x1, x2, x0) → COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2, x1), <=(x0, 100)), x1, x2, x0)
- (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1, x2, x0) → 899_0_MAIN_CONSTANTSTACKPUSH(+(x1, 1), +(x2, -1), x1)
- (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
- (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
- (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
- (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

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

POL(TRUE) = 0
POL(FALSE) = 0
POL(899_0_MAIN_CONSTANTSTACKPUSH(x₁, x₂, x₃)) = x₂ + [-1]x₁
POL(COND_899_0_MAIN_CONSTANTSTACKPUSH(x₁, x₂, x₃, x₄)) = [-1] + x₃ + [-1]x₂ + [-1]x₁
POL(&&(x₁, x₂)) = 0
POL(>=(x₁, x₂)) = [-1]
POL(<=(x₁, x₂)) = [-1]
POL(100) = [100]
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]
POL(-1) = [-1]

The following pairs are in P_>:

899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])
COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])

The following pairs are in P_bound:

899_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_899_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])
COND_899_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 899_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])

The following pairs are in P_≥:
none

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

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

(8) Obligation: