0 JBC
↳1 JBCToGraph (⇒, 360 ms)
↳2 JBCTerminationGraph
↳3 TerminationGraphToSCCProof (⇒, 0 ms)
↳4 JBCTerminationSCC
↳5 SCCToIDPv1Proof (⇒, 80 ms)
↳6 IDP
↳7 IDPNonInfProof (⇒, 160 ms)
↳8 AND
↳9 IDP
↳10 IDependencyGraphProof (⇔, 0 ms)
↳11 TRUE
↳12 IDP
↳13 IDependencyGraphProof (⇔, 0 ms)
↳14 TRUE
/**
* 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 PastaA7 {
public static void main(String[] args) {
Random.args = args;
int x = Random.random();
int y = Random.random();
int z = Random.random();
while (x > y && x > z) {
y++;
z++;
}
}
}
public class Random {
static String[] args;
static int index = 0;
public static int random() {
String string = args[index];
index++;
return string.length();
}
}
Generated 12 rules for P and 0 rules for R.
P rules:
504_0_main_Load(EOS(STATIC_504), i18, i47, i89, i18) → 511_0_main_LE(EOS(STATIC_511), i18, i47, i89, i18, i47)
511_0_main_LE(EOS(STATIC_511), i18, i47, i89, i18, i47) → 527_0_main_LE(EOS(STATIC_527), i18, i47, i89, i18, i47)
527_0_main_LE(EOS(STATIC_527), i18, i47, i89, i18, i47) → 537_0_main_Load(EOS(STATIC_537), i18, i47, i89) | >(i18, i47)
537_0_main_Load(EOS(STATIC_537), i18, i47, i89) → 547_0_main_Load(EOS(STATIC_547), i18, i47, i89, i18)
547_0_main_Load(EOS(STATIC_547), i18, i47, i89, i18) → 557_0_main_LE(EOS(STATIC_557), i18, i47, i89, i18, i89)
557_0_main_LE(EOS(STATIC_557), i18, i47, i89, i18, i89) → 568_0_main_LE(EOS(STATIC_568), i18, i47, i89, i18, i89)
568_0_main_LE(EOS(STATIC_568), i18, i47, i89, i18, i89) → 586_0_main_Inc(EOS(STATIC_586), i18, i47, i89) | >(i18, i89)
586_0_main_Inc(EOS(STATIC_586), i18, i47, i89) → 598_0_main_Inc(EOS(STATIC_598), i18, +(i47, 1), i89) | >=(i47, 0)
598_0_main_Inc(EOS(STATIC_598), i18, i101, i89) → 611_0_main_JMP(EOS(STATIC_611), i18, i101, +(i89, 1)) | >=(i89, 0)
611_0_main_JMP(EOS(STATIC_611), i18, i101, i104) → 639_0_main_Load(EOS(STATIC_639), i18, i101, i104)
639_0_main_Load(EOS(STATIC_639), i18, i101, i104) → 496_0_main_Load(EOS(STATIC_496), i18, i101, i104)
496_0_main_Load(EOS(STATIC_496), i18, i47, i89) → 504_0_main_Load(EOS(STATIC_504), i18, i47, i89, i18)
R rules:
Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.
P rules:
504_0_main_Load(EOS(STATIC_504), x0, x1, x2, x0) → 504_0_main_Load(EOS(STATIC_504), x0, +(x1, 1), +(x2, 1), x0) | &&(&&(&&(>(+(x2, 1), 0), <(x2, x0)), >(+(x1, 1), 0)), <(x1, x0))
R rules:
Filtered ground terms:
504_0_main_Load(x1, x2, x3, x4, x5) → 504_0_main_Load(x2, x3, x4, x5)
EOS(x1) → EOS
Cond_504_0_main_Load(x1, x2, x3, x4, x5, x6) → Cond_504_0_main_Load(x1, x3, x4, x5, x6)
Filtered duplicate args:
504_0_main_Load(x1, x2, x3, x4) → 504_0_main_Load(x2, x3, x4)
Cond_504_0_main_Load(x1, x2, x3, x4, x5) → Cond_504_0_main_Load(x1, x3, x4, x5)
Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.
P rules:
504_0_main_Load(x1, x2, x0) → 504_0_main_Load(+(x1, 1), +(x2, 1), x0) | &&(&&(&&(>(x2, -1), <(x2, x0)), >(x1, -1)), <(x1, x0))
R rules:
Finished conversion. Obtained 2 rules for P and 0 rules for R. System has predefined symbols.
P rules:
504_0_MAIN_LOAD(x1, x2, x0) → COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2, -1), <(x2, x0)), >(x1, -1)), <(x1, x0)), x1, x2, x0)
COND_504_0_MAIN_LOAD(TRUE, x1, x2, x0) → 504_0_MAIN_LOAD(+(x1, 1), +(x2, 1), x0)
R rules:
!= | ~ | 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 |
Boolean, Integer
(0) -> (1), if (x2[0] > -1 && x2[0] < x0[0] && x1[0] > -1 && x1[0] < x0[0] ∧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]∧x0[1] →* x0[0])
(1) (&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0]))=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1] ⇒ 504_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧504_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])∧(UIncreasing(COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥))
(2) (<(x1[0], x0[0])=TRUE∧>(x1[0], -1)=TRUE∧>(x2[0], -1)=TRUE∧<(x2[0], x0[0])=TRUE ⇒ 504_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧504_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])∧(UIncreasing(COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥))
(3) (x0[0] + [-1] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[bni_11 + (-1)Bound*bni_11] + [(2)bni_11]x0[0] + [(-1)bni_11]x2[0] + [(-1)bni_11]x1[0] ≥ 0∧[(-1)bso_12] ≥ 0)
(4) (x0[0] + [-1] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[bni_11 + (-1)Bound*bni_11] + [(2)bni_11]x0[0] + [(-1)bni_11]x2[0] + [(-1)bni_11]x1[0] ≥ 0∧[(-1)bso_12] ≥ 0)
(5) (x0[0] + [-1] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[bni_11 + (-1)Bound*bni_11] + [(2)bni_11]x0[0] + [(-1)bni_11]x2[0] + [(-1)bni_11]x1[0] ≥ 0∧[(-1)bso_12] ≥ 0)
(6) (x0[0] ≥ 0∧x1[0] ≥ 0∧x2[0] ≥ 0∧x1[0] + x0[0] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[(3)bni_11 + (-1)Bound*bni_11] + [bni_11]x1[0] + [(2)bni_11]x0[0] + [(-1)bni_11]x2[0] ≥ 0∧[(-1)bso_12] ≥ 0)
(7) (COND_504_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_504_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥504_0_MAIN_LOAD(+(x1[1], 1), +(x2[1], 1), x0[1])∧(UIncreasing(504_0_MAIN_LOAD(+(x1[1], 1), +(x2[1], 1), x0[1])), ≥))
(8) ((UIncreasing(504_0_MAIN_LOAD(+(x1[1], 1), +(x2[1], 1), x0[1])), ≥)∧[bni_13] = 0∧[2 + (-1)bso_14] ≥ 0)
(9) ((UIncreasing(504_0_MAIN_LOAD(+(x1[1], 1), +(x2[1], 1), x0[1])), ≥)∧[bni_13] = 0∧[2 + (-1)bso_14] ≥ 0)
(10) ((UIncreasing(504_0_MAIN_LOAD(+(x1[1], 1), +(x2[1], 1), x0[1])), ≥)∧[bni_13] = 0∧[2 + (-1)bso_14] ≥ 0)
(11) ((UIncreasing(504_0_MAIN_LOAD(+(x1[1], 1), +(x2[1], 1), x0[1])), ≥)∧[bni_13] = 0∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_14] ≥ 0)
POL(TRUE) = 0
POL(FALSE) = 0
POL(504_0_MAIN_LOAD(x1, x2, x3)) = [1] + [2]x3 + [-1]x2 + [-1]x1
POL(COND_504_0_MAIN_LOAD(x1, x2, x3, x4)) = [1] + [2]x4 + [-1]x3 + [-1]x2
POL(&&(x1, x2)) = [-1]
POL(>(x1, x2)) = [-1]
POL(-1) = [-1]
POL(<(x1, x2)) = [-1]
POL(+(x1, x2)) = x1 + x2
POL(1) = [1]
COND_504_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 504_0_MAIN_LOAD(+(x1[1], 1), +(x2[1], 1), x0[1])
504_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])
504_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_504_0_MAIN_LOAD(&&(&&(&&(>(x2[0], -1), <(x2[0], x0[0])), >(x1[0], -1)), <(x1[0], x0[0])), x1[0], x2[0], x0[0])
!= | ~ | 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 |
Boolean, Integer
!= | ~ | 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 |
Integer