/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 317 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 63 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 41 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (17) IRSwT (18) TempFilterProof [SOUND, 31 ms] (19) IntTRS (20) PolynomialOrderProcessor [EQUIVALENT, 10 ms] (21) YES (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] (24) IRSwT (25) TempFilterProof [SOUND, 19 ms] (26) IntTRS (27) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (28) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: /** * 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 PastaB13 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); int z = Random.random(); while (x > z || y > z) { if (x > z) { x--; } else if (y > z) { y--; } else { continue; } } } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: /** * 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 PastaB13 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); int z = Random.random(); while (x > z || y > z) { if (x > z) { x--; } else if (y > z) { y--; } else { continue; } } } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: PastaB13.main([Ljava/lang/String;)V: Graph of 262 nodes with 1 SCC. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 1 SCCs. ---------------------------------------- (6) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: PastaB13.main([Ljava/lang/String;)V SCC calls the following helper methods: Performed SCC analyses: *Used field analysis yielded the following read fields: *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (7) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 28 IRulesP rules: f516_0_main_Load(EOS(STATIC_516), i75, i48, i71, i75) -> f519_0_main_GT(EOS(STATIC_519), i75, i48, i71, i75, i71) :|: TRUE f519_0_main_GT(EOS(STATIC_519), i75, i48, i71, i75, i71) -> f524_0_main_GT(EOS(STATIC_524), i75, i48, i71, i75, i71) :|: i75 > i71 f519_0_main_GT(EOS(STATIC_519), i75, i48, i71, i75, i71) -> f525_0_main_GT(EOS(STATIC_525), i75, i48, i71, i75, i71) :|: i75 <= i71 f524_0_main_GT(EOS(STATIC_524), i75, i48, i71, i75, i71) -> f528_0_main_Load(EOS(STATIC_528), i75, i48, i71) :|: i75 > i71 f528_0_main_Load(EOS(STATIC_528), i75, i48, i71) -> f531_0_main_Load(EOS(STATIC_531), i75, i48, i71, i75) :|: TRUE f531_0_main_Load(EOS(STATIC_531), i75, i48, i71, i75) -> f535_0_main_LE(EOS(STATIC_535), i75, i48, i71, i75, i71) :|: TRUE f535_0_main_LE(EOS(STATIC_535), i75, i48, i71, i75, i71) -> f549_0_main_LE(EOS(STATIC_549), i75, i48, i71, i75, i71) :|: i75 > i71 f549_0_main_LE(EOS(STATIC_549), i75, i48, i71, i75, i71) -> f553_0_main_Inc(EOS(STATIC_553), i75, i48, i71) :|: i75 > i71 f553_0_main_Inc(EOS(STATIC_553), i75, i48, i71) -> f556_0_main_JMP(EOS(STATIC_556), i75 + -1, i48, i71) :|: TRUE f556_0_main_JMP(EOS(STATIC_556), i80, i48, i71) -> f561_0_main_Load(EOS(STATIC_561), i80, i48, i71) :|: TRUE f561_0_main_Load(EOS(STATIC_561), i80, i48, i71) -> f511_0_main_Load(EOS(STATIC_511), i80, i48, i71) :|: TRUE f511_0_main_Load(EOS(STATIC_511), i75, i48, i71) -> f516_0_main_Load(EOS(STATIC_516), i75, i48, i71, i75) :|: TRUE f525_0_main_GT(EOS(STATIC_525), i75, i48, i71, i75, i71) -> f529_0_main_Load(EOS(STATIC_529), i75, i48, i71) :|: i75 <= i71 f529_0_main_Load(EOS(STATIC_529), i75, i48, i71) -> f532_0_main_Load(EOS(STATIC_532), i75, i48, i71, i48) :|: TRUE f532_0_main_Load(EOS(STATIC_532), i75, i48, i71, i48) -> f536_0_main_LE(EOS(STATIC_536), i75, i48, i71, i48, i71) :|: TRUE f536_0_main_LE(EOS(STATIC_536), i75, i48, i71, i48, i71) -> f551_0_main_LE(EOS(STATIC_551), i75, i48, i71, i48, i71) :|: i48 > i71 f551_0_main_LE(EOS(STATIC_551), i75, i48, i71, i48, i71) -> f555_0_main_Load(EOS(STATIC_555), i75, i48, i71) :|: i48 > i71 f555_0_main_Load(EOS(STATIC_555), i75, i48, i71) -> f558_0_main_Load(EOS(STATIC_558), i75, i48, i71, i75) :|: TRUE f558_0_main_Load(EOS(STATIC_558), i75, i48, i71, i75) -> f574_0_main_LE(EOS(STATIC_574), i75, i48, i71, i75, i71) :|: TRUE f574_0_main_LE(EOS(STATIC_574), i75, i48, i71, i75, i71) -> f576_0_main_LE(EOS(STATIC_576), i75, i48, i71, i75, i71) :|: i75 <= i71 f576_0_main_LE(EOS(STATIC_576), i75, i48, i71, i75, i71) -> f579_0_main_Load(EOS(STATIC_579), i75, i48, i71) :|: i75 <= i71 f579_0_main_Load(EOS(STATIC_579), i75, i48, i71) -> f580_0_main_Load(EOS(STATIC_580), i75, i48, i71, i48) :|: TRUE f580_0_main_Load(EOS(STATIC_580), i75, i48, i71, i48) -> f581_0_main_LE(EOS(STATIC_581), i75, i48, i71, i48, i71) :|: TRUE f581_0_main_LE(EOS(STATIC_581), i75, i48, i71, i48, i71) -> f584_0_main_LE(EOS(STATIC_584), i75, i48, i71, i48, i71) :|: i48 > i71 f584_0_main_LE(EOS(STATIC_584), i75, i48, i71, i48, i71) -> f586_0_main_Inc(EOS(STATIC_586), i75, i48, i71) :|: i48 > i71 f586_0_main_Inc(EOS(STATIC_586), i75, i48, i71) -> f587_0_main_JMP(EOS(STATIC_587), i75, i48 + -1, i71) :|: TRUE f587_0_main_JMP(EOS(STATIC_587), i75, i86, i71) -> f591_0_main_Load(EOS(STATIC_591), i75, i86, i71) :|: TRUE f591_0_main_Load(EOS(STATIC_591), i75, i86, i71) -> f511_0_main_Load(EOS(STATIC_511), i75, i86, i71) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f516_0_main_Load(EOS(STATIC_516), i75:0, i48:0, i71:0, i75:0) -> f516_0_main_Load(EOS(STATIC_516), i75:0 - 1, i48:0, i71:0, i75:0 - 1) :|: i75:0 > i71:0 f516_0_main_Load(EOS(STATIC_516), i75:0, i48:0, i71:0, i75:0) -> f516_0_main_Load(EOS(STATIC_516), i75:0, i48:0 - 1, i71:0, i75:0) :|: i75:0 <= i71:0 && i71:0 < i48:0 Filtered constant ground arguments: f516_0_main_Load(x1, x2, x3, x4, x5) -> f516_0_main_Load(x2, x3, x4, x5) EOS(x1) -> EOS Filtered duplicate arguments: f516_0_main_Load(x1, x2, x3, x4) -> f516_0_main_Load(x2, x3, x4) Finished conversion. Obtained 2 rules.P rules: f516_0_main_Load(i48:0, i71:0, i75:0) -> f516_0_main_Load(i48:0, i71:0, i75:0 - 1) :|: i75:0 > i71:0 f516_0_main_Load(i48:0, i71:0, i75:0) -> f516_0_main_Load(i48:0 - 1, i71:0, i75:0) :|: i75:0 <= i71:0 && i71:0 < i48:0 ---------------------------------------- (8) Obligation: Rules: f516_0_main_Load(i48:0, i71:0, i75:0) -> f516_0_main_Load(i48:0, i71:0, i75:0 - 1) :|: i75:0 > i71:0 f516_0_main_Load(x, x1, x2) -> f516_0_main_Load(x - 1, x1, x2) :|: x2 <= x1 && x1 < x ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f516_0_main_Load(i48:0, i71:0, i75:0) -> f516_0_main_Load(i48:0, i71:0, arith) :|: i75:0 > i71:0 && arith = i75:0 - 1 f516_0_main_Load(x3, x4, x5) -> f516_0_main_Load(x6, x4, x5) :|: x5 <= x4 && x4 < x3 && x6 = x3 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f516_0_main_Load(i48:0, i71:0, i75:0) -> f516_0_main_Load(i48:0, i71:0, arith) :|: i75:0 > i71:0 && arith = i75:0 - 1 (2) f516_0_main_Load(x3, x4, x5) -> f516_0_main_Load(x6, x4, x5) :|: x5 <= x4 && x4 < x3 && x6 = x3 - 1 Arcs: (1) -> (1), (2) (2) -> (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f516_0_main_Load(i48:0, i71:0, i75:0) -> f516_0_main_Load(i48:0, i71:0, arith) :|: i75:0 > i71:0 && arith = i75:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f516_0_main_Load(i48:0:0, i71:0:0, i75:0:0) -> f516_0_main_Load(i48:0:0, i71:0:0, i75:0:0 - 1) :|: i75:0:0 > i71:0:0 ---------------------------------------- (16) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f516_0_main_Load(x1, x2, x3) -> f516_0_main_Load(x2, x3) ---------------------------------------- (17) Obligation: Rules: f516_0_main_Load(i71:0:0, i75:0:0) -> f516_0_main_Load(i71:0:0, i75:0:0 - 1) :|: i75:0:0 > i71:0:0 ---------------------------------------- (18) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f516_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (19) Obligation: Rules: f516_0_main_Load(i71:0:0, i75:0:0) -> f516_0_main_Load(i71:0:0, c) :|: c = i75:0:0 - 1 && i75:0:0 > i71:0:0 ---------------------------------------- (20) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f516_0_main_Load(x, x1)] = -x + x1 The following rules are decreasing: f516_0_main_Load(i71:0:0, i75:0:0) -> f516_0_main_Load(i71:0:0, c) :|: c = i75:0:0 - 1 && i75:0:0 > i71:0:0 The following rules are bounded: f516_0_main_Load(i71:0:0, i75:0:0) -> f516_0_main_Load(i71:0:0, c) :|: c = i75:0:0 - 1 && i75:0:0 > i71:0:0 ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) f516_0_main_Load(x3, x4, x5) -> f516_0_main_Load(x6, x4, x5) :|: x5 <= x4 && x4 < x3 && x6 = x3 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: f516_0_main_Load(x3:0, x4:0, x5:0) -> f516_0_main_Load(x3:0 - 1, x4:0, x5:0) :|: x5:0 <= x4:0 && x4:0 < x3:0 ---------------------------------------- (25) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f516_0_main_Load(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (26) Obligation: Rules: f516_0_main_Load(x3:0, x4:0, x5:0) -> f516_0_main_Load(c, x4:0, x5:0) :|: c = x3:0 - 1 && (x5:0 <= x4:0 && x4:0 < x3:0) ---------------------------------------- (27) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f516_0_main_Load(x, x1, x2)] = x - x1 The following rules are decreasing: f516_0_main_Load(x3:0, x4:0, x5:0) -> f516_0_main_Load(c, x4:0, x5:0) :|: c = x3:0 - 1 && (x5:0 <= x4:0 && x4:0 < x3:0) The following rules are bounded: f516_0_main_Load(x3:0, x4:0, x5:0) -> f516_0_main_Load(c, x4:0, x5:0) :|: c = x3:0 - 1 && (x5:0 <= x4:0 && x4:0 < x3:0) ---------------------------------------- (28) YES