/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 307 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 66 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 34 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 18 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) 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 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(); } } ---------------------------------------- (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 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(); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: PastaA7.main([Ljava/lang/String;)V: Graph of 249 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: PastaA7.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 12 IRulesP rules: f505_0_main_Load(EOS(STATIC_505), i77, i78, i79, i77) -> f509_0_main_LE(EOS(STATIC_509), i77, i78, i79, i77, i78) :|: TRUE f509_0_main_LE(EOS(STATIC_509), i77, i78, i79, i77, i78) -> f526_0_main_LE(EOS(STATIC_526), i77, i78, i79, i77, i78) :|: i77 > i78 f526_0_main_LE(EOS(STATIC_526), i77, i78, i79, i77, i78) -> f529_0_main_Load(EOS(STATIC_529), i77, i78, i79) :|: i77 > i78 f529_0_main_Load(EOS(STATIC_529), i77, i78, i79) -> f532_0_main_Load(EOS(STATIC_532), i77, i78, i79, i77) :|: TRUE f532_0_main_Load(EOS(STATIC_532), i77, i78, i79, i77) -> f534_0_main_LE(EOS(STATIC_534), i77, i78, i79, i77, i79) :|: TRUE f534_0_main_LE(EOS(STATIC_534), i77, i78, i79, i77, i79) -> f546_0_main_LE(EOS(STATIC_546), i77, i78, i79, i77, i79) :|: i77 > i79 f546_0_main_LE(EOS(STATIC_546), i77, i78, i79, i77, i79) -> f552_0_main_Inc(EOS(STATIC_552), i77, i78, i79) :|: i77 > i79 f552_0_main_Inc(EOS(STATIC_552), i77, i78, i79) -> f555_0_main_Inc(EOS(STATIC_555), i77, i78 + 1, i79) :|: TRUE f555_0_main_Inc(EOS(STATIC_555), i77, i87, i79) -> f557_0_main_JMP(EOS(STATIC_557), i77, i87, i79 + 1) :|: TRUE f557_0_main_JMP(EOS(STATIC_557), i77, i87, i88) -> f568_0_main_Load(EOS(STATIC_568), i77, i87, i88) :|: TRUE f568_0_main_Load(EOS(STATIC_568), i77, i87, i88) -> f500_0_main_Load(EOS(STATIC_500), i77, i87, i88) :|: TRUE f500_0_main_Load(EOS(STATIC_500), i77, i78, i79) -> f505_0_main_Load(EOS(STATIC_505), i77, i78, i79, i77) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f505_0_main_Load(EOS(STATIC_505), i77:0, i78:0, i79:0, i77:0) -> f505_0_main_Load(EOS(STATIC_505), i77:0, i78:0 + 1, i79:0 + 1, i77:0) :|: i78:0 < i77:0 && i79:0 < i77:0 Filtered constant ground arguments: f505_0_main_Load(x1, x2, x3, x4, x5) -> f505_0_main_Load(x2, x3, x4, x5) EOS(x1) -> EOS Filtered duplicate arguments: f505_0_main_Load(x1, x2, x3, x4) -> f505_0_main_Load(x2, x3, x4) Finished conversion. Obtained 1 rules.P rules: f505_0_main_Load(i78:0, i79:0, i77:0) -> f505_0_main_Load(i78:0 + 1, i79:0 + 1, i77:0) :|: i78:0 < i77:0 && i79:0 < i77:0 ---------------------------------------- (8) Obligation: Rules: f505_0_main_Load(i78:0, i79:0, i77:0) -> f505_0_main_Load(i78:0 + 1, i79:0 + 1, i77:0) :|: i78:0 < i77:0 && i79:0 < i77:0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f505_0_main_Load(i78:0, i79:0, i77:0) -> f505_0_main_Load(arith, arith1, i77:0) :|: i78:0 < i77:0 && i79:0 < i77:0 && arith = i78:0 + 1 && arith1 = i79:0 + 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f505_0_main_Load(i78:0, i79:0, i77:0) -> f505_0_main_Load(arith, arith1, i77:0) :|: i78:0 < i77:0 && i79:0 < i77:0 && arith = i78:0 + 1 && arith1 = i79:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f505_0_main_Load(i78:0, i79:0, i77:0) -> f505_0_main_Load(arith, arith1, i77:0) :|: i78:0 < i77:0 && i79:0 < i77:0 && arith = i78:0 + 1 && arith1 = i79:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f505_0_main_Load(i78:0:0, i79:0:0, i77:0:0) -> f505_0_main_Load(i78:0:0 + 1, i79:0:0 + 1, i77:0:0) :|: i78:0:0 < i77:0:0 && i79:0:0 < i77:0:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f505_0_main_Load(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f505_0_main_Load(i78:0:0, i79:0:0, i77:0:0) -> f505_0_main_Load(c, c1, i77:0:0) :|: c1 = i79:0:0 + 1 && c = i78:0:0 + 1 && (i78:0:0 < i77:0:0 && i79:0:0 < i77:0:0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f505_0_main_Load(x, x1, x2)] = -x1 + x2 The following rules are decreasing: f505_0_main_Load(i78:0:0, i79:0:0, i77:0:0) -> f505_0_main_Load(c, c1, i77:0:0) :|: c1 = i79:0:0 + 1 && c = i78:0:0 + 1 && (i78:0:0 < i77:0:0 && i79:0:0 < i77:0:0) The following rules are bounded: f505_0_main_Load(i78:0:0, i79:0:0, i77:0:0) -> f505_0_main_Load(c, c1, i77:0:0) :|: c1 = i79:0:0 + 1 && c = i78:0:0 + 1 && (i78:0:0 < i77:0:0 && i79:0:0 < i77:0:0) ---------------------------------------- (18) YES