/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 298 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 4 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 80 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 36 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 30 ms] (16) IntTRS (17) RankingReductionPairProof [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 PastaB7 { 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) { x--; y--; } } } 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 PastaB7 { 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) { x--; y--; } } } 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: PastaB7.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: PastaB7.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: f513_0_main_Load(EOS(STATIC_513), i77, i78, i71, i77) -> f516_0_main_LE(EOS(STATIC_516), i77, i78, i71, i77, i71) :|: TRUE f516_0_main_LE(EOS(STATIC_516), i77, i78, i71, i77, i71) -> f522_0_main_LE(EOS(STATIC_522), i77, i78, i71, i77, i71) :|: i77 > i71 f522_0_main_LE(EOS(STATIC_522), i77, i78, i71, i77, i71) -> f529_0_main_Load(EOS(STATIC_529), i77, i78, i71) :|: i77 > i71 f529_0_main_Load(EOS(STATIC_529), i77, i78, i71) -> f532_0_main_Load(EOS(STATIC_532), i77, i78, i71, i78) :|: TRUE f532_0_main_Load(EOS(STATIC_532), i77, i78, i71, i78) -> f534_0_main_LE(EOS(STATIC_534), i77, i78, i71, i78, i71) :|: TRUE f534_0_main_LE(EOS(STATIC_534), i77, i78, i71, i78, i71) -> f539_0_main_LE(EOS(STATIC_539), i77, i78, i71, i78, i71) :|: i78 > i71 f539_0_main_LE(EOS(STATIC_539), i77, i78, i71, i78, i71) -> f548_0_main_Inc(EOS(STATIC_548), i77, i78, i71) :|: i78 > i71 f548_0_main_Inc(EOS(STATIC_548), i77, i78, i71) -> f549_0_main_Inc(EOS(STATIC_549), i77 + -1, i78, i71) :|: TRUE f549_0_main_Inc(EOS(STATIC_549), i85, i78, i71) -> f550_0_main_JMP(EOS(STATIC_550), i85, i78 + -1, i71) :|: TRUE f550_0_main_JMP(EOS(STATIC_550), i85, i86, i71) -> f558_0_main_Load(EOS(STATIC_558), i85, i86, i71) :|: TRUE f558_0_main_Load(EOS(STATIC_558), i85, i86, i71) -> f509_0_main_Load(EOS(STATIC_509), i85, i86, i71) :|: TRUE f509_0_main_Load(EOS(STATIC_509), i77, i78, i71) -> f513_0_main_Load(EOS(STATIC_513), i77, i78, i71, i77) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f513_0_main_Load(EOS(STATIC_513), i77:0, i78:0, i71:0, i77:0) -> f513_0_main_Load(EOS(STATIC_513), i77:0 - 1, i78:0 - 1, i71:0, i77:0 - 1) :|: i77:0 > i71:0 && i78:0 > i71:0 Filtered constant ground arguments: f513_0_main_Load(x1, x2, x3, x4, x5) -> f513_0_main_Load(x2, x3, x4, x5) EOS(x1) -> EOS Filtered duplicate arguments: f513_0_main_Load(x1, x2, x3, x4) -> f513_0_main_Load(x2, x3, x4) Finished conversion. Obtained 1 rules.P rules: f513_0_main_Load(i78:0, i71:0, i77:0) -> f513_0_main_Load(i78:0 - 1, i71:0, i77:0 - 1) :|: i77:0 > i71:0 && i78:0 > i71:0 ---------------------------------------- (8) Obligation: Rules: f513_0_main_Load(i78:0, i71:0, i77:0) -> f513_0_main_Load(i78:0 - 1, i71:0, i77:0 - 1) :|: i77:0 > i71:0 && i78:0 > i71:0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f513_0_main_Load(i78:0, i71:0, i77:0) -> f513_0_main_Load(arith, i71:0, arith1) :|: i77:0 > i71:0 && i78:0 > i71:0 && arith = i78:0 - 1 && arith1 = i77:0 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f513_0_main_Load(i78:0, i71:0, i77:0) -> f513_0_main_Load(arith, i71:0, arith1) :|: i77:0 > i71:0 && i78:0 > i71:0 && arith = i78:0 - 1 && arith1 = i77:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f513_0_main_Load(i78:0, i71:0, i77:0) -> f513_0_main_Load(arith, i71:0, arith1) :|: i77:0 > i71:0 && i78:0 > i71:0 && arith = i78:0 - 1 && arith1 = i77:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f513_0_main_Load(i78:0:0, i71:0:0, i77:0:0) -> f513_0_main_Load(i78:0:0 - 1, i71:0:0, i77:0:0 - 1) :|: i77:0:0 > i71:0:0 && i78:0:0 > i71:0:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f513_0_main_Load(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f513_0_main_Load(i78:0:0, i71:0:0, i77:0:0) -> f513_0_main_Load(c, i71:0:0, c1) :|: c1 = i77:0:0 - 1 && c = i78:0:0 - 1 && (i77:0:0 > i71:0:0 && i78:0:0 > i71:0:0) ---------------------------------------- (17) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f513_0_main_Load ] = -1*f513_0_main_Load_2 + f513_0_main_Load_1 The following rules are decreasing: f513_0_main_Load(i78:0:0, i71:0:0, i77:0:0) -> f513_0_main_Load(c, i71:0:0, c1) :|: c1 = i77:0:0 - 1 && c = i78:0:0 - 1 && (i77:0:0 > i71:0:0 && i78:0:0 > i71:0:0) The following rules are bounded: f513_0_main_Load(i78:0:0, i71:0:0, i77:0:0) -> f513_0_main_Load(c, i71:0:0, c1) :|: c1 = i77:0:0 - 1 && c = i78:0:0 - 1 && (i77:0:0 > i71:0:0 && i78:0:0 > i71:0:0) ---------------------------------------- (18) YES