/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 316 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 83 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 31 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 41 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 12 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 PastaA9 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); int z = Random.random(); if (y > 0) { while (x >= z) { z += 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 PastaA9 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); int z = Random.random(); if (y > 0) { while (x >= z) { z += 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: PastaA9.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: PastaA9.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 10 IRulesP rules: f448_0_main_LT(EOS(STATIC_448), i19, i74, i72, i19, i72) -> f470_0_main_Load(EOS(STATIC_470), i19, i74, i72) :|: i19 >= i72 f470_0_main_Load(EOS(STATIC_470), i19, i74, i72) -> f481_0_main_Load(EOS(STATIC_481), i19, i74, i72) :|: TRUE f481_0_main_Load(EOS(STATIC_481), i19, i74, i72) -> f484_0_main_IntArithmetic(EOS(STATIC_484), i19, i74, i72, i74) :|: TRUE f484_0_main_IntArithmetic(EOS(STATIC_484), i19, i74, i72, i74) -> f490_0_main_Store(EOS(STATIC_490), i19, i74, i72 + i74) :|: i72 >= 0 && i74 > 0 f490_0_main_Store(EOS(STATIC_490), i19, i74, i76) -> f495_0_main_JMP(EOS(STATIC_495), i19, i74, i76) :|: TRUE f495_0_main_JMP(EOS(STATIC_495), i19, i74, i76) -> f519_0_main_Load(EOS(STATIC_519), i19, i74, i76) :|: TRUE f519_0_main_Load(EOS(STATIC_519), i19, i74, i76) -> f435_0_main_Load(EOS(STATIC_435), i19, i74, i76) :|: TRUE f435_0_main_Load(EOS(STATIC_435), i19, i74, i72) -> f439_0_main_Load(EOS(STATIC_439), i19, i74, i72, i19) :|: TRUE f439_0_main_Load(EOS(STATIC_439), i19, i74, i72, i19) -> f442_0_main_LT(EOS(STATIC_442), i19, i74, i72, i19, i72) :|: TRUE f442_0_main_LT(EOS(STATIC_442), i19, i74, i72, i19, i72) -> f448_0_main_LT(EOS(STATIC_448), i19, i74, i72, i19, i72) :|: i19 >= i72 Combined rules. Obtained 1 IRulesP rules: f448_0_main_LT(EOS(STATIC_448), i19:0, i74:0, i72:0, i19:0, i72:0) -> f448_0_main_LT(EOS(STATIC_448), i19:0, i74:0, i72:0 + i74:0, i19:0, i72:0 + i74:0) :|: i72:0 <= i19:0 && i74:0 > 0 && i72:0 + i74:0 <= i19:0 && i72:0 > -1 Filtered constant ground arguments: f448_0_main_LT(x1, x2, x3, x4, x5, x6) -> f448_0_main_LT(x2, x3, x4, x5, x6) EOS(x1) -> EOS Filtered duplicate arguments: f448_0_main_LT(x1, x2, x3, x4, x5) -> f448_0_main_LT(x2, x4, x5) Finished conversion. Obtained 1 rules.P rules: f448_0_main_LT(i74:0, i19:0, i72:0) -> f448_0_main_LT(i74:0, i19:0, i72:0 + i74:0) :|: i74:0 > 0 && i72:0 <= i19:0 && i72:0 > -1 && i72:0 + i74:0 <= i19:0 ---------------------------------------- (8) Obligation: Rules: f448_0_main_LT(i74:0, i19:0, i72:0) -> f448_0_main_LT(i74:0, i19:0, i72:0 + i74:0) :|: i74:0 > 0 && i72:0 <= i19:0 && i72:0 > -1 && i72:0 + i74:0 <= i19:0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f448_0_main_LT(i74:0, i19:0, i72:0) -> f448_0_main_LT(i74:0, i19:0, arith) :|: i74:0 > 0 && i72:0 <= i19:0 && i72:0 > -1 && i72:0 + i74:0 <= i19:0 && arith = i72:0 + i74:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f448_0_main_LT(i74:0, i19:0, i72:0) -> f448_0_main_LT(i74:0, i19:0, arith) :|: i74:0 > 0 && i72:0 <= i19:0 && i72:0 > -1 && i72:0 + i74:0 <= i19:0 && arith = i72:0 + i74:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f448_0_main_LT(i74:0, i19:0, i72:0) -> f448_0_main_LT(i74:0, i19:0, arith) :|: i74:0 > 0 && i72:0 <= i19:0 && i72:0 > -1 && i72:0 + i74:0 <= i19:0 && arith = i72:0 + i74:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f448_0_main_LT(i74:0:0, i19:0:0, i72:0:0) -> f448_0_main_LT(i74:0:0, i19:0:0, i72:0:0 + i74:0:0) :|: i72:0:0 > -1 && i72:0:0 + i74:0:0 <= i19:0:0 && i72:0:0 <= i19:0:0 && i74:0:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f448_0_main_LT(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f448_0_main_LT(i74:0:0, i19:0:0, i72:0:0) -> f448_0_main_LT(i74:0:0, i19:0:0, c) :|: c = i72:0:0 + i74:0:0 && (i72:0:0 > -1 && i72:0:0 + i74:0:0 <= i19:0:0 && i72:0:0 <= i19:0:0 && i74:0:0 > 0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2)] = x1 - x2 The following rules are decreasing: f448_0_main_LT(i74:0:0, i19:0:0, i72:0:0) -> f448_0_main_LT(i74:0:0, i19:0:0, c) :|: c = i72:0:0 + i74:0:0 && (i72:0:0 > -1 && i72:0:0 + i74:0:0 <= i19:0:0 && i72:0:0 <= i19:0:0 && i74:0:0 > 0) The following rules are bounded: f448_0_main_LT(i74:0:0, i19:0:0, i72:0:0) -> f448_0_main_LT(i74:0:0, i19:0:0, c) :|: c = i72:0:0 + i74:0:0 && (i72:0:0 > -1 && i72:0:0 + i74:0:0 <= i19:0:0 && i72:0:0 <= i19:0:0 && i74:0:0 > 0) ---------------------------------------- (18) YES