/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.jar /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph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, 411 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 131 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 46 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (17) IRSwT (18) TempFilterProof [SOUND, 36 ms] (19) IntTRS (20) RankingReductionPairProof [EQUIVALENT, 11 ms] (21) YES (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] (24) IRSwT (25) TempFilterProof [SOUND, 7 ms] (26) IntTRS (27) PolynomialOrderProcessor [EQUIVALENT, 1 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 PastaB17 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); int z = Random.random(); while (x > z) { while (y > z) { y--; } x--; } } } 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 PastaB17 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); int z = Random.random(); while (x > z) { while (y > z) { y--; } x--; } } } 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: PastaB17.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: PastaB17.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 16 IRulesP rules: f416_0_main_Load(EOS(STATIC_416), i19, i42, i71, i19) -> f419_0_main_LE(EOS(STATIC_419), i19, i42, i71, i19, i71) :|: TRUE f419_0_main_LE(EOS(STATIC_419), i19, i42, i71, i19, i71) -> f424_0_main_LE(EOS(STATIC_424), i19, i42, i71, i19, i71) :|: i19 > i71 f424_0_main_LE(EOS(STATIC_424), i19, i42, i71, i19, i71) -> f434_0_main_Load(EOS(STATIC_434), i19, i42, i71) :|: i19 > i71 f434_0_main_Load(EOS(STATIC_434), i19, i42, i71) -> f442_0_main_Load(EOS(STATIC_442), i19, i42, i71, i42) :|: TRUE f442_0_main_Load(EOS(STATIC_442), i19, i42, i71, i42) -> f445_0_main_LE(EOS(STATIC_445), i19, i42, i71, i42, i71) :|: TRUE f445_0_main_LE(EOS(STATIC_445), i19, i42, i71, i42, i71) -> f452_0_main_LE(EOS(STATIC_452), i19, i42, i71, i42, i71) :|: i42 <= i71 f445_0_main_LE(EOS(STATIC_445), i19, i42, i71, i42, i71) -> f453_0_main_LE(EOS(STATIC_453), i19, i42, i71, i42, i71) :|: i42 > i71 f452_0_main_LE(EOS(STATIC_452), i19, i42, i71, i42, i71) -> f460_0_main_Inc(EOS(STATIC_460), i19, i42, i71) :|: i42 <= i71 f460_0_main_Inc(EOS(STATIC_460), i19, i42, i71) -> f479_0_main_JMP(EOS(STATIC_479), i19 + -1, i42, i71) :|: TRUE f479_0_main_JMP(EOS(STATIC_479), i75, i42, i71) -> f494_0_main_Load(EOS(STATIC_494), i75, i42, i71) :|: TRUE f494_0_main_Load(EOS(STATIC_494), i75, i42, i71) -> f413_0_main_Load(EOS(STATIC_413), i75, i42, i71) :|: TRUE f413_0_main_Load(EOS(STATIC_413), i19, i42, i71) -> f416_0_main_Load(EOS(STATIC_416), i19, i42, i71, i19) :|: TRUE f453_0_main_LE(EOS(STATIC_453), i19, i42, i71, i42, i71) -> f465_0_main_Inc(EOS(STATIC_465), i19, i42, i71) :|: i42 > i71 f465_0_main_Inc(EOS(STATIC_465), i19, i42, i71) -> f483_0_main_JMP(EOS(STATIC_483), i19, i42 + -1, i71) :|: TRUE f483_0_main_JMP(EOS(STATIC_483), i19, i76, i71) -> f507_0_main_Load(EOS(STATIC_507), i19, i76, i71) :|: TRUE f507_0_main_Load(EOS(STATIC_507), i19, i76, i71) -> f434_0_main_Load(EOS(STATIC_434), i19, i76, i71) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f445_0_main_LE(EOS(STATIC_445), i19:0, i42:0, i71:0, i42:0, i71:0) -> f445_0_main_LE(EOS(STATIC_445), i19:0 - 1, i42:0, i71:0, i42:0, i71:0) :|: i71:0 >= i42:0 && i71:0 < i19:0 - 1 f445_0_main_LE(EOS(STATIC_445), i19:0, i42:0, i71:0, i42:0, i71:0) -> f445_0_main_LE(EOS(STATIC_445), i19:0, i42:0 - 1, i71:0, i42:0 - 1, i71:0) :|: i71:0 < i42:0 Filtered constant ground arguments: f445_0_main_LE(x1, x2, x3, x4, x5, x6) -> f445_0_main_LE(x2, x3, x4, x5, x6) EOS(x1) -> EOS Filtered duplicate arguments: f445_0_main_LE(x1, x2, x3, x4, x5) -> f445_0_main_LE(x1, x4, x5) Finished conversion. Obtained 2 rules.P rules: f445_0_main_LE(i19:0, i42:0, i71:0) -> f445_0_main_LE(i19:0 - 1, i42:0, i71:0) :|: i71:0 >= i42:0 && i71:0 < i19:0 - 1 f445_0_main_LE(i19:0, i42:0, i71:0) -> f445_0_main_LE(i19:0, i42:0 - 1, i71:0) :|: i71:0 < i42:0 ---------------------------------------- (8) Obligation: Rules: f445_0_main_LE(i19:0, i42:0, i71:0) -> f445_0_main_LE(i19:0 - 1, i42:0, i71:0) :|: i71:0 >= i42:0 && i71:0 < i19:0 - 1 f445_0_main_LE(x, x1, x2) -> f445_0_main_LE(x, x1 - 1, x2) :|: x2 < x1 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f445_0_main_LE(i19:0, i42:0, i71:0) -> f445_0_main_LE(arith, i42:0, i71:0) :|: i71:0 >= i42:0 && i71:0 < i19:0 - 1 && arith = i19:0 - 1 f445_0_main_LE(x3, x4, x5) -> f445_0_main_LE(x3, x6, x5) :|: x5 < x4 && x6 = x4 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f445_0_main_LE(i19:0, i42:0, i71:0) -> f445_0_main_LE(arith, i42:0, i71:0) :|: i71:0 >= i42:0 && i71:0 < i19:0 - 1 && arith = i19:0 - 1 (2) f445_0_main_LE(x3, x4, x5) -> f445_0_main_LE(x3, x6, x5) :|: x5 < x4 && x6 = x4 - 1 Arcs: (1) -> (1) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f445_0_main_LE(x3, x4, x5) -> f445_0_main_LE(x3, x6, x5) :|: x5 < x4 && x6 = x4 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f445_0_main_LE(x3:0, x4:0, x5:0) -> f445_0_main_LE(x3:0, x4:0 - 1, x5:0) :|: x5:0 < x4:0 ---------------------------------------- (16) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f445_0_main_LE(x1, x2, x3) -> f445_0_main_LE(x2, x3) ---------------------------------------- (17) Obligation: Rules: f445_0_main_LE(x4:0, x5:0) -> f445_0_main_LE(x4:0 - 1, x5:0) :|: x5:0 < x4:0 ---------------------------------------- (18) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f445_0_main_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (19) Obligation: Rules: f445_0_main_LE(x4:0, x5:0) -> f445_0_main_LE(c, x5:0) :|: c = x4:0 - 1 && x5:0 < x4:0 ---------------------------------------- (20) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f445_0_main_LE ] = -1*f445_0_main_LE_2 + f445_0_main_LE_1 The following rules are decreasing: f445_0_main_LE(x4:0, x5:0) -> f445_0_main_LE(c, x5:0) :|: c = x4:0 - 1 && x5:0 < x4:0 The following rules are bounded: f445_0_main_LE(x4:0, x5:0) -> f445_0_main_LE(c, x5:0) :|: c = x4:0 - 1 && x5:0 < x4:0 ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) f445_0_main_LE(i19:0, i42:0, i71:0) -> f445_0_main_LE(arith, i42:0, i71:0) :|: i71:0 >= i42:0 && i71:0 < i19:0 - 1 && arith = i19:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: f445_0_main_LE(i19:0:0, i42:0:0, i71:0:0) -> f445_0_main_LE(i19:0:0 - 1, i42:0:0, i71:0:0) :|: i71:0:0 >= i42:0:0 && i71:0:0 < i19:0:0 - 1 ---------------------------------------- (25) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f445_0_main_LE(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (26) Obligation: Rules: f445_0_main_LE(i19:0:0, i42:0:0, i71:0:0) -> f445_0_main_LE(c, i42:0:0, i71:0:0) :|: c = i19:0:0 - 1 && (i71:0:0 >= i42:0:0 && i71:0:0 < i19:0:0 - 1) ---------------------------------------- (27) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f445_0_main_LE(x, x1, x2)] = x - x2 The following rules are decreasing: f445_0_main_LE(i19:0:0, i42:0:0, i71:0:0) -> f445_0_main_LE(c, i42:0:0, i71:0:0) :|: c = i19:0:0 - 1 && (i71:0:0 >= i42:0:0 && i71:0:0 < i19:0:0 - 1) The following rules are bounded: f445_0_main_LE(i19:0:0, i42:0:0, i71:0:0) -> f445_0_main_LE(c, i42:0:0, i71:0:0) :|: c = i19:0:0 - 1 && (i71:0:0 >= i42:0:0 && i71:0:0 < i19:0:0 - 1) ---------------------------------------- (28) YES