/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 310 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 125 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 42 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (17) IRSwT (18) TempFilterProof [SOUND, 25 ms] (19) IntTRS (20) RankingReductionPairProof [EQUIVALENT, 0 ms] (21) YES (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] (24) IRSwT (25) TempFilterProof [SOUND, 15 ms] (26) IntTRS (27) RankingReductionPairProof [EQUIVALENT, 7 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 250 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: f501_0_main_Load(EOS(STATIC_501), i77, i42, i71, i77) -> f511_0_main_LE(EOS(STATIC_511), i77, i42, i71, i77, i71) :|: TRUE f511_0_main_LE(EOS(STATIC_511), i77, i42, i71, i77, i71) -> f517_0_main_LE(EOS(STATIC_517), i77, i42, i71, i77, i71) :|: i77 > i71 f517_0_main_LE(EOS(STATIC_517), i77, i42, i71, i77, i71) -> f524_0_main_Load(EOS(STATIC_524), i77, i42, i71) :|: i77 > i71 f524_0_main_Load(EOS(STATIC_524), i77, i42, i71) -> f530_0_main_Load(EOS(STATIC_530), i77, i42, i71, i42) :|: TRUE f530_0_main_Load(EOS(STATIC_530), i77, i42, i71, i42) -> f532_0_main_LE(EOS(STATIC_532), i77, i42, i71, i42, i71) :|: TRUE f532_0_main_LE(EOS(STATIC_532), i77, i42, i71, i42, i71) -> f536_0_main_LE(EOS(STATIC_536), i77, i42, i71, i42, i71) :|: i42 <= i71 f532_0_main_LE(EOS(STATIC_532), i77, i42, i71, i42, i71) -> f537_0_main_LE(EOS(STATIC_537), i77, i42, i71, i42, i71) :|: i42 > i71 f536_0_main_LE(EOS(STATIC_536), i77, i42, i71, i42, i71) -> f538_0_main_Inc(EOS(STATIC_538), i77, i42, i71) :|: i42 <= i71 f538_0_main_Inc(EOS(STATIC_538), i77, i42, i71) -> f540_0_main_JMP(EOS(STATIC_540), i77 + -1, i42, i71) :|: TRUE f540_0_main_JMP(EOS(STATIC_540), i82, i42, i71) -> f558_0_main_Load(EOS(STATIC_558), i82, i42, i71) :|: TRUE f558_0_main_Load(EOS(STATIC_558), i82, i42, i71) -> f494_0_main_Load(EOS(STATIC_494), i82, i42, i71) :|: TRUE f494_0_main_Load(EOS(STATIC_494), i77, i42, i71) -> f501_0_main_Load(EOS(STATIC_501), i77, i42, i71, i77) :|: TRUE f537_0_main_LE(EOS(STATIC_537), i77, i42, i71, i42, i71) -> f539_0_main_Inc(EOS(STATIC_539), i77, i42, i71) :|: i42 > i71 f539_0_main_Inc(EOS(STATIC_539), i77, i42, i71) -> f542_0_main_JMP(EOS(STATIC_542), i77, i42 + -1, i71) :|: TRUE f542_0_main_JMP(EOS(STATIC_542), i77, i83, i71) -> f561_0_main_Load(EOS(STATIC_561), i77, i83, i71) :|: TRUE f561_0_main_Load(EOS(STATIC_561), i77, i83, i71) -> f524_0_main_Load(EOS(STATIC_524), i77, i83, i71) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f532_0_main_LE(EOS(STATIC_532), i77:0, i42:0, i71:0, i42:0, i71:0) -> f532_0_main_LE(EOS(STATIC_532), i77:0, i42:0 - 1, i71:0, i42:0 - 1, i71:0) :|: i71:0 < i42:0 f532_0_main_LE(EOS(STATIC_532), i77:0, i42:0, i71:0, i42:0, i71:0) -> f532_0_main_LE(EOS(STATIC_532), i77:0 - 1, i42:0, i71:0, i42:0, i71:0) :|: i71:0 >= i42:0 && i77:0 - 1 > i71:0 Filtered constant ground arguments: f532_0_main_LE(x1, x2, x3, x4, x5, x6) -> f532_0_main_LE(x2, x3, x4, x5, x6) EOS(x1) -> EOS Filtered duplicate arguments: f532_0_main_LE(x1, x2, x3, x4, x5) -> f532_0_main_LE(x1, x4, x5) Finished conversion. Obtained 2 rules.P rules: f532_0_main_LE(i77:0, i42:0, i71:0) -> f532_0_main_LE(i77:0, i42:0 - 1, i71:0) :|: i71:0 < i42:0 f532_0_main_LE(i77:0, i42:0, i71:0) -> f532_0_main_LE(i77:0 - 1, i42:0, i71:0) :|: i71:0 >= i42:0 && i77:0 - 1 > i71:0 ---------------------------------------- (8) Obligation: Rules: f532_0_main_LE(i77:0, i42:0, i71:0) -> f532_0_main_LE(i77:0, i42:0 - 1, i71:0) :|: i71:0 < i42:0 f532_0_main_LE(x, x1, x2) -> f532_0_main_LE(x - 1, x1, x2) :|: x2 >= x1 && x - 1 > x2 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f532_0_main_LE(i77:0, i42:0, i71:0) -> f532_0_main_LE(i77:0, arith, i71:0) :|: i71:0 < i42:0 && arith = i42:0 - 1 f532_0_main_LE(x3, x4, x5) -> f532_0_main_LE(x6, x4, x5) :|: x5 >= x4 && x3 - 1 > x5 && x6 = x3 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f532_0_main_LE(i77:0, i42:0, i71:0) -> f532_0_main_LE(i77:0, arith, i71:0) :|: i71:0 < i42:0 && arith = i42:0 - 1 (2) f532_0_main_LE(x3, x4, x5) -> f532_0_main_LE(x6, x4, x5) :|: x5 >= x4 && x3 - 1 > x5 && x6 = x3 - 1 Arcs: (1) -> (1), (2) (2) -> (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f532_0_main_LE(i77:0, i42:0, i71:0) -> f532_0_main_LE(i77:0, arith, i71:0) :|: i71:0 < i42:0 && arith = i42:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f532_0_main_LE(i77:0:0, i42:0:0, i71:0:0) -> f532_0_main_LE(i77:0:0, i42:0:0 - 1, i71:0:0) :|: i71:0:0 < i42:0:0 ---------------------------------------- (16) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f532_0_main_LE(x1, x2, x3) -> f532_0_main_LE(x2, x3) ---------------------------------------- (17) Obligation: Rules: f532_0_main_LE(i42:0:0, i71:0:0) -> f532_0_main_LE(i42:0:0 - 1, i71:0:0) :|: i71:0:0 < i42:0:0 ---------------------------------------- (18) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f532_0_main_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (19) Obligation: Rules: f532_0_main_LE(i42:0:0, i71:0:0) -> f532_0_main_LE(c, i71:0:0) :|: c = i42:0:0 - 1 && i71:0:0 < i42:0:0 ---------------------------------------- (20) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f532_0_main_LE ] = -1*f532_0_main_LE_2 + f532_0_main_LE_1 The following rules are decreasing: f532_0_main_LE(i42:0:0, i71:0:0) -> f532_0_main_LE(c, i71:0:0) :|: c = i42:0:0 - 1 && i71:0:0 < i42:0:0 The following rules are bounded: f532_0_main_LE(i42:0:0, i71:0:0) -> f532_0_main_LE(c, i71:0:0) :|: c = i42:0:0 - 1 && i71:0:0 < i42:0:0 ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) f532_0_main_LE(x3, x4, x5) -> f532_0_main_LE(x6, x4, x5) :|: x5 >= x4 && x3 - 1 > x5 && x6 = x3 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: f532_0_main_LE(x3:0, x4:0, x5:0) -> f532_0_main_LE(x3:0 - 1, x4:0, x5:0) :|: x5:0 >= x4:0 && x5:0 < x3:0 - 1 ---------------------------------------- (25) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f532_0_main_LE(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (26) Obligation: Rules: f532_0_main_LE(x3:0, x4:0, x5:0) -> f532_0_main_LE(c, x4:0, x5:0) :|: c = x3:0 - 1 && (x5:0 >= x4:0 && x5:0 < x3:0 - 1) ---------------------------------------- (27) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f532_0_main_LE ] = -1*f532_0_main_LE_3 + f532_0_main_LE_1 The following rules are decreasing: f532_0_main_LE(x3:0, x4:0, x5:0) -> f532_0_main_LE(c, x4:0, x5:0) :|: c = x3:0 - 1 && (x5:0 >= x4:0 && x5:0 < x3:0 - 1) The following rules are bounded: f532_0_main_LE(x3:0, x4:0, x5:0) -> f532_0_main_LE(c, x4:0, x5:0) :|: c = x3:0 - 1 && (x5:0 >= x4:0 && x5:0 < x3:0 - 1) ---------------------------------------- (28) YES