/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 432 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 90 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 21 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 PastaB15 { 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) { while (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 PastaB15 { 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) { while (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: PastaB15.main([Ljava/lang/String;)V: Graph of 258 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: PastaB15.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 21 IRulesP rules: f666_0_main_Load(EOS(STATIC_666), i109, i110, i71, i109) -> f667_0_main_NE(EOS(STATIC_667), i109, i110, i71, i109, i110) :|: TRUE f667_0_main_NE(EOS(STATIC_667), i110, i110, i71, i110, i110) -> f670_0_main_NE(EOS(STATIC_670), i110, i110, i71, i110, i110) :|: i109 = i110 f670_0_main_NE(EOS(STATIC_670), i110, i110, i71, i110, i110) -> f677_0_main_Load(EOS(STATIC_677), i110, i110, i71) :|: TRUE f677_0_main_Load(EOS(STATIC_677), i110, i110, i71) -> f680_0_main_Load(EOS(STATIC_680), i110, i110, i71, i110) :|: TRUE f680_0_main_Load(EOS(STATIC_680), i110, i110, i71, i110) -> f681_0_main_LE(EOS(STATIC_681), i110, i110, i71, i110, i71) :|: TRUE f681_0_main_LE(EOS(STATIC_681), i110, i110, i71, i110, i71) -> f683_0_main_LE(EOS(STATIC_683), i110, i110, i71, i110, i71) :|: i110 > i71 f683_0_main_LE(EOS(STATIC_683), i110, i110, i71, i110, i71) -> f687_0_main_Load(EOS(STATIC_687), i110, i110, i71) :|: i110 > i71 f687_0_main_Load(EOS(STATIC_687), i110, i110, i71) -> f714_0_main_Load(EOS(STATIC_714), i110, i110, i71) :|: TRUE f714_0_main_Load(EOS(STATIC_714), i117, i118, i71) -> f756_0_main_Load(EOS(STATIC_756), i117, i118, i71) :|: TRUE f756_0_main_Load(EOS(STATIC_756), i129, i130, i71) -> f757_0_main_Load(EOS(STATIC_757), i129, i130, i71, i130) :|: TRUE f757_0_main_Load(EOS(STATIC_757), i129, i130, i71, i130) -> f758_0_main_LE(EOS(STATIC_758), i129, i130, i71, i130, i71) :|: TRUE f758_0_main_LE(EOS(STATIC_758), i129, i130, i71, i130, i71) -> f762_0_main_LE(EOS(STATIC_762), i129, i130, i71, i130, i71) :|: i130 <= i71 f758_0_main_LE(EOS(STATIC_758), i129, i130, i71, i130, i71) -> f763_0_main_LE(EOS(STATIC_763), i129, i130, i71, i130, i71) :|: i130 > i71 f762_0_main_LE(EOS(STATIC_762), i129, i130, i71, i130, i71) -> f773_0_main_Load(EOS(STATIC_773), i129, i130, i71) :|: i130 <= i71 f773_0_main_Load(EOS(STATIC_773), i129, i130, i71) -> f662_0_main_Load(EOS(STATIC_662), i129, i130, i71) :|: TRUE f662_0_main_Load(EOS(STATIC_662), i109, i110, i71) -> f666_0_main_Load(EOS(STATIC_666), i109, i110, i71, i109) :|: TRUE f763_0_main_LE(EOS(STATIC_763), i129, i130, i71, i130, i71) -> f774_0_main_Inc(EOS(STATIC_774), i129, i130, i71) :|: i130 > i71 f774_0_main_Inc(EOS(STATIC_774), i129, i130, i71) -> f775_0_main_Inc(EOS(STATIC_775), i129 + -1, i130, i71) :|: TRUE f775_0_main_Inc(EOS(STATIC_775), i137, i130, i71) -> f777_0_main_JMP(EOS(STATIC_777), i137, i130 + -1, i71) :|: TRUE f777_0_main_JMP(EOS(STATIC_777), i137, i138, i71) -> f786_0_main_Load(EOS(STATIC_786), i137, i138, i71) :|: TRUE f786_0_main_Load(EOS(STATIC_786), i137, i138, i71) -> f756_0_main_Load(EOS(STATIC_756), i137, i138, i71) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f758_0_main_LE(EOS(STATIC_758), i129:0, i130:0, i71:0, i130:0, i71:0) -> f758_0_main_LE(EOS(STATIC_758), i129:0 - 1, i130:0 - 1, i71:0, i130:0 - 1, i71:0) :|: i71:0 < i130:0 Filtered constant ground arguments: f758_0_main_LE(x1, x2, x3, x4, x5, x6) -> f758_0_main_LE(x2, x3, x4, x5, x6) EOS(x1) -> EOS Filtered duplicate arguments: f758_0_main_LE(x1, x2, x3, x4, x5) -> f758_0_main_LE(x1, x4, x5) Filtered unneeded arguments: f758_0_main_LE(x1, x2, x3) -> f758_0_main_LE(x2, x3) Finished conversion. Obtained 1 rules.P rules: f758_0_main_LE(i130:0, i71:0) -> f758_0_main_LE(i130:0 - 1, i71:0) :|: i71:0 < i130:0 ---------------------------------------- (8) Obligation: Rules: f758_0_main_LE(i130:0, i71:0) -> f758_0_main_LE(i130:0 - 1, i71:0) :|: i71:0 < i130:0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f758_0_main_LE(i130:0, i71:0) -> f758_0_main_LE(arith, i71:0) :|: i71:0 < i130:0 && arith = i130:0 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f758_0_main_LE(i130:0, i71:0) -> f758_0_main_LE(arith, i71:0) :|: i71:0 < i130:0 && arith = i130:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f758_0_main_LE(i130:0, i71:0) -> f758_0_main_LE(arith, i71:0) :|: i71:0 < i130:0 && arith = i130:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f758_0_main_LE(i130:0:0, i71:0:0) -> f758_0_main_LE(i130:0:0 - 1, i71:0:0) :|: i71:0:0 < i130:0:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f758_0_main_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f758_0_main_LE(i130:0:0, i71:0:0) -> f758_0_main_LE(c, i71:0:0) :|: c = i130:0:0 - 1 && i71:0:0 < i130:0:0 ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f758_0_main_LE(x, x1)] = x - x1 The following rules are decreasing: f758_0_main_LE(i130:0:0, i71:0:0) -> f758_0_main_LE(c, i71:0:0) :|: c = i130:0:0 - 1 && i71:0:0 < i130:0:0 The following rules are bounded: f758_0_main_LE(i130:0:0, i71:0:0) -> f758_0_main_LE(c, i71:0:0) :|: c = i130:0:0 - 1 && i71:0:0 < i130:0:0 ---------------------------------------- (18) YES