/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph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, 262 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 74 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 34 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 17 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 PastaB6 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0 && y > 0) { 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 PastaB6 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0 && y > 0) { 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: PastaB6.main([Ljava/lang/String;)V: Graph of 179 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: PastaB6.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: f344_0_main_LE(EOS(STATIC_344), i56, i47, i56) -> f352_0_main_LE(EOS(STATIC_352), i56, i47, i56) :|: TRUE f352_0_main_LE(EOS(STATIC_352), i56, i47, i56) -> f368_0_main_Load(EOS(STATIC_368), i56, i47) :|: i56 > 0 f368_0_main_Load(EOS(STATIC_368), i56, i47) -> f381_0_main_LE(EOS(STATIC_381), i56, i47, i47) :|: TRUE f381_0_main_LE(EOS(STATIC_381), i56, i65, i65) -> f395_0_main_LE(EOS(STATIC_395), i56, i65, i65) :|: TRUE f395_0_main_LE(EOS(STATIC_395), i56, i65, i65) -> f423_0_main_Inc(EOS(STATIC_423), i56, i65) :|: i65 > 0 f423_0_main_Inc(EOS(STATIC_423), i56, i65) -> f438_0_main_Inc(EOS(STATIC_438), i56 + -1, i65) :|: TRUE f438_0_main_Inc(EOS(STATIC_438), i75, i65) -> f450_0_main_JMP(EOS(STATIC_450), i75, i65 + -1) :|: TRUE f450_0_main_JMP(EOS(STATIC_450), i75, i80) -> f484_0_main_Load(EOS(STATIC_484), i75, i80) :|: TRUE f484_0_main_Load(EOS(STATIC_484), i75, i80) -> f332_0_main_Load(EOS(STATIC_332), i75, i80) :|: TRUE f332_0_main_Load(EOS(STATIC_332), i17, i47) -> f344_0_main_LE(EOS(STATIC_344), i17, i47, i17) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f344_0_main_LE(EOS(STATIC_344), i56:0, i47:0, i56:0) -> f344_0_main_LE(EOS(STATIC_344), i56:0 - 1, i47:0 - 1, i56:0 - 1) :|: i47:0 > 0 && i56:0 > 0 Filtered constant ground arguments: f344_0_main_LE(x1, x2, x3, x4) -> f344_0_main_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f344_0_main_LE(x1, x2, x3) -> f344_0_main_LE(x2, x3) Finished conversion. Obtained 1 rules.P rules: f344_0_main_LE(i47:0, i56:0) -> f344_0_main_LE(i47:0 - 1, i56:0 - 1) :|: i47:0 > 0 && i56:0 > 0 ---------------------------------------- (8) Obligation: Rules: f344_0_main_LE(i47:0, i56:0) -> f344_0_main_LE(i47:0 - 1, i56:0 - 1) :|: i47:0 > 0 && i56:0 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f344_0_main_LE(i47:0, i56:0) -> f344_0_main_LE(arith, arith1) :|: i47:0 > 0 && i56:0 > 0 && arith = i47:0 - 1 && arith1 = i56:0 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f344_0_main_LE(i47:0, i56:0) -> f344_0_main_LE(arith, arith1) :|: i47:0 > 0 && i56:0 > 0 && arith = i47:0 - 1 && arith1 = i56:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f344_0_main_LE(i47:0, i56:0) -> f344_0_main_LE(arith, arith1) :|: i47:0 > 0 && i56:0 > 0 && arith = i47:0 - 1 && arith1 = i56:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f344_0_main_LE(i47:0:0, i56:0:0) -> f344_0_main_LE(i47:0:0 - 1, i56:0:0 - 1) :|: i47:0:0 > 0 && i56:0:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f344_0_main_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f344_0_main_LE(i47:0:0, i56:0:0) -> f344_0_main_LE(c, c1) :|: c1 = i56:0:0 - 1 && c = i47:0:0 - 1 && (i47:0:0 > 0 && i56:0:0 > 0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f344_0_main_LE(x, x1)] = x1 The following rules are decreasing: f344_0_main_LE(i47:0:0, i56:0:0) -> f344_0_main_LE(c, c1) :|: c1 = i56:0:0 - 1 && c = i47:0:0 - 1 && (i47:0:0 > 0 && i56:0:0 > 0) The following rules are bounded: f344_0_main_LE(i47:0:0, i56:0:0) -> f344_0_main_LE(c, c1) :|: c1 = i56:0:0 - 1 && c = i47:0:0 - 1 && (i47:0:0 > 0 && i56:0:0 > 0) ---------------------------------------- (18) YES