/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 95 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 381 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 39 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 44 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) PolynomialOrderProcessor [EQUIVALENT, 12 ms] (21) YES (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] (24) IRSwT (25) TempFilterProof [SOUND, 6 ms] (26) IntTRS (27) PolynomialOrderProcessor [EQUIVALENT, 3 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 PastaB16 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0) { while (y > 0) { 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 PastaB16 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0) { while (y > 0) { 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: PastaB16.main([Ljava/lang/String;)V: Graph of 180 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: PastaB16.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 14 IRulesP rules: f349_0_main_LE(EOS(STATIC_349), i58, i48, i58) -> f360_0_main_LE(EOS(STATIC_360), i58, i48, i58) :|: TRUE f360_0_main_LE(EOS(STATIC_360), i58, i48, i58) -> f376_0_main_Load(EOS(STATIC_376), i58, i48) :|: i58 > 0 f376_0_main_Load(EOS(STATIC_376), i58, i48) -> f389_0_main_LE(EOS(STATIC_389), i58, i48, i48) :|: TRUE f389_0_main_LE(EOS(STATIC_389), i58, matching1, matching2) -> f399_0_main_LE(EOS(STATIC_399), i58, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0 f389_0_main_LE(EOS(STATIC_389), i58, i66, i66) -> f400_0_main_LE(EOS(STATIC_400), i58, i66, i66) :|: TRUE f399_0_main_LE(EOS(STATIC_399), i58, matching1, matching2) -> f403_0_main_Inc(EOS(STATIC_403), i58, 0) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 f403_0_main_Inc(EOS(STATIC_403), i58, matching1) -> f407_0_main_JMP(EOS(STATIC_407), i58 + -1, 0) :|: TRUE && matching1 = 0 f407_0_main_JMP(EOS(STATIC_407), i67, matching1) -> f1314_0_main_Load(EOS(STATIC_1314), i67, 0) :|: TRUE && matching1 = 0 f1314_0_main_Load(EOS(STATIC_1314), i67, matching1) -> f338_0_main_Load(EOS(STATIC_338), i67, 0) :|: TRUE && matching1 = 0 f338_0_main_Load(EOS(STATIC_338), i19, i48) -> f349_0_main_LE(EOS(STATIC_349), i19, i48, i19) :|: TRUE f400_0_main_LE(EOS(STATIC_400), i58, i66, i66) -> f404_0_main_Inc(EOS(STATIC_404), i58, i66) :|: i66 > 0 f404_0_main_Inc(EOS(STATIC_404), i58, i66) -> f408_0_main_JMP(EOS(STATIC_408), i58, i66 + -1) :|: TRUE f408_0_main_JMP(EOS(STATIC_408), i58, i68) -> f1330_0_main_Load(EOS(STATIC_1330), i58, i68) :|: TRUE f1330_0_main_Load(EOS(STATIC_1330), i58, i68) -> f376_0_main_Load(EOS(STATIC_376), i58, i68) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f389_0_main_LE(EOS(STATIC_389), i58:0, 0, 0) -> f389_0_main_LE(EOS(STATIC_389), i58:0 - 1, 0, 0) :|: i58:0 > 1 f389_0_main_LE(EOS(STATIC_389), i58:0, i66:0, i66:0) -> f389_0_main_LE(EOS(STATIC_389), i58:0, i66:0 - 1, i66:0 - 1) :|: i66:0 > 0 Filtered constant ground arguments: f389_0_main_LE(x1, x2, x3, x4) -> f389_0_main_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f389_0_main_LE(x1, x2, x3) -> f389_0_main_LE(x1, x3) Finished conversion. Obtained 2 rules.P rules: f389_0_main_LE(i58:0, cons_0) -> f389_0_main_LE(i58:0 - 1, 0) :|: i58:0 > 1 && cons_0 = 0 f389_0_main_LE(i58:0, i66:0) -> f389_0_main_LE(i58:0, i66:0 - 1) :|: i66:0 > 0 ---------------------------------------- (8) Obligation: Rules: f389_0_main_LE(i58:0, cons_0) -> f389_0_main_LE(i58:0 - 1, 0) :|: i58:0 > 1 && cons_0 = 0 f389_0_main_LE(x, x1) -> f389_0_main_LE(x, x1 - 1) :|: x1 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f389_0_main_LE(i58:0, cons_0) -> f389_0_main_LE(arith, 0) :|: i58:0 > 1 && cons_0 = 0 && arith = i58:0 - 1 f389_0_main_LE(x2, x3) -> f389_0_main_LE(x2, x4) :|: x3 > 0 && x4 = x3 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f389_0_main_LE(i58:0, cons_0) -> f389_0_main_LE(arith, 0) :|: i58:0 > 1 && cons_0 = 0 && arith = i58:0 - 1 (2) f389_0_main_LE(x2, x3) -> f389_0_main_LE(x2, x4) :|: x3 > 0 && x4 = x3 - 1 Arcs: (1) -> (1) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f389_0_main_LE(x2, x3) -> f389_0_main_LE(x2, x4) :|: x3 > 0 && x4 = x3 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f389_0_main_LE(x2:0, x3:0) -> f389_0_main_LE(x2:0, x3:0 - 1) :|: x3:0 > 0 ---------------------------------------- (16) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f389_0_main_LE(x1, x2) -> f389_0_main_LE(x2) ---------------------------------------- (17) Obligation: Rules: f389_0_main_LE(x3:0) -> f389_0_main_LE(x3:0 - 1) :|: x3:0 > 0 ---------------------------------------- (18) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f389_0_main_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (19) Obligation: Rules: f389_0_main_LE(x3:0) -> f389_0_main_LE(c) :|: c = x3:0 - 1 && x3:0 > 0 ---------------------------------------- (20) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f389_0_main_LE(x)] = x The following rules are decreasing: f389_0_main_LE(x3:0) -> f389_0_main_LE(c) :|: c = x3:0 - 1 && x3:0 > 0 The following rules are bounded: f389_0_main_LE(x3:0) -> f389_0_main_LE(c) :|: c = x3:0 - 1 && x3:0 > 0 ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) f389_0_main_LE(i58:0, cons_0) -> f389_0_main_LE(arith, 0) :|: i58:0 > 1 && cons_0 = 0 && arith = i58:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: f389_0_main_LE(i58:0:0, cons_0) -> f389_0_main_LE(i58:0:0 - 1, 0) :|: i58:0:0 > 1 && cons_0 = 0 ---------------------------------------- (25) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f389_0_main_LE(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (26) Obligation: Rules: f389_0_main_LE(i58:0:0, c) -> f389_0_main_LE(c1, c2) :|: c2 = 0 && (c1 = i58:0:0 - 1 && c = 0) && (i58:0:0 > 1 && cons_0 = 0) ---------------------------------------- (27) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f389_0_main_LE(x, x1)] = x + c1*x1 The following rules are decreasing: f389_0_main_LE(i58:0:0, c) -> f389_0_main_LE(c1, c2) :|: c2 = 0 && (c1 = i58:0:0 - 1 && c = 0) && (i58:0:0 > 1 && cons_0 = 0) The following rules are bounded: f389_0_main_LE(i58:0:0, c) -> f389_0_main_LE(c1, c2) :|: c2 = 0 && (c1 = i58:0:0 - 1 && c = 0) && (i58:0:0 > 1 && cons_0 = 0) ---------------------------------------- (28) YES