/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph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, 523 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 33 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) TempFilterProof [SOUND, 4 ms] (17) IntTRS (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (19) YES (20) IRSwT (21) IntTRSCompressionProof [EQUIVALENT, 0 ms] (22) IRSwT (23) TempFilterProof [SOUND, 21 ms] (24) IntTRS (25) PolynomialOrderProcessor [EQUIVALENT, 11 ms] (26) 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 PastaA10 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x != y) { if (x > y) { y++; } else { 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 PastaA10 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x != y) { if (x > y) { y++; } else { 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: PastaA10.main([Ljava/lang/String;)V: Graph of 182 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: PastaA10.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: f282_0_main_Load(EOS(STATIC_282), i19, i42, i19) -> f285_0_main_EQ(EOS(STATIC_285), i19, i42, i19, i42) :|: TRUE f285_0_main_EQ(EOS(STATIC_285), i19, i42, i19, i42) -> f290_0_main_EQ(EOS(STATIC_290), i19, i42, i19, i42) :|: !(i19 = i42) f290_0_main_EQ(EOS(STATIC_290), i19, i42, i19, i42) -> f299_0_main_Load(EOS(STATIC_299), i19, i42) :|: !(i19 = i42) f299_0_main_Load(EOS(STATIC_299), i19, i42) -> f311_0_main_Load(EOS(STATIC_311), i19, i42, i19) :|: TRUE f311_0_main_Load(EOS(STATIC_311), i19, i42, i19) -> f314_0_main_LE(EOS(STATIC_314), i19, i42, i19, i42) :|: TRUE f314_0_main_LE(EOS(STATIC_314), i19, i42, i19, i42) -> f320_0_main_LE(EOS(STATIC_320), i19, i42, i19, i42) :|: i19 <= i42 f314_0_main_LE(EOS(STATIC_314), i19, i42, i19, i42) -> f321_0_main_LE(EOS(STATIC_321), i19, i42, i19, i42) :|: i19 > i42 f320_0_main_LE(EOS(STATIC_320), i19, i42, i19, i42) -> f340_0_main_Inc(EOS(STATIC_340), i19, i42) :|: i19 < i42 f340_0_main_Inc(EOS(STATIC_340), i19, i42) -> f349_0_main_JMP(EOS(STATIC_349), i19 + 1, i42) :|: TRUE f349_0_main_JMP(EOS(STATIC_349), i46, i42) -> f363_0_main_Load(EOS(STATIC_363), i46, i42) :|: TRUE f363_0_main_Load(EOS(STATIC_363), i46, i42) -> f279_0_main_Load(EOS(STATIC_279), i46, i42) :|: TRUE f279_0_main_Load(EOS(STATIC_279), i19, i42) -> f282_0_main_Load(EOS(STATIC_282), i19, i42, i19) :|: TRUE f321_0_main_LE(EOS(STATIC_321), i19, i42, i19, i42) -> f346_0_main_Inc(EOS(STATIC_346), i19, i42) :|: i19 > i42 f346_0_main_Inc(EOS(STATIC_346), i19, i42) -> f350_0_main_JMP(EOS(STATIC_350), i19, i42 + 1) :|: TRUE f350_0_main_JMP(EOS(STATIC_350), i19, i47) -> f372_0_main_Load(EOS(STATIC_372), i19, i47) :|: TRUE f372_0_main_Load(EOS(STATIC_372), i19, i47) -> f279_0_main_Load(EOS(STATIC_279), i19, i47) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f282_0_main_Load(EOS(STATIC_282), i19:0, i42:0, i19:0) -> f282_0_main_Load(EOS(STATIC_282), i19:0 + 1, i42:0, i19:0 + 1) :|: i42:0 > i19:0 f282_0_main_Load(EOS(STATIC_282), i19:0, i42:0, i19:0) -> f282_0_main_Load(EOS(STATIC_282), i19:0, i42:0 + 1, i19:0) :|: i42:0 < i19:0 Filtered constant ground arguments: f282_0_main_Load(x1, x2, x3, x4) -> f282_0_main_Load(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f282_0_main_Load(x1, x2, x3) -> f282_0_main_Load(x2, x3) Finished conversion. Obtained 2 rules.P rules: f282_0_main_Load(i42:0, i19:0) -> f282_0_main_Load(i42:0, i19:0 + 1) :|: i42:0 > i19:0 f282_0_main_Load(i42:0, i19:0) -> f282_0_main_Load(i42:0 + 1, i19:0) :|: i42:0 < i19:0 ---------------------------------------- (8) Obligation: Rules: f282_0_main_Load(i42:0, i19:0) -> f282_0_main_Load(i42:0, i19:0 + 1) :|: i42:0 > i19:0 f282_0_main_Load(x, x1) -> f282_0_main_Load(x + 1, x1) :|: x < x1 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f282_0_main_Load(i42:0, i19:0) -> f282_0_main_Load(i42:0, arith) :|: i42:0 > i19:0 && arith = i19:0 + 1 f282_0_main_Load(x2, x3) -> f282_0_main_Load(x4, x3) :|: x2 < x3 && x4 = x2 + 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f282_0_main_Load(i42:0, i19:0) -> f282_0_main_Load(i42:0, arith) :|: i42:0 > i19:0 && arith = i19:0 + 1 (2) f282_0_main_Load(x2, x3) -> f282_0_main_Load(x4, x3) :|: x2 < x3 && x4 = x2 + 1 Arcs: (1) -> (1) (2) -> (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f282_0_main_Load(x2, x3) -> f282_0_main_Load(x4, x3) :|: x2 < x3 && x4 = x2 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f282_0_main_Load(x2:0, x3:0) -> f282_0_main_Load(x2:0 + 1, x3:0) :|: x3:0 > x2:0 ---------------------------------------- (16) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f282_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (17) Obligation: Rules: f282_0_main_Load(x2:0, x3:0) -> f282_0_main_Load(c, x3:0) :|: c = x2:0 + 1 && x3:0 > x2:0 ---------------------------------------- (18) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f282_0_main_Load(x, x1)] = -x + x1 The following rules are decreasing: f282_0_main_Load(x2:0, x3:0) -> f282_0_main_Load(c, x3:0) :|: c = x2:0 + 1 && x3:0 > x2:0 The following rules are bounded: f282_0_main_Load(x2:0, x3:0) -> f282_0_main_Load(c, x3:0) :|: c = x2:0 + 1 && x3:0 > x2:0 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Termination digraph: Nodes: (1) f282_0_main_Load(i42:0, i19:0) -> f282_0_main_Load(i42:0, arith) :|: i42:0 > i19:0 && arith = i19:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (21) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (22) Obligation: Rules: f282_0_main_Load(i42:0:0, i19:0:0) -> f282_0_main_Load(i42:0:0, i19:0:0 + 1) :|: i42:0:0 > i19:0:0 ---------------------------------------- (23) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f282_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (24) Obligation: Rules: f282_0_main_Load(i42:0:0, i19:0:0) -> f282_0_main_Load(i42:0:0, c) :|: c = i19:0:0 + 1 && i42:0:0 > i19:0:0 ---------------------------------------- (25) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f282_0_main_Load(x, x1)] = x - x1 The following rules are decreasing: f282_0_main_Load(i42:0:0, i19:0:0) -> f282_0_main_Load(i42:0:0, c) :|: c = i19:0:0 + 1 && i42:0:0 > i19:0:0 The following rules are bounded: f282_0_main_Load(i42:0:0, i19:0:0) -> f282_0_main_Load(i42:0:0, c) :|: c = i19:0:0 + 1 && i42:0:0 > i19:0:0 ---------------------------------------- (26) YES