/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph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, 382 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 87 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 1 ms] (14) IRSwT (15) TempFilterProof [SOUND, 32 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 PastaB14 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x == y && x > 0) { while (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 PastaB14 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x == y && x > 0) { while (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: PastaB14.main([Ljava/lang/String;)V: Graph of 189 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: PastaB14.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 20 IRulesP rules: f1006_0_main_Load(EOS(STATIC_1006), i200, i201, i200) -> f1007_0_main_NE(EOS(STATIC_1007), i200, i201, i200, i201) :|: TRUE f1007_0_main_NE(EOS(STATIC_1007), i201, i201, i201, i201) -> f1022_0_main_NE(EOS(STATIC_1022), i201, i201, i201, i201) :|: i200 = i201 f1022_0_main_NE(EOS(STATIC_1022), i201, i201, i201, i201) -> f1029_0_main_Load(EOS(STATIC_1029), i201, i201) :|: TRUE f1029_0_main_Load(EOS(STATIC_1029), i201, i201) -> f1031_0_main_LE(EOS(STATIC_1031), i201, i201, i201) :|: TRUE f1031_0_main_LE(EOS(STATIC_1031), i212, i212, i212) -> f1033_0_main_LE(EOS(STATIC_1033), i212, i212, i212) :|: TRUE f1033_0_main_LE(EOS(STATIC_1033), i212, i212, i212) -> f1039_0_main_Load(EOS(STATIC_1039), i212, i212) :|: i212 > 0 f1039_0_main_Load(EOS(STATIC_1039), i212, i212) -> f1059_0_main_Load(EOS(STATIC_1059), i212, i212) :|: TRUE f1059_0_main_Load(EOS(STATIC_1059), i218, i219) -> f1118_0_main_Load(EOS(STATIC_1118), i218, i219) :|: TRUE f1118_0_main_Load(EOS(STATIC_1118), i235, i236) -> f1180_0_main_Load(EOS(STATIC_1180), i235, i236) :|: TRUE f1180_0_main_Load(EOS(STATIC_1180), i256, i257) -> f1182_0_main_LE(EOS(STATIC_1182), i256, i257, i257) :|: TRUE f1182_0_main_LE(EOS(STATIC_1182), i256, matching1, matching2) -> f1183_0_main_LE(EOS(STATIC_1183), i256, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0 f1182_0_main_LE(EOS(STATIC_1182), i256, i264, i264) -> f1184_0_main_LE(EOS(STATIC_1184), i256, i264, i264) :|: TRUE f1183_0_main_LE(EOS(STATIC_1183), i256, matching1, matching2) -> f1202_0_main_Load(EOS(STATIC_1202), i256, 0) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 f1202_0_main_Load(EOS(STATIC_1202), i256, matching1) -> f1003_0_main_Load(EOS(STATIC_1003), i256, 0) :|: TRUE && matching1 = 0 f1003_0_main_Load(EOS(STATIC_1003), i200, i201) -> f1006_0_main_Load(EOS(STATIC_1006), i200, i201, i200) :|: TRUE f1184_0_main_LE(EOS(STATIC_1184), i256, i264, i264) -> f1204_0_main_Inc(EOS(STATIC_1204), i256, i264) :|: i264 > 0 f1204_0_main_Inc(EOS(STATIC_1204), i256, i264) -> f1205_0_main_Inc(EOS(STATIC_1205), i256 + -1, i264) :|: TRUE f1205_0_main_Inc(EOS(STATIC_1205), i271, i264) -> f1206_0_main_JMP(EOS(STATIC_1206), i271, i264 + -1) :|: TRUE f1206_0_main_JMP(EOS(STATIC_1206), i271, i272) -> f1218_0_main_Load(EOS(STATIC_1218), i271, i272) :|: TRUE f1218_0_main_Load(EOS(STATIC_1218), i271, i272) -> f1180_0_main_Load(EOS(STATIC_1180), i271, i272) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f1182_0_main_LE(EOS(STATIC_1182), i256:0, i264:0, i264:0) -> f1182_0_main_LE(EOS(STATIC_1182), i256:0 - 1, i264:0 - 1, i264:0 - 1) :|: i264:0 > 0 Filtered constant ground arguments: f1182_0_main_LE(x1, x2, x3, x4) -> f1182_0_main_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f1182_0_main_LE(x1, x2, x3) -> f1182_0_main_LE(x1, x3) Filtered unneeded arguments: f1182_0_main_LE(x1, x2) -> f1182_0_main_LE(x2) Finished conversion. Obtained 1 rules.P rules: f1182_0_main_LE(i264:0) -> f1182_0_main_LE(i264:0 - 1) :|: i264:0 > 0 ---------------------------------------- (8) Obligation: Rules: f1182_0_main_LE(i264:0) -> f1182_0_main_LE(i264:0 - 1) :|: i264:0 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f1182_0_main_LE(i264:0) -> f1182_0_main_LE(arith) :|: i264:0 > 0 && arith = i264:0 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1182_0_main_LE(i264:0) -> f1182_0_main_LE(arith) :|: i264:0 > 0 && arith = i264:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f1182_0_main_LE(i264:0) -> f1182_0_main_LE(arith) :|: i264:0 > 0 && arith = i264:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f1182_0_main_LE(i264:0:0) -> f1182_0_main_LE(i264:0:0 - 1) :|: i264:0:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1182_0_main_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f1182_0_main_LE(i264:0:0) -> f1182_0_main_LE(c) :|: c = i264:0:0 - 1 && i264:0:0 > 0 ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1182_0_main_LE(x)] = x The following rules are decreasing: f1182_0_main_LE(i264:0:0) -> f1182_0_main_LE(c) :|: c = i264:0:0 - 1 && i264:0:0 > 0 The following rules are bounded: f1182_0_main_LE(i264:0:0) -> f1182_0_main_LE(c) :|: c = i264:0:0 - 1 && i264:0:0 > 0 ---------------------------------------- (18) YES