/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 316 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 4 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 115 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 47 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (17) IRSwT (18) TempFilterProof [SOUND, 9 ms] (19) IntTRS (20) RankingReductionPairProof [EQUIVALENT, 0 ms] (21) YES (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] (24) IRSwT (25) TempFilterProof [SOUND, 34 ms] (26) IntTRS (27) PolynomialOrderProcessor [EQUIVALENT, 0 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 181 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: f1149_0_main_LE(EOS(STATIC_1149), i232, i81, i232) -> f1164_0_main_LE(EOS(STATIC_1164), i232, i81, i232) :|: TRUE f1164_0_main_LE(EOS(STATIC_1164), i232, i81, i232) -> f1178_0_main_Load(EOS(STATIC_1178), i232, i81) :|: i232 > 0 f1178_0_main_Load(EOS(STATIC_1178), i232, i81) -> f1189_0_main_LE(EOS(STATIC_1189), i232, i81, i81) :|: TRUE f1189_0_main_LE(EOS(STATIC_1189), i232, matching1, matching2) -> f1201_0_main_LE(EOS(STATIC_1201), i232, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0 f1189_0_main_LE(EOS(STATIC_1189), i232, i239, i239) -> f1202_0_main_LE(EOS(STATIC_1202), i232, i239, i239) :|: TRUE f1201_0_main_LE(EOS(STATIC_1201), i232, matching1, matching2) -> f1207_0_main_Inc(EOS(STATIC_1207), i232, 0) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 f1207_0_main_Inc(EOS(STATIC_1207), i232, matching1) -> f1216_0_main_JMP(EOS(STATIC_1216), i232 + -1, 0) :|: TRUE && matching1 = 0 f1216_0_main_JMP(EOS(STATIC_1216), i242, matching1) -> f1309_0_main_Load(EOS(STATIC_1309), i242, 0) :|: TRUE && matching1 = 0 f1309_0_main_Load(EOS(STATIC_1309), i242, matching1) -> f1127_0_main_Load(EOS(STATIC_1127), i242, 0) :|: TRUE && matching1 = 0 f1127_0_main_Load(EOS(STATIC_1127), i80, i81) -> f1149_0_main_LE(EOS(STATIC_1149), i80, i81, i80) :|: TRUE f1202_0_main_LE(EOS(STATIC_1202), i232, i239, i239) -> f1210_0_main_Inc(EOS(STATIC_1210), i232, i239) :|: i239 > 0 f1210_0_main_Inc(EOS(STATIC_1210), i232, i239) -> f1219_0_main_JMP(EOS(STATIC_1219), i232, i239 + -1) :|: TRUE f1219_0_main_JMP(EOS(STATIC_1219), i232, i243) -> f1324_0_main_Load(EOS(STATIC_1324), i232, i243) :|: TRUE f1324_0_main_Load(EOS(STATIC_1324), i232, i243) -> f1178_0_main_Load(EOS(STATIC_1178), i232, i243) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f1189_0_main_LE(EOS(STATIC_1189), i232:0, 0, 0) -> f1189_0_main_LE(EOS(STATIC_1189), i232:0 - 1, 0, 0) :|: i232:0 > 1 f1189_0_main_LE(EOS(STATIC_1189), i232:0, i239:0, i239:0) -> f1189_0_main_LE(EOS(STATIC_1189), i232:0, i239:0 - 1, i239:0 - 1) :|: i239:0 > 0 Filtered constant ground arguments: f1189_0_main_LE(x1, x2, x3, x4) -> f1189_0_main_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f1189_0_main_LE(x1, x2, x3) -> f1189_0_main_LE(x1, x3) Finished conversion. Obtained 2 rules.P rules: f1189_0_main_LE(i232:0, cons_0) -> f1189_0_main_LE(i232:0 - 1, 0) :|: i232:0 > 1 && cons_0 = 0 f1189_0_main_LE(i232:0, i239:0) -> f1189_0_main_LE(i232:0, i239:0 - 1) :|: i239:0 > 0 ---------------------------------------- (8) Obligation: Rules: f1189_0_main_LE(i232:0, cons_0) -> f1189_0_main_LE(i232:0 - 1, 0) :|: i232:0 > 1 && cons_0 = 0 f1189_0_main_LE(x, x1) -> f1189_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: f1189_0_main_LE(i232:0, cons_0) -> f1189_0_main_LE(arith, 0) :|: i232:0 > 1 && cons_0 = 0 && arith = i232:0 - 1 f1189_0_main_LE(x2, x3) -> f1189_0_main_LE(x2, x4) :|: x3 > 0 && x4 = x3 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1189_0_main_LE(i232:0, cons_0) -> f1189_0_main_LE(arith, 0) :|: i232:0 > 1 && cons_0 = 0 && arith = i232:0 - 1 (2) f1189_0_main_LE(x2, x3) -> f1189_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) f1189_0_main_LE(x2, x3) -> f1189_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: f1189_0_main_LE(x2:0, x3:0) -> f1189_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: f1189_0_main_LE(x1, x2) -> f1189_0_main_LE(x2) ---------------------------------------- (17) Obligation: Rules: f1189_0_main_LE(x3:0) -> f1189_0_main_LE(x3:0 - 1) :|: x3:0 > 0 ---------------------------------------- (18) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1189_0_main_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (19) Obligation: Rules: f1189_0_main_LE(x3:0) -> f1189_0_main_LE(c) :|: c = x3:0 - 1 && x3:0 > 0 ---------------------------------------- (20) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f1189_0_main_LE ] = f1189_0_main_LE_1 The following rules are decreasing: f1189_0_main_LE(x3:0) -> f1189_0_main_LE(c) :|: c = x3:0 - 1 && x3:0 > 0 The following rules are bounded: f1189_0_main_LE(x3:0) -> f1189_0_main_LE(c) :|: c = x3:0 - 1 && x3:0 > 0 ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) f1189_0_main_LE(i232:0, cons_0) -> f1189_0_main_LE(arith, 0) :|: i232:0 > 1 && cons_0 = 0 && arith = i232:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: f1189_0_main_LE(i232:0:0, cons_0) -> f1189_0_main_LE(i232:0:0 - 1, 0) :|: i232:0:0 > 1 && cons_0 = 0 ---------------------------------------- (25) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1189_0_main_LE(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (26) Obligation: Rules: f1189_0_main_LE(i232:0:0, c) -> f1189_0_main_LE(c1, c2) :|: c2 = 0 && (c1 = i232:0:0 - 1 && c = 0) && (i232:0:0 > 1 && cons_0 = 0) ---------------------------------------- (27) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1189_0_main_LE(x, x1)] = x + c1*x1 The following rules are decreasing: f1189_0_main_LE(i232:0:0, c) -> f1189_0_main_LE(c1, c2) :|: c2 = 0 && (c1 = i232:0:0 - 1 && c = 0) && (i232:0:0 > 1 && cons_0 = 0) The following rules are bounded: f1189_0_main_LE(i232:0:0, c) -> f1189_0_main_LE(c1, c2) :|: c2 = 0 && (c1 = i232:0:0 - 1 && c = 0) && (i232:0:0 > 1 && cons_0 = 0) ---------------------------------------- (28) YES