/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 92 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 210 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) AND (7) JBCTerminationSCC (8) SCCToQDPProof [SOUND, 120 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) JBCTerminationSCC (13) SCCToIRSProof [SOUND, 37 ms] (14) IRSwT (15) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (16) IRSwT (17) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (18) IRSwT (19) IntTRSCompressionProof [EQUIVALENT, 0 ms] (20) IRSwT (21) TempFilterProof [SOUND, 16 ms] (22) IntTRS (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class ListReverseAcyclicList { public static void main(String... args) { List x = List.createList(args[0].length(), null); List.reverse(x); } } class List { List n; public List(List next) { this.n = next; } public static void reverse(List x) { List y = null; while (x != null) { List z = x; x = x.n; z.n = y; y = z; } } public static List createList(int l, List end) { while (--l > 0) { end = new List(end); } return end; } public static List createCycle(int l) { List last = new List(null); List first = createList(l - 1, last); last.n = first; return first; } public static List createPanhandleList(int pl, int cl) { return createList(pl, createCycle(cl)); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: public class ListReverseAcyclicList { public static void main(String... args) { List x = List.createList(args[0].length(), null); List.reverse(x); } } class List { List n; public List(List next) { this.n = next; } public static void reverse(List x) { List y = null; while (x != null) { List z = x; x = x.n; z.n = y; y = z; } } public static List createList(int l, List end) { while (--l > 0) { end = new List(end); } return end; } public static List createCycle(int l) { List last = new List(null); List first = createList(l - 1, last); last.n = first; return first; } public static List createPanhandleList(int pl, int cl) { return createList(pl, createCycle(cl)); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: ListReverseAcyclicList.main([Ljava/lang/String;)V: Graph of 147 nodes with 2 SCCs. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 2 SCCss. ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: ListReverseAcyclicList.main([Ljava/lang/String;)V SCC calls the following helper methods: Performed SCC analyses: *Used field analysis yielded the following read fields: *List: [n] *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (8) SCCToQDPProof (SOUND) Transformed TerminationGraph SCC to QDP. Log: Generated 16 rules for P and 0 rules for R.P rules: f736_0_reverse_NULL(EOS(STATIC_736), java.lang.Object(o206sub), java.lang.Object(List(EOC, o185)), java.lang.Object(o206sub)) -> f741_0_reverse_Load(EOS(STATIC_741), java.lang.Object(o206sub), java.lang.Object(List(EOC, o185))) :|: TRUE f741_0_reverse_Load(EOS(STATIC_741), java.lang.Object(o206sub), java.lang.Object(List(EOC, o185))) -> f754_0_reverse_Store(EOS(STATIC_754), java.lang.Object(o206sub), java.lang.Object(List(EOC, o185)), java.lang.Object(o206sub)) :|: TRUE f754_0_reverse_Store(EOS(STATIC_754), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216))) -> f755_0_reverse_Store(EOS(STATIC_755), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216))) :|: TRUE f755_0_reverse_Store(EOS(STATIC_755), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216))) -> f756_0_reverse_Load(EOS(STATIC_756), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216))) :|: TRUE f756_0_reverse_Load(EOS(STATIC_756), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216))) -> f759_0_reverse_FieldAccess(EOS(STATIC_759), java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o216))) :|: TRUE f759_0_reverse_FieldAccess(EOS(STATIC_759), java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o216))) -> f763_0_reverse_Store(EOS(STATIC_763), java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216)), o216) :|: TRUE f763_0_reverse_Store(EOS(STATIC_763), java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216)), o216) -> f766_0_reverse_Load(EOS(STATIC_766), o216, java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216))) :|: TRUE f766_0_reverse_Load(EOS(STATIC_766), o216, java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216))) -> f769_0_reverse_Load(EOS(STATIC_769), o216, java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o216))) :|: TRUE f769_0_reverse_Load(EOS(STATIC_769), o216, java.lang.Object(List(EOC, o185)), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o216))) -> f772_0_reverse_FieldAccess(EOS(STATIC_772), o216, java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o185))) :|: TRUE f772_0_reverse_FieldAccess(EOS(STATIC_772), o216, java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o216)), java.lang.Object(List(EOC, o185))) -> f792_0_reverse_Load(EOS(STATIC_792), o216, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185))))) :|: TRUE f792_0_reverse_Load(EOS(STATIC_792), o216, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185))))) -> f797_0_reverse_Store(EOS(STATIC_797), o216, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185))))) :|: TRUE f797_0_reverse_Store(EOS(STATIC_797), o216, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185))))) -> f801_0_reverse_JMP(EOS(STATIC_801), o216, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185))))) :|: TRUE f801_0_reverse_JMP(EOS(STATIC_801), o216, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185))))) -> f821_0_reverse_Load(EOS(STATIC_821), o216, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185))))) :|: TRUE f821_0_reverse_Load(EOS(STATIC_821), o216, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185))))) -> f725_0_reverse_Load(EOS(STATIC_725), o216, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185))))) :|: TRUE f725_0_reverse_Load(EOS(STATIC_725), o183, java.lang.Object(List(EOC, o185))) -> f733_0_reverse_NULL(EOS(STATIC_733), o183, java.lang.Object(List(EOC, o185)), o183) :|: TRUE f733_0_reverse_NULL(EOS(STATIC_733), java.lang.Object(o206sub), java.lang.Object(List(EOC, o185)), java.lang.Object(o206sub)) -> f736_0_reverse_NULL(EOS(STATIC_736), java.lang.Object(o206sub), java.lang.Object(List(EOC, o185)), java.lang.Object(o206sub)) :|: TRUE R rules: Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules: f736_0_reverse_NULL(EOS(STATIC_736), java.lang.Object(List(EOC, java.lang.Object(o206sub:0))), java.lang.Object(List(EOC, o185:0)), java.lang.Object(List(EOC, java.lang.Object(o206sub:0)))) -> f736_0_reverse_NULL(EOS(STATIC_736), java.lang.Object(o206sub:0), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o185:0)))), java.lang.Object(o206sub:0)) :|: TRUE R rules: Filtered ground terms: f736_0_reverse_NULL(x1, x2, x3, x4) -> f736_0_reverse_NULL(x2, x3, x4) EOS(x1) -> EOS List(x1, x2) -> List(x2) Filtered duplicate args: f736_0_reverse_NULL(x1, x2, x3) -> f736_0_reverse_NULL(x2, x3) Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules: F736_0_REVERSE_NULL(java.lang.Object(List(o185:0:0)), java.lang.Object(List(java.lang.Object(o206sub:0:0)))) -> F736_0_REVERSE_NULL(java.lang.Object(List(java.lang.Object(List(o185:0:0)))), java.lang.Object(o206sub:0:0)) :|: TRUE R rules: ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: F736_0_REVERSE_NULL(java.lang.Object(List(o185:0:0)), java.lang.Object(List(java.lang.Object(o206sub:0:0)))) -> F736_0_REVERSE_NULL(java.lang.Object(List(java.lang.Object(List(o185:0:0)))), java.lang.Object(o206sub:0:0)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (10) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *F736_0_REVERSE_NULL(java.lang.Object(List(o185:0:0)), java.lang.Object(List(java.lang.Object(o206sub:0:0)))) -> F736_0_REVERSE_NULL(java.lang.Object(List(java.lang.Object(List(o185:0:0)))), java.lang.Object(o206sub:0:0)) The graph contains the following edges 2 > 2 ---------------------------------------- (11) YES ---------------------------------------- (12) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: ListReverseAcyclicList.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: ---------------------------------------- (13) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 17 IRulesP rules: f483_0_createList_LE(EOS(STATIC_483), i71, i71) -> f487_0_createList_New(EOS(STATIC_487), i71) :|: i71 > 0 f487_0_createList_New(EOS(STATIC_487), i71) -> f490_0_createList_Duplicate(EOS(STATIC_490), i71) :|: TRUE f490_0_createList_Duplicate(EOS(STATIC_490), i71) -> f496_0_createList_Load(EOS(STATIC_496), i71) :|: TRUE f496_0_createList_Load(EOS(STATIC_496), i71) -> f501_0_createList_InvokeMethod(EOS(STATIC_501), i71) :|: TRUE f501_0_createList_InvokeMethod(EOS(STATIC_501), i71) -> f507_0__init__Load(EOS(STATIC_507), i71) :|: TRUE f507_0__init__Load(EOS(STATIC_507), i71) -> f517_0__init__InvokeMethod(EOS(STATIC_517), i71) :|: TRUE f517_0__init__InvokeMethod(EOS(STATIC_517), i71) -> f525_0__init__Load(EOS(STATIC_525), i71) :|: TRUE f525_0__init__Load(EOS(STATIC_525), i71) -> f531_0__init__Load(EOS(STATIC_531), i71) :|: TRUE f531_0__init__Load(EOS(STATIC_531), i71) -> f536_0__init__FieldAccess(EOS(STATIC_536), i71) :|: TRUE f536_0__init__FieldAccess(EOS(STATIC_536), i71) -> f561_0__init__Return(EOS(STATIC_561), i71) :|: TRUE f561_0__init__Return(EOS(STATIC_561), i71) -> f563_0_createList_Store(EOS(STATIC_563), i71) :|: TRUE f563_0_createList_Store(EOS(STATIC_563), i71) -> f565_0_createList_JMP(EOS(STATIC_565), i71) :|: TRUE f565_0_createList_JMP(EOS(STATIC_565), i71) -> f597_0_createList_Inc(EOS(STATIC_597), i71) :|: TRUE f597_0_createList_Inc(EOS(STATIC_597), i71) -> f471_0_createList_Inc(EOS(STATIC_471), i71) :|: TRUE f471_0_createList_Inc(EOS(STATIC_471), i63) -> f478_0_createList_Load(EOS(STATIC_478), i63 + -1) :|: TRUE f478_0_createList_Load(EOS(STATIC_478), i67) -> f481_0_createList_LE(EOS(STATIC_481), i67, i67) :|: TRUE f481_0_createList_LE(EOS(STATIC_481), i71, i71) -> f483_0_createList_LE(EOS(STATIC_483), i71, i71) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f483_0_createList_LE(EOS(STATIC_483), i71:0, i71:0) -> f483_0_createList_LE(EOS(STATIC_483), i71:0 - 1, i71:0 - 1) :|: i71:0 > 0 Filtered constant ground arguments: f483_0_createList_LE(x1, x2, x3) -> f483_0_createList_LE(x2, x3) EOS(x1) -> EOS Filtered duplicate arguments: f483_0_createList_LE(x1, x2) -> f483_0_createList_LE(x2) Finished conversion. Obtained 1 rules.P rules: f483_0_createList_LE(i71:0) -> f483_0_createList_LE(i71:0 - 1) :|: i71:0 > 0 ---------------------------------------- (14) Obligation: Rules: f483_0_createList_LE(i71:0) -> f483_0_createList_LE(i71:0 - 1) :|: i71:0 > 0 ---------------------------------------- (15) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (16) Obligation: Rules: f483_0_createList_LE(i71:0) -> f483_0_createList_LE(arith) :|: i71:0 > 0 && arith = i71:0 - 1 ---------------------------------------- (17) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f483_0_createList_LE(i71:0) -> f483_0_createList_LE(arith) :|: i71:0 > 0 && arith = i71:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (18) Obligation: Termination digraph: Nodes: (1) f483_0_createList_LE(i71:0) -> f483_0_createList_LE(arith) :|: i71:0 > 0 && arith = i71:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (19) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (20) Obligation: Rules: f483_0_createList_LE(i71:0:0) -> f483_0_createList_LE(i71:0:0 - 1) :|: i71:0:0 > 0 ---------------------------------------- (21) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f483_0_createList_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (22) Obligation: Rules: f483_0_createList_LE(i71:0:0) -> f483_0_createList_LE(c) :|: c = i71:0:0 - 1 && i71:0:0 > 0 ---------------------------------------- (23) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f483_0_createList_LE(x)] = x The following rules are decreasing: f483_0_createList_LE(i71:0:0) -> f483_0_createList_LE(c) :|: c = i71:0:0 - 1 && i71:0:0 > 0 The following rules are bounded: f483_0_createList_LE(i71:0:0) -> f483_0_createList_LE(c) :|: c = i71:0:0 - 1 && i71:0:0 > 0 ---------------------------------------- (24) YES