/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


MAYBE
proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


termination of the given Bare JBC problem could not be shown:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 498 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 89 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 65 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) IRSwTChainingProof [EQUIVALENT, 0 ms]
(16) IRSwT
(17) IRSwTTerminationDigraphProof [EQUIVALENT, 14 ms]
(18) IRSwT
(19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(20) IRSwT
(21) IRSwTChainingProof [EQUIVALENT, 0 ms]
(22) IRSwT
(23) IRSwTTerminationDigraphProof [EQUIVALENT, 70 ms]
(24) IRSwT
(25) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(26) IRSwT
(27) TempFilterProof [SOUND, 2320 ms]
(28) IRSwT
(29) IRSwTTerminationDigraphProof [EQUIVALENT, 4 ms]
(30) IRSwT
(31) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(32) IRSwT


----------------------------------------

(0)
Obligation:
need to prove termination of the following program:
public class MinusUserDefined{
  public static boolean gt(int x, int y) {

    while (x > 0 && y > 0) {
      x--;
      y--;
    }

    return x > 0;
  }


  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    int res = 0;

    while (gt(x,y)) {

      y++;
      res++;

    }
  }
}


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:
public class MinusUserDefined{
  public static boolean gt(int x, int y) {

    while (x > 0 && y > 0) {
      x--;
      y--;
    }

    return x > 0;
  }


  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    int res = 0;

    while (gt(x,y)) {

      y++;
      res++;

    }
  }
}


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:
MinusUserDefined.main([Ljava/lang/String;)V: Graph of 202 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: MinusUserDefined.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 26 IRulesP rules:
f2803_0_main_Load(EOS(STATIC_2803), i545, i546, i545) -> f2805_0_main_InvokeMethod(EOS(STATIC_2805), i545, i546, i545, i546) :|: TRUE
f2805_0_main_InvokeMethod(EOS(STATIC_2805), i545, i546, i545, i546) -> f2807_0_gt_Load(EOS(STATIC_2807), i545, i546, i545, i546) :|: TRUE
f2807_0_gt_Load(EOS(STATIC_2807), i545, i546, i545, i546) -> f3007_0_gt_Load(EOS(STATIC_3007), i545, i546, i545, i546) :|: TRUE
f3007_0_gt_Load(EOS(STATIC_3007), i593, i594, i591, i592) -> f3011_0_gt_LE(EOS(STATIC_3011), i593, i594, i591, i592, i591) :|: TRUE
f3011_0_gt_LE(EOS(STATIC_3011), i639, i594, i638, i592, i638) -> f3017_0_gt_LE(EOS(STATIC_3017), i639, i594, i638, i592, i638) :|: TRUE
f3017_0_gt_LE(EOS(STATIC_3017), i639, i594, i638, i592, i638) -> f3021_0_gt_Load(EOS(STATIC_3021), i639, i594, i638, i592) :|: i638 > 0
f3021_0_gt_Load(EOS(STATIC_3021), i639, i594, i638, i592) -> f3025_0_gt_LE(EOS(STATIC_3025), i639, i594, i638, i592, i592) :|: TRUE
f3025_0_gt_LE(EOS(STATIC_3025), i639, i594, i638, matching1, matching2) -> f3030_0_gt_LE(EOS(STATIC_3030), i639, i594, i638, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f3025_0_gt_LE(EOS(STATIC_3025), i639, i643, i638, i642, i642) -> f3031_0_gt_LE(EOS(STATIC_3031), i639, i643, i638, i642, i642) :|: TRUE
f3030_0_gt_LE(EOS(STATIC_3030), i639, i594, i638, matching1, matching2) -> f3038_0_gt_Load(EOS(STATIC_3038), i639, i594, i638) :|: 0 <= 0 && matching1 = 0 && matching2 = 0
f3038_0_gt_Load(EOS(STATIC_3038), i639, i594, i638) -> f3047_0_gt_LE(EOS(STATIC_3047), i639, i594, i638) :|: TRUE
f3047_0_gt_LE(EOS(STATIC_3047), i639, i594, i638) -> f3056_0_gt_ConstantStackPush(EOS(STATIC_3056), i639, i594) :|: i638 > 0
f3056_0_gt_ConstantStackPush(EOS(STATIC_3056), i639, i594) -> f3063_0_gt_JMP(EOS(STATIC_3063), i639, i594, 1) :|: TRUE
f3063_0_gt_JMP(EOS(STATIC_3063), i639, i594, matching1) -> f3153_0_gt_Return(EOS(STATIC_3153), i639, i594, 1) :|: TRUE && matching1 = 1
f3153_0_gt_Return(EOS(STATIC_3153), i639, i594, matching1) -> f3157_0_main_EQ(EOS(STATIC_3157), i639, i594, 1) :|: TRUE && matching1 = 1
f3157_0_main_EQ(EOS(STATIC_3157), i639, i594, matching1) -> f3160_0_main_Inc(EOS(STATIC_3160), i639, i594) :|: 1 > 0 && matching1 = 1
f3160_0_main_Inc(EOS(STATIC_3160), i639, i594) -> f3163_0_main_Inc(EOS(STATIC_3163), i639, i594 + 1) :|: TRUE
f3163_0_main_Inc(EOS(STATIC_3163), i639, i663) -> f3165_0_main_JMP(EOS(STATIC_3165), i639, i663) :|: TRUE
f3165_0_main_JMP(EOS(STATIC_3165), i639, i663) -> f3193_0_main_Load(EOS(STATIC_3193), i639, i663) :|: TRUE
f3193_0_main_Load(EOS(STATIC_3193), i639, i663) -> f2796_0_main_Load(EOS(STATIC_2796), i639, i663) :|: TRUE
f2796_0_main_Load(EOS(STATIC_2796), i545, i546) -> f2803_0_main_Load(EOS(STATIC_2803), i545, i546, i545) :|: TRUE
f3031_0_gt_LE(EOS(STATIC_3031), i639, i643, i638, i642, i642) -> f3041_0_gt_Inc(EOS(STATIC_3041), i639, i643, i638, i642) :|: i642 > 0
f3041_0_gt_Inc(EOS(STATIC_3041), i639, i643, i638, i642) -> f3050_0_gt_Inc(EOS(STATIC_3050), i639, i643, i638 + -1, i642) :|: TRUE
f3050_0_gt_Inc(EOS(STATIC_3050), i639, i643, i645, i642) -> f3059_0_gt_JMP(EOS(STATIC_3059), i639, i643, i645, i642 + -1) :|: TRUE
f3059_0_gt_JMP(EOS(STATIC_3059), i639, i643, i645, i646) -> f3148_0_gt_Load(EOS(STATIC_3148), i639, i643, i645, i646) :|: TRUE
f3148_0_gt_Load(EOS(STATIC_3148), i639, i643, i645, i646) -> f3007_0_gt_Load(EOS(STATIC_3007), i639, i643, i645, i646) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f3025_0_gt_LE(EOS(STATIC_3025), i639:0, i594:0, i638:0, 0, 0) -> f3025_0_gt_LE(EOS(STATIC_3025), i639:0, i594:0 + 1, i639:0, i594:0 + 1, i594:0 + 1) :|: i639:0 > 0 && i638:0 > 0
f3025_0_gt_LE(EOS(STATIC_3025), i639:0, i643:0, i638:0, i642:0, i642:0) -> f3025_0_gt_LE(EOS(STATIC_3025), i639:0, i643:0, i638:0 - 1, i642:0 - 1, i642:0 - 1) :|: i638:0 > 1 && i642:0 > 0
Filtered constant ground arguments:
   f3025_0_gt_LE(x1, x2, x3, x4, x5, x6) -> f3025_0_gt_LE(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f3025_0_gt_LE(x1, x2, x3, x4, x5) -> f3025_0_gt_LE(x1, x2, x3, x5)
Finished conversion. Obtained 2 rules.P rules:
f3025_0_gt_LE(i639:0, i594:0, i638:0, cons_0) -> f3025_0_gt_LE(i639:0, i594:0 + 1, i639:0, i594:0 + 1) :|: i639:0 > 0 && i638:0 > 0 && cons_0 = 0
f3025_0_gt_LE(i639:0, i643:0, i638:0, i642:0) -> f3025_0_gt_LE(i639:0, i643:0, i638:0 - 1, i642:0 - 1) :|: i638:0 > 1 && i642:0 > 0

----------------------------------------

(8)
Obligation:
Rules:
f3025_0_gt_LE(i639:0, i594:0, i638:0, cons_0) -> f3025_0_gt_LE(i639:0, i594:0 + 1, i639:0, i594:0 + 1) :|: i639:0 > 0 && i638:0 > 0 && cons_0 = 0
f3025_0_gt_LE(x, x1, x2, x3) -> f3025_0_gt_LE(x, x1, x2 - 1, x3 - 1) :|: x2 > 1 && x3 > 0

----------------------------------------

(9) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(10)
Obligation:
Rules:
f3025_0_gt_LE(i639:0, i594:0, i638:0, cons_0) -> f3025_0_gt_LE(i639:0, arith, i639:0, arith) :|: i639:0 > 0 && i638:0 > 0 && cons_0 = 0 && arith = i594:0 + 1 && arith = i594:0 + 1
f3025_0_gt_LE(x4, x5, x6, x7) -> f3025_0_gt_LE(x4, x5, x8, x9) :|: x6 > 1 && x7 > 0 && x8 = x6 - 1 && x9 = x7 - 1

----------------------------------------

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f3025_0_gt_LE(i639:0, i594:0, i638:0, cons_0) -> f3025_0_gt_LE(i639:0, arith, i639:0, arith) :|: i639:0 > 0 && i638:0 > 0 && cons_0 = 0 && arith = i594:0 + 1 && arith = i594:0 + 1
(2) f3025_0_gt_LE(x4, x5, x6, x7) -> f3025_0_gt_LE(x4, x5, x8, x9) :|: x6 > 1 && x7 > 0 && x8 = x6 - 1 && x9 = x7 - 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!
----------------------------------------

(12)
Obligation:

Termination digraph:
Nodes:
(1) f3025_0_gt_LE(i639:0, i594:0, i638:0, cons_0) -> f3025_0_gt_LE(i639:0, arith, i639:0, arith) :|: i639:0 > 0 && i638:0 > 0 && cons_0 = 0 && arith = i594:0 + 1 && arith = i594:0 + 1
(2) f3025_0_gt_LE(x4, x5, x6, x7) -> f3025_0_gt_LE(x4, x5, x8, x9) :|: x6 > 1 && x7 > 0 && x8 = x6 - 1 && x9 = x7 - 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!

----------------------------------------

(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(14)
Obligation:
Rules:
f3025_0_gt_LE(x4:0, x5:0, x6:0, x7:0) -> f3025_0_gt_LE(x4:0, x5:0, x6:0 - 1, x7:0 - 1) :|: x6:0 > 1 && x7:0 > 0
f3025_0_gt_LE(i639:0:0, i594:0:0, i638:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0, i594:0:0 + 1, i639:0:0, i594:0:0 + 1) :|: i639:0:0 > 0 && i638:0:0 > 0 && cons_0 = 0

----------------------------------------

(15) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(16)
Obligation:
Rules:
f3025_0_gt_LE(x, x1, x2, x3) -> f3025_0_gt_LE(x, x1, x2 + -2, x3 + -2) :|: TRUE && x2 >= 3 && x3 >= 2
f3025_0_gt_LE(i639:0:0, i594:0:0, i638:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0, i594:0:0 + 1, i639:0:0, i594:0:0 + 1) :|: i639:0:0 > 0 && i638:0:0 > 0 && cons_0 = 0
f3025_0_gt_LE(x8, x9, x10, x11) -> f3025_0_gt_LE(x8, x9 + 1, x8, x9 + 1) :|: TRUE && x10 >= 2 && x8 >= 1 && x11 = 1

----------------------------------------

(17) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f3025_0_gt_LE(x, x1, x2, x3) -> f3025_0_gt_LE(x, x1, x2 + -2, x3 + -2) :|: TRUE && x2 >= 3 && x3 >= 2
(2) f3025_0_gt_LE(i639:0:0, i594:0:0, i638:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0, i594:0:0 + 1, i639:0:0, i594:0:0 + 1) :|: i639:0:0 > 0 && i638:0:0 > 0 && cons_0 = 0
(3) f3025_0_gt_LE(x8, x9, x10, x11) -> f3025_0_gt_LE(x8, x9 + 1, x8, x9 + 1) :|: TRUE && x10 >= 2 && x8 >= 1 && x11 = 1

Arcs:
(1) -> (1), (2), (3)
(2) -> (1), (2), (3)
(3) -> (1), (2), (3)

This digraph is fully evaluated!
----------------------------------------

(18)
Obligation:

Termination digraph:
Nodes:
(1) f3025_0_gt_LE(x, x1, x2, x3) -> f3025_0_gt_LE(x, x1, x2 + -2, x3 + -2) :|: TRUE && x2 >= 3 && x3 >= 2
(2) f3025_0_gt_LE(i639:0:0, i594:0:0, i638:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0, i594:0:0 + 1, i639:0:0, i594:0:0 + 1) :|: i639:0:0 > 0 && i638:0:0 > 0 && cons_0 = 0
(3) f3025_0_gt_LE(x8, x9, x10, x11) -> f3025_0_gt_LE(x8, x9 + 1, x8, x9 + 1) :|: TRUE && x10 >= 2 && x8 >= 1 && x11 = 1

Arcs:
(1) -> (1), (2), (3)
(2) -> (1), (2), (3)
(3) -> (1), (2), (3)

This digraph is fully evaluated!

----------------------------------------

(19) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(20)
Obligation:
Rules:
f3025_0_gt_LE(x8:0, x9:0, x10:0, cons_1) -> f3025_0_gt_LE(x8:0, x9:0 + 1, x8:0, x9:0 + 1) :|: x8:0 > 0 && x10:0 > 1 && cons_1 = 1
f3025_0_gt_LE(x:0, x1:0, x2:0, x3:0) -> f3025_0_gt_LE(x:0, x1:0, x2:0 - 2, x3:0 - 2) :|: x3:0 > 1 && x2:0 > 2
f3025_0_gt_LE(i639:0:0:0, i594:0:0:0, i638:0:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0:0, i594:0:0:0 + 1, i639:0:0:0, i594:0:0:0 + 1) :|: i639:0:0:0 > 0 && i638:0:0:0 > 0 && cons_0 = 0

----------------------------------------

(21) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(22)
Obligation:
Rules:
f3025_0_gt_LE(x, x1, x2, x3) -> f3025_0_gt_LE(x, 0 + 2, x, 0 + 2) :|: TRUE && x2 >= 2 && x3 = 1 && x >= 2 && x1 = 0
f3025_0_gt_LE(x:0, x1:0, x2:0, x3:0) -> f3025_0_gt_LE(x:0, x1:0, x2:0 - 2, x3:0 - 2) :|: x3:0 > 1 && x2:0 > 2
f3025_0_gt_LE(x8, x9, x10, x11) -> f3025_0_gt_LE(x8, x9 + 1, x8 + -2, x9 + -1) :|: TRUE && x10 >= 2 && x11 = 1 && x9 >= 1 && x8 >= 3
f3025_0_gt_LE(i639:0:0:0, i594:0:0:0, i638:0:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0:0, i594:0:0:0 + 1, i639:0:0:0, i594:0:0:0 + 1) :|: i639:0:0:0 > 0 && i638:0:0:0 > 0 && cons_0 = 0
f3025_0_gt_LE(x16, x17, x18, x19) -> f3025_0_gt_LE(x16, x17 + 2, x16, x17 + 2) :|: TRUE && x16 >= 1 && x18 >= 2 && x19 = 1 && x17 = -1

----------------------------------------

(23) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f3025_0_gt_LE(x, x1, x2, x3) -> f3025_0_gt_LE(x, 0 + 2, x, 0 + 2) :|: TRUE && x2 >= 2 && x3 = 1 && x >= 2 && x1 = 0
(2) f3025_0_gt_LE(x:0, x1:0, x2:0, x3:0) -> f3025_0_gt_LE(x:0, x1:0, x2:0 - 2, x3:0 - 2) :|: x3:0 > 1 && x2:0 > 2
(3) f3025_0_gt_LE(x8, x9, x10, x11) -> f3025_0_gt_LE(x8, x9 + 1, x8 + -2, x9 + -1) :|: TRUE && x10 >= 2 && x11 = 1 && x9 >= 1 && x8 >= 3
(4) f3025_0_gt_LE(i639:0:0:0, i594:0:0:0, i638:0:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0:0, i594:0:0:0 + 1, i639:0:0:0, i594:0:0:0 + 1) :|: i639:0:0:0 > 0 && i638:0:0:0 > 0 && cons_0 = 0
(5) f3025_0_gt_LE(x16, x17, x18, x19) -> f3025_0_gt_LE(x16, x17 + 2, x16, x17 + 2) :|: TRUE && x16 >= 1 && x18 >= 2 && x19 = 1 && x17 = -1

Arcs:
(1) -> (2)
(2) -> (1), (2), (3), (4), (5)
(3) -> (2), (3), (4)
(4) -> (2), (3), (4)
(5) -> (3)

This digraph is fully evaluated!
----------------------------------------

(24)
Obligation:

Termination digraph:
Nodes:
(1) f3025_0_gt_LE(x, x1, x2, x3) -> f3025_0_gt_LE(x, 0 + 2, x, 0 + 2) :|: TRUE && x2 >= 2 && x3 = 1 && x >= 2 && x1 = 0
(2) f3025_0_gt_LE(x:0, x1:0, x2:0, x3:0) -> f3025_0_gt_LE(x:0, x1:0, x2:0 - 2, x3:0 - 2) :|: x3:0 > 1 && x2:0 > 2
(3) f3025_0_gt_LE(x8, x9, x10, x11) -> f3025_0_gt_LE(x8, x9 + 1, x8 + -2, x9 + -1) :|: TRUE && x10 >= 2 && x11 = 1 && x9 >= 1 && x8 >= 3
(4) f3025_0_gt_LE(x16, x17, x18, x19) -> f3025_0_gt_LE(x16, x17 + 2, x16, x17 + 2) :|: TRUE && x16 >= 1 && x18 >= 2 && x19 = 1 && x17 = -1
(5) f3025_0_gt_LE(i639:0:0:0, i594:0:0:0, i638:0:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0:0, i594:0:0:0 + 1, i639:0:0:0, i594:0:0:0 + 1) :|: i639:0:0:0 > 0 && i638:0:0:0 > 0 && cons_0 = 0

Arcs:
(1) -> (2)
(2) -> (1), (2), (3), (4), (5)
(3) -> (2), (3), (5)
(4) -> (3)
(5) -> (2), (3), (5)

This digraph is fully evaluated!

----------------------------------------

(25) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(26)
Obligation:
Rules:
f3025_0_gt_LE(x16:0, cons_-1, x18:0, cons_1) -> f3025_0_gt_LE(x16:0, 1, x16:0, 1) :|: x18:0 > 1 && x16:0 > 0 && cons_-1 = -1 && cons_1 = 1
f3025_0_gt_LE(x, x1, x2, x3) -> f3025_0_gt_LE(x, 2, x, 2) :|: x > 1 && x2 > 1 && x1 = 0 && x3 = 1
f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0) -> f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0 - 2, x3:0:0 - 2) :|: x3:0:0 > 1 && x2:0:0 > 2
f3025_0_gt_LE(x4, x5, x6, x7) -> f3025_0_gt_LE(x4, x5 + 1, x4 - 2, x5 - 1) :|: x5 > 0 && x6 > 1 && x4 > 2 && x7 = 1
f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0, i638:0:0:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0 + 1, i639:0:0:0:0, i594:0:0:0:0 + 1) :|: i639:0:0:0:0 > 0 && i638:0:0:0:0 > 0 && cons_0 = 0

----------------------------------------

(27) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f3025_0_gt_LE(VARIABLE, VARIABLE, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.The following proof was generated: 
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given IntTRS could not be shown:



- IntTRS
  - PolynomialOrderProcessor

Rules:
f3025_0_gt_LE(x16:0, c, x18:0, c1) -> f3025_0_gt_LE(x16:0, c2, x16:0, c3) :|: c3 = 1 && (c2 = 1 && (c1 = 1 && c = -1)) && (x18:0 > 1 && x16:0 > 0 && cons_-1 = -1 && cons_1 = 1)
f3025_0_gt_LE(x, c4, x2, c5) -> f3025_0_gt_LE(x, c6, x, c7) :|: c7 = 2 && (c6 = 2 && (c5 = 1 && c4 = 0)) && (x > 1 && x2 > 1 && x1 = 0 && x3 = 1)
f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0) -> f3025_0_gt_LE(x:0:0, x1:0:0, c8, c9) :|: c9 = x3:0:0 - 2 && c8 = x2:0:0 - 2 && (x3:0:0 > 1 && x2:0:0 > 2)
f3025_0_gt_LE(x4, x5, x6, c10) -> f3025_0_gt_LE(x4, c11, c12, c13) :|: c13 = x5 - 1 && (c12 = x4 - 2 && (c11 = x5 + 1 && c10 = 1)) && (x5 > 0 && x6 > 1 && x4 > 2 && x7 = 1)
f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0, i638:0:0:0:0, c14) -> f3025_0_gt_LE(i639:0:0:0:0, c15, i639:0:0:0:0, c16) :|: c16 = i594:0:0:0:0 + 1 && (c15 = i594:0:0:0:0 + 1 && c14 = 0) && (i639:0:0:0:0 > 0 && i638:0:0:0:0 > 0 && cons_0 = 0)

Found the following polynomial interpretation:
[f3025_0_gt_LE(x, x1, x2, x3)] = -2 + x - 2*x1

The following rules are decreasing:
f3025_0_gt_LE(x16:0, c, x18:0, c1) -> f3025_0_gt_LE(x16:0, c2, x16:0, c3) :|: c3 = 1 && (c2 = 1 && (c1 = 1 && c = -1)) && (x18:0 > 1 && x16:0 > 0 && cons_-1 = -1 && cons_1 = 1)
f3025_0_gt_LE(x, c4, x2, c5) -> f3025_0_gt_LE(x, c6, x, c7) :|: c7 = 2 && (c6 = 2 && (c5 = 1 && c4 = 0)) && (x > 1 && x2 > 1 && x1 = 0 && x3 = 1)
f3025_0_gt_LE(x4, x5, x6, c10) -> f3025_0_gt_LE(x4, c11, c12, c13) :|: c13 = x5 - 1 && (c12 = x4 - 2 && (c11 = x5 + 1 && c10 = 1)) && (x5 > 0 && x6 > 1 && x4 > 2 && x7 = 1)
f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0, i638:0:0:0:0, c14) -> f3025_0_gt_LE(i639:0:0:0:0, c15, i639:0:0:0:0, c16) :|: c16 = i594:0:0:0:0 + 1 && (c15 = i594:0:0:0:0 + 1 && c14 = 0) && (i639:0:0:0:0 > 0 && i638:0:0:0:0 > 0 && cons_0 = 0)
The following rules are bounded:
f3025_0_gt_LE(x16:0, c, x18:0, c1) -> f3025_0_gt_LE(x16:0, c2, x16:0, c3) :|: c3 = 1 && (c2 = 1 && (c1 = 1 && c = -1)) && (x18:0 > 1 && x16:0 > 0 && cons_-1 = -1 && cons_1 = 1)
f3025_0_gt_LE(x, c4, x2, c5) -> f3025_0_gt_LE(x, c6, x, c7) :|: c7 = 2 && (c6 = 2 && (c5 = 1 && c4 = 0)) && (x > 1 && x2 > 1 && x1 = 0 && x3 = 1)


- IntTRS
  - PolynomialOrderProcessor
    - IntTRS

Rules:
f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0) -> f3025_0_gt_LE(x:0:0, x1:0:0, c8, c9) :|: c9 = x3:0:0 - 2 && c8 = x2:0:0 - 2 && (x3:0:0 > 1 && x2:0:0 > 2)
f3025_0_gt_LE(x4, x5, x6, c10) -> f3025_0_gt_LE(x4, c11, c12, c13) :|: c13 = x5 - 1 && (c12 = x4 - 2 && (c11 = x5 + 1 && c10 = 1)) && (x5 > 0 && x6 > 1 && x4 > 2 && x7 = 1)
f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0, i638:0:0:0:0, c14) -> f3025_0_gt_LE(i639:0:0:0:0, c15, i639:0:0:0:0, c16) :|: c16 = i594:0:0:0:0 + 1 && (c15 = i594:0:0:0:0 + 1 && c14 = 0) && (i639:0:0:0:0 > 0 && i638:0:0:0:0 > 0 && cons_0 = 0)



----------------------------------------

(28)
Obligation:
Rules:
f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0) -> f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0 - 2, x3:0:0 - 2) :|: x3:0:0 > 1 && x2:0:0 > 2
f3025_0_gt_LE(x4, x5, x6, x7) -> f3025_0_gt_LE(x4, x5 + 1, x4 - 2, x5 - 1) :|: x5 > 0 && x6 > 1 && x4 > 2 && x7 = 1
f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0, i638:0:0:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0 + 1, i639:0:0:0:0, i594:0:0:0:0 + 1) :|: i639:0:0:0:0 > 0 && i638:0:0:0:0 > 0 && cons_0 = 0

----------------------------------------

(29) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0) -> f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0 - 2, x3:0:0 - 2) :|: x3:0:0 > 1 && x2:0:0 > 2
(2) f3025_0_gt_LE(x4, x5, x6, x7) -> f3025_0_gt_LE(x4, x5 + 1, x4 - 2, x5 - 1) :|: x5 > 0 && x6 > 1 && x4 > 2 && x7 = 1
(3) f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0, i638:0:0:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0 + 1, i639:0:0:0:0, i594:0:0:0:0 + 1) :|: i639:0:0:0:0 > 0 && i638:0:0:0:0 > 0 && cons_0 = 0

Arcs:
(1) -> (1), (2), (3)
(2) -> (1), (2), (3)
(3) -> (1), (2), (3)

This digraph is fully evaluated!
----------------------------------------

(30)
Obligation:

Termination digraph:
Nodes:
(1) f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0) -> f3025_0_gt_LE(x:0:0, x1:0:0, x2:0:0 - 2, x3:0:0 - 2) :|: x3:0:0 > 1 && x2:0:0 > 2
(2) f3025_0_gt_LE(x4, x5, x6, x7) -> f3025_0_gt_LE(x4, x5 + 1, x4 - 2, x5 - 1) :|: x5 > 0 && x6 > 1 && x4 > 2 && x7 = 1
(3) f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0, i638:0:0:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0:0:0, i594:0:0:0:0 + 1, i639:0:0:0:0, i594:0:0:0:0 + 1) :|: i639:0:0:0:0 > 0 && i638:0:0:0:0 > 0 && cons_0 = 0

Arcs:
(1) -> (1), (2), (3)
(2) -> (1), (2), (3)
(3) -> (1), (2), (3)

This digraph is fully evaluated!

----------------------------------------

(31) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(32)
Obligation:
Rules:
f3025_0_gt_LE(x4:0, x5:0, x6:0, cons_1) -> f3025_0_gt_LE(x4:0, x5:0 + 1, x4:0 - 2, x5:0 - 1) :|: x5:0 > 0 && x6:0 > 1 && x4:0 > 2 && cons_1 = 1
f3025_0_gt_LE(x:0:0:0, x1:0:0:0, x2:0:0:0, x3:0:0:0) -> f3025_0_gt_LE(x:0:0:0, x1:0:0:0, x2:0:0:0 - 2, x3:0:0:0 - 2) :|: x3:0:0:0 > 1 && x2:0:0:0 > 2
f3025_0_gt_LE(i639:0:0:0:0:0, i594:0:0:0:0:0, i638:0:0:0:0:0, cons_0) -> f3025_0_gt_LE(i639:0:0:0:0:0, i594:0:0:0:0:0 + 1, i639:0:0:0:0:0, i594:0:0:0:0:0 + 1) :|: i639:0:0:0:0:0 > 0 && i638:0:0:0:0:0 > 0 && cons_0 = 0