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


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


MAYBE
proof of /export/starexec/sandbox/benchmark/theBenchmark.jar
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 259 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 95 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 31 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) IRSwTChainingProof [EQUIVALENT, 0 ms]
(16) IRSwT
(17) IRSwTTerminationDigraphProof [EQUIVALENT, 2 ms]
(18) IRSwT
(19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(20) IRSwT
(21) IRSwTChainingProof [EQUIVALENT, 0 ms]
(22) IRSwT
(23) IRSwTTerminationDigraphProof [EQUIVALENT, 55 ms]
(24) IRSwT
(25) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(26) IRSwT
(27) IRSwTChainingProof [EQUIVALENT, 0 ms]
(28) IRSwT
(29) IRSwTTerminationDigraphProof [EQUIVALENT, 79 ms]
(30) IRSwT
(31) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(32) IRSwT
(33) TempFilterProof [SOUND, 547 ms]
(34) IRSwT
(35) IRSwTTerminationDigraphProof [EQUIVALENT, 35 ms]
(36) IRSwT
(37) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(38) IRSwT


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

(0)
Obligation:
need to prove termination of the following program:
/**
 * All lasso-shaped runs of this program are terminating.
 */
public class MultiLasso {
    
    public static void main(String[] args) {
        int x = args[0].length() - args[1].length();
        int y;

        while (x > 0) {
            x++;
            y = x;
            while (y > 0) {
                y--;
            }
        }
    }
}



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

(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
----------------------------------------

(2)
Obligation:
need to prove termination of the following program:
/**
 * All lasso-shaped runs of this program are terminating.
 */
public class MultiLasso {
    
    public static void main(String[] args) {
        int x = args[0].length() - args[1].length();
        int y;

        while (x > 0) {
            x++;
            y = x;
            while (y > 0) {
                y--;
            }
        }
    }
}



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

(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
----------------------------------------

(4)
Obligation:
Termination Graph based on JBC Program:
MultiLasso.main([Ljava/lang/String;)V: Graph of 134 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: MultiLasso.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 17 IRulesP rules:
f178_0_main_LE(EOS(STATIC_178), i39, i39) -> f191_0_main_LE(EOS(STATIC_191), i39, i39) :|: TRUE
f191_0_main_LE(EOS(STATIC_191), i39, i39) -> f198_0_main_Inc(EOS(STATIC_198), i39) :|: i39 > 0
f198_0_main_Inc(EOS(STATIC_198), i39) -> f244_0_main_Load(EOS(STATIC_244), i39 + 1) :|: TRUE
f244_0_main_Load(EOS(STATIC_244), i46) -> f258_0_main_Store(EOS(STATIC_258), i46, i46) :|: TRUE
f258_0_main_Store(EOS(STATIC_258), i46, i46) -> f269_0_main_Load(EOS(STATIC_269), i46, i46) :|: TRUE
f269_0_main_Load(EOS(STATIC_269), i46, i46) -> f896_0_main_Load(EOS(STATIC_896), i46, i46) :|: TRUE
f896_0_main_Load(EOS(STATIC_896), i46, i82) -> f1099_0_main_Load(EOS(STATIC_1099), i46, i82) :|: TRUE
f1099_0_main_Load(EOS(STATIC_1099), i46, i218) -> f1112_0_main_LE(EOS(STATIC_1112), i46, i218, i218) :|: TRUE
f1112_0_main_LE(EOS(STATIC_1112), i46, matching1, matching2) -> f1120_0_main_LE(EOS(STATIC_1120), i46, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f1112_0_main_LE(EOS(STATIC_1112), i46, i264, i264) -> f1122_0_main_LE(EOS(STATIC_1122), i46, i264, i264) :|: TRUE
f1120_0_main_LE(EOS(STATIC_1120), i46, matching1, matching2) -> f1165_0_main_Load(EOS(STATIC_1165), i46) :|: 0 <= 0 && matching1 = 0 && matching2 = 0
f1165_0_main_Load(EOS(STATIC_1165), i46) -> f165_0_main_Load(EOS(STATIC_165), i46) :|: TRUE
f165_0_main_Load(EOS(STATIC_165), i34) -> f178_0_main_LE(EOS(STATIC_178), i34, i34) :|: TRUE
f1122_0_main_LE(EOS(STATIC_1122), i46, i264, i264) -> f1169_0_main_Inc(EOS(STATIC_1169), i46, i264) :|: i264 > 0
f1169_0_main_Inc(EOS(STATIC_1169), i46, i264) -> f1172_0_main_JMP(EOS(STATIC_1172), i46, i264 + -1) :|: TRUE
f1172_0_main_JMP(EOS(STATIC_1172), i46, i274) -> f1207_0_main_Load(EOS(STATIC_1207), i46, i274) :|: TRUE
f1207_0_main_Load(EOS(STATIC_1207), i46, i274) -> f1099_0_main_Load(EOS(STATIC_1099), i46, i274) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f1112_0_main_LE(EOS(STATIC_1112), i46:0, i264:0, i264:0) -> f1112_0_main_LE(EOS(STATIC_1112), i46:0, i264:0 - 1, i264:0 - 1) :|: i264:0 > 0
f1112_0_main_LE(EOS(STATIC_1112), i46:0, 0, 0) -> f1112_0_main_LE(EOS(STATIC_1112), i46:0 + 1, i46:0 + 1, i46:0 + 1) :|: i46:0 > 0
Filtered constant ground arguments:
   f1112_0_main_LE(x1, x2, x3, x4) -> f1112_0_main_LE(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f1112_0_main_LE(x1, x2, x3) -> f1112_0_main_LE(x1, x3)
Finished conversion. Obtained 2 rules.P rules:
f1112_0_main_LE(i46:0, i264:0) -> f1112_0_main_LE(i46:0, i264:0 - 1) :|: i264:0 > 0
f1112_0_main_LE(i46:0, cons_0) -> f1112_0_main_LE(i46:0 + 1, i46:0 + 1) :|: i46:0 > 0 && cons_0 = 0

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

(8)
Obligation:
Rules:
f1112_0_main_LE(i46:0, i264:0) -> f1112_0_main_LE(i46:0, i264:0 - 1) :|: i264:0 > 0
f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x + 1, x + 1) :|: x > 0 && x1 = 0

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

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

(10)
Obligation:
Rules:
f1112_0_main_LE(i46:0, i264:0) -> f1112_0_main_LE(i46:0, arith) :|: i264:0 > 0 && arith = i264:0 - 1
f1112_0_main_LE(x2, x3) -> f1112_0_main_LE(x4, x4) :|: x2 > 0 && x3 = 0 && x4 = x2 + 1 && x4 = x2 + 1

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1112_0_main_LE(i46:0, i264:0) -> f1112_0_main_LE(i46:0, arith) :|: i264:0 > 0 && arith = i264:0 - 1
(2) f1112_0_main_LE(x2, x3) -> f1112_0_main_LE(x4, x4) :|: x2 > 0 && x3 = 0 && x4 = x2 + 1 && x4 = x2 + 1

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f1112_0_main_LE(i46:0, i264:0) -> f1112_0_main_LE(i46:0, arith) :|: i264:0 > 0 && arith = i264:0 - 1
(2) f1112_0_main_LE(x2, x3) -> f1112_0_main_LE(x4, x4) :|: x2 > 0 && x3 = 0 && x4 = x2 + 1 && x4 = x2 + 1

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f1112_0_main_LE(i46:0:0, i264:0:0) -> f1112_0_main_LE(i46:0:0, i264:0:0 - 1) :|: i264:0:0 > 0
f1112_0_main_LE(x2:0, cons_0) -> f1112_0_main_LE(x2:0 + 1, x2:0 + 1) :|: x2:0 > 0 && cons_0 = 0

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

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

(16)
Obligation:
Rules:
f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x, x1 + -2) :|: TRUE && x1 >= 2
f1112_0_main_LE(x2:0, cons_0) -> f1112_0_main_LE(x2:0 + 1, x2:0 + 1) :|: x2:0 > 0 && cons_0 = 0
f1112_0_main_LE(x4, x5) -> f1112_0_main_LE(x4 + 1, x4 + 1) :|: TRUE && x4 >= 1 && x5 = 1

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

(17) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x, x1 + -2) :|: TRUE && x1 >= 2
(2) f1112_0_main_LE(x2:0, cons_0) -> f1112_0_main_LE(x2:0 + 1, x2:0 + 1) :|: x2:0 > 0 && cons_0 = 0
(3) f1112_0_main_LE(x4, x5) -> f1112_0_main_LE(x4 + 1, x4 + 1) :|: TRUE && x4 >= 1 && x5 = 1

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

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

(18)
Obligation:

Termination digraph:
Nodes:
(1) f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x, x1 + -2) :|: TRUE && x1 >= 2
(2) f1112_0_main_LE(x4, x5) -> f1112_0_main_LE(x4 + 1, x4 + 1) :|: TRUE && x4 >= 1 && x5 = 1
(3) f1112_0_main_LE(x2:0, cons_0) -> f1112_0_main_LE(x2:0 + 1, x2:0 + 1) :|: x2:0 > 0 && cons_0 = 0

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

This digraph is fully evaluated!

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

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

(20)
Obligation:
Rules:
f1112_0_main_LE(x:0, x1:0) -> f1112_0_main_LE(x:0, x1:0 - 2) :|: x1:0 > 1
f1112_0_main_LE(x4:0, cons_1) -> f1112_0_main_LE(x4:0 + 1, x4:0 + 1) :|: x4:0 > 0 && cons_1 = 1
f1112_0_main_LE(x2:0:0, cons_0) -> f1112_0_main_LE(x2:0:0 + 1, x2:0:0 + 1) :|: x2:0:0 > 0 && cons_0 = 0

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

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

(22)
Obligation:
Rules:
f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x, x1 + -4) :|: TRUE && x1 >= 4
f1112_0_main_LE(x4:0, cons_1) -> f1112_0_main_LE(x4:0 + 1, x4:0 + 1) :|: x4:0 > 0 && cons_1 = 1
f1112_0_main_LE(x4, x5) -> f1112_0_main_LE(x4 + 1, x4 + 1) :|: TRUE && x4 >= 1 && x5 = 3
f1112_0_main_LE(x2:0:0, cons_0) -> f1112_0_main_LE(x2:0:0 + 1, x2:0:0 + 1) :|: x2:0:0 > 0 && cons_0 = 0
f1112_0_main_LE(x8, x9) -> f1112_0_main_LE(x8 + 1, x8 + 1) :|: TRUE && x8 >= 1 && x9 = 2

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

(23) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x, x1 + -4) :|: TRUE && x1 >= 4
(2) f1112_0_main_LE(x4:0, cons_1) -> f1112_0_main_LE(x4:0 + 1, x4:0 + 1) :|: x4:0 > 0 && cons_1 = 1
(3) f1112_0_main_LE(x4, x5) -> f1112_0_main_LE(x4 + 1, x4 + 1) :|: TRUE && x4 >= 1 && x5 = 3
(4) f1112_0_main_LE(x2:0:0, cons_0) -> f1112_0_main_LE(x2:0:0 + 1, x2:0:0 + 1) :|: x2:0:0 > 0 && cons_0 = 0
(5) f1112_0_main_LE(x8, x9) -> f1112_0_main_LE(x8 + 1, x8 + 1) :|: TRUE && x8 >= 1 && x9 = 2

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

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

(24)
Obligation:

Termination digraph:
Nodes:
(1) f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x, x1 + -4) :|: TRUE && x1 >= 4
(2) f1112_0_main_LE(x4, x5) -> f1112_0_main_LE(x4 + 1, x4 + 1) :|: TRUE && x4 >= 1 && x5 = 3
(3) f1112_0_main_LE(x8, x9) -> f1112_0_main_LE(x8 + 1, x8 + 1) :|: TRUE && x8 >= 1 && x9 = 2
(4) f1112_0_main_LE(x2:0:0, cons_0) -> f1112_0_main_LE(x2:0:0 + 1, x2:0:0 + 1) :|: x2:0:0 > 0 && cons_0 = 0
(5) f1112_0_main_LE(x4:0, cons_1) -> f1112_0_main_LE(x4:0 + 1, x4:0 + 1) :|: x4:0 > 0 && cons_1 = 1

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

This digraph is fully evaluated!

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

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

(26)
Obligation:
Rules:
f1112_0_main_LE(x4:0, cons_3) -> f1112_0_main_LE(x4:0 + 1, x4:0 + 1) :|: x4:0 > 0 && cons_3 = 3
f1112_0_main_LE(x8:0, cons_2) -> f1112_0_main_LE(x8:0 + 1, x8:0 + 1) :|: x8:0 > 0 && cons_2 = 2
f1112_0_main_LE(x2:0:0:0, cons_0) -> f1112_0_main_LE(x2:0:0:0 + 1, x2:0:0:0 + 1) :|: x2:0:0:0 > 0 && cons_0 = 0
f1112_0_main_LE(x4:0:0, cons_1) -> f1112_0_main_LE(x4:0:0 + 1, x4:0:0 + 1) :|: x4:0:0 > 0 && cons_1 = 1
f1112_0_main_LE(x:0, x1:0) -> f1112_0_main_LE(x:0, x1:0 - 4) :|: x1:0 > 3

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

(27) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(28)
Obligation:
Rules:
f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x + 2, x + 2) :|: TRUE && x1 = 3 && x = 2
f1112_0_main_LE(x8:0, cons_2) -> f1112_0_main_LE(x8:0 + 1, x8:0 + 1) :|: x8:0 > 0 && cons_2 = 2
f1112_0_main_LE(x4, x5) -> f1112_0_main_LE(x4 + 2, x4 + 2) :|: TRUE && x5 = 3 && x4 = 1
f1112_0_main_LE(x2:0:0:0, cons_0) -> f1112_0_main_LE(x2:0:0:0 + 1, x2:0:0:0 + 1) :|: x2:0:0:0 > 0 && cons_0 = 0
f1112_0_main_LE(x4:0:0, cons_1) -> f1112_0_main_LE(x4:0:0 + 1, x4:0:0 + 1) :|: x4:0:0 > 0 && cons_1 = 1
f1112_0_main_LE(x:0, x1:0) -> f1112_0_main_LE(x:0, x1:0 - 4) :|: x1:0 > 3
f1112_0_main_LE(x16, x17) -> f1112_0_main_LE(x16 + 1, x16 + -3) :|: TRUE && x17 = 3 && x16 >= 3

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

(29) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x + 2, x + 2) :|: TRUE && x1 = 3 && x = 2
(2) f1112_0_main_LE(x8:0, cons_2) -> f1112_0_main_LE(x8:0 + 1, x8:0 + 1) :|: x8:0 > 0 && cons_2 = 2
(3) f1112_0_main_LE(x4, x5) -> f1112_0_main_LE(x4 + 2, x4 + 2) :|: TRUE && x5 = 3 && x4 = 1
(4) f1112_0_main_LE(x2:0:0:0, cons_0) -> f1112_0_main_LE(x2:0:0:0 + 1, x2:0:0:0 + 1) :|: x2:0:0:0 > 0 && cons_0 = 0
(5) f1112_0_main_LE(x4:0:0, cons_1) -> f1112_0_main_LE(x4:0:0 + 1, x4:0:0 + 1) :|: x4:0:0 > 0 && cons_1 = 1
(6) f1112_0_main_LE(x:0, x1:0) -> f1112_0_main_LE(x:0, x1:0 - 4) :|: x1:0 > 3
(7) f1112_0_main_LE(x16, x17) -> f1112_0_main_LE(x16 + 1, x16 + -3) :|: TRUE && x17 = 3 && x16 >= 3

Arcs:
(1) -> (6)
(2) -> (2), (6), (7)
(3) -> (7)
(4) -> (2), (6), (7)
(5) -> (2), (6), (7)
(6) -> (1), (2), (3), (4), (5), (6), (7)
(7) -> (2), (4), (5), (6), (7)

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

(30)
Obligation:

Termination digraph:
Nodes:
(1) f1112_0_main_LE(x, x1) -> f1112_0_main_LE(x + 2, x + 2) :|: TRUE && x1 = 3 && x = 2
(2) f1112_0_main_LE(x:0, x1:0) -> f1112_0_main_LE(x:0, x1:0 - 4) :|: x1:0 > 3
(3) f1112_0_main_LE(x8:0, cons_2) -> f1112_0_main_LE(x8:0 + 1, x8:0 + 1) :|: x8:0 > 0 && cons_2 = 2
(4) f1112_0_main_LE(x2:0:0:0, cons_0) -> f1112_0_main_LE(x2:0:0:0 + 1, x2:0:0:0 + 1) :|: x2:0:0:0 > 0 && cons_0 = 0
(5) f1112_0_main_LE(x16, x17) -> f1112_0_main_LE(x16 + 1, x16 + -3) :|: TRUE && x17 = 3 && x16 >= 3
(6) f1112_0_main_LE(x4:0:0, cons_1) -> f1112_0_main_LE(x4:0:0 + 1, x4:0:0 + 1) :|: x4:0:0 > 0 && cons_1 = 1
(7) f1112_0_main_LE(x4, x5) -> f1112_0_main_LE(x4 + 2, x4 + 2) :|: TRUE && x5 = 3 && x4 = 1

Arcs:
(1) -> (2)
(2) -> (1), (2), (3), (4), (5), (6), (7)
(3) -> (2), (3), (5)
(4) -> (2), (3), (5)
(5) -> (2), (3), (4), (5), (6)
(6) -> (2), (3), (5)
(7) -> (5)

This digraph is fully evaluated!

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

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

(32)
Obligation:
Rules:
f1112_0_main_LE(x8:0:0, cons_2) -> f1112_0_main_LE(x8:0:0 + 1, x8:0:0 + 1) :|: x8:0:0 > 0 && cons_2 = 2
f1112_0_main_LE(x2:0:0:0:0, cons_0) -> f1112_0_main_LE(x2:0:0:0:0 + 1, x2:0:0:0:0 + 1) :|: x2:0:0:0:0 > 0 && cons_0 = 0
f1112_0_main_LE(x4:0:0:0, cons_1) -> f1112_0_main_LE(x4:0:0:0 + 1, x4:0:0:0 + 1) :|: x4:0:0:0 > 0 && cons_1 = 1
f1112_0_main_LE(x, x1) -> f1112_0_main_LE(3, 3) :|: TRUE && x = 1 && x1 = 3
f1112_0_main_LE(x2, x3) -> f1112_0_main_LE(4, 4) :|: TRUE && x2 = 2 && x3 = 3
f1112_0_main_LE(x:0:0, x1:0:0) -> f1112_0_main_LE(x:0:0, x1:0:0 - 4) :|: x1:0:0 > 3
f1112_0_main_LE(x16:0, cons_3) -> f1112_0_main_LE(x16:0 + 1, x16:0 - 3) :|: x16:0 > 2 && cons_3 = 3

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

(33) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1112_0_main_LE(VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.The following proof was generated: 
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IntTRS could not be shown:



- IntTRS
  - PolynomialOrderProcessor

Rules:
f1112_0_main_LE(x8:0:0, c) -> f1112_0_main_LE(c1, c2) :|: c2 = x8:0:0 + 1 && (c1 = x8:0:0 + 1 && c = 2) && (x8:0:0 > 0 && cons_2 = 2)
f1112_0_main_LE(x2:0:0:0:0, c3) -> f1112_0_main_LE(c4, c5) :|: c5 = x2:0:0:0:0 + 1 && (c4 = x2:0:0:0:0 + 1 && c3 = 0) && (x2:0:0:0:0 > 0 && cons_0 = 0)
f1112_0_main_LE(x4:0:0:0, c6) -> f1112_0_main_LE(c7, c8) :|: c8 = x4:0:0:0 + 1 && (c7 = x4:0:0:0 + 1 && c6 = 1) && (x4:0:0:0 > 0 && cons_1 = 1)
f1112_0_main_LE(c9, c10) -> f1112_0_main_LE(c11, c12) :|: c12 = 3 && (c11 = 3 && (c10 = 3 && c9 = 1)) && (TRUE && x = 1 && x1 = 3)
f1112_0_main_LE(c13, c14) -> f1112_0_main_LE(c15, c16) :|: c16 = 4 && (c15 = 4 && (c14 = 3 && c13 = 2)) && (TRUE && x2 = 2 && x3 = 3)
f1112_0_main_LE(x:0:0, x1:0:0) -> f1112_0_main_LE(x:0:0, c17) :|: c17 = x1:0:0 - 4 && x1:0:0 > 3
f1112_0_main_LE(x16:0, c18) -> f1112_0_main_LE(c19, c20) :|: c20 = x16:0 - 3 && (c19 = x16:0 + 1 && c18 = 3) && (x16:0 > 2 && cons_3 = 3)

Found the following polynomial interpretation:
[f1112_0_main_LE(x, x1)] = 1 - x

The following rules are decreasing:
f1112_0_main_LE(x8:0:0, c) -> f1112_0_main_LE(c1, c2) :|: c2 = x8:0:0 + 1 && (c1 = x8:0:0 + 1 && c = 2) && (x8:0:0 > 0 && cons_2 = 2)
f1112_0_main_LE(x2:0:0:0:0, c3) -> f1112_0_main_LE(c4, c5) :|: c5 = x2:0:0:0:0 + 1 && (c4 = x2:0:0:0:0 + 1 && c3 = 0) && (x2:0:0:0:0 > 0 && cons_0 = 0)
f1112_0_main_LE(x4:0:0:0, c6) -> f1112_0_main_LE(c7, c8) :|: c8 = x4:0:0:0 + 1 && (c7 = x4:0:0:0 + 1 && c6 = 1) && (x4:0:0:0 > 0 && cons_1 = 1)
f1112_0_main_LE(c9, c10) -> f1112_0_main_LE(c11, c12) :|: c12 = 3 && (c11 = 3 && (c10 = 3 && c9 = 1)) && (TRUE && x = 1 && x1 = 3)
f1112_0_main_LE(c13, c14) -> f1112_0_main_LE(c15, c16) :|: c16 = 4 && (c15 = 4 && (c14 = 3 && c13 = 2)) && (TRUE && x2 = 2 && x3 = 3)
f1112_0_main_LE(x16:0, c18) -> f1112_0_main_LE(c19, c20) :|: c20 = x16:0 - 3 && (c19 = x16:0 + 1 && c18 = 3) && (x16:0 > 2 && cons_3 = 3)
The following rules are bounded:
f1112_0_main_LE(c9, c10) -> f1112_0_main_LE(c11, c12) :|: c12 = 3 && (c11 = 3 && (c10 = 3 && c9 = 1)) && (TRUE && x = 1 && x1 = 3)


- IntTRS
  - PolynomialOrderProcessor
    - IntTRS
      - PolynomialOrderProcessor

Rules:
f1112_0_main_LE(x8:0:0, c) -> f1112_0_main_LE(c1, c2) :|: c2 = x8:0:0 + 1 && (c1 = x8:0:0 + 1 && c = 2) && (x8:0:0 > 0 && cons_2 = 2)
f1112_0_main_LE(x2:0:0:0:0, c3) -> f1112_0_main_LE(c4, c5) :|: c5 = x2:0:0:0:0 + 1 && (c4 = x2:0:0:0:0 + 1 && c3 = 0) && (x2:0:0:0:0 > 0 && cons_0 = 0)
f1112_0_main_LE(x4:0:0:0, c6) -> f1112_0_main_LE(c7, c8) :|: c8 = x4:0:0:0 + 1 && (c7 = x4:0:0:0 + 1 && c6 = 1) && (x4:0:0:0 > 0 && cons_1 = 1)
f1112_0_main_LE(c13, c14) -> f1112_0_main_LE(c15, c16) :|: c16 = 4 && (c15 = 4 && (c14 = 3 && c13 = 2)) && (TRUE && x2 = 2 && x3 = 3)
f1112_0_main_LE(x:0:0, x1:0:0) -> f1112_0_main_LE(x:0:0, c17) :|: c17 = x1:0:0 - 4 && x1:0:0 > 3
f1112_0_main_LE(x16:0, c18) -> f1112_0_main_LE(c19, c20) :|: c20 = x16:0 - 3 && (c19 = x16:0 + 1 && c18 = 3) && (x16:0 > 2 && cons_3 = 3)

Found the following polynomial interpretation:
[f1112_0_main_LE(x, x1)] = 2 - x

The following rules are decreasing:
f1112_0_main_LE(x8:0:0, c) -> f1112_0_main_LE(c1, c2) :|: c2 = x8:0:0 + 1 && (c1 = x8:0:0 + 1 && c = 2) && (x8:0:0 > 0 && cons_2 = 2)
f1112_0_main_LE(x2:0:0:0:0, c3) -> f1112_0_main_LE(c4, c5) :|: c5 = x2:0:0:0:0 + 1 && (c4 = x2:0:0:0:0 + 1 && c3 = 0) && (x2:0:0:0:0 > 0 && cons_0 = 0)
f1112_0_main_LE(x4:0:0:0, c6) -> f1112_0_main_LE(c7, c8) :|: c8 = x4:0:0:0 + 1 && (c7 = x4:0:0:0 + 1 && c6 = 1) && (x4:0:0:0 > 0 && cons_1 = 1)
f1112_0_main_LE(c13, c14) -> f1112_0_main_LE(c15, c16) :|: c16 = 4 && (c15 = 4 && (c14 = 3 && c13 = 2)) && (TRUE && x2 = 2 && x3 = 3)
f1112_0_main_LE(x16:0, c18) -> f1112_0_main_LE(c19, c20) :|: c20 = x16:0 - 3 && (c19 = x16:0 + 1 && c18 = 3) && (x16:0 > 2 && cons_3 = 3)
The following rules are bounded:
f1112_0_main_LE(c13, c14) -> f1112_0_main_LE(c15, c16) :|: c16 = 4 && (c15 = 4 && (c14 = 3 && c13 = 2)) && (TRUE && x2 = 2 && x3 = 3)


- IntTRS
  - PolynomialOrderProcessor
    - IntTRS
      - PolynomialOrderProcessor
        - IntTRS

Rules:
f1112_0_main_LE(x8:0:0, c) -> f1112_0_main_LE(c1, c2) :|: c2 = x8:0:0 + 1 && (c1 = x8:0:0 + 1 && c = 2) && (x8:0:0 > 0 && cons_2 = 2)
f1112_0_main_LE(x2:0:0:0:0, c3) -> f1112_0_main_LE(c4, c5) :|: c5 = x2:0:0:0:0 + 1 && (c4 = x2:0:0:0:0 + 1 && c3 = 0) && (x2:0:0:0:0 > 0 && cons_0 = 0)
f1112_0_main_LE(x4:0:0:0, c6) -> f1112_0_main_LE(c7, c8) :|: c8 = x4:0:0:0 + 1 && (c7 = x4:0:0:0 + 1 && c6 = 1) && (x4:0:0:0 > 0 && cons_1 = 1)
f1112_0_main_LE(x:0:0, x1:0:0) -> f1112_0_main_LE(x:0:0, c17) :|: c17 = x1:0:0 - 4 && x1:0:0 > 3
f1112_0_main_LE(x16:0, c18) -> f1112_0_main_LE(c19, c20) :|: c20 = x16:0 - 3 && (c19 = x16:0 + 1 && c18 = 3) && (x16:0 > 2 && cons_3 = 3)



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(34)
Obligation:
Rules:
f1112_0_main_LE(x8:0:0, cons_2) -> f1112_0_main_LE(x8:0:0 + 1, x8:0:0 + 1) :|: x8:0:0 > 0 && cons_2 = 2
f1112_0_main_LE(x2:0:0:0:0, cons_0) -> f1112_0_main_LE(x2:0:0:0:0 + 1, x2:0:0:0:0 + 1) :|: x2:0:0:0:0 > 0 && cons_0 = 0
f1112_0_main_LE(x4:0:0:0, cons_1) -> f1112_0_main_LE(x4:0:0:0 + 1, x4:0:0:0 + 1) :|: x4:0:0:0 > 0 && cons_1 = 1
f1112_0_main_LE(x:0:0, x1:0:0) -> f1112_0_main_LE(x:0:0, x1:0:0 - 4) :|: x1:0:0 > 3
f1112_0_main_LE(x16:0, cons_3) -> f1112_0_main_LE(x16:0 + 1, x16:0 - 3) :|: x16:0 > 2 && cons_3 = 3

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(35) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1112_0_main_LE(x8:0:0, cons_2) -> f1112_0_main_LE(x8:0:0 + 1, x8:0:0 + 1) :|: x8:0:0 > 0 && cons_2 = 2
(2) f1112_0_main_LE(x2:0:0:0:0, cons_0) -> f1112_0_main_LE(x2:0:0:0:0 + 1, x2:0:0:0:0 + 1) :|: x2:0:0:0:0 > 0 && cons_0 = 0
(3) f1112_0_main_LE(x4:0:0:0, cons_1) -> f1112_0_main_LE(x4:0:0:0 + 1, x4:0:0:0 + 1) :|: x4:0:0:0 > 0 && cons_1 = 1
(4) f1112_0_main_LE(x:0:0, x1:0:0) -> f1112_0_main_LE(x:0:0, x1:0:0 - 4) :|: x1:0:0 > 3
(5) f1112_0_main_LE(x16:0, cons_3) -> f1112_0_main_LE(x16:0 + 1, x16:0 - 3) :|: x16:0 > 2 && cons_3 = 3

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

This digraph is fully evaluated!
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(36)
Obligation:

Termination digraph:
Nodes:
(1) f1112_0_main_LE(x8:0:0, cons_2) -> f1112_0_main_LE(x8:0:0 + 1, x8:0:0 + 1) :|: x8:0:0 > 0 && cons_2 = 2
(2) f1112_0_main_LE(x2:0:0:0:0, cons_0) -> f1112_0_main_LE(x2:0:0:0:0 + 1, x2:0:0:0:0 + 1) :|: x2:0:0:0:0 > 0 && cons_0 = 0
(3) f1112_0_main_LE(x:0:0, x1:0:0) -> f1112_0_main_LE(x:0:0, x1:0:0 - 4) :|: x1:0:0 > 3
(4) f1112_0_main_LE(x4:0:0:0, cons_1) -> f1112_0_main_LE(x4:0:0:0 + 1, x4:0:0:0 + 1) :|: x4:0:0:0 > 0 && cons_1 = 1
(5) f1112_0_main_LE(x16:0, cons_3) -> f1112_0_main_LE(x16:0 + 1, x16:0 - 3) :|: x16:0 > 2 && cons_3 = 3

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

This digraph is fully evaluated!

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(37) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(38)
Obligation:
Rules:
f1112_0_main_LE(x8:0:0:0, cons_2) -> f1112_0_main_LE(x8:0:0:0 + 1, x8:0:0:0 + 1) :|: x8:0:0:0 > 0 && cons_2 = 2
f1112_0_main_LE(x2:0:0:0:0:0, cons_0) -> f1112_0_main_LE(x2:0:0:0:0:0 + 1, x2:0:0:0:0:0 + 1) :|: x2:0:0:0:0:0 > 0 && cons_0 = 0
f1112_0_main_LE(x16:0:0, cons_3) -> f1112_0_main_LE(x16:0:0 + 1, x16:0:0 - 3) :|: x16:0:0 > 2 && cons_3 = 3
f1112_0_main_LE(x4:0:0:0:0, cons_1) -> f1112_0_main_LE(x4:0:0:0:0 + 1, x4:0:0:0:0 + 1) :|: x4:0:0:0:0 > 0 && cons_1 = 1
f1112_0_main_LE(x:0:0:0, x1:0:0:0) -> f1112_0_main_LE(x:0:0:0, x1:0:0:0 - 4) :|: x1:0:0:0 > 3