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


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 192 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 91 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 50 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 14 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) YES


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(0)
Obligation:
need to prove termination of the following program:
package Nest;

public class Nest{
    public static int nest(int x){
		if (x == 0) return 0;
		else return nest(nest(x-1));
    }

    
    public static void main(final String[] args) {
        final int x = args[0].length();
        final int y = nest(x);
    }
}



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(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
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(2)
Obligation:
need to prove termination of the following program:
package Nest;

public class Nest{
    public static int nest(int x){
		if (x == 0) return 0;
		else return nest(nest(x-1));
    }

    
    public static void main(final String[] args) {
        final int x = args[0].length();
        final int y = nest(x);
    }
}



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

(4)
Obligation:
Termination Graph based on JBC Program:
Nest.Nest.main([Ljava/lang/String;)V: Graph of 68 nodes with 0 SCCs.



Nest.Nest.nest(I)I: Graph of 22 nodes with 0 SCCs.





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(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: Nest.Nest.nest(I)I
SCC calls the following helper methods: Nest.Nest.nest(I)I
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 19 IRulesP rules:
f96_0_nest_NE(EOS(STATIC_96), i17, i17, i17) -> f99_0_nest_NE(EOS(STATIC_99), i17, i17, i17) :|: TRUE
f99_0_nest_NE(EOS(STATIC_99), i17, i17, i17) -> f111_0_nest_Load(EOS(STATIC_111), i17, i17) :|: i17 > 0
f111_0_nest_Load(EOS(STATIC_111), i17, i17) -> f120_0_nest_ConstantStackPush(EOS(STATIC_120), i17, i17) :|: TRUE
f120_0_nest_ConstantStackPush(EOS(STATIC_120), i17, i17) -> f132_0_nest_IntArithmetic(EOS(STATIC_132), i17, i17, 1) :|: TRUE
f132_0_nest_IntArithmetic(EOS(STATIC_132), i17, i17, matching1) -> f142_0_nest_InvokeMethod(EOS(STATIC_142), i17, i17 - 1) :|: i17 > 0 && matching1 = 1
f142_0_nest_InvokeMethod(EOS(STATIC_142), i17, i19) -> f175_0_nest_Load(EOS(STATIC_175), i19, i19) :|: i17 >= 1 && i19 < i17
f142_0_nest_InvokeMethod(EOS(STATIC_142), i17, i19) -> f175_1_nest_Load(EOS(STATIC_175), i17, i19) :|: i17 >= 1 && i19 < i17
f175_0_nest_Load(EOS(STATIC_175), i19, i19) -> f185_0_nest_Load(EOS(STATIC_185), i19, i19) :|: TRUE
f185_0_nest_Load(EOS(STATIC_185), i19, i19) -> f93_0_nest_Load(EOS(STATIC_93), i19, i19) :|: TRUE
f93_0_nest_Load(EOS(STATIC_93), i13, i13) -> f96_0_nest_NE(EOS(STATIC_96), i13, i13, i13) :|: TRUE
f777_0_nest_Return(EOS(STATIC_777), i17, matching1) -> f778_0_nest_InvokeMethod(EOS(STATIC_778), i17, 0) :|: TRUE && matching1 = 0
f778_0_nest_InvokeMethod(EOS(STATIC_778), i17, matching1) -> f779_0_nest_Load(EOS(STATIC_779), 0, 0) :|: i17 >= 1 && matching1 = 0
f778_0_nest_InvokeMethod(EOS(STATIC_778), i17, matching1) -> f779_1_nest_Load(EOS(STATIC_779), i17, 0) :|: i17 >= 1 && matching1 = 0
f779_0_nest_Load(EOS(STATIC_779), matching1, matching2) -> f780_0_nest_Load(EOS(STATIC_780), 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f780_0_nest_Load(EOS(STATIC_780), matching1, matching2) -> f93_0_nest_Load(EOS(STATIC_93), 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f1925_0_nest_Return(EOS(STATIC_1925), i17, matching1) -> f1952_0_nest_InvokeMethod(EOS(STATIC_1952), i17, 0) :|: TRUE && matching1 = 0
f1952_0_nest_InvokeMethod(EOS(STATIC_1952), i17, matching1) -> f778_0_nest_InvokeMethod(EOS(STATIC_778), i17, 0) :|: TRUE && matching1 = 0
f175_1_nest_Load(EOS(STATIC_175), i17, matching1) -> f777_0_nest_Return(EOS(STATIC_777), i17, 0) :|: TRUE && matching1 = 0
f175_1_nest_Load(EOS(STATIC_175), i17, i19) -> f1925_0_nest_Return(EOS(STATIC_1925), i17, 0) :|: TRUE
Combined rules. Obtained 5 IRulesP rules:
f96_0_nest_NE(EOS(STATIC_96), 1, 1, 1) -> f778_0_nest_InvokeMethod(EOS(STATIC_778), 1, 0) :|: TRUE
f96_0_nest_NE(EOS(STATIC_96), i17:0, i17:0, i17:0) -> f96_0_nest_NE(EOS(STATIC_96), i17:0 - 1, i17:0 - 1, i17:0 - 1) :|: i17:0 > 0 && i17:0 - 1 < i17:0
f96_0_nest_NE(EOS(STATIC_96), i17:0, i17:0, i17:0) -> f778_0_nest_InvokeMethod(EOS(STATIC_778), i17:0, 0) :|: i17:0 > 0 && i17:0 - 1 < i17:0
f778_0_nest_InvokeMethod(EOS(STATIC_778), i17:0, 0) -> f96_0_nest_NE(EOS(STATIC_96), 0, 0, 0) :|: i17:0 > 0
Removed following non-SCC rules:
f778_0_nest_InvokeMethod(EOS(STATIC_778), i17:0, 0) -> f779_1_nest_Load(EOS(STATIC_779), i17:0, 0) :|: i17:0 > 0
Filtered constant ground arguments:
   f96_0_nest_NE(x1, x2, x3, x4) -> f96_0_nest_NE(x2, x3, x4)
   f778_0_nest_InvokeMethod(x1, x2, x3) -> f778_0_nest_InvokeMethod(x2)
Filtered duplicate arguments:
   f96_0_nest_NE(x1, x2, x3) -> f96_0_nest_NE(x3)
Finished conversion. Obtained 4 rules.P rules:
f96_0_nest_NE(cons_1) -> f778_0_nest_InvokeMethod(1) :|: TRUE && cons_1 = 1
f96_0_nest_NE(i17:0) -> f96_0_nest_NE(i17:0 - 1) :|: i17:0 > 0 && i17:0 - 1 < i17:0
f96_0_nest_NE(i17:0) -> f778_0_nest_InvokeMethod(i17:0) :|: i17:0 > 0 && i17:0 - 1 < i17:0
f778_0_nest_InvokeMethod(i17:0) -> f96_0_nest_NE(0) :|: i17:0 > 0

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(8)
Obligation:
Rules:
f96_0_nest_NE(cons_1) -> f778_0_nest_InvokeMethod(1) :|: TRUE && cons_1 = 1
f96_0_nest_NE(i17:0) -> f96_0_nest_NE(i17:0 - 1) :|: i17:0 > 0 && i17:0 - 1 < i17:0
f96_0_nest_NE(x) -> f778_0_nest_InvokeMethod(x) :|: x > 0 && x - 1 < x
f778_0_nest_InvokeMethod(x1) -> f96_0_nest_NE(0) :|: x1 > 0

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

(10)
Obligation:
Rules:
f96_0_nest_NE(cons_1) -> f778_0_nest_InvokeMethod(1) :|: TRUE && cons_1 = 1
f96_0_nest_NE(i17:0) -> f96_0_nest_NE(arith) :|: i17:0 > 0 && i17:0 - 1 < i17:0 && arith = i17:0 - 1
f96_0_nest_NE(x) -> f778_0_nest_InvokeMethod(x) :|: x > 0 && x - 1 < x
f778_0_nest_InvokeMethod(x1) -> f96_0_nest_NE(0) :|: x1 > 0

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f96_0_nest_NE(cons_1) -> f778_0_nest_InvokeMethod(1) :|: TRUE && cons_1 = 1
(2) f96_0_nest_NE(i17:0) -> f96_0_nest_NE(arith) :|: i17:0 > 0 && i17:0 - 1 < i17:0 && arith = i17:0 - 1
(3) f96_0_nest_NE(x) -> f778_0_nest_InvokeMethod(x) :|: x > 0 && x - 1 < x
(4) f778_0_nest_InvokeMethod(x1) -> f96_0_nest_NE(0) :|: x1 > 0

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f96_0_nest_NE(i17:0) -> f96_0_nest_NE(arith) :|: i17:0 > 0 && i17:0 - 1 < i17:0 && arith = i17:0 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f96_0_nest_NE(i17:0:0) -> f96_0_nest_NE(i17:0:0 - 1) :|: i17:0:0 > 0 && i17:0:0 - 1 < i17:0:0

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f96_0_nest_NE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f96_0_nest_NE(i17:0:0) -> f96_0_nest_NE(c) :|: c = i17:0:0 - 1 && (i17:0:0 > 0 && i17:0:0 - 1 < i17:0:0)

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f96_0_nest_NE(x)] = x

The following rules are decreasing:
f96_0_nest_NE(i17:0:0) -> f96_0_nest_NE(c) :|: c = i17:0:0 - 1 && (i17:0:0 > 0 && i17:0:0 - 1 < i17:0:0)
The following rules are bounded:
f96_0_nest_NE(i17:0:0) -> f96_0_nest_NE(c) :|: c = i17:0:0 - 1 && (i17:0:0 > 0 && i17:0:0 - 1 < i17:0:0)

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(18)
YES