Logic Progr 19030 pair #381919866

details

property	value
status	complete
benchmark	exercise_squareroot.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	Art-of-prolog

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.03006792068 seconds
cpu usage	8.298445059
max memory	6.72980992E8

stage attributes

key	value
output-size	136203
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

squareroot(g,a)

w.r.t. the given Prolog program could successfully be proven:

(0) Prolog
(1) PrologToIRSwTTransformerProof [SOUND, 76 ms]
(2) IRSwT
(3) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 18 ms]
(6) IRSwT
(7) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 27 ms]
(10) IRSwT
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IRSwT
(13) TempFilterProof [SOUND, 40 ms]
(14) IntTRS
(15) RankingReductionPairProof [EQUIVALENT, 21 ms]
(16) YES


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

(0)
Obligation:
Clauses:

squareroot(N, I) :- ','(>=(N, 0), ','(between(0, N, I), ','(=<(*(I, I), N), ','(>(*(+(I, 1), +(I, 1)), N), !)))).
between(I, J, I) :- =<(I, J).
between(I, J, K) :- ','(<(I, J), ','(is(I1, +(I, 1)), between(I1, J, K))).


Query: squareroot(g,a)
----------------------------------------

(1) PrologToIRSwTTransformerProof (SOUND)
Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert

{
    "root": 2,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(squareroot N I)",
                "(',' (>= N (0)) (',' (between (0) N I) (',' (=< (* I I) N) (',' (> (* (+ I (1)) (+ I (1))) N) (!)))))"
            ],
            [
                "(between I J I)",
                "(=< I J)"
            ],
            [
                "(between I J K)",
                "(',' (< I J) (',' (is I1 (+ I (1))) (between I1 J K)))"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "3167": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<="
                            },
                            {
                                "lhs": {
                                    "name": "T18",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",

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