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


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

map(a)

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

(0) Prolog
(1) PrologToIRSwTTransformerProof [SOUND, 0 ms]
(2) TRUE


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

(0)
Obligation:
Clauses:

color_map([], X1).
color_map(.(Region, Regions), Colors) :- ','(color_region(Region, Colors), color_map(Regions, Colors)).
color_region(region(X2, Color, Neighbors), Colors) :- ','(select(Color, Colors, Colors1), subset(Neighbors, Colors1)).
select(X, .(X, Xs), Xs).
select(X, .(Y, Xs), .(Y, Zs)) :- select(X, Xs, Zs).
subset([], X3).
subset(.(X, Xs), Ys) :- ','(member(X, Ys), subset(Xs, Ys)).
member(X, .(X, X4)).
member(X, .(X5, Xs)) :- member(X, Xs).
map(.(region(belize, Belize, .(Guatemala, [])), .(region(guatemala, Guatemala, .(Belize, .(El_Salvador, .(Honduras, [])))), .(region(el_salvador, El_Salvador, .(Guatemala, .(Honduras, []))), .(region(honduras, Honduras, .(Guatemala, .(El_Salvador, .(Nicaragua, [])))), .(region(nicaragua, Nicaragua, .(Honduras, .(Costa_rica, []))), .(region(costa_rica, Costa_rica, .(Nicaragua, .(Panama, []))), .(region(panama, Panama, .(Costa_rica, [])), [])))))))).
query :- ','(map(X), color_map(X, .(red, .(blue, .(green, []))))).


Query: map(a)
----------------------------------------

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

{
    "root": 2,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(color_map ([]) X1)",
                null
            ],
            [
                "(color_map (. Region Regions) Colors)",
                "(',' (color_region Region Colors) (color_map Regions Colors))"
            ],
            [
                "(color_region (region X2 Color Neighbors) Colors)",
                "(',' (select Color Colors Colors1) (subset Neighbors Colors1))"
            ],
            [
                "(select X (. X Xs) Xs)",
                null
            ],
            [
                "(select X (. Y Xs) (. Y Zs))",
                "(select X Xs Zs)"
            ],
            [
                "(subset ([]) X3)",
                null
            ],
            [
                "(subset (. X Xs) Ys)",
                "(',' (member X Ys) (subset Xs Ys))"
            ],
            [
                "(member X (. X X4))",
                null
            ],
            [
                "(member X (. X5 Xs))",
                "(member X Xs)"
            ],
            [
                "(map (. (region (belize) Belize (. Guatemala ([]))) (. (region (guatemala) Guatemala (. Belize (. El_Salvador (. Honduras ([]))))) (. (region (el_salvador) El_Salvador (. Guatemala (. Honduras ([])))) (. (region (honduras) Honduras (. Guatemala (. El_Salvador (. Nicaragua ([]))))) (. (region (nicaragua) Nicaragua (. Honduras (. Costa_rica ([])))) (. (region (costa_rica) Costa_rica (. Nicaragua (. Panama ([])))) (. (region (panama) Panama (. Costa_rica ([]))) ([])))))))))",
                null
            ],
            [
                "(query)",
                "(',' (map X) (color_map X (. (red) (. (blue) (. (green) ([]))))))"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "2": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(map T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "245": {
                "goal": [{
                    "clause": 9,
                    "scope": 1,
                    "term": "(map T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "322": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "304": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "327": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes"
        },
        "edges": [
            {
                "from": 2,
                "to": 245,
                "label": "CASE"
            },
            {
                "from": 245,
                "to": 304,
                "label": "EVAL with clause\nmap(.(region(belize, X20, .(X21, [])), .(region(guatemala, X21, .(X20, .(X22, .(X23, [])))), .(region(el_salvador, X22, .(X21, .(X23, []))), .(region(honduras, X23, .(X21, .(X22, .(X24, [])))), .(region(nicaragua, X24, .(X23, .(X25, []))), .(region(costa_rica, X25, .(X24, .(X26, []))), .(region(panama, X26, .(X25, [])), [])))))))).\nand substitutionX20 -> T16,\nX21 -> T17,\nX22 -> T18,\nX23 -> T19,\nX24 -> T20,\nX25 -> T21,\nX26 -> T22,\nT1 -> .(region(belize, T16, .(T17, [])), .(region(guatemala, T17, .(T16, .(T18, .(T19, [])))), .(region(el_salvador, T18, .(T17, .(T19, []))), .(region(honduras, T19, .(T17, .(T18, .(T20, [])))), .(region(nicaragua, T20, .(T19, .(T21, []))), .(region(costa_rica, T21, .(T20, .(T22, []))), .(region(panama, T22, .(T21, [])), [])))))))"
            },
            {
                "from": 245,
                "to": 322,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 304,
                "to": 327,
                "label": "SUCCESS"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE