3.39/1.66	YES
3.39/1.67	proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
3.39/1.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.39/1.67	
3.39/1.67	
3.39/1.67	Left Termination of the query pattern
3.39/1.67	
3.39/1.67	p(g,a)
3.39/1.67	
3.39/1.67	w.r.t. the given Prolog program could successfully be proven:
3.39/1.67	
3.39/1.67	(0) Prolog
3.39/1.67	(1) PrologToDTProblemTransformerProof [SOUND, 0 ms]
3.39/1.67	(2) TRIPLES
3.39/1.67	(3) TPisEmptyProof [EQUIVALENT, 0 ms]
3.39/1.67	(4) YES
3.39/1.67	
3.39/1.67	
3.39/1.67	----------------------------------------
3.39/1.67	
3.39/1.67	(0)
3.39/1.67	Obligation:
3.39/1.67	Clauses:
3.39/1.67	
3.39/1.67	p(X, g(X)).
3.39/1.67	p(X, f(Y)) :- p(X, g(Y)).
3.39/1.67	
3.39/1.67	
3.39/1.67	Query: p(g,a)
3.39/1.67	----------------------------------------
3.39/1.67	
3.39/1.67	(1) PrologToDTProblemTransformerProof (SOUND)
3.39/1.67	Built DT problem from termination graph DT10.
3.39/1.67	
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3.39/1.67	    "root": 2,
3.39/1.67	    "program": {
3.39/1.67	        "directives": [],
3.39/1.67	        "clauses": [
3.39/1.67	            [
3.39/1.67	                "(p X (g X))",
3.39/1.67	                null
3.39/1.67	            ],
3.39/1.67	            [
3.39/1.67	                "(p X (f Y))",
3.39/1.67	                "(p X (g Y))"
3.39/1.67	            ]
3.39/1.67	        ]
3.39/1.67	    },
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3.39/1.67	            },
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3.39/1.67	            },
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3.39/1.67	                        "(p T18 T2)",
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3.39/1.67	                ],
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3.39/1.67	                        "(p T18 T2)",
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3.39/1.67	                    ]],
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3.39/1.67	                        "(p T18 T2)",
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3.39/1.67	                        "(p T18 T2)",
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3.39/1.67	        },
3.39/1.67	        "edges": [
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3.39/1.67	            {
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3.39/1.67	                "label": "EVAL with clause\np(X2, g(X2)).\nand substitutionT1 -> T4,\nX2 -> T4,\nT2 -> g(T4)"
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3.39/1.67	            },
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3.39/1.67	            {
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3.39/1.67	                "to": 67,
3.39/1.67	                "label": "EVAL with clause\np(X5, f(X6)) :- p(X5, g(X6)).\nand substitutionT4 -> T7,\nX5 -> T7,\nX6 -> T9,\nT2 -> f(T9),\nT8 -> T9"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 66,
3.39/1.67	                "to": 68,
3.39/1.67	                "label": "EVAL-BACKTRACK"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 67,
3.39/1.67	                "to": 69,
3.39/1.67	                "label": "CASE"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 69,
3.39/1.67	                "to": 109,
3.39/1.67	                "label": "PARALLEL"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 69,
3.39/1.67	                "to": 110,
3.39/1.67	                "label": "PARALLEL"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 109,
3.39/1.67	                "to": 111,
3.39/1.67	                "label": "EVAL with clause\np(X11, g(X11)).\nand substitutionT7 -> T14,\nX11 -> T14,\nT9 -> T14"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 109,
3.39/1.67	                "to": 112,
3.39/1.67	                "label": "EVAL-BACKTRACK"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 110,
3.39/1.67	                "to": 114,
3.39/1.67	                "label": "BACKTRACK\nfor clause: p(X, f(Y)) :- p(X, g(Y))because of non-unification"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 111,
3.39/1.67	                "to": 113,
3.39/1.67	                "label": "SUCCESS"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 115,
3.39/1.67	                "to": 117,
3.39/1.67	                "label": "CASE"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 117,
3.39/1.67	                "to": 118,
3.39/1.67	                "label": "PARALLEL"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 117,
3.39/1.67	                "to": 119,
3.39/1.67	                "label": "PARALLEL"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 118,
3.39/1.67	                "to": 120,
3.39/1.67	                "label": "EVAL with clause\np(X22, g(X22)).\nand substitutionT18 -> T25,\nX22 -> T25,\nT20 -> T25"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 118,
3.39/1.67	                "to": 121,
3.39/1.67	                "label": "EVAL-BACKTRACK"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 119,
3.39/1.67	                "to": 123,
3.39/1.67	                "label": "BACKTRACK\nfor clause: p(X, f(Y)) :- p(X, g(Y))because of non-unification"
3.39/1.67	            },
3.39/1.67	            {
3.39/1.67	                "from": 120,
3.39/1.67	                "to": 122,
3.39/1.67	                "label": "SUCCESS"
3.39/1.67	            }
3.39/1.67	        ],
3.39/1.67	        "type": "Graph"
3.39/1.67	    }
3.39/1.67	}
3.39/1.67	
3.39/1.67	----------------------------------------
3.39/1.67	
3.39/1.67	(2)
3.39/1.67	Obligation:
3.39/1.67	Triples:
3.39/1.67	
3.39/1.67	
3.39/1.67	Clauses:
3.39/1.67	
3.39/1.67	
3.39/1.67	Afs:
3.39/1.67	
3.39/1.67	
3.39/1.67	----------------------------------------
3.39/1.67	
3.39/1.67	(3) TPisEmptyProof (EQUIVALENT)
3.39/1.67	There are no more dependency triples. Hence, the dependency triple problem trivially terminates.
3.39/1.67	----------------------------------------
3.39/1.67	
3.39/1.67	(4)
3.39/1.67	YES
3.46/1.70	EOF