3.39/1.68	YES
3.70/1.71	proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
3.70/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.70/1.71	
3.70/1.71	
3.70/1.71	Left Termination of the query pattern
3.70/1.71	
3.70/1.71	tc(g,a)
3.70/1.71	
3.70/1.71	w.r.t. the given Prolog program could successfully be proven:
3.70/1.71	
3.70/1.71	(0) Prolog
3.70/1.71	(1) PrologToDTProblemTransformerProof [SOUND, 0 ms]
3.70/1.71	(2) TRIPLES
3.70/1.71	(3) TriplesToPiDPProof [SOUND, 5 ms]
3.70/1.71	(4) PiDP
3.70/1.71	(5) DependencyGraphProof [EQUIVALENT, 0 ms]
3.70/1.71	(6) TRUE
3.70/1.71	
3.70/1.71	
3.70/1.71	----------------------------------------
3.70/1.71	
3.70/1.71	(0)
3.70/1.71	Obligation:
3.70/1.71	Clauses:
3.70/1.71	
3.70/1.71	p(a, b).
3.70/1.71	p(b, c).
3.70/1.71	tc(X, X).
3.70/1.71	tc(X, Y) :- ','(p(X, Z), tc(Z, Y)).
3.70/1.71	
3.70/1.71	
3.70/1.71	Query: tc(g,a)
3.70/1.71	----------------------------------------
3.70/1.71	
3.70/1.71	(1) PrologToDTProblemTransformerProof (SOUND)
3.70/1.71	Built DT problem from termination graph DT10.
3.70/1.71	
3.70/1.71	{
3.70/1.71	    "root": 2,
3.70/1.71	    "program": {
3.70/1.71	        "directives": [],
3.70/1.71	        "clauses": [
3.70/1.71	            [
3.70/1.71	                "(p (a) (b))",
3.70/1.71	                null
3.70/1.71	            ],
3.70/1.71	            [
3.70/1.71	                "(p (b) (c))",
3.70/1.71	                null
3.70/1.71	            ],
3.70/1.71	            [
3.70/1.71	                "(tc X X)",
3.70/1.71	                null
3.70/1.71	            ],
3.70/1.71	            [
3.70/1.71	                "(tc X Y)",
3.70/1.71	                "(',' (p X Z) (tc Z Y))"
3.70/1.71	            ]
3.70/1.71	        ]
3.70/1.71	    },
3.70/1.71	    "graph": {
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3.70/1.71	                        "scope": 1,
3.70/1.71	                        "term": "(tc T1 T2)"
3.70/1.71	                    },
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3.70/1.71	                        "clause": 3,
3.70/1.71	                        "scope": 1,
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3.70/1.71	                    }
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3.70/1.71	                }
3.70/1.71	            },
3.70/1.71	            "type": "Nodes",
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3.70/1.71	                }],
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3.70/1.71	                        "(tc T12 T2)",
3.70/1.71	                        "(tc X2 X2)"
3.70/1.71	                    ]],
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3.70/1.71	                        "X2",
3.70/1.71	                        "X16"
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3.70/1.71	                    }
3.70/1.71	                ],
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3.70/1.71	                        "(tc T12 T2)",
3.70/1.71	                        "(tc X2 X2)"
3.70/1.71	                    ]],
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3.70/1.71	                        "X2",
3.70/1.71	                        "X16"
3.70/1.71	                    ],
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3.70/1.71	                }
3.70/1.71	            },
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3.70/1.71	                }],
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3.70/1.71	                        "(tc T12 T2)",
3.70/1.71	                        "(tc X2 X2)"
3.70/1.71	                    ]],
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3.70/1.71	                        "X2",
3.70/1.71	                        "X16"
3.70/1.71	                    ],
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3.70/1.71	            },
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3.70/1.71	            },
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3.70/1.71	                    },
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3.70/1.71	                    }
3.70/1.71	                ],
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3.70/1.71	                    },
3.70/1.71	                    "ground": ["T7"],
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3.70/1.71	                    "exprvars": []
3.70/1.71	                }
3.70/1.71	            },
3.70/1.71	            "134": {
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3.70/1.71	                    "scope": -1,
3.70/1.71	                    "term": "(tc (c) T9)"
3.70/1.71	                }],
3.70/1.71	                "kb": {
3.70/1.71	                    "nonunifying": [],
3.70/1.71	                    "intvars": {},
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3.70/1.71	                        "type": "PlainIntegerRelationState",
3.70/1.71	                        "relations": []
3.70/1.71	                    },
3.70/1.71	                    "ground": [],
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3.70/1.71	                }
3.70/1.71	            },
3.70/1.71	            "145": {
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3.70/1.71	                    "scope": 3,
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3.70/1.71	                }],
3.70/1.71	                "kb": {
3.70/1.71	                    "nonunifying": [[
3.70/1.71	                        "(tc T12 T2)",
3.70/1.71	                        "(tc X2 X2)"
3.70/1.71	                    ]],
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3.70/1.71	                        "X2",
3.70/1.71	                        "X16"
3.70/1.71	                    ],
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3.70/1.71	            },
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3.70/1.71	                }],
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3.70/1.71	            },
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3.70/1.71	                }],
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3.70/1.71	                }
3.70/1.71	            },
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3.70/1.71	                }
3.70/1.71	            },
3.70/1.71	            "104": {
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3.70/1.71	                    {
3.70/1.71	                        "clause": -1,
3.70/1.71	                        "scope": -1,
3.70/1.71	                        "term": "(true)"
3.70/1.71	                    },
3.70/1.71	                    {
3.70/1.71	                        "clause": 3,
3.70/1.71	                        "scope": 1,
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3.70/1.71	                    }
3.70/1.71	                ],
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3.70/1.71	            },
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3.70/1.71	            },
3.70/1.71	            "137": {
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3.70/1.71	            },
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3.70/1.71	            },
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3.70/1.71	                        "(tc T1 T2)",
3.70/1.71	                        "(tc X2 X2)"
3.70/1.71	                    ]],
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3.70/1.71	            },
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3.70/1.71	            },
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3.70/1.71	            },
3.70/1.71	            "106": {
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3.70/1.71	                }],
3.70/1.71	                "kb": {
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3.70/1.71	                    },
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3.70/1.71	                }
3.70/1.71	            }
3.70/1.71	        },
3.70/1.71	        "edges": [
3.70/1.71	            {
3.70/1.71	                "from": 2,
3.70/1.71	                "to": 18,
3.70/1.71	                "label": "CASE"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 18,
3.70/1.71	                "to": 104,
3.70/1.71	                "label": "EVAL with clause\ntc(X2, X2).\nand substitutionT1 -> T4,\nX2 -> T4,\nT2 -> T4"
3.70/1.71	            },
3.70/1.71	            {
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3.70/1.71	            },
3.70/1.71	            {
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3.70/1.71	            {
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3.70/1.71	                "to": 142,
3.70/1.71	                "label": "ONLY EVAL with clause\ntc(X14, X15) :- ','(p(X14, X16), tc(X16, X15)).\nand substitutionT1 -> T12,\nX14 -> T12,\nT2 -> T14,\nX15 -> T14,\nT13 -> T14"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 106,
3.70/1.71	                "to": 120,
3.70/1.71	                "label": "ONLY EVAL with clause\ntc(X5, X6) :- ','(p(X5, X7), tc(X7, X6)).\nand substitutionT4 -> T7,\nX5 -> T7,\nT2 -> T9,\nX6 -> T9,\nT8 -> T9"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 120,
3.70/1.71	                "to": 123,
3.70/1.71	                "label": "CASE"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 123,
3.70/1.71	                "to": 124,
3.70/1.71	                "label": "PARALLEL"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 123,
3.70/1.71	                "to": 125,
3.70/1.71	                "label": "PARALLEL"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 124,
3.70/1.71	                "to": 126,
3.70/1.71	                "label": "EVAL with clause\np(a, b).\nand substitutionT7 -> a,\nX7 -> b"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 124,
3.70/1.71	                "to": 127,
3.70/1.71	                "label": "EVAL-BACKTRACK"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 125,
3.70/1.71	                "to": 134,
3.70/1.71	                "label": "EVAL with clause\np(b, c).\nand substitutionT7 -> b,\nX7 -> c"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 125,
3.70/1.71	                "to": 137,
3.70/1.71	                "label": "EVAL-BACKTRACK"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 126,
3.70/1.71	                "to": 2,
3.70/1.71	                "label": "INSTANCE with matching:\nT1 -> b\nT2 -> T9"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 134,
3.70/1.71	                "to": 2,
3.70/1.71	                "label": "INSTANCE with matching:\nT1 -> c\nT2 -> T9"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 142,
3.70/1.71	                "to": 143,
3.70/1.71	                "label": "CASE"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 143,
3.70/1.71	                "to": 144,
3.70/1.71	                "label": "PARALLEL"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 143,
3.70/1.71	                "to": 145,
3.70/1.71	                "label": "PARALLEL"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 144,
3.70/1.71	                "to": 146,
3.70/1.71	                "label": "EVAL with clause\np(a, b).\nand substitutionT12 -> a,\nX16 -> b"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 144,
3.70/1.71	                "to": 147,
3.70/1.71	                "label": "EVAL-BACKTRACK"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 145,
3.70/1.71	                "to": 148,
3.70/1.71	                "label": "EVAL with clause\np(b, c).\nand substitutionT12 -> b,\nX16 -> c"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 145,
3.70/1.71	                "to": 149,
3.70/1.71	                "label": "EVAL-BACKTRACK"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 146,
3.70/1.71	                "to": 2,
3.70/1.71	                "label": "INSTANCE with matching:\nT1 -> b\nT2 -> T14"
3.70/1.71	            },
3.70/1.71	            {
3.70/1.71	                "from": 148,
3.70/1.71	                "to": 2,
3.70/1.71	                "label": "INSTANCE with matching:\nT1 -> c\nT2 -> T14"
3.70/1.71	            }
3.70/1.71	        ],
3.70/1.71	        "type": "Graph"
3.70/1.71	    }
3.70/1.71	}
3.70/1.71	
3.70/1.71	----------------------------------------
3.70/1.71	
3.70/1.71	(2)
3.70/1.71	Obligation:
3.70/1.71	Triples:
3.70/1.71	
3.70/1.71	tcA(a, X1) :- tcA(b, X1).
3.70/1.71	tcA(b, X1) :- tcA(c, X1).
3.70/1.71	tcA(a, X1) :- tcA(b, X1).
3.70/1.71	tcA(b, X1) :- tcA(c, X1).
3.70/1.71	
3.70/1.71	Clauses:
3.70/1.71	
3.70/1.71	tccA(X1, X1).
3.70/1.71	tccA(a, X1) :- tccA(b, X1).
3.70/1.71	tccA(b, X1) :- tccA(c, X1).
3.70/1.71	tccA(a, X1) :- tccA(b, X1).
3.70/1.71	tccA(b, X1) :- tccA(c, X1).
3.70/1.71	
3.70/1.71	Afs:
3.70/1.71	
3.70/1.71	tcA(x1, x2)  =  tcA(x1)
3.70/1.71	
3.70/1.71	
3.70/1.71	----------------------------------------
3.70/1.71	
3.70/1.71	(3) TriplesToPiDPProof (SOUND)
3.70/1.71	We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes:
3.70/1.71	
3.70/1.71	tcA_in_2: (b,f)
3.70/1.71	
3.70/1.71	Transforming TRIPLES into the following Term Rewriting System:
3.70/1.71	
3.70/1.71	Pi DP problem:
3.70/1.71	The TRS P consists of the following rules:
3.70/1.71	
3.70/1.71	   TCA_IN_GA(a, X1) -> U1_GA(X1, tcA_in_ga(b, X1))
3.70/1.71	   TCA_IN_GA(a, X1) -> TCA_IN_GA(b, X1)
3.70/1.71	   TCA_IN_GA(b, X1) -> U2_GA(X1, tcA_in_ga(c, X1))
3.70/1.71	   TCA_IN_GA(b, X1) -> TCA_IN_GA(c, X1)
3.70/1.71	
3.70/1.71	R is empty.
3.70/1.71	The argument filtering Pi contains the following mapping:
3.70/1.71	tcA_in_ga(x1, x2)  =  tcA_in_ga(x1)
3.70/1.71	
3.70/1.71	a  =  a
3.70/1.71	
3.70/1.71	b  =  b
3.70/1.71	
3.70/1.71	c  =  c
3.70/1.71	
3.70/1.71	TCA_IN_GA(x1, x2)  =  TCA_IN_GA(x1)
3.70/1.71	
3.70/1.71	U1_GA(x1, x2)  =  U1_GA(x2)
3.70/1.71	
3.70/1.71	U2_GA(x1, x2)  =  U2_GA(x2)
3.70/1.71	
3.70/1.71	
3.70/1.71	We have to consider all (P,R,Pi)-chains
3.70/1.71	
3.70/1.71	
3.70/1.71	Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES
3.70/1.71	
3.70/1.71	
3.70/1.71	
3.70/1.71	----------------------------------------
3.70/1.71	
3.70/1.71	(4)
3.70/1.71	Obligation:
3.70/1.71	Pi DP problem:
3.70/1.71	The TRS P consists of the following rules:
3.70/1.71	
3.70/1.71	   TCA_IN_GA(a, X1) -> U1_GA(X1, tcA_in_ga(b, X1))
3.70/1.71	   TCA_IN_GA(a, X1) -> TCA_IN_GA(b, X1)
3.70/1.71	   TCA_IN_GA(b, X1) -> U2_GA(X1, tcA_in_ga(c, X1))
3.70/1.71	   TCA_IN_GA(b, X1) -> TCA_IN_GA(c, X1)
3.70/1.71	
3.70/1.71	R is empty.
3.70/1.71	The argument filtering Pi contains the following mapping:
3.70/1.71	tcA_in_ga(x1, x2)  =  tcA_in_ga(x1)
3.70/1.71	
3.70/1.71	a  =  a
3.70/1.71	
3.70/1.71	b  =  b
3.70/1.71	
3.70/1.71	c  =  c
3.70/1.71	
3.70/1.71	TCA_IN_GA(x1, x2)  =  TCA_IN_GA(x1)
3.70/1.71	
3.70/1.71	U1_GA(x1, x2)  =  U1_GA(x2)
3.70/1.71	
3.70/1.71	U2_GA(x1, x2)  =  U2_GA(x2)
3.70/1.71	
3.70/1.71	
3.70/1.71	We have to consider all (P,R,Pi)-chains
3.70/1.71	----------------------------------------
3.70/1.71	
3.70/1.71	(5) DependencyGraphProof (EQUIVALENT)
3.70/1.71	The approximation of the Dependency Graph [LOPSTR] contains 0 SCCs with 4 less nodes.
3.70/1.71	----------------------------------------
3.70/1.71	
3.70/1.71	(6)
3.70/1.71	TRUE
3.70/1.76	EOF