3.06/1.58	YES
3.06/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
3.06/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.06/1.59	
3.06/1.59	
3.06/1.59	Left Termination of the query pattern
3.06/1.59	
3.06/1.59	q()
3.06/1.59	
3.06/1.59	w.r.t. the given Prolog program could successfully be proven:
3.06/1.59	
3.06/1.59	(0) Prolog
3.06/1.59	(1) PrologToIRSwTTransformerProof [SOUND, 0 ms]
3.06/1.59	(2) TRUE
3.06/1.59	
3.06/1.59	
3.06/1.59	----------------------------------------
3.06/1.59	
3.06/1.59	(0)
3.06/1.59	Obligation:
3.06/1.59	Clauses:
3.06/1.59	
3.06/1.59	q :- p(s(s(0))).
3.06/1.59	p(s(X)) :- p(X).
3.06/1.59	p(0).
3.06/1.59	p(s(s(s(0)))) :- p(s(s(s(0)))).
3.06/1.59	
3.06/1.59	
3.06/1.59	Query: q()
3.06/1.59	----------------------------------------
3.06/1.59	
3.06/1.59	(1) PrologToIRSwTTransformerProof (SOUND)
3.06/1.59	Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert
3.06/1.59	
3.06/1.59	{
3.06/1.59	    "root": 2,
3.06/1.59	    "program": {
3.06/1.59	        "directives": [],
3.06/1.59	        "clauses": [
3.06/1.59	            [
3.06/1.59	                "(q)",
3.06/1.59	                "(p (s (s (0))))"
3.06/1.59	            ],
3.06/1.59	            [
3.06/1.59	                "(p (s X))",
3.06/1.59	                "(p X)"
3.06/1.59	            ],
3.06/1.59	            [
3.06/1.59	                "(p (0))",
3.06/1.59	                null
3.06/1.59	            ],
3.06/1.59	            [
3.06/1.59	                "(p (s (s (s (0)))))",
3.06/1.59	                "(p (s (s (s (0)))))"
3.06/1.59	            ]
3.06/1.59	        ]
3.06/1.59	    },
3.06/1.59	    "graph": {
3.06/1.59	        "nodes": {
3.06/1.59	            "99": {
3.06/1.59	                "goal": [
3.06/1.59	                    {
3.06/1.59	                        "clause": 2,
3.06/1.59	                        "scope": 4,
3.06/1.59	                        "term": "(p (0))"
3.06/1.59	                    },
3.06/1.59	                    {
3.06/1.59	                        "clause": 3,
3.06/1.59	                        "scope": 4,
3.06/1.59	                        "term": "(p (0))"
3.06/1.59	                    }
3.06/1.59	                ],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "27": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": 0,
3.06/1.59	                    "scope": 1,
3.06/1.59	                    "term": "(q)"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "28": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": -1,
3.06/1.59	                    "scope": -1,
3.06/1.59	                    "term": "(p (s (s (0))))"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "type": "Nodes",
3.06/1.59	            "110": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": 3,
3.06/1.59	                    "scope": 3,
3.06/1.59	                    "term": "(p (s (0)))"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "2": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": -1,
3.06/1.59	                    "scope": -1,
3.06/1.59	                    "term": "(q)"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "112": {
3.06/1.59	                "goal": [],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "102": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": 2,
3.06/1.59	                    "scope": 4,
3.06/1.59	                    "term": "(p (0))"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "103": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": 3,
3.06/1.59	                    "scope": 4,
3.06/1.59	                    "term": "(p (0))"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "114": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": 3,
3.06/1.59	                    "scope": 2,
3.06/1.59	                    "term": "(p (s (s (0))))"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "115": {
3.06/1.59	                "goal": [],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "105": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": -1,
3.06/1.59	                    "scope": -1,
3.06/1.59	                    "term": "(true)"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "106": {
3.06/1.59	                "goal": [],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "91": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": 1,
3.06/1.59	                    "scope": 3,
3.06/1.59	                    "term": "(p (s (0)))"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "81": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": -1,
3.06/1.59	                    "scope": -1,
3.06/1.59	                    "term": "(p (s (0)))"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "92": {
3.06/1.59	                "goal": [
3.06/1.59	                    {
3.06/1.59	                        "clause": 2,
3.06/1.59	                        "scope": 3,
3.06/1.59	                        "term": "(p (s (0)))"
3.06/1.59	                    },
3.06/1.59	                    {
3.06/1.59	                        "clause": 3,
3.06/1.59	                        "scope": 3,
3.06/1.59	                        "term": "(p (s (0)))"
3.06/1.59	                    }
3.06/1.59	                ],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "108": {
3.06/1.59	                "goal": [],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "95": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": -1,
3.06/1.59	                    "scope": -1,
3.06/1.59	                    "term": "(p (0))"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "30": {
3.06/1.59	                "goal": [
3.06/1.59	                    {
3.06/1.59	                        "clause": 1,
3.06/1.59	                        "scope": 2,
3.06/1.59	                        "term": "(p (s (s (0))))"
3.06/1.59	                    },
3.06/1.59	                    {
3.06/1.59	                        "clause": 2,
3.06/1.59	                        "scope": 2,
3.06/1.59	                        "term": "(p (s (s (0))))"
3.06/1.59	                    },
3.06/1.59	                    {
3.06/1.59	                        "clause": 3,
3.06/1.59	                        "scope": 2,
3.06/1.59	                        "term": "(p (s (s (0))))"
3.06/1.59	                    }
3.06/1.59	                ],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "64": {
3.06/1.59	                "goal": [{
3.06/1.59	                    "clause": 1,
3.06/1.59	                    "scope": 2,
3.06/1.59	                    "term": "(p (s (s (0))))"
3.06/1.59	                }],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "86": {
3.06/1.59	                "goal": [
3.06/1.59	                    {
3.06/1.59	                        "clause": 1,
3.06/1.59	                        "scope": 3,
3.06/1.59	                        "term": "(p (s (0)))"
3.06/1.59	                    },
3.06/1.59	                    {
3.06/1.59	                        "clause": 2,
3.06/1.59	                        "scope": 3,
3.06/1.59	                        "term": "(p (s (0)))"
3.06/1.59	                    },
3.06/1.59	                    {
3.06/1.59	                        "clause": 3,
3.06/1.59	                        "scope": 3,
3.06/1.59	                        "term": "(p (s (0)))"
3.06/1.59	                    }
3.06/1.59	                ],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "65": {
3.06/1.59	                "goal": [
3.06/1.59	                    {
3.06/1.59	                        "clause": 2,
3.06/1.59	                        "scope": 2,
3.06/1.59	                        "term": "(p (s (s (0))))"
3.06/1.59	                    },
3.06/1.59	                    {
3.06/1.59	                        "clause": 3,
3.06/1.59	                        "scope": 2,
3.06/1.59	                        "term": "(p (s (s (0))))"
3.06/1.59	                    }
3.06/1.59	                ],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            },
3.06/1.59	            "98": {
3.06/1.59	                "goal": [
3.06/1.59	                    {
3.06/1.59	                        "clause": 1,
3.06/1.59	                        "scope": 4,
3.06/1.59	                        "term": "(p (0))"
3.06/1.59	                    },
3.06/1.59	                    {
3.06/1.59	                        "clause": 2,
3.06/1.59	                        "scope": 4,
3.06/1.59	                        "term": "(p (0))"
3.06/1.59	                    },
3.06/1.59	                    {
3.06/1.59	                        "clause": 3,
3.06/1.59	                        "scope": 4,
3.06/1.59	                        "term": "(p (0))"
3.06/1.59	                    }
3.06/1.59	                ],
3.06/1.59	                "kb": {
3.06/1.59	                    "nonunifying": [],
3.06/1.59	                    "intvars": {},
3.06/1.59	                    "arithmetic": {
3.06/1.59	                        "type": "PlainIntegerRelationState",
3.06/1.59	                        "relations": []
3.06/1.59	                    },
3.06/1.59	                    "ground": [],
3.06/1.59	                    "free": [],
3.06/1.59	                    "exprvars": []
3.06/1.59	                }
3.06/1.59	            }
3.06/1.59	        },
3.06/1.59	        "edges": [
3.06/1.59	            {
3.06/1.59	                "from": 2,
3.06/1.59	                "to": 27,
3.06/1.59	                "label": "CASE"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 27,
3.06/1.59	                "to": 28,
3.06/1.59	                "label": "ONLY EVAL with clause\nq :- p(s(s(0))).\nand substitution"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 28,
3.06/1.59	                "to": 30,
3.06/1.59	                "label": "CASE"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 30,
3.06/1.59	                "to": 64,
3.06/1.59	                "label": "PARALLEL"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 30,
3.06/1.59	                "to": 65,
3.06/1.59	                "label": "PARALLEL"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 64,
3.06/1.59	                "to": 81,
3.06/1.59	                "label": "ONLY EVAL with clause\np(s(X9)) :- p(X9).\nand substitutionX9 -> s(0)"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 65,
3.06/1.59	                "to": 114,
3.06/1.59	                "label": "BACKTRACK\nfor clause: p(0)because of non-unification"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 81,
3.06/1.59	                "to": 86,
3.06/1.59	                "label": "CASE"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 86,
3.06/1.59	                "to": 91,
3.06/1.59	                "label": "PARALLEL"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 86,
3.06/1.59	                "to": 92,
3.06/1.59	                "label": "PARALLEL"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 91,
3.06/1.59	                "to": 95,
3.06/1.59	                "label": "ONLY EVAL with clause\np(s(X17)) :- p(X17).\nand substitutionX17 -> 0"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 92,
3.06/1.59	                "to": 110,
3.06/1.59	                "label": "BACKTRACK\nfor clause: p(0)because of non-unification"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 95,
3.06/1.59	                "to": 98,
3.06/1.59	                "label": "CASE"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 98,
3.06/1.59	                "to": 99,
3.06/1.59	                "label": "BACKTRACK\nfor clause: p(s(X)) :- p(X)because of non-unification"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 99,
3.06/1.59	                "to": 102,
3.06/1.59	                "label": "PARALLEL"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 99,
3.06/1.59	                "to": 103,
3.06/1.59	                "label": "PARALLEL"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 102,
3.06/1.59	                "to": 105,
3.06/1.59	                "label": "ONLY EVAL with clause\np(0).\nand substitution"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 103,
3.06/1.59	                "to": 108,
3.06/1.59	                "label": "BACKTRACK\nfor clause: p(s(s(s(0)))) :- p(s(s(s(0))))because of non-unification"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 105,
3.06/1.59	                "to": 106,
3.06/1.59	                "label": "SUCCESS"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 110,
3.06/1.59	                "to": 112,
3.06/1.59	                "label": "BACKTRACK\nfor clause: p(s(s(s(0)))) :- p(s(s(s(0))))because of non-unification"
3.06/1.59	            },
3.06/1.59	            {
3.06/1.59	                "from": 114,
3.06/1.59	                "to": 115,
3.06/1.59	                "label": "BACKTRACK\nfor clause: p(s(s(s(0)))) :- p(s(s(s(0))))because of non-unification"
3.06/1.59	            }
3.06/1.59	        ],
3.06/1.59	        "type": "Graph"
3.06/1.59	    }
3.06/1.59	}
3.06/1.59	
3.06/1.59	----------------------------------------
3.06/1.59	
3.06/1.59	(2)
3.06/1.59	TRUE
3.35/1.62	EOF