3.52/1.71	YES
3.67/1.72	proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
3.67/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.67/1.72	
3.67/1.72	
3.67/1.72	Left Termination of the query pattern
3.67/1.72	
3.67/1.72	plus(g,a,a)
3.67/1.72	
3.67/1.72	w.r.t. the given Prolog program could successfully be proven:
3.67/1.72	
3.67/1.72	(0) Prolog
3.67/1.72	(1) PrologToDTProblemTransformerProof [SOUND, 0 ms]
3.67/1.72	(2) TRIPLES
3.67/1.72	(3) TriplesToPiDPProof [SOUND, 0 ms]
3.67/1.72	(4) PiDP
3.67/1.72	(5) DependencyGraphProof [EQUIVALENT, 0 ms]
3.67/1.72	(6) PiDP
3.67/1.72	(7) PiDPToQDPProof [SOUND, 0 ms]
3.67/1.72	(8) QDP
3.67/1.72	(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
3.67/1.72	(10) YES
3.67/1.72	
3.67/1.72	
3.67/1.72	----------------------------------------
3.67/1.72	
3.67/1.72	(0)
3.67/1.72	Obligation:
3.67/1.72	Clauses:
3.67/1.72	
3.67/1.72	plus(0, Y, Y).
3.67/1.72	plus(s(X), Y, Z) :- plus(X, s(Y), Z).
3.67/1.72	
3.67/1.72	
3.67/1.72	Query: plus(g,a,a)
3.67/1.72	----------------------------------------
3.67/1.72	
3.67/1.72	(1) PrologToDTProblemTransformerProof (SOUND)
3.67/1.72	Built DT problem from termination graph DT10.
3.67/1.72	
3.67/1.72	{
3.67/1.72	    "root": 1,
3.67/1.72	    "program": {
3.67/1.72	        "directives": [],
3.67/1.72	        "clauses": [
3.67/1.72	            [
3.67/1.72	                "(plus (0) Y Y)",
3.67/1.72	                null
3.67/1.72	            ],
3.67/1.72	            [
3.67/1.72	                "(plus (s X) Y Z)",
3.67/1.72	                "(plus X (s Y) Z)"
3.67/1.72	            ]
3.67/1.72	        ]
3.67/1.72	    },
3.67/1.72	    "graph": {
3.67/1.72	        "nodes": {
3.67/1.72	            "88": {
3.67/1.72	                "goal": [
3.67/1.72	                    {
3.67/1.72	                        "clause": 0,
3.67/1.72	                        "scope": 2,
3.67/1.72	                        "term": "(plus T9 (s T13) T12)"
3.67/1.72	                    },
3.67/1.72	                    {
3.67/1.72	                        "clause": 1,
3.67/1.72	                        "scope": 2,
3.67/1.72	                        "term": "(plus T9 (s T13) T12)"
3.67/1.72	                    }
3.67/1.72	                ],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": ["T9"],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "89": {
3.67/1.72	                "goal": [{
3.67/1.72	                    "clause": 0,
3.67/1.72	                    "scope": 2,
3.67/1.72	                    "term": "(plus T9 (s T13) T12)"
3.67/1.72	                }],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": ["T9"],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "type": "Nodes",
3.67/1.72	            "1": {
3.67/1.72	                "goal": [{
3.67/1.72	                    "clause": -1,
3.67/1.72	                    "scope": -1,
3.67/1.72	                    "term": "(plus T1 T2 T3)"
3.67/1.72	                }],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": ["T1"],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "90": {
3.67/1.72	                "goal": [{
3.67/1.72	                    "clause": 1,
3.67/1.72	                    "scope": 2,
3.67/1.72	                    "term": "(plus T9 (s T13) T12)"
3.67/1.72	                }],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": ["T9"],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "91": {
3.67/1.72	                "goal": [{
3.67/1.72	                    "clause": -1,
3.67/1.72	                    "scope": -1,
3.67/1.72	                    "term": "(true)"
3.67/1.72	                }],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": [],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "92": {
3.67/1.72	                "goal": [],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": [],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "82": {
3.67/1.72	                "goal": [
3.67/1.72	                    {
3.67/1.72	                        "clause": -1,
3.67/1.72	                        "scope": -1,
3.67/1.72	                        "term": "(true)"
3.67/1.72	                    },
3.67/1.72	                    {
3.67/1.72	                        "clause": 1,
3.67/1.72	                        "scope": 1,
3.67/1.72	                        "term": "(plus (0) T2 T3)"
3.67/1.72	                    }
3.67/1.72	                ],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": [],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "93": {
3.67/1.72	                "goal": [],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": [],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "83": {
3.67/1.72	                "goal": [{
3.67/1.72	                    "clause": 1,
3.67/1.72	                    "scope": 1,
3.67/1.72	                    "term": "(plus T1 T2 T3)"
3.67/1.72	                }],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [[
3.67/1.72	                        "(plus T1 T2 T3)",
3.67/1.72	                        "(plus (0) X2 X2)"
3.67/1.72	                    ]],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": ["T1"],
3.67/1.72	                    "free": ["X2"],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "94": {
3.67/1.72	                "goal": [{
3.67/1.72	                    "clause": -1,
3.67/1.72	                    "scope": -1,
3.67/1.72	                    "term": "(plus T25 (s (s T29)) T28)"
3.67/1.72	                }],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": ["T25"],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "84": {
3.67/1.72	                "goal": [{
3.67/1.72	                    "clause": 1,
3.67/1.72	                    "scope": 1,
3.67/1.72	                    "term": "(plus (0) T2 T3)"
3.67/1.72	                }],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": [],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "95": {
3.67/1.72	                "goal": [],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": [],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "85": {
3.67/1.72	                "goal": [],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": [],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "86": {
3.67/1.72	                "goal": [{
3.67/1.72	                    "clause": -1,
3.67/1.72	                    "scope": -1,
3.67/1.72	                    "term": "(plus T9 (s T13) T12)"
3.67/1.72	                }],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": ["T9"],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "32": {
3.67/1.72	                "goal": [
3.67/1.72	                    {
3.67/1.72	                        "clause": 0,
3.67/1.72	                        "scope": 1,
3.67/1.72	                        "term": "(plus T1 T2 T3)"
3.67/1.72	                    },
3.67/1.72	                    {
3.67/1.72	                        "clause": 1,
3.67/1.72	                        "scope": 1,
3.67/1.72	                        "term": "(plus T1 T2 T3)"
3.67/1.72	                    }
3.67/1.72	                ],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": ["T1"],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            },
3.67/1.72	            "87": {
3.67/1.72	                "goal": [],
3.67/1.72	                "kb": {
3.67/1.72	                    "nonunifying": [],
3.67/1.72	                    "intvars": {},
3.67/1.72	                    "arithmetic": {
3.67/1.72	                        "type": "PlainIntegerRelationState",
3.67/1.72	                        "relations": []
3.67/1.72	                    },
3.67/1.72	                    "ground": [],
3.67/1.72	                    "free": [],
3.67/1.72	                    "exprvars": []
3.67/1.72	                }
3.67/1.72	            }
3.67/1.72	        },
3.67/1.72	        "edges": [
3.67/1.72	            {
3.67/1.72	                "from": 1,
3.67/1.72	                "to": 32,
3.67/1.72	                "label": "CASE"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 32,
3.67/1.72	                "to": 82,
3.67/1.72	                "label": "EVAL with clause\nplus(0, X2, X2).\nand substitutionT1 -> 0,\nT2 -> T5,\nX2 -> T5,\nT3 -> T5"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 32,
3.67/1.72	                "to": 83,
3.67/1.72	                "label": "EVAL-BACKTRACK"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 82,
3.67/1.72	                "to": 84,
3.67/1.72	                "label": "SUCCESS"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 83,
3.67/1.72	                "to": 86,
3.67/1.72	                "label": "EVAL with clause\nplus(s(X9), X10, X11) :- plus(X9, s(X10), X11).\nand substitutionX9 -> T9,\nT1 -> s(T9),\nT2 -> T13,\nX10 -> T13,\nT3 -> T12,\nX11 -> T12,\nT11 -> T12,\nT10 -> T13"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 83,
3.67/1.72	                "to": 87,
3.67/1.72	                "label": "EVAL-BACKTRACK"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 84,
3.67/1.72	                "to": 85,
3.67/1.72	                "label": "BACKTRACK\nfor clause: plus(s(X), Y, Z) :- plus(X, s(Y), Z)because of non-unification"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 86,
3.67/1.72	                "to": 88,
3.67/1.72	                "label": "CASE"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 88,
3.67/1.72	                "to": 89,
3.67/1.72	                "label": "PARALLEL"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 88,
3.67/1.72	                "to": 90,
3.67/1.72	                "label": "PARALLEL"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 89,
3.67/1.72	                "to": 91,
3.67/1.72	                "label": "EVAL with clause\nplus(0, X16, X16).\nand substitutionT9 -> 0,\nT13 -> T18,\nX16 -> s(T18),\nT12 -> s(T18)"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 89,
3.67/1.72	                "to": 92,
3.67/1.72	                "label": "EVAL-BACKTRACK"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 90,
3.67/1.72	                "to": 94,
3.67/1.72	                "label": "EVAL with clause\nplus(s(X23), X24, X25) :- plus(X23, s(X24), X25).\nand substitutionX23 -> T25,\nT9 -> s(T25),\nT13 -> T29,\nX24 -> s(T29),\nT12 -> T28,\nX25 -> T28,\nT27 -> T28,\nT26 -> T29"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 90,
3.67/1.72	                "to": 95,
3.67/1.72	                "label": "EVAL-BACKTRACK"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 91,
3.67/1.72	                "to": 93,
3.67/1.72	                "label": "SUCCESS"
3.67/1.72	            },
3.67/1.72	            {
3.67/1.72	                "from": 94,
3.67/1.72	                "to": 1,
3.67/1.72	                "label": "INSTANCE with matching:\nT1 -> T25\nT2 -> s(s(T29))\nT3 -> T28"
3.67/1.72	            }
3.67/1.72	        ],
3.67/1.72	        "type": "Graph"
3.67/1.72	    }
3.67/1.72	}
3.67/1.72	
3.67/1.72	----------------------------------------
3.67/1.72	
3.67/1.72	(2)
3.67/1.72	Obligation:
3.67/1.72	Triples:
3.67/1.72	
3.67/1.72	plusA(s(s(X1)), X2, X3) :- plusA(X1, s(s(X2)), X3).
3.67/1.72	
3.67/1.72	Clauses:
3.67/1.72	
3.67/1.72	pluscA(0, X1, X1).
3.67/1.72	pluscA(s(0), X1, s(X1)).
3.67/1.72	pluscA(s(s(X1)), X2, X3) :- pluscA(X1, s(s(X2)), X3).
3.67/1.72	
3.67/1.72	Afs:
3.67/1.72	
3.67/1.72	plusA(x1, x2, x3)  =  plusA(x1)
3.67/1.72	
3.67/1.72	
3.67/1.72	----------------------------------------
3.67/1.72	
3.67/1.72	(3) TriplesToPiDPProof (SOUND)
3.67/1.72	We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes:
3.67/1.72	
3.67/1.72	plusA_in_3: (b,f,f)
3.67/1.72	
3.67/1.72	Transforming TRIPLES into the following Term Rewriting System:
3.67/1.72	
3.67/1.72	Pi DP problem:
3.67/1.72	The TRS P consists of the following rules:
3.67/1.72	
3.67/1.72	   PLUSA_IN_GAA(s(s(X1)), X2, X3) -> U1_GAA(X1, X2, X3, plusA_in_gaa(X1, s(s(X2)), X3))
3.67/1.72	   PLUSA_IN_GAA(s(s(X1)), X2, X3) -> PLUSA_IN_GAA(X1, s(s(X2)), X3)
3.67/1.72	
3.67/1.72	R is empty.
3.67/1.72	The argument filtering Pi contains the following mapping:
3.67/1.72	plusA_in_gaa(x1, x2, x3)  =  plusA_in_gaa(x1)
3.67/1.72	
3.67/1.72	s(x1)  =  s(x1)
3.67/1.72	
3.67/1.72	PLUSA_IN_GAA(x1, x2, x3)  =  PLUSA_IN_GAA(x1)
3.67/1.72	
3.67/1.72	U1_GAA(x1, x2, x3, x4)  =  U1_GAA(x1, x4)
3.67/1.72	
3.67/1.72	
3.67/1.72	We have to consider all (P,R,Pi)-chains
3.67/1.72	
3.67/1.72	
3.67/1.72	Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES
3.67/1.72	
3.67/1.72	
3.67/1.72	
3.67/1.72	----------------------------------------
3.67/1.72	
3.67/1.72	(4)
3.67/1.72	Obligation:
3.67/1.72	Pi DP problem:
3.67/1.72	The TRS P consists of the following rules:
3.67/1.72	
3.67/1.72	   PLUSA_IN_GAA(s(s(X1)), X2, X3) -> U1_GAA(X1, X2, X3, plusA_in_gaa(X1, s(s(X2)), X3))
3.67/1.72	   PLUSA_IN_GAA(s(s(X1)), X2, X3) -> PLUSA_IN_GAA(X1, s(s(X2)), X3)
3.67/1.72	
3.67/1.72	R is empty.
3.67/1.72	The argument filtering Pi contains the following mapping:
3.67/1.72	plusA_in_gaa(x1, x2, x3)  =  plusA_in_gaa(x1)
3.67/1.72	
3.67/1.72	s(x1)  =  s(x1)
3.67/1.72	
3.67/1.72	PLUSA_IN_GAA(x1, x2, x3)  =  PLUSA_IN_GAA(x1)
3.67/1.72	
3.67/1.72	U1_GAA(x1, x2, x3, x4)  =  U1_GAA(x1, x4)
3.67/1.72	
3.67/1.72	
3.67/1.72	We have to consider all (P,R,Pi)-chains
3.67/1.72	----------------------------------------
3.67/1.72	
3.67/1.72	(5) DependencyGraphProof (EQUIVALENT)
3.67/1.72	The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 1 less node.
3.67/1.72	----------------------------------------
3.67/1.72	
3.67/1.72	(6)
3.67/1.72	Obligation:
3.67/1.72	Pi DP problem:
3.67/1.72	The TRS P consists of the following rules:
3.67/1.72	
3.67/1.72	   PLUSA_IN_GAA(s(s(X1)), X2, X3) -> PLUSA_IN_GAA(X1, s(s(X2)), X3)
3.67/1.72	
3.67/1.72	R is empty.
3.67/1.72	The argument filtering Pi contains the following mapping:
3.67/1.72	s(x1)  =  s(x1)
3.67/1.72	
3.67/1.72	PLUSA_IN_GAA(x1, x2, x3)  =  PLUSA_IN_GAA(x1)
3.67/1.72	
3.67/1.72	
3.67/1.72	We have to consider all (P,R,Pi)-chains
3.67/1.72	----------------------------------------
3.67/1.73	
3.67/1.73	(7) PiDPToQDPProof (SOUND)
3.67/1.73	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
3.67/1.73	----------------------------------------
3.67/1.73	
3.67/1.73	(8)
3.67/1.73	Obligation:
3.67/1.73	Q DP problem:
3.67/1.73	The TRS P consists of the following rules:
3.67/1.73	
3.67/1.73	   PLUSA_IN_GAA(s(s(X1))) -> PLUSA_IN_GAA(X1)
3.67/1.73	
3.67/1.73	R is empty.
3.67/1.73	Q is empty.
3.67/1.73	We have to consider all (P,Q,R)-chains.
3.67/1.73	----------------------------------------
3.67/1.73	
3.67/1.73	(9) QDPSizeChangeProof (EQUIVALENT)
3.67/1.73	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
3.67/1.73	
3.67/1.73	From the DPs we obtained the following set of size-change graphs:
3.67/1.73	*PLUSA_IN_GAA(s(s(X1))) -> PLUSA_IN_GAA(X1)
3.67/1.73	The graph contains the following edges 1 > 1
3.67/1.73	
3.67/1.73	
3.67/1.73	----------------------------------------
3.67/1.73	
3.67/1.73	(10)
3.67/1.73	YES
3.75/1.77	EOF