6.45/2.53	MAYBE
6.45/2.56	proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
6.45/2.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.45/2.56	
6.45/2.56	
6.45/2.56	Left Termination of the query pattern
6.45/2.56	
6.45/2.56	tree_member(g,a)
6.45/2.56	
6.45/2.56	w.r.t. the given Prolog program could not be shown:
6.45/2.56	
6.45/2.56	(0) Prolog
6.45/2.56	(1) PrologToPiTRSProof [SOUND, 0 ms]
6.45/2.56	(2) PiTRS
6.45/2.56	    (3) DependencyPairsProof [EQUIVALENT, 0 ms]
6.45/2.56	    (4) PiDP
6.45/2.56	    (5) DependencyGraphProof [EQUIVALENT, 0 ms]
6.45/2.56	    (6) PiDP
6.45/2.56	    (7) UsableRulesProof [EQUIVALENT, 0 ms]
6.45/2.56	    (8) PiDP
6.45/2.56	    (9) PiDPToQDPProof [SOUND, 0 ms]
6.45/2.56	    (10) QDP
6.45/2.56	(11) PrologToTRSTransformerProof [SOUND, 0 ms]
6.45/2.56	(12) QTRS
6.45/2.56	    (13) DependencyPairsProof [EQUIVALENT, 0 ms]
6.45/2.56	    (14) QDP
6.45/2.56	    (15) DependencyGraphProof [EQUIVALENT, 0 ms]
6.45/2.56	    (16) QDP
6.45/2.56	    (17) MNOCProof [EQUIVALENT, 0 ms]
6.45/2.56	    (18) QDP
6.45/2.56	    (19) UsableRulesProof [EQUIVALENT, 0 ms]
6.45/2.56	    (20) QDP
6.45/2.56	    (21) QReductionProof [EQUIVALENT, 0 ms]
6.45/2.56	    (22) QDP
6.45/2.56	(23) PrologToPiTRSProof [SOUND, 0 ms]
6.45/2.56	(24) PiTRS
6.45/2.56	    (25) DependencyPairsProof [EQUIVALENT, 0 ms]
6.45/2.56	    (26) PiDP
6.45/2.56	    (27) DependencyGraphProof [EQUIVALENT, 0 ms]
6.45/2.56	    (28) PiDP
6.45/2.56	    (29) UsableRulesProof [EQUIVALENT, 0 ms]
6.45/2.56	    (30) PiDP
6.45/2.56	    (31) PiDPToQDPProof [SOUND, 0 ms]
6.45/2.56	    (32) QDP
6.45/2.56	(33) PrologToIRSwTTransformerProof [SOUND, 0 ms]
6.45/2.56	(34) IRSwT
6.45/2.56	    (35) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms]
6.45/2.56	    (36) IRSwT
6.45/2.56	    (37) IntTRSCompressionProof [EQUIVALENT, 22 ms]
6.45/2.56	    (38) IRSwT
6.45/2.56	    (39) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
6.45/2.56	    (40) IRSwT
6.45/2.56	    (41) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
6.45/2.56	    (42) IRSwT
6.45/2.56	    (43) FilterProof [EQUIVALENT, 4 ms]
6.45/2.56	    (44) IntTRS
6.45/2.56	    (45) IntTRSNonPeriodicNontermProof [COMPLETE, 0 ms]
6.45/2.56	    (46) NO
6.45/2.56	(47) PrologToDTProblemTransformerProof [SOUND, 70 ms]
6.45/2.56	(48) TRIPLES
6.45/2.56	    (49) TriplesToPiDPProof [SOUND, 23 ms]
6.45/2.56	    (50) PiDP
6.45/2.56	    (51) DependencyGraphProof [EQUIVALENT, 0 ms]
6.45/2.56	    (52) PiDP
6.45/2.56	    (53) PiDPToQDPProof [SOUND, 0 ms]
6.45/2.56	    (54) QDP
6.45/2.56	
6.45/2.56	
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(0)
6.45/2.56	Obligation:
6.45/2.56	Clauses:
6.45/2.56	
6.45/2.56	tree_member(X, tree(X, X1, X2)).
6.45/2.56	tree_member(X, tree(X3, Left, X4)) :- tree_member(X, Left).
6.45/2.56	tree_member(X, tree(X5, X6, Right)) :- tree_member(X, Right).
6.45/2.56	
6.45/2.56	
6.45/2.56	Query: tree_member(g,a)
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(1) PrologToPiTRSProof (SOUND)
6.45/2.56	We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
6.45/2.56	
6.45/2.56	tree_member_in_2: (b,f)
6.45/2.56	
6.45/2.56	Transforming Prolog into the following Term Rewriting System:
6.45/2.56	
6.45/2.56	Pi-finite rewrite system:
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.45/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.45/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.45/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.45/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.45/2.56	
6.45/2.56	The argument filtering Pi contains the following mapping:
6.45/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.45/2.56	
6.45/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga
6.45/2.56	
6.45/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
6.45/2.56	
6.45/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
6.45/2.56	
6.45/2.56	
6.45/2.56	
6.45/2.56	
6.45/2.56	
6.45/2.56	Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
6.45/2.56	
6.45/2.56	
6.45/2.56	
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(2)
6.45/2.56	Obligation:
6.45/2.56	Pi-finite rewrite system:
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.45/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.45/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.45/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.45/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.45/2.56	
6.45/2.56	The argument filtering Pi contains the following mapping:
6.45/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.45/2.56	
6.45/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga
6.45/2.56	
6.45/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
6.45/2.56	
6.45/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
6.45/2.56	
6.45/2.56	
6.45/2.56	
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(3) DependencyPairsProof (EQUIVALENT)
6.45/2.56	Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
6.45/2.56	Pi DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> U1_GA(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> TREE_MEMBER_IN_GA(X, Left)
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> U2_GA(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> TREE_MEMBER_IN_GA(X, Right)
6.45/2.56	
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.45/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.45/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.45/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.45/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.45/2.56	
6.45/2.56	The argument filtering Pi contains the following mapping:
6.45/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.45/2.56	
6.45/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga
6.45/2.56	
6.45/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
6.45/2.56	
6.45/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
6.45/2.56	
6.45/2.56	TREE_MEMBER_IN_GA(x1, x2)  =  TREE_MEMBER_IN_GA(x1)
6.45/2.56	
6.45/2.56	U1_GA(x1, x2, x3, x4, x5)  =  U1_GA(x5)
6.45/2.56	
6.45/2.56	U2_GA(x1, x2, x3, x4, x5)  =  U2_GA(x5)
6.45/2.56	
6.45/2.56	
6.45/2.56	We have to consider all (P,R,Pi)-chains
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(4)
6.45/2.56	Obligation:
6.45/2.56	Pi DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> U1_GA(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> TREE_MEMBER_IN_GA(X, Left)
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> U2_GA(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> TREE_MEMBER_IN_GA(X, Right)
6.45/2.56	
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.45/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.45/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.45/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.45/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.45/2.56	
6.45/2.56	The argument filtering Pi contains the following mapping:
6.45/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.45/2.56	
6.45/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga
6.45/2.56	
6.45/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
6.45/2.56	
6.45/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
6.45/2.56	
6.45/2.56	TREE_MEMBER_IN_GA(x1, x2)  =  TREE_MEMBER_IN_GA(x1)
6.45/2.56	
6.45/2.56	U1_GA(x1, x2, x3, x4, x5)  =  U1_GA(x5)
6.45/2.56	
6.45/2.56	U2_GA(x1, x2, x3, x4, x5)  =  U2_GA(x5)
6.45/2.56	
6.45/2.56	
6.45/2.56	We have to consider all (P,R,Pi)-chains
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(5) DependencyGraphProof (EQUIVALENT)
6.45/2.56	The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 2 less nodes.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(6)
6.45/2.56	Obligation:
6.45/2.56	Pi DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> TREE_MEMBER_IN_GA(X, Right)
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> TREE_MEMBER_IN_GA(X, Left)
6.45/2.56	
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.45/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.45/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.45/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.45/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.45/2.56	
6.45/2.56	The argument filtering Pi contains the following mapping:
6.45/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.45/2.56	
6.45/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga
6.45/2.56	
6.45/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
6.45/2.56	
6.45/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
6.45/2.56	
6.45/2.56	TREE_MEMBER_IN_GA(x1, x2)  =  TREE_MEMBER_IN_GA(x1)
6.45/2.56	
6.45/2.56	
6.45/2.56	We have to consider all (P,R,Pi)-chains
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(7) UsableRulesProof (EQUIVALENT)
6.45/2.56	For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(8)
6.45/2.56	Obligation:
6.45/2.56	Pi DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> TREE_MEMBER_IN_GA(X, Right)
6.45/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> TREE_MEMBER_IN_GA(X, Left)
6.45/2.56	
6.45/2.56	R is empty.
6.45/2.56	The argument filtering Pi contains the following mapping:
6.45/2.56	TREE_MEMBER_IN_GA(x1, x2)  =  TREE_MEMBER_IN_GA(x1)
6.45/2.56	
6.45/2.56	
6.45/2.56	We have to consider all (P,R,Pi)-chains
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(9) PiDPToQDPProof (SOUND)
6.45/2.56	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(10)
6.45/2.56	Obligation:
6.45/2.56	Q DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   TREE_MEMBER_IN_GA(X) -> TREE_MEMBER_IN_GA(X)
6.45/2.56	
6.45/2.56	R is empty.
6.45/2.56	Q is empty.
6.45/2.56	We have to consider all (P,Q,R)-chains.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(11) PrologToTRSTransformerProof (SOUND)
6.45/2.56	Transformed Prolog program to TRS.
6.45/2.56	
6.45/2.56	{
6.45/2.56	    "root": 8,
6.45/2.56	    "program": {
6.45/2.56	        "directives": [],
6.45/2.56	        "clauses": [
6.45/2.56	            [
6.45/2.56	                "(tree_member X (tree X X1 X2))",
6.45/2.56	                null
6.45/2.56	            ],
6.45/2.56	            [
6.45/2.56	                "(tree_member X (tree X3 Left X4))",
6.45/2.56	                "(tree_member X Left)"
6.45/2.56	            ],
6.45/2.56	            [
6.45/2.56	                "(tree_member X (tree X5 X6 Right))",
6.45/2.56	                "(tree_member X Right)"
6.45/2.56	            ]
6.45/2.56	        ]
6.45/2.56	    },
6.45/2.56	    "graph": {
6.45/2.56	        "nodes": {
6.45/2.56	            "78": {
6.45/2.56	                "goal": [{
6.45/2.56	                    "clause": 0,
6.45/2.56	                    "scope": 1,
6.45/2.56	                    "term": "(tree_member T1 T2)"
6.45/2.56	                }],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": ["T1"],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "79": {
6.45/2.56	                "goal": [
6.45/2.56	                    {
6.45/2.56	                        "clause": 1,
6.45/2.56	                        "scope": 1,
6.45/2.56	                        "term": "(tree_member T1 T2)"
6.45/2.56	                    },
6.45/2.56	                    {
6.45/2.56	                        "clause": 2,
6.45/2.56	                        "scope": 1,
6.45/2.56	                        "term": "(tree_member T1 T2)"
6.45/2.56	                    }
6.45/2.56	                ],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": ["T1"],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "16": {
6.45/2.56	                "goal": [
6.45/2.56	                    {
6.45/2.56	                        "clause": 0,
6.45/2.56	                        "scope": 1,
6.45/2.56	                        "term": "(tree_member T1 T2)"
6.45/2.56	                    },
6.45/2.56	                    {
6.45/2.56	                        "clause": 1,
6.45/2.56	                        "scope": 1,
6.45/2.56	                        "term": "(tree_member T1 T2)"
6.45/2.56	                    },
6.45/2.56	                    {
6.45/2.56	                        "clause": 2,
6.45/2.56	                        "scope": 1,
6.45/2.56	                        "term": "(tree_member T1 T2)"
6.45/2.56	                    }
6.45/2.56	                ],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": ["T1"],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "type": "Nodes",
6.45/2.56	            "138": {
6.45/2.56	                "goal": [{
6.45/2.56	                    "clause": -1,
6.45/2.56	                    "scope": -1,
6.45/2.56	                    "term": "(tree_member T53 T57)"
6.45/2.56	                }],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": ["T53"],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "139": {
6.45/2.56	                "goal": [],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": [],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "8": {
6.45/2.56	                "goal": [{
6.45/2.56	                    "clause": -1,
6.45/2.56	                    "scope": -1,
6.45/2.56	                    "term": "(tree_member T1 T2)"
6.45/2.56	                }],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": ["T1"],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "80": {
6.45/2.56	                "goal": [{
6.45/2.56	                    "clause": -1,
6.45/2.56	                    "scope": -1,
6.45/2.56	                    "term": "(true)"
6.45/2.56	                }],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": [],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "81": {
6.45/2.56	                "goal": [],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": [],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "82": {
6.45/2.56	                "goal": [],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": [],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "83": {
6.45/2.56	                "goal": [{
6.45/2.56	                    "clause": 1,
6.45/2.56	                    "scope": 1,
6.45/2.56	                    "term": "(tree_member T1 T2)"
6.45/2.56	                }],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": ["T1"],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "84": {
6.45/2.56	                "goal": [{
6.45/2.56	                    "clause": 2,
6.45/2.56	                    "scope": 1,
6.45/2.56	                    "term": "(tree_member T1 T2)"
6.45/2.56	                }],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": ["T1"],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "85": {
6.45/2.56	                "goal": [{
6.45/2.56	                    "clause": -1,
6.45/2.56	                    "scope": -1,
6.45/2.56	                    "term": "(tree_member T34 T38)"
6.45/2.56	                }],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": ["T34"],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            },
6.45/2.56	            "86": {
6.45/2.56	                "goal": [],
6.45/2.56	                "kb": {
6.45/2.56	                    "nonunifying": [],
6.45/2.56	                    "intvars": {},
6.45/2.56	                    "arithmetic": {
6.45/2.56	                        "type": "PlainIntegerRelationState",
6.45/2.56	                        "relations": []
6.45/2.56	                    },
6.45/2.56	                    "ground": [],
6.45/2.56	                    "free": [],
6.45/2.56	                    "exprvars": []
6.45/2.56	                }
6.45/2.56	            }
6.45/2.56	        },
6.45/2.56	        "edges": [
6.45/2.56	            {
6.45/2.56	                "from": 8,
6.45/2.56	                "to": 16,
6.45/2.56	                "label": "CASE"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 16,
6.45/2.56	                "to": 78,
6.45/2.56	                "label": "PARALLEL"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 16,
6.45/2.56	                "to": 79,
6.45/2.56	                "label": "PARALLEL"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 78,
6.45/2.56	                "to": 80,
6.45/2.56	                "label": "EVAL with clause\ntree_member(X19, tree(X19, X20, X21)).\nand substitutionT1 -> T15,\nX19 -> T15,\nX20 -> T16,\nX21 -> T17,\nT2 -> tree(T15, T16, T17)"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 78,
6.45/2.56	                "to": 81,
6.45/2.56	                "label": "EVAL-BACKTRACK"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 79,
6.45/2.56	                "to": 83,
6.45/2.56	                "label": "PARALLEL"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 79,
6.45/2.56	                "to": 84,
6.45/2.56	                "label": "PARALLEL"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 80,
6.45/2.56	                "to": 82,
6.45/2.56	                "label": "SUCCESS"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 83,
6.45/2.56	                "to": 85,
6.45/2.56	                "label": "EVAL with clause\ntree_member(X38, tree(X39, X40, X41)) :- tree_member(X38, X40).\nand substitutionT1 -> T34,\nX38 -> T34,\nX39 -> T35,\nX40 -> T38,\nX41 -> T37,\nT2 -> tree(T35, T38, T37),\nT36 -> T38"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 83,
6.45/2.56	                "to": 86,
6.45/2.56	                "label": "EVAL-BACKTRACK"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 84,
6.45/2.56	                "to": 138,
6.45/2.56	                "label": "EVAL with clause\ntree_member(X56, tree(X57, X58, X59)) :- tree_member(X56, X59).\nand substitutionT1 -> T53,\nX56 -> T53,\nX57 -> T54,\nX58 -> T55,\nX59 -> T57,\nT2 -> tree(T54, T55, T57),\nT56 -> T57"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 84,
6.45/2.56	                "to": 139,
6.45/2.56	                "label": "EVAL-BACKTRACK"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 85,
6.45/2.56	                "to": 8,
6.45/2.56	                "label": "INSTANCE with matching:\nT1 -> T34\nT2 -> T38"
6.45/2.56	            },
6.45/2.56	            {
6.45/2.56	                "from": 138,
6.45/2.56	                "to": 8,
6.45/2.56	                "label": "INSTANCE with matching:\nT1 -> T53\nT2 -> T57"
6.45/2.56	            }
6.45/2.56	        ],
6.45/2.56	        "type": "Graph"
6.45/2.56	    }
6.45/2.56	}
6.45/2.56	
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(12)
6.45/2.56	Obligation:
6.45/2.56	Q restricted rewrite system:
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   f8_in(T15) -> f8_out1
6.45/2.56	   f8_in(T34) -> U1(f8_in(T34), T34)
6.45/2.56	   U1(f8_out1, T34) -> f8_out1
6.45/2.56	   f8_in(T53) -> U2(f8_in(T53), T53)
6.45/2.56	   U2(f8_out1, T53) -> f8_out1
6.45/2.56	
6.45/2.56	Q is empty.
6.45/2.56	
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(13) DependencyPairsProof (EQUIVALENT)
6.45/2.56	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(14)
6.45/2.56	Obligation:
6.45/2.56	Q DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   F8_IN(T34) -> U1^1(f8_in(T34), T34)
6.45/2.56	   F8_IN(T34) -> F8_IN(T34)
6.45/2.56	   F8_IN(T53) -> U2^1(f8_in(T53), T53)
6.45/2.56	
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   f8_in(T15) -> f8_out1
6.45/2.56	   f8_in(T34) -> U1(f8_in(T34), T34)
6.45/2.56	   U1(f8_out1, T34) -> f8_out1
6.45/2.56	   f8_in(T53) -> U2(f8_in(T53), T53)
6.45/2.56	   U2(f8_out1, T53) -> f8_out1
6.45/2.56	
6.45/2.56	Q is empty.
6.45/2.56	We have to consider all minimal (P,Q,R)-chains.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(15) DependencyGraphProof (EQUIVALENT)
6.45/2.56	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(16)
6.45/2.56	Obligation:
6.45/2.56	Q DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   F8_IN(T34) -> F8_IN(T34)
6.45/2.56	
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   f8_in(T15) -> f8_out1
6.45/2.56	   f8_in(T34) -> U1(f8_in(T34), T34)
6.45/2.56	   U1(f8_out1, T34) -> f8_out1
6.45/2.56	   f8_in(T53) -> U2(f8_in(T53), T53)
6.45/2.56	   U2(f8_out1, T53) -> f8_out1
6.45/2.56	
6.45/2.56	Q is empty.
6.45/2.56	We have to consider all minimal (P,Q,R)-chains.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(17) MNOCProof (EQUIVALENT)
6.45/2.56	We use the modular non-overlap check [LPAR04] to enlarge Q to all left-hand sides of R.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(18)
6.45/2.56	Obligation:
6.45/2.56	Q DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   F8_IN(T34) -> F8_IN(T34)
6.45/2.56	
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   f8_in(T15) -> f8_out1
6.45/2.56	   f8_in(T34) -> U1(f8_in(T34), T34)
6.45/2.56	   U1(f8_out1, T34) -> f8_out1
6.45/2.56	   f8_in(T53) -> U2(f8_in(T53), T53)
6.45/2.56	   U2(f8_out1, T53) -> f8_out1
6.45/2.56	
6.45/2.56	The set Q consists of the following terms:
6.45/2.56	
6.45/2.56	   f8_in(x0)
6.45/2.56	   U1(f8_out1, x0)
6.45/2.56	   U2(f8_out1, x0)
6.45/2.56	
6.45/2.56	We have to consider all minimal (P,Q,R)-chains.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(19) UsableRulesProof (EQUIVALENT)
6.45/2.56	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(20)
6.45/2.56	Obligation:
6.45/2.56	Q DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   F8_IN(T34) -> F8_IN(T34)
6.45/2.56	
6.45/2.56	R is empty.
6.45/2.56	The set Q consists of the following terms:
6.45/2.56	
6.45/2.56	   f8_in(x0)
6.45/2.56	   U1(f8_out1, x0)
6.45/2.56	   U2(f8_out1, x0)
6.45/2.56	
6.45/2.56	We have to consider all minimal (P,Q,R)-chains.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(21) QReductionProof (EQUIVALENT)
6.45/2.56	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
6.45/2.56	
6.45/2.56	   f8_in(x0)
6.45/2.56	   U1(f8_out1, x0)
6.45/2.56	   U2(f8_out1, x0)
6.45/2.56	
6.45/2.56	
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(22)
6.45/2.56	Obligation:
6.45/2.56	Q DP problem:
6.45/2.56	The TRS P consists of the following rules:
6.45/2.56	
6.45/2.56	   F8_IN(T34) -> F8_IN(T34)
6.45/2.56	
6.45/2.56	R is empty.
6.45/2.56	Q is empty.
6.45/2.56	We have to consider all minimal (P,Q,R)-chains.
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(23) PrologToPiTRSProof (SOUND)
6.45/2.56	We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
6.45/2.56	
6.45/2.56	tree_member_in_2: (b,f)
6.45/2.56	
6.45/2.56	Transforming Prolog into the following Term Rewriting System:
6.45/2.56	
6.45/2.56	Pi-finite rewrite system:
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.45/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.45/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.45/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.45/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.45/2.56	
6.45/2.56	The argument filtering Pi contains the following mapping:
6.45/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.45/2.56	
6.45/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga(x1)
6.45/2.56	
6.45/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x5)
6.45/2.56	
6.45/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x5)
6.45/2.56	
6.45/2.56	
6.45/2.56	
6.45/2.56	
6.45/2.56	
6.45/2.56	Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
6.45/2.56	
6.45/2.56	
6.45/2.56	
6.45/2.56	----------------------------------------
6.45/2.56	
6.45/2.56	(24)
6.45/2.56	Obligation:
6.45/2.56	Pi-finite rewrite system:
6.45/2.56	The TRS R consists of the following rules:
6.45/2.56	
6.45/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.80/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.80/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.80/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.80/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.80/2.56	
6.80/2.56	The argument filtering Pi contains the following mapping:
6.80/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.80/2.56	
6.80/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga(x1)
6.80/2.56	
6.80/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x5)
6.80/2.56	
6.80/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x5)
6.80/2.56	
6.80/2.56	
6.80/2.56	
6.80/2.56	----------------------------------------
6.80/2.56	
6.80/2.56	(25) DependencyPairsProof (EQUIVALENT)
6.80/2.56	Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
6.80/2.56	Pi DP problem:
6.80/2.56	The TRS P consists of the following rules:
6.80/2.56	
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> U1_GA(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> TREE_MEMBER_IN_GA(X, Left)
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> U2_GA(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> TREE_MEMBER_IN_GA(X, Right)
6.80/2.56	
6.80/2.56	The TRS R consists of the following rules:
6.80/2.56	
6.80/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.80/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.80/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.80/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.80/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.80/2.56	
6.80/2.56	The argument filtering Pi contains the following mapping:
6.80/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.80/2.56	
6.80/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga(x1)
6.80/2.56	
6.80/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x5)
6.80/2.56	
6.80/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x5)
6.80/2.56	
6.80/2.56	TREE_MEMBER_IN_GA(x1, x2)  =  TREE_MEMBER_IN_GA(x1)
6.80/2.56	
6.80/2.56	U1_GA(x1, x2, x3, x4, x5)  =  U1_GA(x1, x5)
6.80/2.56	
6.80/2.56	U2_GA(x1, x2, x3, x4, x5)  =  U2_GA(x1, x5)
6.80/2.56	
6.80/2.56	
6.80/2.56	We have to consider all (P,R,Pi)-chains
6.80/2.56	----------------------------------------
6.80/2.56	
6.80/2.56	(26)
6.80/2.56	Obligation:
6.80/2.56	Pi DP problem:
6.80/2.56	The TRS P consists of the following rules:
6.80/2.56	
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> U1_GA(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> TREE_MEMBER_IN_GA(X, Left)
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> U2_GA(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> TREE_MEMBER_IN_GA(X, Right)
6.80/2.56	
6.80/2.56	The TRS R consists of the following rules:
6.80/2.56	
6.80/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.80/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.80/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.80/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.80/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.80/2.56	
6.80/2.56	The argument filtering Pi contains the following mapping:
6.80/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.80/2.56	
6.80/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga(x1)
6.80/2.56	
6.80/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x5)
6.80/2.56	
6.80/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x5)
6.80/2.56	
6.80/2.56	TREE_MEMBER_IN_GA(x1, x2)  =  TREE_MEMBER_IN_GA(x1)
6.80/2.56	
6.80/2.56	U1_GA(x1, x2, x3, x4, x5)  =  U1_GA(x1, x5)
6.80/2.56	
6.80/2.56	U2_GA(x1, x2, x3, x4, x5)  =  U2_GA(x1, x5)
6.80/2.56	
6.80/2.56	
6.80/2.56	We have to consider all (P,R,Pi)-chains
6.80/2.56	----------------------------------------
6.80/2.56	
6.80/2.56	(27) DependencyGraphProof (EQUIVALENT)
6.80/2.56	The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 2 less nodes.
6.80/2.56	----------------------------------------
6.80/2.56	
6.80/2.56	(28)
6.80/2.56	Obligation:
6.80/2.56	Pi DP problem:
6.80/2.56	The TRS P consists of the following rules:
6.80/2.56	
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> TREE_MEMBER_IN_GA(X, Right)
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> TREE_MEMBER_IN_GA(X, Left)
6.80/2.56	
6.80/2.56	The TRS R consists of the following rules:
6.80/2.56	
6.80/2.56	   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
6.80/2.56	   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
6.80/2.56	   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
6.80/2.56	   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
6.80/2.56	   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))
6.80/2.56	
6.80/2.56	The argument filtering Pi contains the following mapping:
6.80/2.56	tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)
6.80/2.56	
6.80/2.56	tree_member_out_ga(x1, x2)  =  tree_member_out_ga(x1)
6.80/2.56	
6.80/2.56	U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x5)
6.80/2.56	
6.80/2.56	U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x5)
6.80/2.56	
6.80/2.56	TREE_MEMBER_IN_GA(x1, x2)  =  TREE_MEMBER_IN_GA(x1)
6.80/2.56	
6.80/2.56	
6.80/2.56	We have to consider all (P,R,Pi)-chains
6.80/2.56	----------------------------------------
6.80/2.56	
6.80/2.56	(29) UsableRulesProof (EQUIVALENT)
6.80/2.56	For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.
6.80/2.56	----------------------------------------
6.80/2.56	
6.80/2.56	(30)
6.80/2.56	Obligation:
6.80/2.56	Pi DP problem:
6.80/2.56	The TRS P consists of the following rules:
6.80/2.56	
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X5, X6, Right)) -> TREE_MEMBER_IN_GA(X, Right)
6.80/2.56	   TREE_MEMBER_IN_GA(X, tree(X3, Left, X4)) -> TREE_MEMBER_IN_GA(X, Left)
6.80/2.56	
6.80/2.56	R is empty.
6.80/2.56	The argument filtering Pi contains the following mapping:
6.80/2.56	TREE_MEMBER_IN_GA(x1, x2)  =  TREE_MEMBER_IN_GA(x1)
6.80/2.56	
6.80/2.56	
6.80/2.56	We have to consider all (P,R,Pi)-chains
6.80/2.56	----------------------------------------
6.80/2.56	
6.80/2.56	(31) PiDPToQDPProof (SOUND)
6.80/2.56	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
6.80/2.56	----------------------------------------
6.80/2.56	
6.80/2.56	(32)
6.80/2.56	Obligation:
6.80/2.56	Q DP problem:
6.80/2.56	The TRS P consists of the following rules:
6.80/2.56	
6.80/2.56	   TREE_MEMBER_IN_GA(X) -> TREE_MEMBER_IN_GA(X)
6.80/2.56	
6.80/2.56	R is empty.
6.80/2.56	Q is empty.
6.80/2.56	We have to consider all (P,Q,R)-chains.
6.80/2.56	----------------------------------------
6.80/2.56	
6.80/2.56	(33) PrologToIRSwTTransformerProof (SOUND)
6.80/2.56	Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert
6.80/2.56	
6.80/2.56	{
6.80/2.56	    "root": 17,
6.80/2.56	    "program": {
6.80/2.56	        "directives": [],
6.80/2.56	        "clauses": [
6.80/2.56	            [
6.80/2.56	                "(tree_member X (tree X X1 X2))",
6.80/2.56	                null
6.80/2.56	            ],
6.80/2.56	            [
6.80/2.56	                "(tree_member X (tree X3 Left X4))",
6.80/2.56	                "(tree_member X Left)"
6.80/2.56	            ],
6.80/2.56	            [
6.80/2.56	                "(tree_member X (tree X5 X6 Right))",
6.80/2.56	                "(tree_member X Right)"
6.80/2.56	            ]
6.80/2.56	        ]
6.80/2.56	    },
6.80/2.56	    "graph": {
6.80/2.56	        "nodes": {
6.80/2.56	            "89": {
6.80/2.56	                "goal": [{
6.80/2.56	                    "clause": -1,
6.80/2.56	                    "scope": -1,
6.80/2.56	                    "term": "(true)"
6.80/2.56	                }],
6.80/2.56	                "kb": {
6.80/2.56	                    "nonunifying": [],
6.80/2.56	                    "intvars": {},
6.80/2.56	                    "arithmetic": {
6.80/2.56	                        "type": "PlainIntegerRelationState",
6.80/2.56	                        "relations": []
6.80/2.56	                    },
6.80/2.56	                    "ground": [],
6.80/2.56	                    "free": [],
6.80/2.56	                    "exprvars": []
6.80/2.56	                }
6.80/2.56	            },
6.80/2.56	            "17": {
6.80/2.56	                "goal": [{
6.80/2.56	                    "clause": -1,
6.80/2.56	                    "scope": -1,
6.80/2.56	                    "term": "(tree_member T1 T2)"
6.80/2.56	                }],
6.80/2.56	                "kb": {
6.80/2.56	                    "nonunifying": [],
6.80/2.56	                    "intvars": {},
6.80/2.56	                    "arithmetic": {
6.80/2.56	                        "type": "PlainIntegerRelationState",
6.80/2.56	                        "relations": []
6.80/2.56	                    },
6.80/2.56	                    "ground": ["T1"],
6.80/2.56	                    "free": [],
6.80/2.56	                    "exprvars": []
6.80/2.56	                }
6.80/2.56	            },
6.80/2.56	            "18": {
6.80/2.56	                "goal": [
6.80/2.56	                    {
6.80/2.56	                        "clause": 0,
6.80/2.56	                        "scope": 1,
6.80/2.56	                        "term": "(tree_member T1 T2)"
6.80/2.56	                    },
6.80/2.56	                    {
6.80/2.56	                        "clause": 1,
6.80/2.56	                        "scope": 1,
6.80/2.56	                        "term": "(tree_member T1 T2)"
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 1,
6.80/2.57	                        "term": "(tree_member T1 T2)"
6.80/2.57	                    }
6.80/2.57	                ],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T1"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "type": "Nodes",
6.80/2.57	            "150": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "130": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": 1,
6.80/2.57	                    "scope": 1,
6.80/2.57	                    "term": "(tree_member T1 T2)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T1"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "131": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": 2,
6.80/2.57	                    "scope": 1,
6.80/2.57	                    "term": "(tree_member T1 T2)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T1"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "101": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "136": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": -1,
6.80/2.57	                    "scope": -1,
6.80/2.57	                    "term": "(tree_member T34 T38)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T34"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "147": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": -1,
6.80/2.57	                    "scope": -1,
6.80/2.57	                    "term": "(tree_member T53 T57)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T53"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "137": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "74": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": 0,
6.80/2.57	                    "scope": 1,
6.80/2.57	                    "term": "(tree_member T1 T2)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T1"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "76": {
6.80/2.57	                "goal": [
6.80/2.57	                    {
6.80/2.57	                        "clause": 1,
6.80/2.57	                        "scope": 1,
6.80/2.57	                        "term": "(tree_member T1 T2)"
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 1,
6.80/2.57	                        "term": "(tree_member T1 T2)"
6.80/2.57	                    }
6.80/2.57	                ],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T1"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "98": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            }
6.80/2.57	        },
6.80/2.57	        "edges": [
6.80/2.57	            {
6.80/2.57	                "from": 17,
6.80/2.57	                "to": 18,
6.80/2.57	                "label": "CASE"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 18,
6.80/2.57	                "to": 74,
6.80/2.57	                "label": "PARALLEL"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 18,
6.80/2.57	                "to": 76,
6.80/2.57	                "label": "PARALLEL"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 74,
6.80/2.57	                "to": 89,
6.80/2.57	                "label": "EVAL with clause\ntree_member(X19, tree(X19, X20, X21)).\nand substitutionT1 -> T15,\nX19 -> T15,\nX20 -> T16,\nX21 -> T17,\nT2 -> tree(T15, T16, T17)"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 74,
6.80/2.57	                "to": 98,
6.80/2.57	                "label": "EVAL-BACKTRACK"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 76,
6.80/2.57	                "to": 130,
6.80/2.57	                "label": "PARALLEL"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 76,
6.80/2.57	                "to": 131,
6.80/2.57	                "label": "PARALLEL"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 89,
6.80/2.57	                "to": 101,
6.80/2.57	                "label": "SUCCESS"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 130,
6.80/2.57	                "to": 136,
6.80/2.57	                "label": "EVAL with clause\ntree_member(X38, tree(X39, X40, X41)) :- tree_member(X38, X40).\nand substitutionT1 -> T34,\nX38 -> T34,\nX39 -> T35,\nX40 -> T38,\nX41 -> T37,\nT2 -> tree(T35, T38, T37),\nT36 -> T38"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 130,
6.80/2.57	                "to": 137,
6.80/2.57	                "label": "EVAL-BACKTRACK"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 131,
6.80/2.57	                "to": 147,
6.80/2.57	                "label": "EVAL with clause\ntree_member(X56, tree(X57, X58, X59)) :- tree_member(X56, X59).\nand substitutionT1 -> T53,\nX56 -> T53,\nX57 -> T54,\nX58 -> T55,\nX59 -> T57,\nT2 -> tree(T54, T55, T57),\nT56 -> T57"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 131,
6.80/2.57	                "to": 150,
6.80/2.57	                "label": "EVAL-BACKTRACK"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 136,
6.80/2.57	                "to": 17,
6.80/2.57	                "label": "INSTANCE with matching:\nT1 -> T34\nT2 -> T38"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 147,
6.80/2.57	                "to": 17,
6.80/2.57	                "label": "INSTANCE with matching:\nT1 -> T53\nT2 -> T57"
6.80/2.57	            }
6.80/2.57	        ],
6.80/2.57	        "type": "Graph"
6.80/2.57	    }
6.80/2.57	}
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(34)
6.80/2.57	Obligation:
6.80/2.57	Rules:
6.80/2.57	f17_out(T53) -> f147_out(T53) :|: TRUE
6.80/2.57	f147_in(x) -> f17_in(x) :|: TRUE
6.80/2.57	f18_in(T1) -> f76_in(T1) :|: TRUE
6.80/2.57	f74_out(x1) -> f18_out(x1) :|: TRUE
6.80/2.57	f18_in(x2) -> f74_in(x2) :|: TRUE
6.80/2.57	f76_out(x3) -> f18_out(x3) :|: TRUE
6.80/2.57	f17_out(T34) -> f136_out(T34) :|: TRUE
6.80/2.57	f136_in(x4) -> f17_in(x4) :|: TRUE
6.80/2.57	f76_in(x5) -> f130_in(x5) :|: TRUE
6.80/2.57	f130_out(x6) -> f76_out(x6) :|: TRUE
6.80/2.57	f76_in(x7) -> f131_in(x7) :|: TRUE
6.80/2.57	f131_out(x8) -> f76_out(x8) :|: TRUE
6.80/2.57	f130_in(x9) -> f136_in(x9) :|: TRUE
6.80/2.57	f130_in(x10) -> f137_in :|: TRUE
6.80/2.57	f136_out(x11) -> f130_out(x11) :|: TRUE
6.80/2.57	f137_out -> f130_out(x12) :|: TRUE
6.80/2.57	f147_out(x13) -> f131_out(x13) :|: TRUE
6.80/2.57	f131_in(x14) -> f150_in :|: TRUE
6.80/2.57	f131_in(x15) -> f147_in(x15) :|: TRUE
6.80/2.57	f150_out -> f131_out(x16) :|: TRUE
6.80/2.57	f18_out(x17) -> f17_out(x17) :|: TRUE
6.80/2.57	f17_in(x18) -> f18_in(x18) :|: TRUE
6.80/2.57	Start term: f17_in(T1)
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(35) IRSwTSimpleDependencyGraphProof (EQUIVALENT)
6.80/2.57	Constructed simple dependency graph.
6.80/2.57	
6.80/2.57	Simplified to the following IRSwTs:
6.80/2.57	
6.80/2.57	intTRSProblem:
6.80/2.57	f147_in(x) -> f17_in(x) :|: TRUE
6.80/2.57	f18_in(T1) -> f76_in(T1) :|: TRUE
6.80/2.57	f136_in(x4) -> f17_in(x4) :|: TRUE
6.80/2.57	f76_in(x5) -> f130_in(x5) :|: TRUE
6.80/2.57	f76_in(x7) -> f131_in(x7) :|: TRUE
6.80/2.57	f130_in(x9) -> f136_in(x9) :|: TRUE
6.80/2.57	f131_in(x15) -> f147_in(x15) :|: TRUE
6.80/2.57	f17_in(x18) -> f18_in(x18) :|: TRUE
6.80/2.57	
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(36)
6.80/2.57	Obligation:
6.80/2.57	Rules:
6.80/2.57	f147_in(x) -> f17_in(x) :|: TRUE
6.80/2.57	f18_in(T1) -> f76_in(T1) :|: TRUE
6.80/2.57	f136_in(x4) -> f17_in(x4) :|: TRUE
6.80/2.57	f76_in(x5) -> f130_in(x5) :|: TRUE
6.80/2.57	f76_in(x7) -> f131_in(x7) :|: TRUE
6.80/2.57	f130_in(x9) -> f136_in(x9) :|: TRUE
6.80/2.57	f131_in(x15) -> f147_in(x15) :|: TRUE
6.80/2.57	f17_in(x18) -> f18_in(x18) :|: TRUE
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(37) IntTRSCompressionProof (EQUIVALENT)
6.80/2.57	Compressed rules.
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(38)
6.80/2.57	Obligation:
6.80/2.57	Rules:
6.80/2.57	f18_in(T1:0) -> f18_in(T1:0) :|: TRUE
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(39) IRSFormatTransformerProof (EQUIVALENT)
6.80/2.57	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(40)
6.80/2.57	Obligation:
6.80/2.57	Rules:
6.80/2.57	f18_in(T1:0) -> f18_in(T1:0) :|: TRUE
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(41) IRSwTTerminationDigraphProof (EQUIVALENT)
6.80/2.57	Constructed termination digraph!
6.80/2.57	Nodes:
6.80/2.57	(1) f18_in(T1:0) -> f18_in(T1:0) :|: TRUE
6.80/2.57	
6.80/2.57	Arcs:
6.80/2.57	(1) -> (1)
6.80/2.57	
6.80/2.57	This digraph is fully evaluated!
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(42)
6.80/2.57	Obligation:
6.80/2.57	
6.80/2.57	Termination digraph:
6.80/2.57	Nodes:
6.80/2.57	(1) f18_in(T1:0) -> f18_in(T1:0) :|: TRUE
6.80/2.57	
6.80/2.57	Arcs:
6.80/2.57	(1) -> (1)
6.80/2.57	
6.80/2.57	This digraph is fully evaluated!
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(43) FilterProof (EQUIVALENT)
6.80/2.57	Used the following sort dictionary for filtering: 
6.80/2.57	f18_in(VARIABLE)
6.80/2.57	Replaced non-predefined constructor symbols by 0.
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(44)
6.80/2.57	Obligation:
6.80/2.57	Rules:
6.80/2.57	f18_in(T1:0) -> f18_in(T1:0) :|: TRUE
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(45) IntTRSNonPeriodicNontermProof (COMPLETE)
6.80/2.57	Normalized system to the following form:
6.80/2.57	f(pc, T1:0) -> f(1, T1:0) :|: pc = 1 && TRUE
6.80/2.57	Proved unsatisfiability of the following formula, indicating that the system is never left after entering:
6.80/2.57	(((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T)) and !(((run2_0 * 1)) = ((1 * 1)) and T))
6.80/2.57	Proved satisfiability of the following formula, indicating that the system is entered at least once:
6.80/2.57	((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T))
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(46)
6.80/2.57	NO
6.80/2.57	
6.80/2.57	----------------------------------------
6.80/2.57	
6.80/2.57	(47) PrologToDTProblemTransformerProof (SOUND)
6.80/2.57	Built DT problem from termination graph DT10.
6.80/2.57	
6.80/2.57	{
6.80/2.57	    "root": 7,
6.80/2.57	    "program": {
6.80/2.57	        "directives": [],
6.80/2.57	        "clauses": [
6.80/2.57	            [
6.80/2.57	                "(tree_member X (tree X X1 X2))",
6.80/2.57	                null
6.80/2.57	            ],
6.80/2.57	            [
6.80/2.57	                "(tree_member X (tree X3 Left X4))",
6.80/2.57	                "(tree_member X Left)"
6.80/2.57	            ],
6.80/2.57	            [
6.80/2.57	                "(tree_member X (tree X5 X6 Right))",
6.80/2.57	                "(tree_member X Right)"
6.80/2.57	            ]
6.80/2.57	        ]
6.80/2.57	    },
6.80/2.57	    "graph": {
6.80/2.57	        "nodes": {
6.80/2.57	            "190": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": 2,
6.80/2.57	                    "scope": 1,
6.80/2.57	                    "term": "(tree_member T180 T2)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T180 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T180"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "191": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": -1,
6.80/2.57	                    "scope": -1,
6.80/2.57	                    "term": "(tree_member T262 T266)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T262 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T262"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "192": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "193": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": -1,
6.80/2.57	                    "scope": -1,
6.80/2.57	                    "term": "(tree_member T277 T281)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T277 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T277"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "type": "Nodes",
6.80/2.57	            "194": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "151": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": -1,
6.80/2.57	                    "scope": -1,
6.80/2.57	                    "term": "(tree_member T49 T53)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T49"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "195": {
6.80/2.57	                "goal": [
6.80/2.57	                    {
6.80/2.57	                        "clause": 0,
6.80/2.57	                        "scope": 5,
6.80/2.57	                        "term": "(tree_member T277 T281)"
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 1,
6.80/2.57	                        "scope": 5,
6.80/2.57	                        "term": "(tree_member T277 T281)"
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 5,
6.80/2.57	                        "term": "(tree_member T277 T281)"
6.80/2.57	                    }
6.80/2.57	                ],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T277 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T277"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "152": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "196": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": 0,
6.80/2.57	                    "scope": 5,
6.80/2.57	                    "term": "(tree_member T277 T281)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T277 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T277"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "153": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": 2,
6.80/2.57	                    "scope": 2,
6.80/2.57	                    "term": "(tree_member T13 T17)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T13"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "197": {
6.80/2.57	                "goal": [
6.80/2.57	                    {
6.80/2.57	                        "clause": 1,
6.80/2.57	                        "scope": 5,
6.80/2.57	                        "term": "(tree_member T277 T281)"
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 5,
6.80/2.57	                        "term": "(tree_member T277 T281)"
6.80/2.57	                    }
6.80/2.57	                ],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T277 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T277"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
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6.80/2.57	                        "term": "(tree_member T13 T17)"
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 2,
6.80/2.57	                        "term": "(tree_member T13 T17)"
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": -1,
6.80/2.57	                        "scope": 2,
6.80/2.57	                        "term": null
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 1,
6.80/2.57	                        "term": "(tree_member T13 T2)"
6.80/2.57	                    }
6.80/2.57	                ],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T13"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "180": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "181": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "182": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": 1,
6.80/2.57	                    "scope": 4,
6.80/2.57	                    "term": "(tree_member T180 T184)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T180 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T180"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "183": {
6.80/2.57	                "goal": [
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 4,
6.80/2.57	                        "term": "(tree_member T180 T184)"
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": -1,
6.80/2.57	                        "scope": 4,
6.80/2.57	                        "term": null
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 1,
6.80/2.57	                        "term": "(tree_member T180 T2)"
6.80/2.57	                    }
6.80/2.57	                ],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T180 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T180"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "184": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": -1,
6.80/2.57	                    "scope": -1,
6.80/2.57	                    "term": "(tree_member T216 T220)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T216 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T216"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "185": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "186": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": 2,
6.80/2.57	                    "scope": 4,
6.80/2.57	                    "term": "(tree_member T180 T184)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T180 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T180"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "187": {
6.80/2.57	                "goal": [
6.80/2.57	                    {
6.80/2.57	                        "clause": -1,
6.80/2.57	                        "scope": 4,
6.80/2.57	                        "term": null
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 1,
6.80/2.57	                        "term": "(tree_member T180 T2)"
6.80/2.57	                    }
6.80/2.57	                ],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T180 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T180"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "144": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": -1,
6.80/2.57	                    "scope": -1,
6.80/2.57	                    "term": "(true)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "188": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": -1,
6.80/2.57	                    "scope": -1,
6.80/2.57	                    "term": "(tree_member T243 T247)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [[
6.80/2.57	                        "(tree_member T243 T2)",
6.80/2.57	                        "(tree_member X10 (tree X10 X11 X12))"
6.80/2.57	                    ]],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T243"],
6.80/2.57	                    "free": [
6.80/2.57	                        "X10",
6.80/2.57	                        "X11",
6.80/2.57	                        "X12"
6.80/2.57	                    ],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "145": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "189": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "146": {
6.80/2.57	                "goal": [],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": [],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "148": {
6.80/2.57	                "goal": [{
6.80/2.57	                    "clause": 1,
6.80/2.57	                    "scope": 2,
6.80/2.57	                    "term": "(tree_member T13 T17)"
6.80/2.57	                }],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T13"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            },
6.80/2.57	            "149": {
6.80/2.57	                "goal": [
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 2,
6.80/2.57	                        "term": "(tree_member T13 T17)"
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": -1,
6.80/2.57	                        "scope": 2,
6.80/2.57	                        "term": null
6.80/2.57	                    },
6.80/2.57	                    {
6.80/2.57	                        "clause": 2,
6.80/2.57	                        "scope": 1,
6.80/2.57	                        "term": "(tree_member T13 T2)"
6.80/2.57	                    }
6.80/2.57	                ],
6.80/2.57	                "kb": {
6.80/2.57	                    "nonunifying": [],
6.80/2.57	                    "intvars": {},
6.80/2.57	                    "arithmetic": {
6.80/2.57	                        "type": "PlainIntegerRelationState",
6.80/2.57	                        "relations": []
6.80/2.57	                    },
6.80/2.57	                    "ground": ["T13"],
6.80/2.57	                    "free": [],
6.80/2.57	                    "exprvars": []
6.80/2.57	                }
6.80/2.57	            }
6.80/2.57	        },
6.80/2.57	        "edges": [
6.80/2.57	            {
6.80/2.57	                "from": 7,
6.80/2.57	                "to": 10,
6.80/2.57	                "label": "CASE"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 10,
6.80/2.57	                "to": 58,
6.80/2.57	                "label": "EVAL with clause\ntree_member(X10, tree(X10, X11, X12)).\nand substitutionT1 -> T6,\nX10 -> T6,\nX11 -> T7,\nX12 -> T8,\nT2 -> tree(T6, T7, T8)"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 10,
6.80/2.57	                "to": 59,
6.80/2.57	                "label": "EVAL-BACKTRACK"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 58,
6.80/2.57	                "to": 60,
6.80/2.57	                "label": "SUCCESS"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 59,
6.80/2.57	                "to": 174,
6.80/2.57	                "label": "EVAL with clause\ntree_member(X177, tree(X178, X179, X180)) :- tree_member(X177, X179).\nand substitutionT1 -> T180,\nX177 -> T180,\nX178 -> T181,\nX179 -> T184,\nX180 -> T183,\nT2 -> tree(T181, T184, T183),\nT182 -> T184"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 59,
6.80/2.57	                "to": 175,
6.80/2.57	                "label": "EVAL-BACKTRACK"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 60,
6.80/2.57	                "to": 64,
6.80/2.57	                "label": "EVAL with clause\ntree_member(X17, tree(X18, X19, X20)) :- tree_member(X17, X19).\nand substitutionT6 -> T13,\nX17 -> T13,\nX18 -> T14,\nX19 -> T17,\nX20 -> T16,\nT2 -> tree(T14, T17, T16),\nT15 -> T17"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 60,
6.80/2.57	                "to": 67,
6.80/2.57	                "label": "EVAL-BACKTRACK"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 64,
6.80/2.57	                "to": 69,
6.80/2.57	                "label": "CASE"
6.80/2.57	            },
6.80/2.57	            {
6.80/2.57	                "from": 67,
6.80/2.58	                "to": 160,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X110, tree(X111, X112, X113)) :- tree_member(X110, X113).\nand substitutionT6 -> T110,\nX110 -> T110,\nX111 -> T111,\nX112 -> T112,\nX113 -> T114,\nT2 -> tree(T111, T112, T114),\nT113 -> T114"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 67,
6.80/2.58	                "to": 161,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 69,
6.80/2.58	                "to": 75,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 69,
6.80/2.58	                "to": 77,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 75,
6.80/2.58	                "to": 144,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X33, tree(X33, X34, X35)).\nand substitutionT13 -> T30,\nX33 -> T30,\nX34 -> T31,\nX35 -> T32,\nT17 -> tree(T30, T31, T32)"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 75,
6.80/2.58	                "to": 145,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 77,
6.80/2.58	                "to": 148,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 77,
6.80/2.58	                "to": 149,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 144,
6.80/2.58	                "to": 146,
6.80/2.58	                "label": "SUCCESS"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 148,
6.80/2.58	                "to": 151,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X52, tree(X53, X54, X55)) :- tree_member(X52, X54).\nand substitutionT13 -> T49,\nX52 -> T49,\nX53 -> T50,\nX54 -> T53,\nX55 -> T52,\nT17 -> tree(T50, T53, T52),\nT51 -> T53"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 148,
6.80/2.58	                "to": 152,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 149,
6.80/2.58	                "to": 153,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 149,
6.80/2.58	                "to": 154,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 151,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T49\nT2 -> T53"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 153,
6.80/2.58	                "to": 155,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X78, tree(X79, X80, X81)) :- tree_member(X78, X81).\nand substitutionT13 -> T76,\nX78 -> T76,\nX79 -> T77,\nX80 -> T78,\nX81 -> T80,\nT17 -> tree(T77, T78, T80),\nT79 -> T80"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 153,
6.80/2.58	                "to": 156,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 154,
6.80/2.58	                "to": 157,
6.80/2.58	                "label": "FAILURE"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 155,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T76\nT2 -> T80"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 157,
6.80/2.58	                "to": 158,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X96, tree(X97, X98, X99)) :- tree_member(X96, X99).\nand substitutionT13 -> T95,\nX96 -> T95,\nX97 -> T96,\nX98 -> T97,\nX99 -> T99,\nT2 -> tree(T96, T97, T99),\nT98 -> T99"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 157,
6.80/2.58	                "to": 159,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 158,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T95\nT2 -> T99"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 160,
6.80/2.58	                "to": 162,
6.80/2.58	                "label": "CASE"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 162,
6.80/2.58	                "to": 163,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 162,
6.80/2.58	                "to": 164,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 163,
6.80/2.58	                "to": 165,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X126, tree(X126, X127, X128)).\nand substitutionT110 -> T127,\nX126 -> T127,\nX127 -> T128,\nX128 -> T129,\nT114 -> tree(T127, T128, T129)"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 163,
6.80/2.58	                "to": 166,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 164,
6.80/2.58	                "to": 168,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 164,
6.80/2.58	                "to": 169,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 165,
6.80/2.58	                "to": 167,
6.80/2.58	                "label": "SUCCESS"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 168,
6.80/2.58	                "to": 170,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X145, tree(X146, X147, X148)) :- tree_member(X145, X147).\nand substitutionT110 -> T146,\nX145 -> T146,\nX146 -> T147,\nX147 -> T150,\nX148 -> T149,\nT114 -> tree(T147, T150, T149),\nT148 -> T150"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 168,
6.80/2.58	                "to": 171,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 169,
6.80/2.58	                "to": 172,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X163, tree(X164, X165, X166)) :- tree_member(X163, X166).\nand substitutionT110 -> T165,\nX163 -> T165,\nX164 -> T166,\nX165 -> T167,\nX166 -> T169,\nT114 -> tree(T166, T167, T169),\nT168 -> T169"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 169,
6.80/2.58	                "to": 173,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 170,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T146\nT2 -> T150"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 172,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T165\nT2 -> T169"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 174,
6.80/2.58	                "to": 176,
6.80/2.58	                "label": "CASE"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 175,
6.80/2.58	                "to": 193,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X270, tree(X271, X272, X273)) :- tree_member(X270, X273).\nand substitutionT1 -> T277,\nX270 -> T277,\nX271 -> T278,\nX272 -> T279,\nX273 -> T281,\nT2 -> tree(T278, T279, T281),\nT280 -> T281"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 175,
6.80/2.58	                "to": 194,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 176,
6.80/2.58	                "to": 177,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 176,
6.80/2.58	                "to": 178,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 177,
6.80/2.58	                "to": 179,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X193, tree(X193, X194, X195)).\nand substitutionT180 -> T197,\nX193 -> T197,\nX194 -> T198,\nX195 -> T199,\nT184 -> tree(T197, T198, T199)"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 177,
6.80/2.58	                "to": 180,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 178,
6.80/2.58	                "to": 182,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 178,
6.80/2.58	                "to": 183,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 179,
6.80/2.58	                "to": 181,
6.80/2.58	                "label": "SUCCESS"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 182,
6.80/2.58	                "to": 184,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X212, tree(X213, X214, X215)) :- tree_member(X212, X214).\nand substitutionT180 -> T216,\nX212 -> T216,\nX213 -> T217,\nX214 -> T220,\nX215 -> T219,\nT184 -> tree(T217, T220, T219),\nT218 -> T220"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 182,
6.80/2.58	                "to": 185,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 183,
6.80/2.58	                "to": 186,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 183,
6.80/2.58	                "to": 187,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 184,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T216\nT2 -> T220"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 186,
6.80/2.58	                "to": 188,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X238, tree(X239, X240, X241)) :- tree_member(X238, X241).\nand substitutionT180 -> T243,\nX238 -> T243,\nX239 -> T244,\nX240 -> T245,\nX241 -> T247,\nT184 -> tree(T244, T245, T247),\nT246 -> T247"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 186,
6.80/2.58	                "to": 189,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 187,
6.80/2.58	                "to": 190,
6.80/2.58	                "label": "FAILURE"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 188,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T243\nT2 -> T247"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 190,
6.80/2.58	                "to": 191,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X256, tree(X257, X258, X259)) :- tree_member(X256, X259).\nand substitutionT180 -> T262,\nX256 -> T262,\nX257 -> T263,\nX258 -> T264,\nX259 -> T266,\nT2 -> tree(T263, T264, T266),\nT265 -> T266"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 190,
6.80/2.58	                "to": 192,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 191,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T262\nT2 -> T266"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 193,
6.80/2.58	                "to": 195,
6.80/2.58	                "label": "CASE"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 195,
6.80/2.58	                "to": 196,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 195,
6.80/2.58	                "to": 197,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 196,
6.80/2.58	                "to": 198,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X286, tree(X286, X287, X288)).\nand substitutionT277 -> T294,\nX286 -> T294,\nX287 -> T295,\nX288 -> T296,\nT281 -> tree(T294, T295, T296)"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 196,
6.80/2.58	                "to": 199,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 197,
6.80/2.58	                "to": 201,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 197,
6.80/2.58	                "to": 202,
6.80/2.58	                "label": "PARALLEL"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 198,
6.80/2.58	                "to": 200,
6.80/2.58	                "label": "SUCCESS"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 201,
6.80/2.58	                "to": 203,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X305, tree(X306, X307, X308)) :- tree_member(X305, X307).\nand substitutionT277 -> T313,\nX305 -> T313,\nX306 -> T314,\nX307 -> T317,\nX308 -> T316,\nT281 -> tree(T314, T317, T316),\nT315 -> T317"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 201,
6.80/2.58	                "to": 204,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 202,
6.80/2.58	                "to": 205,
6.80/2.58	                "label": "EVAL with clause\ntree_member(X323, tree(X324, X325, X326)) :- tree_member(X323, X326).\nand substitutionT277 -> T332,\nX323 -> T332,\nX324 -> T333,\nX325 -> T334,\nX326 -> T336,\nT281 -> tree(T333, T334, T336),\nT335 -> T336"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 202,
6.80/2.58	                "to": 206,
6.80/2.58	                "label": "EVAL-BACKTRACK"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 203,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T313\nT2 -> T317"
6.80/2.58	            },
6.80/2.58	            {
6.80/2.58	                "from": 205,
6.80/2.58	                "to": 7,
6.80/2.58	                "label": "INSTANCE with matching:\nT1 -> T332\nT2 -> T336"
6.80/2.58	            }
6.80/2.58	        ],
6.80/2.58	        "type": "Graph"
6.80/2.58	    }
6.80/2.58	}
6.80/2.58	
6.80/2.58	----------------------------------------
6.80/2.58	
6.80/2.58	(48)
6.80/2.58	Obligation:
6.80/2.58	Triples:
6.80/2.58	
6.80/2.58	tree_memberA(X1, tree(X2, tree(X3, X4, X5), X6)) :- tree_memberA(X1, X4).
6.80/2.58	tree_memberA(X1, tree(X2, tree(X3, X4, X5), X6)) :- tree_memberA(X1, X5).
6.80/2.58	tree_memberA(X1, tree(X2, X3, X4)) :- tree_memberA(X1, X4).
6.80/2.58	tree_memberA(X1, tree(X2, X3, tree(X4, X5, X6))) :- tree_memberA(X1, X5).
6.80/2.58	tree_memberA(X1, tree(X2, X3, tree(X4, X5, X6))) :- tree_memberA(X1, X6).
6.80/2.58	tree_memberA(X1, tree(X2, tree(X3, X4, X5), X6)) :- tree_memberA(X1, X4).
6.80/2.58	tree_memberA(X1, tree(X2, tree(X3, X4, X5), X6)) :- tree_memberA(X1, X5).
6.80/2.58	tree_memberA(X1, tree(X2, X3, X4)) :- tree_memberA(X1, X4).
6.80/2.58	tree_memberA(X1, tree(X2, X3, tree(X4, X5, X6))) :- tree_memberA(X1, X5).
6.80/2.58	tree_memberA(X1, tree(X2, X3, tree(X4, X5, X6))) :- tree_memberA(X1, X6).
6.80/2.58	
6.80/2.58	Clauses:
6.80/2.58	
6.80/2.58	tree_membercA(X1, tree(X1, X2, X3)).
6.80/2.58	tree_membercA(X1, tree(X2, tree(X1, X3, X4), X5)).
6.80/2.58	tree_membercA(X1, tree(X2, tree(X3, X4, X5), X6)) :- tree_membercA(X1, X4).
6.80/2.58	tree_membercA(X1, tree(X2, tree(X3, X4, X5), X6)) :- tree_membercA(X1, X5).
6.80/2.58	tree_membercA(X1, tree(X2, X3, X4)) :- tree_membercA(X1, X4).
6.80/2.58	tree_membercA(X1, tree(X2, X3, tree(X1, X4, X5))).
6.80/2.58	tree_membercA(X1, tree(X2, X3, tree(X4, X5, X6))) :- tree_membercA(X1, X5).
6.80/2.58	tree_membercA(X1, tree(X2, X3, tree(X4, X5, X6))) :- tree_membercA(X1, X6).
6.80/2.58	tree_membercA(X1, tree(X2, tree(X1, X3, X4), X5)).
6.80/2.58	tree_membercA(X1, tree(X2, tree(X3, X4, X5), X6)) :- tree_membercA(X1, X4).
6.80/2.58	tree_membercA(X1, tree(X2, tree(X3, X4, X5), X6)) :- tree_membercA(X1, X5).
6.80/2.58	tree_membercA(X1, tree(X2, X3, X4)) :- tree_membercA(X1, X4).
6.80/2.58	tree_membercA(X1, tree(X2, X3, tree(X1, X4, X5))).
6.80/2.58	tree_membercA(X1, tree(X2, X3, tree(X4, X5, X6))) :- tree_membercA(X1, X5).
6.80/2.58	tree_membercA(X1, tree(X2, X3, tree(X4, X5, X6))) :- tree_membercA(X1, X6).
6.80/2.58	
6.80/2.58	Afs:
6.80/2.58	
6.80/2.58	tree_memberA(x1, x2)  =  tree_memberA(x1)
6.80/2.58	
6.80/2.58	
6.80/2.58	----------------------------------------
6.80/2.58	
6.80/2.58	(49) TriplesToPiDPProof (SOUND)
6.80/2.58	We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes:
6.80/2.58	
6.80/2.58	tree_memberA_in_2: (b,f)
6.80/2.58	
6.80/2.58	Transforming TRIPLES into the following Term Rewriting System:
6.80/2.58	
6.80/2.58	Pi DP problem:
6.80/2.58	The TRS P consists of the following rules:
6.80/2.58	
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> U1_GA(X1, X2, X3, X4, X5, X6, tree_memberA_in_ga(X1, X4))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> TREE_MEMBERA_IN_GA(X1, X4)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> U2_GA(X1, X2, X3, X4, X5, X6, tree_memberA_in_ga(X1, X5))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> TREE_MEMBERA_IN_GA(X1, X5)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, X4)) -> U3_GA(X1, X2, X3, X4, tree_memberA_in_ga(X1, X4))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, X4)) -> TREE_MEMBERA_IN_GA(X1, X4)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> U4_GA(X1, X2, X3, X4, X5, X6, tree_memberA_in_ga(X1, X5))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> TREE_MEMBERA_IN_GA(X1, X5)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> U5_GA(X1, X2, X3, X4, X5, X6, tree_memberA_in_ga(X1, X6))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> TREE_MEMBERA_IN_GA(X1, X6)
6.80/2.58	
6.80/2.58	R is empty.
6.80/2.58	The argument filtering Pi contains the following mapping:
6.80/2.58	tree_memberA_in_ga(x1, x2)  =  tree_memberA_in_ga(x1)
6.80/2.58	
6.80/2.58	TREE_MEMBERA_IN_GA(x1, x2)  =  TREE_MEMBERA_IN_GA(x1)
6.80/2.58	
6.80/2.58	U1_GA(x1, x2, x3, x4, x5, x6, x7)  =  U1_GA(x1, x7)
6.80/2.58	
6.80/2.58	U2_GA(x1, x2, x3, x4, x5, x6, x7)  =  U2_GA(x1, x7)
6.80/2.58	
6.80/2.58	U3_GA(x1, x2, x3, x4, x5)  =  U3_GA(x1, x5)
6.80/2.58	
6.80/2.58	U4_GA(x1, x2, x3, x4, x5, x6, x7)  =  U4_GA(x1, x7)
6.80/2.58	
6.80/2.58	U5_GA(x1, x2, x3, x4, x5, x6, x7)  =  U5_GA(x1, x7)
6.80/2.58	
6.80/2.58	
6.80/2.58	We have to consider all (P,R,Pi)-chains
6.80/2.58	
6.80/2.58	
6.80/2.58	Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES
6.80/2.58	
6.80/2.58	
6.80/2.58	
6.80/2.58	----------------------------------------
6.80/2.58	
6.80/2.58	(50)
6.80/2.58	Obligation:
6.80/2.58	Pi DP problem:
6.80/2.58	The TRS P consists of the following rules:
6.80/2.58	
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> U1_GA(X1, X2, X3, X4, X5, X6, tree_memberA_in_ga(X1, X4))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> TREE_MEMBERA_IN_GA(X1, X4)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> U2_GA(X1, X2, X3, X4, X5, X6, tree_memberA_in_ga(X1, X5))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> TREE_MEMBERA_IN_GA(X1, X5)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, X4)) -> U3_GA(X1, X2, X3, X4, tree_memberA_in_ga(X1, X4))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, X4)) -> TREE_MEMBERA_IN_GA(X1, X4)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> U4_GA(X1, X2, X3, X4, X5, X6, tree_memberA_in_ga(X1, X5))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> TREE_MEMBERA_IN_GA(X1, X5)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> U5_GA(X1, X2, X3, X4, X5, X6, tree_memberA_in_ga(X1, X6))
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> TREE_MEMBERA_IN_GA(X1, X6)
6.80/2.58	
6.80/2.58	R is empty.
6.80/2.58	The argument filtering Pi contains the following mapping:
6.80/2.58	tree_memberA_in_ga(x1, x2)  =  tree_memberA_in_ga(x1)
6.80/2.58	
6.80/2.58	TREE_MEMBERA_IN_GA(x1, x2)  =  TREE_MEMBERA_IN_GA(x1)
6.80/2.58	
6.80/2.58	U1_GA(x1, x2, x3, x4, x5, x6, x7)  =  U1_GA(x1, x7)
6.80/2.58	
6.80/2.58	U2_GA(x1, x2, x3, x4, x5, x6, x7)  =  U2_GA(x1, x7)
6.80/2.58	
6.80/2.58	U3_GA(x1, x2, x3, x4, x5)  =  U3_GA(x1, x5)
6.80/2.58	
6.80/2.58	U4_GA(x1, x2, x3, x4, x5, x6, x7)  =  U4_GA(x1, x7)
6.80/2.58	
6.80/2.58	U5_GA(x1, x2, x3, x4, x5, x6, x7)  =  U5_GA(x1, x7)
6.80/2.58	
6.80/2.58	
6.80/2.58	We have to consider all (P,R,Pi)-chains
6.80/2.58	----------------------------------------
6.80/2.58	
6.80/2.58	(51) DependencyGraphProof (EQUIVALENT)
6.80/2.58	The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 5 less nodes.
6.80/2.58	----------------------------------------
6.80/2.58	
6.80/2.58	(52)
6.80/2.58	Obligation:
6.80/2.58	Pi DP problem:
6.80/2.58	The TRS P consists of the following rules:
6.80/2.58	
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> TREE_MEMBERA_IN_GA(X1, X5)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, tree(X3, X4, X5), X6)) -> TREE_MEMBERA_IN_GA(X1, X4)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, X4)) -> TREE_MEMBERA_IN_GA(X1, X4)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> TREE_MEMBERA_IN_GA(X1, X5)
6.80/2.58	   TREE_MEMBERA_IN_GA(X1, tree(X2, X3, tree(X4, X5, X6))) -> TREE_MEMBERA_IN_GA(X1, X6)
6.80/2.58	
6.80/2.58	R is empty.
6.80/2.58	The argument filtering Pi contains the following mapping:
6.80/2.58	TREE_MEMBERA_IN_GA(x1, x2)  =  TREE_MEMBERA_IN_GA(x1)
6.80/2.58	
6.80/2.58	
6.80/2.58	We have to consider all (P,R,Pi)-chains
6.80/2.58	----------------------------------------
6.80/2.58	
6.80/2.58	(53) PiDPToQDPProof (SOUND)
6.80/2.58	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
6.80/2.58	----------------------------------------
6.80/2.58	
6.80/2.58	(54)
6.80/2.58	Obligation:
6.80/2.58	Q DP problem:
6.80/2.58	The TRS P consists of the following rules:
6.80/2.58	
6.80/2.58	   TREE_MEMBERA_IN_GA(X1) -> TREE_MEMBERA_IN_GA(X1)
6.80/2.58	
6.80/2.58	R is empty.
6.80/2.58	Q is empty.
6.80/2.58	We have to consider all (P,Q,R)-chains.
6.89/2.62	EOF