6.63/2.59	MAYBE
6.63/2.60	proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
6.63/2.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.63/2.60	
6.63/2.60	
6.63/2.60	Left Termination of the query pattern
6.63/2.60	
6.63/2.60	reverse(a,g)
6.63/2.60	
6.63/2.60	w.r.t. the given Prolog program could not be shown:
6.63/2.60	
6.63/2.60	(0) Prolog
6.63/2.60	(1) PrologToPiTRSProof [SOUND, 0 ms]
6.63/2.60	(2) PiTRS
6.63/2.60	    (3) DependencyPairsProof [EQUIVALENT, 0 ms]
6.63/2.60	    (4) PiDP
6.63/2.60	    (5) DependencyGraphProof [EQUIVALENT, 0 ms]
6.63/2.60	    (6) PiDP
6.63/2.60	    (7) UsableRulesProof [EQUIVALENT, 0 ms]
6.63/2.60	    (8) PiDP
6.63/2.60	    (9) PiDPToQDPProof [SOUND, 0 ms]
6.63/2.60	    (10) QDP
6.63/2.60	    (11) TransformationProof [EQUIVALENT, 0 ms]
6.63/2.60	    (12) QDP
6.63/2.60	(13) PrologToPiTRSProof [SOUND, 0 ms]
6.63/2.60	(14) PiTRS
6.63/2.60	    (15) DependencyPairsProof [EQUIVALENT, 0 ms]
6.63/2.60	    (16) PiDP
6.63/2.60	    (17) DependencyGraphProof [EQUIVALENT, 0 ms]
6.63/2.60	    (18) PiDP
6.63/2.60	    (19) UsableRulesProof [EQUIVALENT, 0 ms]
6.63/2.60	    (20) PiDP
6.63/2.60	    (21) PiDPToQDPProof [SOUND, 0 ms]
6.63/2.60	    (22) QDP
6.63/2.60	    (23) TransformationProof [EQUIVALENT, 0 ms]
6.63/2.60	    (24) QDP
6.63/2.60	(25) PrologToDTProblemTransformerProof [SOUND, 48 ms]
6.63/2.60	(26) TRIPLES
6.63/2.60	    (27) TriplesToPiDPProof [SOUND, 0 ms]
6.63/2.60	    (28) PiDP
6.63/2.60	    (29) DependencyGraphProof [EQUIVALENT, 0 ms]
6.63/2.60	    (30) PiDP
6.63/2.60	    (31) PiDPToQDPProof [SOUND, 0 ms]
6.63/2.60	    (32) QDP
6.63/2.60	    (33) TransformationProof [EQUIVALENT, 0 ms]
6.63/2.60	    (34) QDP
6.63/2.60	(35) PrologToTRSTransformerProof [SOUND, 33 ms]
6.63/2.60	(36) QTRS
6.63/2.60	(37) PrologToIRSwTTransformerProof [SOUND, 100 ms]
6.63/2.60	(38) IRSwT
6.63/2.60	    (39) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms]
6.63/2.60	    (40) IRSwT
6.63/2.60	    (41) IntTRSCompressionProof [EQUIVALENT, 10 ms]
6.63/2.60	    (42) IRSwT
6.63/2.60	    (43) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
6.63/2.60	    (44) IRSwT
6.63/2.60	    (45) IRSwTTerminationDigraphProof [EQUIVALENT, 7 ms]
6.63/2.60	    (46) IRSwT
6.63/2.60	    (47) FilterProof [EQUIVALENT, 2 ms]
6.63/2.60	    (48) IntTRS
6.63/2.60	    (49) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
6.63/2.60	    (50) NO
6.63/2.60	
6.63/2.60	
6.63/2.60	----------------------------------------
6.63/2.60	
6.63/2.60	(0)
6.63/2.60	Obligation:
6.63/2.60	Clauses:
6.63/2.60	
6.63/2.60	reverse(X1s, X2s) :- reverse(X1s, [], X2s).
6.63/2.60	reverse([], Xs, Xs).
6.63/2.60	reverse(.(X, X1s), X2s, Ys) :- reverse(X1s, .(X, X2s), Ys).
6.63/2.60	
6.63/2.60	
6.63/2.60	Query: reverse(a,g)
6.63/2.60	----------------------------------------
6.63/2.60	
6.63/2.60	(1) PrologToPiTRSProof (SOUND)
6.63/2.60	We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
6.63/2.60	
6.63/2.60	reverse_in_2: (f,b)
6.63/2.60	
6.63/2.60	reverse_in_3: (f,b,b)
6.63/2.60	
6.63/2.60	Transforming Prolog into the following Term Rewriting System:
6.63/2.60	
6.63/2.60	Pi-finite rewrite system:
6.63/2.60	The TRS R consists of the following rules:
6.63/2.60	
6.63/2.60	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
6.63/2.60	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
6.63/2.60	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
6.63/2.60	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
6.63/2.60	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
6.63/2.60	
6.63/2.60	The argument filtering Pi contains the following mapping:
6.63/2.60	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
6.63/2.60	
6.63/2.60	U1_ag(x1, x2, x3)  =  U1_ag(x3)
6.63/2.60	
6.63/2.60	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
6.63/2.60	
6.63/2.60	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1)
6.63/2.60	
6.63/2.60	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x5)
6.63/2.60	
6.63/2.60	.(x1, x2)  =  .(x2)
6.63/2.60	
6.63/2.60	[]  =  []
6.63/2.60	
6.63/2.60	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1)
6.63/2.60	
6.63/2.60	
6.63/2.60	
6.63/2.60	
6.63/2.60	
6.63/2.60	Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
6.63/2.60	
6.63/2.60	
6.63/2.60	
6.63/2.60	----------------------------------------
6.63/2.60	
6.63/2.60	(2)
6.63/2.60	Obligation:
6.63/2.60	Pi-finite rewrite system:
6.63/2.60	The TRS R consists of the following rules:
6.63/2.60	
6.63/2.60	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
6.63/2.60	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
6.63/2.60	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
6.63/2.60	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
6.63/2.60	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
6.63/2.60	
6.63/2.60	The argument filtering Pi contains the following mapping:
6.63/2.60	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
6.63/2.60	
6.63/2.60	U1_ag(x1, x2, x3)  =  U1_ag(x3)
6.63/2.60	
6.63/2.60	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
6.63/2.60	
6.63/2.60	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1)
6.63/2.60	
6.63/2.60	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x5)
6.63/2.60	
6.63/2.60	.(x1, x2)  =  .(x2)
6.63/2.60	
6.63/2.60	[]  =  []
6.63/2.60	
6.63/2.60	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1)
6.63/2.60	
6.63/2.60	
6.63/2.60	
6.63/2.60	----------------------------------------
6.63/2.60	
6.63/2.60	(3) DependencyPairsProof (EQUIVALENT)
6.63/2.60	Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
6.63/2.60	Pi DP problem:
6.63/2.60	The TRS P consists of the following rules:
6.63/2.60	
6.63/2.60	   REVERSE_IN_AG(X1s, X2s) -> U1_AG(X1s, X2s, reverse_in_agg(X1s, [], X2s))
6.63/2.60	   REVERSE_IN_AG(X1s, X2s) -> REVERSE_IN_AGG(X1s, [], X2s)
6.63/2.60	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> U2_AGG(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
6.63/2.60	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> REVERSE_IN_AGG(X1s, .(X, X2s), Ys)
6.63/2.60	
6.63/2.60	The TRS R consists of the following rules:
6.63/2.60	
6.63/2.60	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
6.63/2.60	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
6.63/2.60	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
6.63/2.60	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
6.63/2.60	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
6.63/2.60	
6.63/2.60	The argument filtering Pi contains the following mapping:
6.63/2.60	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
6.63/2.60	
6.63/2.60	U1_ag(x1, x2, x3)  =  U1_ag(x3)
6.63/2.60	
6.63/2.60	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
6.63/2.60	
6.63/2.60	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1)
6.63/2.60	
6.63/2.60	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x5)
6.63/2.60	
6.63/2.60	.(x1, x2)  =  .(x2)
6.63/2.60	
6.63/2.60	[]  =  []
6.63/2.60	
6.63/2.60	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1)
6.63/2.60	
6.63/2.60	REVERSE_IN_AG(x1, x2)  =  REVERSE_IN_AG(x2)
6.63/2.60	
6.63/2.60	U1_AG(x1, x2, x3)  =  U1_AG(x3)
6.63/2.60	
6.63/2.60	REVERSE_IN_AGG(x1, x2, x3)  =  REVERSE_IN_AGG(x2, x3)
6.63/2.60	
6.63/2.60	U2_AGG(x1, x2, x3, x4, x5)  =  U2_AGG(x5)
6.63/2.60	
6.63/2.60	
6.63/2.60	We have to consider all (P,R,Pi)-chains
6.63/2.60	----------------------------------------
6.63/2.60	
6.63/2.60	(4)
6.63/2.60	Obligation:
6.63/2.60	Pi DP problem:
6.63/2.60	The TRS P consists of the following rules:
6.63/2.60	
6.63/2.60	   REVERSE_IN_AG(X1s, X2s) -> U1_AG(X1s, X2s, reverse_in_agg(X1s, [], X2s))
6.63/2.60	   REVERSE_IN_AG(X1s, X2s) -> REVERSE_IN_AGG(X1s, [], X2s)
6.63/2.60	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> U2_AGG(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
6.63/2.60	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> REVERSE_IN_AGG(X1s, .(X, X2s), Ys)
6.63/2.60	
6.63/2.60	The TRS R consists of the following rules:
6.63/2.60	
6.63/2.60	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
6.63/2.60	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
6.63/2.60	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
6.63/2.60	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
6.63/2.60	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
6.63/2.60	
6.63/2.60	The argument filtering Pi contains the following mapping:
6.63/2.60	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
6.63/2.60	
6.63/2.60	U1_ag(x1, x2, x3)  =  U1_ag(x3)
6.63/2.60	
6.63/2.60	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
6.63/2.60	
6.63/2.60	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1)
6.63/2.60	
6.63/2.60	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x5)
6.63/2.60	
6.63/2.60	.(x1, x2)  =  .(x2)
6.63/2.60	
6.63/2.60	[]  =  []
6.63/2.60	
6.63/2.60	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1)
6.63/2.60	
6.63/2.60	REVERSE_IN_AG(x1, x2)  =  REVERSE_IN_AG(x2)
6.63/2.60	
6.63/2.60	U1_AG(x1, x2, x3)  =  U1_AG(x3)
6.63/2.60	
6.63/2.60	REVERSE_IN_AGG(x1, x2, x3)  =  REVERSE_IN_AGG(x2, x3)
6.63/2.60	
6.63/2.60	U2_AGG(x1, x2, x3, x4, x5)  =  U2_AGG(x5)
6.63/2.60	
6.63/2.60	
6.63/2.60	We have to consider all (P,R,Pi)-chains
6.63/2.60	----------------------------------------
6.63/2.60	
6.63/2.60	(5) DependencyGraphProof (EQUIVALENT)
6.63/2.60	The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 3 less nodes.
6.63/2.60	----------------------------------------
6.63/2.60	
6.63/2.60	(6)
6.63/2.60	Obligation:
6.63/2.60	Pi DP problem:
6.63/2.60	The TRS P consists of the following rules:
6.63/2.60	
6.63/2.60	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> REVERSE_IN_AGG(X1s, .(X, X2s), Ys)
6.63/2.60	
6.63/2.60	The TRS R consists of the following rules:
6.63/2.60	
6.63/2.60	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
6.63/2.60	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
6.63/2.60	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
6.63/2.60	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
6.63/2.60	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
6.63/2.60	
6.63/2.60	The argument filtering Pi contains the following mapping:
6.63/2.60	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
6.63/2.60	
6.63/2.60	U1_ag(x1, x2, x3)  =  U1_ag(x3)
6.63/2.60	
6.63/2.60	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
7.03/2.63	
7.03/2.63	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1)
7.03/2.63	
7.03/2.63	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x5)
7.03/2.63	
7.03/2.63	.(x1, x2)  =  .(x2)
7.03/2.63	
7.03/2.63	[]  =  []
7.03/2.63	
7.03/2.63	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1)
7.03/2.63	
7.03/2.63	REVERSE_IN_AGG(x1, x2, x3)  =  REVERSE_IN_AGG(x2, x3)
7.03/2.63	
7.03/2.63	
7.03/2.63	We have to consider all (P,R,Pi)-chains
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(7) UsableRulesProof (EQUIVALENT)
7.03/2.63	For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(8)
7.03/2.63	Obligation:
7.03/2.63	Pi DP problem:
7.03/2.63	The TRS P consists of the following rules:
7.03/2.63	
7.03/2.63	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> REVERSE_IN_AGG(X1s, .(X, X2s), Ys)
7.03/2.63	
7.03/2.63	R is empty.
7.03/2.63	The argument filtering Pi contains the following mapping:
7.03/2.63	.(x1, x2)  =  .(x2)
7.03/2.63	
7.03/2.63	REVERSE_IN_AGG(x1, x2, x3)  =  REVERSE_IN_AGG(x2, x3)
7.03/2.63	
7.03/2.63	
7.03/2.63	We have to consider all (P,R,Pi)-chains
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(9) PiDPToQDPProof (SOUND)
7.03/2.63	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(10)
7.03/2.63	Obligation:
7.03/2.63	Q DP problem:
7.03/2.63	The TRS P consists of the following rules:
7.03/2.63	
7.03/2.63	   REVERSE_IN_AGG(X2s, Ys) -> REVERSE_IN_AGG(.(X2s), Ys)
7.03/2.63	
7.03/2.63	R is empty.
7.03/2.63	Q is empty.
7.03/2.63	We have to consider all (P,Q,R)-chains.
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(11) TransformationProof (EQUIVALENT)
7.03/2.63	By instantiating [LPAR04] the rule REVERSE_IN_AGG(X2s, Ys) -> REVERSE_IN_AGG(.(X2s), Ys) we obtained the following new rules [LPAR04]:
7.03/2.63	
7.03/2.63	   (REVERSE_IN_AGG(.(z0), z1) -> REVERSE_IN_AGG(.(.(z0)), z1),REVERSE_IN_AGG(.(z0), z1) -> REVERSE_IN_AGG(.(.(z0)), z1))
7.03/2.63	
7.03/2.63	
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(12)
7.03/2.63	Obligation:
7.03/2.63	Q DP problem:
7.03/2.63	The TRS P consists of the following rules:
7.03/2.63	
7.03/2.63	   REVERSE_IN_AGG(.(z0), z1) -> REVERSE_IN_AGG(.(.(z0)), z1)
7.03/2.63	
7.03/2.63	R is empty.
7.03/2.63	Q is empty.
7.03/2.63	We have to consider all (P,Q,R)-chains.
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(13) PrologToPiTRSProof (SOUND)
7.03/2.63	We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
7.03/2.63	
7.03/2.63	reverse_in_2: (f,b)
7.03/2.63	
7.03/2.63	reverse_in_3: (f,b,b)
7.03/2.63	
7.03/2.63	Transforming Prolog into the following Term Rewriting System:
7.03/2.63	
7.03/2.63	Pi-finite rewrite system:
7.03/2.63	The TRS R consists of the following rules:
7.03/2.63	
7.03/2.63	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
7.03/2.63	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
7.03/2.63	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
7.03/2.63	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
7.03/2.63	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
7.03/2.63	
7.03/2.63	The argument filtering Pi contains the following mapping:
7.03/2.63	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
7.03/2.63	
7.03/2.63	U1_ag(x1, x2, x3)  =  U1_ag(x2, x3)
7.03/2.63	
7.03/2.63	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
7.03/2.63	
7.03/2.63	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1, x2, x3)
7.03/2.63	
7.03/2.63	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x3, x4, x5)
7.03/2.63	
7.03/2.63	.(x1, x2)  =  .(x2)
7.03/2.63	
7.03/2.63	[]  =  []
7.03/2.63	
7.03/2.63	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1, x2)
7.03/2.63	
7.03/2.63	
7.03/2.63	
7.03/2.63	
7.03/2.63	
7.03/2.63	Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
7.03/2.63	
7.03/2.63	
7.03/2.63	
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(14)
7.03/2.63	Obligation:
7.03/2.63	Pi-finite rewrite system:
7.03/2.63	The TRS R consists of the following rules:
7.03/2.63	
7.03/2.63	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
7.03/2.63	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
7.03/2.63	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
7.03/2.63	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
7.03/2.63	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
7.03/2.63	
7.03/2.63	The argument filtering Pi contains the following mapping:
7.03/2.63	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
7.03/2.63	
7.03/2.63	U1_ag(x1, x2, x3)  =  U1_ag(x2, x3)
7.03/2.63	
7.03/2.63	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
7.03/2.63	
7.03/2.63	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1, x2, x3)
7.03/2.63	
7.03/2.63	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x3, x4, x5)
7.03/2.63	
7.03/2.63	.(x1, x2)  =  .(x2)
7.03/2.63	
7.03/2.63	[]  =  []
7.03/2.63	
7.03/2.63	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1, x2)
7.03/2.63	
7.03/2.63	
7.03/2.63	
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(15) DependencyPairsProof (EQUIVALENT)
7.03/2.63	Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
7.03/2.63	Pi DP problem:
7.03/2.63	The TRS P consists of the following rules:
7.03/2.63	
7.03/2.63	   REVERSE_IN_AG(X1s, X2s) -> U1_AG(X1s, X2s, reverse_in_agg(X1s, [], X2s))
7.03/2.63	   REVERSE_IN_AG(X1s, X2s) -> REVERSE_IN_AGG(X1s, [], X2s)
7.03/2.63	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> U2_AGG(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
7.03/2.63	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> REVERSE_IN_AGG(X1s, .(X, X2s), Ys)
7.03/2.63	
7.03/2.63	The TRS R consists of the following rules:
7.03/2.63	
7.03/2.63	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
7.03/2.63	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
7.03/2.63	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
7.03/2.63	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
7.03/2.63	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
7.03/2.63	
7.03/2.63	The argument filtering Pi contains the following mapping:
7.03/2.63	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
7.03/2.63	
7.03/2.63	U1_ag(x1, x2, x3)  =  U1_ag(x2, x3)
7.03/2.63	
7.03/2.63	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
7.03/2.63	
7.03/2.63	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1, x2, x3)
7.03/2.63	
7.03/2.63	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x3, x4, x5)
7.03/2.63	
7.03/2.63	.(x1, x2)  =  .(x2)
7.03/2.63	
7.03/2.63	[]  =  []
7.03/2.63	
7.03/2.63	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1, x2)
7.03/2.63	
7.03/2.63	REVERSE_IN_AG(x1, x2)  =  REVERSE_IN_AG(x2)
7.03/2.63	
7.03/2.63	U1_AG(x1, x2, x3)  =  U1_AG(x2, x3)
7.03/2.63	
7.03/2.63	REVERSE_IN_AGG(x1, x2, x3)  =  REVERSE_IN_AGG(x2, x3)
7.03/2.63	
7.03/2.63	U2_AGG(x1, x2, x3, x4, x5)  =  U2_AGG(x3, x4, x5)
7.03/2.63	
7.03/2.63	
7.03/2.63	We have to consider all (P,R,Pi)-chains
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(16)
7.03/2.63	Obligation:
7.03/2.63	Pi DP problem:
7.03/2.63	The TRS P consists of the following rules:
7.03/2.63	
7.03/2.63	   REVERSE_IN_AG(X1s, X2s) -> U1_AG(X1s, X2s, reverse_in_agg(X1s, [], X2s))
7.03/2.63	   REVERSE_IN_AG(X1s, X2s) -> REVERSE_IN_AGG(X1s, [], X2s)
7.03/2.63	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> U2_AGG(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
7.03/2.63	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> REVERSE_IN_AGG(X1s, .(X, X2s), Ys)
7.03/2.63	
7.03/2.63	The TRS R consists of the following rules:
7.03/2.63	
7.03/2.63	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
7.03/2.63	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
7.03/2.63	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
7.03/2.63	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
7.03/2.63	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
7.03/2.63	
7.03/2.63	The argument filtering Pi contains the following mapping:
7.03/2.63	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
7.03/2.63	
7.03/2.63	U1_ag(x1, x2, x3)  =  U1_ag(x2, x3)
7.03/2.63	
7.03/2.63	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
7.03/2.63	
7.03/2.63	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1, x2, x3)
7.03/2.63	
7.03/2.63	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x3, x4, x5)
7.03/2.63	
7.03/2.63	.(x1, x2)  =  .(x2)
7.03/2.63	
7.03/2.63	[]  =  []
7.03/2.63	
7.03/2.63	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1, x2)
7.03/2.63	
7.03/2.63	REVERSE_IN_AG(x1, x2)  =  REVERSE_IN_AG(x2)
7.03/2.63	
7.03/2.63	U1_AG(x1, x2, x3)  =  U1_AG(x2, x3)
7.03/2.63	
7.03/2.63	REVERSE_IN_AGG(x1, x2, x3)  =  REVERSE_IN_AGG(x2, x3)
7.03/2.63	
7.03/2.63	U2_AGG(x1, x2, x3, x4, x5)  =  U2_AGG(x3, x4, x5)
7.03/2.63	
7.03/2.63	
7.03/2.63	We have to consider all (P,R,Pi)-chains
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(17) DependencyGraphProof (EQUIVALENT)
7.03/2.63	The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 3 less nodes.
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(18)
7.03/2.63	Obligation:
7.03/2.63	Pi DP problem:
7.03/2.63	The TRS P consists of the following rules:
7.03/2.63	
7.03/2.63	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> REVERSE_IN_AGG(X1s, .(X, X2s), Ys)
7.03/2.63	
7.03/2.63	The TRS R consists of the following rules:
7.03/2.63	
7.03/2.63	   reverse_in_ag(X1s, X2s) -> U1_ag(X1s, X2s, reverse_in_agg(X1s, [], X2s))
7.03/2.63	   reverse_in_agg([], Xs, Xs) -> reverse_out_agg([], Xs, Xs)
7.03/2.63	   reverse_in_agg(.(X, X1s), X2s, Ys) -> U2_agg(X, X1s, X2s, Ys, reverse_in_agg(X1s, .(X, X2s), Ys))
7.03/2.63	   U2_agg(X, X1s, X2s, Ys, reverse_out_agg(X1s, .(X, X2s), Ys)) -> reverse_out_agg(.(X, X1s), X2s, Ys)
7.03/2.63	   U1_ag(X1s, X2s, reverse_out_agg(X1s, [], X2s)) -> reverse_out_ag(X1s, X2s)
7.03/2.63	
7.03/2.63	The argument filtering Pi contains the following mapping:
7.03/2.63	reverse_in_ag(x1, x2)  =  reverse_in_ag(x2)
7.03/2.63	
7.03/2.63	U1_ag(x1, x2, x3)  =  U1_ag(x2, x3)
7.03/2.63	
7.03/2.63	reverse_in_agg(x1, x2, x3)  =  reverse_in_agg(x2, x3)
7.03/2.63	
7.03/2.63	reverse_out_agg(x1, x2, x3)  =  reverse_out_agg(x1, x2, x3)
7.03/2.63	
7.03/2.63	U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x3, x4, x5)
7.03/2.63	
7.03/2.63	.(x1, x2)  =  .(x2)
7.03/2.63	
7.03/2.63	[]  =  []
7.03/2.63	
7.03/2.63	reverse_out_ag(x1, x2)  =  reverse_out_ag(x1, x2)
7.03/2.63	
7.03/2.63	REVERSE_IN_AGG(x1, x2, x3)  =  REVERSE_IN_AGG(x2, x3)
7.03/2.63	
7.03/2.63	
7.03/2.63	We have to consider all (P,R,Pi)-chains
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(19) UsableRulesProof (EQUIVALENT)
7.03/2.63	For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(20)
7.03/2.63	Obligation:
7.03/2.63	Pi DP problem:
7.03/2.63	The TRS P consists of the following rules:
7.03/2.63	
7.03/2.63	   REVERSE_IN_AGG(.(X, X1s), X2s, Ys) -> REVERSE_IN_AGG(X1s, .(X, X2s), Ys)
7.03/2.63	
7.03/2.63	R is empty.
7.03/2.63	The argument filtering Pi contains the following mapping:
7.03/2.63	.(x1, x2)  =  .(x2)
7.03/2.63	
7.03/2.63	REVERSE_IN_AGG(x1, x2, x3)  =  REVERSE_IN_AGG(x2, x3)
7.03/2.63	
7.03/2.63	
7.03/2.63	We have to consider all (P,R,Pi)-chains
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(21) PiDPToQDPProof (SOUND)
7.03/2.63	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(22)
7.03/2.63	Obligation:
7.03/2.63	Q DP problem:
7.03/2.63	The TRS P consists of the following rules:
7.03/2.63	
7.03/2.63	   REVERSE_IN_AGG(X2s, Ys) -> REVERSE_IN_AGG(.(X2s), Ys)
7.03/2.63	
7.03/2.63	R is empty.
7.03/2.63	Q is empty.
7.03/2.63	We have to consider all (P,Q,R)-chains.
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(23) TransformationProof (EQUIVALENT)
7.03/2.63	By instantiating [LPAR04] the rule REVERSE_IN_AGG(X2s, Ys) -> REVERSE_IN_AGG(.(X2s), Ys) we obtained the following new rules [LPAR04]:
7.03/2.63	
7.03/2.63	   (REVERSE_IN_AGG(.(z0), z1) -> REVERSE_IN_AGG(.(.(z0)), z1),REVERSE_IN_AGG(.(z0), z1) -> REVERSE_IN_AGG(.(.(z0)), z1))
7.03/2.63	
7.03/2.63	
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(24)
7.03/2.63	Obligation:
7.03/2.63	Q DP problem:
7.03/2.63	The TRS P consists of the following rules:
7.03/2.63	
7.03/2.63	   REVERSE_IN_AGG(.(z0), z1) -> REVERSE_IN_AGG(.(.(z0)), z1)
7.03/2.63	
7.03/2.63	R is empty.
7.03/2.63	Q is empty.
7.03/2.63	We have to consider all (P,Q,R)-chains.
7.03/2.63	----------------------------------------
7.03/2.63	
7.03/2.63	(25) PrologToDTProblemTransformerProof (SOUND)
7.03/2.63	Built DT problem from termination graph DT10.
7.03/2.63	
7.03/2.63	{
7.03/2.63	    "root": 1,
7.03/2.63	    "program": {
7.03/2.63	        "directives": [],
7.03/2.63	        "clauses": [
7.03/2.63	            [
7.03/2.63	                "(reverse X1s X2s)",
7.03/2.63	                "(reverse X1s ([]) X2s)"
7.03/2.63	            ],
7.03/2.63	            [
7.03/2.63	                "(reverse ([]) Xs Xs)",
7.03/2.63	                null
7.03/2.63	            ],
7.03/2.63	            [
7.03/2.63	                "(reverse (. X X1s) X2s Ys)",
7.03/2.63	                "(reverse X1s (. X X2s) Ys)"
7.03/2.63	            ]
7.03/2.63	        ]
7.03/2.63	    },
7.03/2.63	    "graph": {
7.03/2.63	        "nodes": {
7.03/2.63	            "type": "Nodes",
7.03/2.63	            "150": {
7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": 1,
7.03/2.63	                    "scope": 2,
7.03/2.63	                    "term": "(reverse T7 ([]) T6)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T6"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "151": {
7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": 2,
7.03/2.63	                    "scope": 2,
7.03/2.63	                    "term": "(reverse T7 ([]) T6)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T6"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "230": {
7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": -1,
7.03/2.63	                    "scope": -1,
7.03/2.63	                    "term": "(reverse T167 (. T168 (. T169 (. T170 (. T171 (. T172 ([])))))) T166)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T166"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "231": {
7.03/2.63	                "goal": [],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": [],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "155": {
7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": -1,
7.03/2.63	                    "scope": -1,
7.03/2.63	                    "term": "(true)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": [],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "156": {
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7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": 2,
7.03/2.63	                    "scope": 6,
7.03/2.63	                    "term": "(reverse T113 (. T114 (. T115 (. T116 (. T117 ([]))))) T112)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T112"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "265": {
7.03/2.63	                "goal": [
7.03/2.63	                    {
7.03/2.63	                        "clause": 1,
7.03/2.63	                        "scope": 8,
7.03/2.63	                        "term": "(reverse T232 (. T233 (. T234 (. T235 (. T236 (. T237 (. T238 ([]))))))) T231)"
7.03/2.63	                    },
7.03/2.63	                    {
7.03/2.63	                        "clause": 2,
7.03/2.63	                        "scope": 8,
7.03/2.63	                        "term": "(reverse T232 (. T233 (. T234 (. T235 (. T236 (. T237 (. T238 ([]))))))) T231)"
7.03/2.63	                    }
7.03/2.63	                ],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T231"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "222": {
7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": -1,
7.03/2.63	                    "scope": -1,
7.03/2.63	                    "term": "(true)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": [],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "266": {
7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": 1,
7.03/2.63	                    "scope": 8,
7.03/2.63	                    "term": "(reverse T232 (. T233 (. T234 (. T235 (. T236 (. T237 (. T238 ([]))))))) T231)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T231"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "267": {
7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": 2,
7.03/2.63	                    "scope": 8,
7.03/2.63	                    "term": "(reverse T232 (. T233 (. T234 (. T235 (. T236 (. T237 (. T238 ([]))))))) T231)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T231"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "224": {
7.03/2.63	                "goal": [],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": [],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "268": {
7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": -1,
7.03/2.63	                    "scope": -1,
7.03/2.63	                    "term": "(true)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": [],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "148": {
7.03/2.63	                "goal": [{
7.03/2.63	                    "clause": -1,
7.03/2.63	                    "scope": -1,
7.03/2.63	                    "term": "(reverse T7 ([]) T6)"
7.03/2.63	                }],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T6"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "149": {
7.03/2.63	                "goal": [
7.03/2.63	                    {
7.03/2.63	                        "clause": 1,
7.03/2.63	                        "scope": 2,
7.03/2.63	                        "term": "(reverse T7 ([]) T6)"
7.03/2.63	                    },
7.03/2.63	                    {
7.03/2.63	                        "clause": 2,
7.03/2.63	                        "scope": 2,
7.03/2.63	                        "term": "(reverse T7 ([]) T6)"
7.03/2.63	                    }
7.03/2.63	                ],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T6"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "226": {
7.03/2.63	                "goal": [],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": [],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            },
7.03/2.63	            "308": {
7.03/2.63	                "goal": [
7.03/2.63	                    {
7.03/2.63	                        "clause": 1,
7.03/2.63	                        "scope": 9,
7.03/2.63	                        "term": "(reverse T308 (. T309 (. T310 (. T311 (. T312 (. T313 (. T314 (. T315 ([])))))))) T307)"
7.03/2.63	                    },
7.03/2.63	                    {
7.03/2.63	                        "clause": 2,
7.03/2.63	                        "scope": 9,
7.03/2.63	                        "term": "(reverse T308 (. T309 (. T310 (. T311 (. T312 (. T313 (. T314 (. T315 ([])))))))) T307)"
7.03/2.63	                    }
7.03/2.63	                ],
7.03/2.63	                "kb": {
7.03/2.63	                    "nonunifying": [],
7.03/2.63	                    "intvars": {},
7.03/2.63	                    "arithmetic": {
7.03/2.63	                        "type": "PlainIntegerRelationState",
7.03/2.63	                        "relations": []
7.03/2.63	                    },
7.03/2.63	                    "ground": ["T307"],
7.03/2.63	                    "free": [],
7.03/2.63	                    "exprvars": []
7.03/2.63	                }
7.03/2.63	            }
7.03/2.63	        },
7.03/2.63	        "edges": [
7.03/2.63	            {
7.03/2.63	                "from": 1,
7.03/2.63	                "to": 4,
7.03/2.63	                "label": "CASE"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 4,
7.03/2.63	                "to": 148,
7.03/2.63	                "label": "ONLY EVAL with clause\nreverse(X3, X4) :- reverse(X3, [], X4).\nand substitutionT1 -> T7,\nX3 -> T7,\nT2 -> T6,\nX4 -> T6,\nT5 -> T7"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 148,
7.03/2.63	                "to": 149,
7.03/2.63	                "label": "CASE"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 149,
7.03/2.63	                "to": 150,
7.03/2.63	                "label": "PARALLEL"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 149,
7.03/2.63	                "to": 151,
7.03/2.63	                "label": "PARALLEL"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 150,
7.03/2.63	                "to": 155,
7.03/2.63	                "label": "EVAL with clause\nreverse([], X9, X9).\nand substitutionT7 -> [],\nX9 -> [],\nT6 -> []"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 150,
7.03/2.63	                "to": 156,
7.03/2.63	                "label": "EVAL-BACKTRACK"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 151,
7.03/2.63	                "to": 158,
7.03/2.63	                "label": "EVAL with clause\nreverse(.(X18, X19), X20, X21) :- reverse(X19, .(X18, X20), X21).\nand substitutionX18 -> T18,\nX19 -> T17,\nT7 -> .(T18, T17),\nX20 -> [],\nT6 -> T16,\nX21 -> T16,\nT15 -> T17,\nT14 -> T18"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 151,
7.03/2.63	                "to": 159,
7.03/2.63	                "label": "EVAL-BACKTRACK"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 155,
7.03/2.63	                "to": 157,
7.03/2.63	                "label": "SUCCESS"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 158,
7.03/2.63	                "to": 162,
7.03/2.63	                "label": "CASE"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 162,
7.03/2.63	                "to": 163,
7.03/2.63	                "label": "PARALLEL"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 162,
7.03/2.63	                "to": 164,
7.03/2.63	                "label": "PARALLEL"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 163,
7.03/2.63	                "to": 166,
7.03/2.63	                "label": "EVAL with clause\nreverse([], X28, X28).\nand substitutionT17 -> [],\nT18 -> T25,\nX28 -> .(T25, []),\nT16 -> .(T25, [])"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 163,
7.03/2.63	                "to": 167,
7.03/2.63	                "label": "EVAL-BACKTRACK"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 164,
7.03/2.63	                "to": 171,
7.03/2.63	                "label": "EVAL with clause\nreverse(.(X37, X38), X39, X40) :- reverse(X38, .(X37, X39), X40).\nand substitutionX37 -> T39,\nX38 -> T38,\nT17 -> .(T39, T38),\nT18 -> T40,\nX39 -> .(T40, []),\nT16 -> T37,\nX40 -> T37,\nT35 -> T38,\nT34 -> T39,\nT36 -> T40"
7.03/2.63	            },
7.03/2.63	            {
7.03/2.63	                "from": 164,
7.03/2.63	                "to": 172,
7.03/2.63	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 166,
7.03/2.64	                "to": 168,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 171,
7.03/2.64	                "to": 176,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 176,
7.03/2.64	                "to": 177,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 176,
7.03/2.64	                "to": 178,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 177,
7.03/2.64	                "to": 179,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X47, X47).\nand substitutionT38 -> [],\nT39 -> T53,\nT40 -> T54,\nX47 -> .(T53, .(T54, [])),\nT37 -> .(T53, .(T54, []))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 177,
7.03/2.64	                "to": 180,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 178,
7.03/2.64	                "to": 184,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X56, X57), X58, X59) :- reverse(X57, .(X56, X58), X59).\nand substitutionX56 -> T71,\nX57 -> T70,\nT38 -> .(T71, T70),\nT39 -> T72,\nT40 -> T73,\nX58 -> .(T72, .(T73, [])),\nT37 -> T69,\nX59 -> T69,\nT66 -> T70,\nT65 -> T71,\nT67 -> T72,\nT68 -> T73"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 178,
7.03/2.64	                "to": 185,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 179,
7.03/2.64	                "to": 181,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 184,
7.03/2.64	                "to": 187,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 187,
7.03/2.64	                "to": 206,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 187,
7.03/2.64	                "to": 207,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 206,
7.03/2.64	                "to": 208,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X66, X66).\nand substitutionT70 -> [],\nT71 -> T92,\nT72 -> T93,\nT73 -> T94,\nX66 -> .(T92, .(T93, .(T94, []))),\nT69 -> .(T92, .(T93, .(T94, [])))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 206,
7.03/2.64	                "to": 209,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 207,
7.03/2.64	                "to": 214,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X75, X76), X77, X78) :- reverse(X76, .(X75, X77), X78).\nand substitutionX75 -> T114,\nX76 -> T113,\nT70 -> .(T114, T113),\nT71 -> T115,\nT72 -> T116,\nT73 -> T117,\nX77 -> .(T115, .(T116, .(T117, []))),\nT69 -> T112,\nX78 -> T112,\nT108 -> T113,\nT107 -> T114,\nT109 -> T115,\nT110 -> T116,\nT111 -> T117"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 207,
7.03/2.64	                "to": 215,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 208,
7.03/2.64	                "to": 210,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 214,
7.03/2.64	                "to": 217,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 217,
7.03/2.64	                "to": 220,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 217,
7.03/2.64	                "to": 221,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 220,
7.03/2.64	                "to": 222,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X85, X85).\nand substitutionT113 -> [],\nT114 -> T142,\nT115 -> T143,\nT116 -> T144,\nT117 -> T145,\nX85 -> .(T142, .(T143, .(T144, .(T145, [])))),\nT112 -> .(T142, .(T143, .(T144, .(T145, []))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 220,
7.03/2.64	                "to": 224,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 221,
7.03/2.64	                "to": 230,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X94, X95), X96, X97) :- reverse(X95, .(X94, X96), X97).\nand substitutionX94 -> T168,\nX95 -> T167,\nT113 -> .(T168, T167),\nT114 -> T169,\nT115 -> T170,\nT116 -> T171,\nT117 -> T172,\nX96 -> .(T169, .(T170, .(T171, .(T172, [])))),\nT112 -> T166,\nX97 -> T166,\nT161 -> T167,\nT160 -> T168,\nT162 -> T169,\nT163 -> T170,\nT164 -> T171,\nT165 -> T172"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 221,
7.03/2.64	                "to": 231,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 222,
7.03/2.64	                "to": 226,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 230,
7.03/2.64	                "to": 235,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 235,
7.03/2.64	                "to": 236,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 235,
7.03/2.64	                "to": 237,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 236,
7.03/2.64	                "to": 246,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X104, X104).\nand substitutionT167 -> [],\nT168 -> T203,\nT169 -> T204,\nT170 -> T205,\nT171 -> T206,\nT172 -> T207,\nX104 -> .(T203, .(T204, .(T205, .(T206, .(T207, []))))),\nT166 -> .(T203, .(T204, .(T205, .(T206, .(T207, [])))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 236,
7.03/2.64	                "to": 247,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 237,
7.03/2.64	                "to": 251,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X113, X114), X115, X116) :- reverse(X114, .(X113, X115), X116).\nand substitutionX113 -> T233,\nX114 -> T232,\nT167 -> .(T233, T232),\nT168 -> T234,\nT169 -> T235,\nT170 -> T236,\nT171 -> T237,\nT172 -> T238,\nX115 -> .(T234, .(T235, .(T236, .(T237, .(T238, []))))),\nT166 -> T231,\nX116 -> T231,\nT225 -> T232,\nT224 -> T233,\nT226 -> T234,\nT227 -> T235,\nT228 -> T236,\nT229 -> T237,\nT230 -> T238"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 237,
7.03/2.64	                "to": 252,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 246,
7.03/2.64	                "to": 248,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 251,
7.03/2.64	                "to": 265,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 265,
7.03/2.64	                "to": 266,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 265,
7.03/2.64	                "to": 267,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 266,
7.03/2.64	                "to": 268,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X123, X123).\nand substitutionT232 -> [],\nT233 -> T275,\nT234 -> T276,\nT235 -> T277,\nT236 -> T278,\nT237 -> T279,\nT238 -> T280,\nX123 -> .(T275, .(T276, .(T277, .(T278, .(T279, .(T280, [])))))),\nT231 -> .(T275, .(T276, .(T277, .(T278, .(T279, .(T280, []))))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 266,
7.03/2.64	                "to": 281,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 267,
7.03/2.64	                "to": 285,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X132, X133), X134, X135) :- reverse(X133, .(X132, X134), X135).\nand substitutionX132 -> T309,\nX133 -> T308,\nT232 -> .(T309, T308),\nT233 -> T310,\nT234 -> T311,\nT235 -> T312,\nT236 -> T313,\nT237 -> T314,\nT238 -> T315,\nX134 -> .(T310, .(T311, .(T312, .(T313, .(T314, .(T315, [])))))),\nT231 -> T307,\nX135 -> T307,\nT300 -> T308,\nT299 -> T309,\nT301 -> T310,\nT302 -> T311,\nT303 -> T312,\nT304 -> T313,\nT305 -> T314,\nT306 -> T315"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 267,
7.03/2.64	                "to": 286,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 268,
7.03/2.64	                "to": 282,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 285,
7.03/2.64	                "to": 308,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 308,
7.03/2.64	                "to": 311,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 308,
7.03/2.64	                "to": 312,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 311,
7.03/2.64	                "to": 317,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X142, X142).\nand substitutionT308 -> [],\nT309 -> T358,\nT310 -> T359,\nT311 -> T360,\nT312 -> T361,\nT313 -> T362,\nT314 -> T363,\nT315 -> T364,\nX142 -> .(T358, .(T359, .(T360, .(T361, .(T362, .(T363, .(T364, []))))))),\nT307 -> .(T358, .(T359, .(T360, .(T361, .(T362, .(T363, .(T364, [])))))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 311,
7.03/2.64	                "to": 318,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 312,
7.03/2.64	                "to": 322,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X151, X152), X153, X154) :- reverse(X152, .(X151, X153), X154).\nand substitutionX151 -> T396,\nX152 -> T395,\nT308 -> .(T396, T395),\nT309 -> T397,\nT310 -> T398,\nT311 -> T399,\nT312 -> T400,\nT313 -> T401,\nT314 -> T402,\nT315 -> T403,\nX153 -> .(T397, .(T398, .(T399, .(T400, .(T401, .(T402, .(T403, []))))))),\nT307 -> T394,\nX154 -> T394,\nT386 -> T395,\nT385 -> T396,\nT387 -> T397,\nT388 -> T398,\nT389 -> T399,\nT390 -> T400,\nT391 -> T401,\nT392 -> T402,\nT393 -> T403"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 312,
7.03/2.64	                "to": 323,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 317,
7.03/2.64	                "to": 319,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 322,
7.03/2.64	                "to": 327,
7.03/2.64	                "label": "GENERALIZATION\nT420 <-- .(T397, .(T398, .(T399, .(T400, .(T401, .(T402, .(T403, [])))))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 327,
7.03/2.64	                "to": 328,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 328,
7.03/2.64	                "to": 329,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 328,
7.03/2.64	                "to": 330,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 329,
7.03/2.64	                "to": 331,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X163, X163).\nand substitutionT395 -> [],\nT396 -> T433,\nT420 -> T434,\nX163 -> .(T433, T434),\nT394 -> .(T433, T434)"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 329,
7.03/2.64	                "to": 332,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 330,
7.03/2.64	                "to": 336,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X172, X173), X174, X175) :- reverse(X173, .(X172, X174), X175).\nand substitutionX172 -> T451,\nX173 -> T450,\nT395 -> .(T451, T450),\nT396 -> T452,\nT420 -> T453,\nX174 -> .(T452, T453),\nT394 -> T449,\nX175 -> T449,\nT446 -> T450,\nT445 -> T451,\nT447 -> T452,\nT448 -> T453"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 330,
7.03/2.64	                "to": 337,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 331,
7.03/2.64	                "to": 333,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 336,
7.03/2.64	                "to": 327,
7.03/2.64	                "label": "INSTANCE with matching:\nT395 -> T450\nT396 -> T451\nT420 -> .(T452, T453)\nT394 -> T449"
7.03/2.64	            }
7.03/2.64	        ],
7.03/2.64	        "type": "Graph"
7.03/2.64	    }
7.03/2.64	}
7.03/2.64	
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(26)
7.03/2.64	Obligation:
7.03/2.64	Triples:
7.03/2.64	
7.03/2.64	reverseA(.(X1, X2), X3, X4, X5) :- reverseA(X2, X1, .(X3, X4), X5).
7.03/2.64	reverseB(.(X1, .(X2, .(X3, .(X4, .(X5, .(X6, .(X7, .(X8, X9)))))))), X10) :- reverseA(X9, X8, .(X7, .(X6, .(X5, .(X4, .(X3, .(X2, .(X1, []))))))), X10).
7.03/2.64	
7.03/2.64	Clauses:
7.03/2.64	
7.03/2.64	reversecA([], X1, X2, .(X1, X2)).
7.03/2.64	reversecA(.(X1, X2), X3, X4, X5) :- reversecA(X2, X1, .(X3, X4), X5).
7.03/2.64	
7.03/2.64	Afs:
7.03/2.64	
7.03/2.64	reverseB(x1, x2)  =  reverseB(x2)
7.03/2.64	
7.03/2.64	
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(27) TriplesToPiDPProof (SOUND)
7.03/2.64	We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes:
7.03/2.64	
7.03/2.64	reverseB_in_2: (f,b)
7.03/2.64	
7.03/2.64	reverseA_in_4: (f,f,b,b)
7.03/2.64	
7.03/2.64	Transforming TRIPLES into the following Term Rewriting System:
7.03/2.64	
7.03/2.64	Pi DP problem:
7.03/2.64	The TRS P consists of the following rules:
7.03/2.64	
7.03/2.64	   REVERSEB_IN_AG(.(X1, .(X2, .(X3, .(X4, .(X5, .(X6, .(X7, .(X8, X9)))))))), X10) -> U2_AG(X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, reverseA_in_aagg(X9, X8, .(X7, .(X6, .(X5, .(X4, .(X3, .(X2, .(X1, []))))))), X10))
7.03/2.64	   REVERSEB_IN_AG(.(X1, .(X2, .(X3, .(X4, .(X5, .(X6, .(X7, .(X8, X9)))))))), X10) -> REVERSEA_IN_AAGG(X9, X8, .(X7, .(X6, .(X5, .(X4, .(X3, .(X2, .(X1, []))))))), X10)
7.03/2.64	   REVERSEA_IN_AAGG(.(X1, X2), X3, X4, X5) -> U1_AAGG(X1, X2, X3, X4, X5, reverseA_in_aagg(X2, X1, .(X3, X4), X5))
7.03/2.64	   REVERSEA_IN_AAGG(.(X1, X2), X3, X4, X5) -> REVERSEA_IN_AAGG(X2, X1, .(X3, X4), X5)
7.03/2.64	
7.03/2.64	R is empty.
7.03/2.64	The argument filtering Pi contains the following mapping:
7.03/2.64	reverseA_in_aagg(x1, x2, x3, x4)  =  reverseA_in_aagg(x3, x4)
7.03/2.64	
7.03/2.64	.(x1, x2)  =  .(x2)
7.03/2.64	
7.03/2.64	[]  =  []
7.03/2.64	
7.03/2.64	REVERSEB_IN_AG(x1, x2)  =  REVERSEB_IN_AG(x2)
7.03/2.64	
7.03/2.64	U2_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)  =  U2_AG(x10, x11)
7.03/2.64	
7.03/2.64	REVERSEA_IN_AAGG(x1, x2, x3, x4)  =  REVERSEA_IN_AAGG(x3, x4)
7.03/2.64	
7.03/2.64	U1_AAGG(x1, x2, x3, x4, x5, x6)  =  U1_AAGG(x4, x5, x6)
7.03/2.64	
7.03/2.64	
7.03/2.64	We have to consider all (P,R,Pi)-chains
7.03/2.64	
7.03/2.64	
7.03/2.64	Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES
7.03/2.64	
7.03/2.64	
7.03/2.64	
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(28)
7.03/2.64	Obligation:
7.03/2.64	Pi DP problem:
7.03/2.64	The TRS P consists of the following rules:
7.03/2.64	
7.03/2.64	   REVERSEB_IN_AG(.(X1, .(X2, .(X3, .(X4, .(X5, .(X6, .(X7, .(X8, X9)))))))), X10) -> U2_AG(X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, reverseA_in_aagg(X9, X8, .(X7, .(X6, .(X5, .(X4, .(X3, .(X2, .(X1, []))))))), X10))
7.03/2.64	   REVERSEB_IN_AG(.(X1, .(X2, .(X3, .(X4, .(X5, .(X6, .(X7, .(X8, X9)))))))), X10) -> REVERSEA_IN_AAGG(X9, X8, .(X7, .(X6, .(X5, .(X4, .(X3, .(X2, .(X1, []))))))), X10)
7.03/2.64	   REVERSEA_IN_AAGG(.(X1, X2), X3, X4, X5) -> U1_AAGG(X1, X2, X3, X4, X5, reverseA_in_aagg(X2, X1, .(X3, X4), X5))
7.03/2.64	   REVERSEA_IN_AAGG(.(X1, X2), X3, X4, X5) -> REVERSEA_IN_AAGG(X2, X1, .(X3, X4), X5)
7.03/2.64	
7.03/2.64	R is empty.
7.03/2.64	The argument filtering Pi contains the following mapping:
7.03/2.64	reverseA_in_aagg(x1, x2, x3, x4)  =  reverseA_in_aagg(x3, x4)
7.03/2.64	
7.03/2.64	.(x1, x2)  =  .(x2)
7.03/2.64	
7.03/2.64	[]  =  []
7.03/2.64	
7.03/2.64	REVERSEB_IN_AG(x1, x2)  =  REVERSEB_IN_AG(x2)
7.03/2.64	
7.03/2.64	U2_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)  =  U2_AG(x10, x11)
7.03/2.64	
7.03/2.64	REVERSEA_IN_AAGG(x1, x2, x3, x4)  =  REVERSEA_IN_AAGG(x3, x4)
7.03/2.64	
7.03/2.64	U1_AAGG(x1, x2, x3, x4, x5, x6)  =  U1_AAGG(x4, x5, x6)
7.03/2.64	
7.03/2.64	
7.03/2.64	We have to consider all (P,R,Pi)-chains
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(29) DependencyGraphProof (EQUIVALENT)
7.03/2.64	The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 3 less nodes.
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(30)
7.03/2.64	Obligation:
7.03/2.64	Pi DP problem:
7.03/2.64	The TRS P consists of the following rules:
7.03/2.64	
7.03/2.64	   REVERSEA_IN_AAGG(.(X1, X2), X3, X4, X5) -> REVERSEA_IN_AAGG(X2, X1, .(X3, X4), X5)
7.03/2.64	
7.03/2.64	R is empty.
7.03/2.64	The argument filtering Pi contains the following mapping:
7.03/2.64	.(x1, x2)  =  .(x2)
7.03/2.64	
7.03/2.64	REVERSEA_IN_AAGG(x1, x2, x3, x4)  =  REVERSEA_IN_AAGG(x3, x4)
7.03/2.64	
7.03/2.64	
7.03/2.64	We have to consider all (P,R,Pi)-chains
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(31) PiDPToQDPProof (SOUND)
7.03/2.64	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(32)
7.03/2.64	Obligation:
7.03/2.64	Q DP problem:
7.03/2.64	The TRS P consists of the following rules:
7.03/2.64	
7.03/2.64	   REVERSEA_IN_AAGG(X4, X5) -> REVERSEA_IN_AAGG(.(X4), X5)
7.03/2.64	
7.03/2.64	R is empty.
7.03/2.64	Q is empty.
7.03/2.64	We have to consider all (P,Q,R)-chains.
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(33) TransformationProof (EQUIVALENT)
7.03/2.64	By instantiating [LPAR04] the rule REVERSEA_IN_AAGG(X4, X5) -> REVERSEA_IN_AAGG(.(X4), X5) we obtained the following new rules [LPAR04]:
7.03/2.64	
7.03/2.64	   (REVERSEA_IN_AAGG(.(z0), z1) -> REVERSEA_IN_AAGG(.(.(z0)), z1),REVERSEA_IN_AAGG(.(z0), z1) -> REVERSEA_IN_AAGG(.(.(z0)), z1))
7.03/2.64	
7.03/2.64	
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(34)
7.03/2.64	Obligation:
7.03/2.64	Q DP problem:
7.03/2.64	The TRS P consists of the following rules:
7.03/2.64	
7.03/2.64	   REVERSEA_IN_AAGG(.(z0), z1) -> REVERSEA_IN_AAGG(.(.(z0)), z1)
7.03/2.64	
7.03/2.64	R is empty.
7.03/2.64	Q is empty.
7.03/2.64	We have to consider all (P,Q,R)-chains.
7.03/2.64	----------------------------------------
7.03/2.64	
7.03/2.64	(35) PrologToTRSTransformerProof (SOUND)
7.03/2.64	Transformed Prolog program to TRS.
7.03/2.64	
7.03/2.64	{
7.03/2.64	    "root": 2,
7.03/2.64	    "program": {
7.03/2.64	        "directives": [],
7.03/2.64	        "clauses": [
7.03/2.64	            [
7.03/2.64	                "(reverse X1s X2s)",
7.03/2.64	                "(reverse X1s ([]) X2s)"
7.03/2.64	            ],
7.03/2.64	            [
7.03/2.64	                "(reverse ([]) Xs Xs)",
7.03/2.64	                null
7.03/2.64	            ],
7.03/2.64	            [
7.03/2.64	                "(reverse (. X X1s) X2s Ys)",
7.03/2.64	                "(reverse X1s (. X X2s) Ys)"
7.03/2.64	            ]
7.03/2.64	        ]
7.03/2.64	    },
7.03/2.64	    "graph": {
7.03/2.64	        "nodes": {
7.03/2.64	            "190": {
7.03/2.64	                "goal": [],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": [],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "191": {
7.03/2.64	                "goal": [],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": [],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "192": {
7.03/2.64	                "goal": [{
7.03/2.64	                    "clause": -1,
7.03/2.64	                    "scope": -1,
7.03/2.64	                    "term": "(reverse T73 (. T74 (. T75 (. T76 ([])))) T72)"
7.03/2.64	                }],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
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7.03/2.64	                    },
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7.03/2.64	                    "clause": 1,
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7.03/2.64	                }],
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7.03/2.64	                    },
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7.03/2.64	            },
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7.03/2.64	                    "clause": 2,
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7.03/2.64	                }],
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7.03/2.64	                    },
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7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "262": {
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7.03/2.64	                    "clause": -1,
7.03/2.64	                    "scope": -1,
7.03/2.64	                    "term": "(true)"
7.03/2.64	                }],
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7.03/2.64	            },
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7.03/2.64	                    },
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7.03/2.64	            },
7.03/2.64	            "264": {
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7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": [],
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7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "189": {
7.03/2.64	                "goal": [{
7.03/2.64	                    "clause": -1,
7.03/2.64	                    "scope": -1,
7.03/2.64	                    "term": "(true)"
7.03/2.64	                }],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": [],
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7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "223": {
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7.03/2.64	                    "clause": -1,
7.03/2.64	                    "scope": -1,
7.03/2.64	                    "term": "(reverse T116 (. T117 (. T118 (. T119 (. T120 ([]))))) T115)"
7.03/2.64	                }],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": ["T115"],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "300": {
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7.03/2.64	                    "nonunifying": [],
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7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": [],
7.03/2.64	                    "free": [],
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7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "301": {
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7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": [],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "225": {
7.03/2.64	                "goal": [],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": [],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "227": {
7.03/2.64	                "goal": [
7.03/2.64	                    {
7.03/2.64	                        "clause": 1,
7.03/2.64	                        "scope": 6,
7.03/2.64	                        "term": "(reverse T116 (. T117 (. T118 (. T119 (. T120 ([]))))) T115)"
7.03/2.64	                    },
7.03/2.64	                    {
7.03/2.64	                        "clause": 2,
7.03/2.64	                        "scope": 6,
7.03/2.64	                        "term": "(reverse T116 (. T117 (. T118 (. T119 (. T120 ([]))))) T115)"
7.03/2.64	                    }
7.03/2.64	                ],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": ["T115"],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "80": {
7.03/2.64	                "goal": [],
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7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": [],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "228": {
7.03/2.64	                "goal": [{
7.03/2.64	                    "clause": 1,
7.03/2.64	                    "scope": 6,
7.03/2.64	                    "term": "(reverse T116 (. T117 (. T118 (. T119 (. T120 ([]))))) T115)"
7.03/2.64	                }],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": ["T115"],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "229": {
7.03/2.64	                "goal": [{
7.03/2.64	                    "clause": 2,
7.03/2.64	                    "scope": 6,
7.03/2.64	                    "term": "(reverse T116 (. T117 (. T118 (. T119 (. T120 ([]))))) T115)"
7.03/2.64	                }],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": ["T115"],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            },
7.03/2.64	            "309": {
7.03/2.64	                "goal": [{
7.03/2.64	                    "clause": -1,
7.03/2.64	                    "scope": -1,
7.03/2.64	                    "term": "(reverse T398 (. T399 (. T400 (. T401 (. T402 (. T403 (. T404 (. T405 (. T406 ([]))))))))) T397)"
7.03/2.64	                }],
7.03/2.64	                "kb": {
7.03/2.64	                    "nonunifying": [],
7.03/2.64	                    "intvars": {},
7.03/2.64	                    "arithmetic": {
7.03/2.64	                        "type": "PlainIntegerRelationState",
7.03/2.64	                        "relations": []
7.03/2.64	                    },
7.03/2.64	                    "ground": ["T397"],
7.03/2.64	                    "free": [],
7.03/2.64	                    "exprvars": []
7.03/2.64	                }
7.03/2.64	            }
7.03/2.64	        },
7.03/2.64	        "edges": [
7.03/2.64	            {
7.03/2.64	                "from": 2,
7.03/2.64	                "to": 18,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 18,
7.03/2.64	                "to": 19,
7.03/2.64	                "label": "ONLY EVAL with clause\nreverse(X7, X8) :- reverse(X7, [], X8).\nand substitutionT1 -> T10,\nX7 -> T10,\nT2 -> T9,\nX8 -> T9,\nT8 -> T10"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 19,
7.03/2.64	                "to": 57,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 57,
7.03/2.64	                "to": 58,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 57,
7.03/2.64	                "to": 59,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 58,
7.03/2.64	                "to": 62,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X15, X15).\nand substitutionT10 -> [],\nX15 -> [],\nT9 -> []"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 58,
7.03/2.64	                "to": 64,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 59,
7.03/2.64	                "to": 73,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X24, X25), X26, X27) :- reverse(X25, .(X24, X26), X27).\nand substitutionX24 -> T21,\nX25 -> T20,\nT10 -> .(T21, T20),\nX26 -> [],\nT9 -> T19,\nX27 -> T19,\nT18 -> T20,\nT17 -> T21"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 59,
7.03/2.64	                "to": 74,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 62,
7.03/2.64	                "to": 65,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 73,
7.03/2.64	                "to": 75,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 75,
7.03/2.64	                "to": 76,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 75,
7.03/2.64	                "to": 77,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 76,
7.03/2.64	                "to": 78,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X34, X34).\nand substitutionT20 -> [],\nT21 -> T28,\nX34 -> .(T28, []),\nT19 -> .(T28, [])"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 76,
7.03/2.64	                "to": 79,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 77,
7.03/2.64	                "to": 93,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X43, X44), X45, X46) :- reverse(X44, .(X43, X45), X46).\nand substitutionX43 -> T42,\nX44 -> T41,\nT20 -> .(T42, T41),\nT21 -> T43,\nX45 -> .(T43, []),\nT19 -> T40,\nX46 -> T40,\nT38 -> T41,\nT37 -> T42,\nT39 -> T43"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 77,
7.03/2.64	                "to": 94,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 78,
7.03/2.64	                "to": 80,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 93,
7.03/2.64	                "to": 95,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 95,
7.03/2.64	                "to": 96,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 95,
7.03/2.64	                "to": 97,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 96,
7.03/2.64	                "to": 189,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X53, X53).\nand substitutionT41 -> [],\nT42 -> T56,\nT43 -> T57,\nX53 -> .(T56, .(T57, [])),\nT40 -> .(T56, .(T57, []))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 96,
7.03/2.64	                "to": 190,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 97,
7.03/2.64	                "to": 192,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X62, X63), X64, X65) :- reverse(X63, .(X62, X64), X65).\nand substitutionX62 -> T74,\nX63 -> T73,\nT41 -> .(T74, T73),\nT42 -> T75,\nT43 -> T76,\nX64 -> .(T75, .(T76, [])),\nT40 -> T72,\nX65 -> T72,\nT69 -> T73,\nT68 -> T74,\nT70 -> T75,\nT71 -> T76"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 97,
7.03/2.64	                "to": 193,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 189,
7.03/2.64	                "to": 191,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 192,
7.03/2.64	                "to": 194,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 194,
7.03/2.64	                "to": 195,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 194,
7.03/2.64	                "to": 196,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 195,
7.03/2.64	                "to": 197,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X72, X72).\nand substitutionT73 -> [],\nT74 -> T95,\nT75 -> T96,\nT76 -> T97,\nX72 -> .(T95, .(T96, .(T97, []))),\nT72 -> .(T95, .(T96, .(T97, [])))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 195,
7.03/2.64	                "to": 198,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 196,
7.03/2.64	                "to": 223,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X81, X82), X83, X84) :- reverse(X82, .(X81, X83), X84).\nand substitutionX81 -> T117,\nX82 -> T116,\nT73 -> .(T117, T116),\nT74 -> T118,\nT75 -> T119,\nT76 -> T120,\nX83 -> .(T118, .(T119, .(T120, []))),\nT72 -> T115,\nX84 -> T115,\nT111 -> T116,\nT110 -> T117,\nT112 -> T118,\nT113 -> T119,\nT114 -> T120"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 196,
7.03/2.64	                "to": 225,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 197,
7.03/2.64	                "to": 199,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 223,
7.03/2.64	                "to": 227,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 227,
7.03/2.64	                "to": 228,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 227,
7.03/2.64	                "to": 229,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 228,
7.03/2.64	                "to": 232,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X91, X91).\nand substitutionT116 -> [],\nT117 -> T145,\nT118 -> T146,\nT119 -> T147,\nT120 -> T148,\nX91 -> .(T145, .(T146, .(T147, .(T148, [])))),\nT115 -> .(T145, .(T146, .(T147, .(T148, []))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 228,
7.03/2.64	                "to": 233,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 229,
7.03/2.64	                "to": 238,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X100, X101), X102, X103) :- reverse(X101, .(X100, X102), X103).\nand substitutionX100 -> T171,\nX101 -> T170,\nT116 -> .(T171, T170),\nT117 -> T172,\nT118 -> T173,\nT119 -> T174,\nT120 -> T175,\nX102 -> .(T172, .(T173, .(T174, .(T175, [])))),\nT115 -> T169,\nX103 -> T169,\nT164 -> T170,\nT163 -> T171,\nT165 -> T172,\nT166 -> T173,\nT167 -> T174,\nT168 -> T175"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 229,
7.03/2.64	                "to": 239,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 232,
7.03/2.64	                "to": 234,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 238,
7.03/2.64	                "to": 240,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 240,
7.03/2.64	                "to": 241,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 240,
7.03/2.64	                "to": 242,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 241,
7.03/2.64	                "to": 243,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X110, X110).\nand substitutionT170 -> [],\nT171 -> T206,\nT172 -> T207,\nT173 -> T208,\nT174 -> T209,\nT175 -> T210,\nX110 -> .(T206, .(T207, .(T208, .(T209, .(T210, []))))),\nT169 -> .(T206, .(T207, .(T208, .(T209, .(T210, [])))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 241,
7.03/2.64	                "to": 244,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 242,
7.03/2.64	                "to": 253,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X119, X120), X121, X122) :- reverse(X120, .(X119, X121), X122).\nand substitutionX119 -> T236,\nX120 -> T235,\nT170 -> .(T236, T235),\nT171 -> T237,\nT172 -> T238,\nT173 -> T239,\nT174 -> T240,\nT175 -> T241,\nX121 -> .(T237, .(T238, .(T239, .(T240, .(T241, []))))),\nT169 -> T234,\nX122 -> T234,\nT228 -> T235,\nT227 -> T236,\nT229 -> T237,\nT230 -> T238,\nT231 -> T239,\nT232 -> T240,\nT233 -> T241"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 242,
7.03/2.64	                "to": 254,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 243,
7.03/2.64	                "to": 245,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 253,
7.03/2.64	                "to": 259,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 259,
7.03/2.64	                "to": 260,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 259,
7.03/2.64	                "to": 261,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 260,
7.03/2.64	                "to": 262,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X129, X129).\nand substitutionT235 -> [],\nT236 -> T278,\nT237 -> T279,\nT238 -> T280,\nT239 -> T281,\nT240 -> T282,\nT241 -> T283,\nX129 -> .(T278, .(T279, .(T280, .(T281, .(T282, .(T283, [])))))),\nT234 -> .(T278, .(T279, .(T280, .(T281, .(T282, .(T283, []))))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 260,
7.03/2.64	                "to": 263,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 261,
7.03/2.64	                "to": 279,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X138, X139), X140, X141) :- reverse(X139, .(X138, X140), X141).\nand substitutionX138 -> T312,\nX139 -> T311,\nT235 -> .(T312, T311),\nT236 -> T313,\nT237 -> T314,\nT238 -> T315,\nT239 -> T316,\nT240 -> T317,\nT241 -> T318,\nX140 -> .(T313, .(T314, .(T315, .(T316, .(T317, .(T318, [])))))),\nT234 -> T310,\nX141 -> T310,\nT303 -> T311,\nT302 -> T312,\nT304 -> T313,\nT305 -> T314,\nT306 -> T315,\nT307 -> T316,\nT308 -> T317,\nT309 -> T318"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 261,
7.03/2.64	                "to": 280,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 262,
7.03/2.64	                "to": 264,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 279,
7.03/2.64	                "to": 295,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 295,
7.03/2.64	                "to": 296,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 295,
7.03/2.64	                "to": 297,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 296,
7.03/2.64	                "to": 299,
7.03/2.64	                "label": "EVAL with clause\nreverse([], X148, X148).\nand substitutionT311 -> [],\nT312 -> T361,\nT313 -> T362,\nT314 -> T363,\nT315 -> T364,\nT316 -> T365,\nT317 -> T366,\nT318 -> T367,\nX148 -> .(T361, .(T362, .(T363, .(T364, .(T365, .(T366, .(T367, []))))))),\nT310 -> .(T361, .(T362, .(T363, .(T364, .(T365, .(T366, .(T367, [])))))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 296,
7.03/2.64	                "to": 300,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 297,
7.03/2.64	                "to": 309,
7.03/2.64	                "label": "EVAL with clause\nreverse(.(X157, X158), X159, X160) :- reverse(X158, .(X157, X159), X160).\nand substitutionX157 -> T399,\nX158 -> T398,\nT311 -> .(T399, T398),\nT312 -> T400,\nT313 -> T401,\nT314 -> T402,\nT315 -> T403,\nT316 -> T404,\nT317 -> T405,\nT318 -> T406,\nX159 -> .(T400, .(T401, .(T402, .(T403, .(T404, .(T405, .(T406, []))))))),\nT310 -> T397,\nX160 -> T397,\nT389 -> T398,\nT388 -> T399,\nT390 -> T400,\nT391 -> T401,\nT392 -> T402,\nT393 -> T403,\nT394 -> T404,\nT395 -> T405,\nT396 -> T406"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 297,
7.03/2.64	                "to": 310,
7.03/2.64	                "label": "EVAL-BACKTRACK"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 299,
7.03/2.64	                "to": 301,
7.03/2.64	                "label": "SUCCESS"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 309,
7.03/2.64	                "to": 313,
7.03/2.64	                "label": "GENERALIZATION\nT423 <-- .(T400, .(T401, .(T402, .(T403, .(T404, .(T405, .(T406, [])))))))"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 313,
7.03/2.64	                "to": 316,
7.03/2.64	                "label": "CASE"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 316,
7.03/2.64	                "to": 320,
7.03/2.64	                "label": "PARALLEL"
7.03/2.64	            },
7.03/2.64	            {
7.03/2.64	                "from": 316,
7.03/2.64	                "to": 321,
7.03/2.64	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 320,
7.03/2.65	                "to": 324,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X169, X169).\nand substitutionT398 -> [],\nT399 -> T436,\nT423 -> T437,\nX169 -> .(T436, T437),\nT397 -> .(T436, T437)"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 320,
7.03/2.65	                "to": 325,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 321,
7.03/2.65	                "to": 334,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X178, X179), X180, X181) :- reverse(X179, .(X178, X180), X181).\nand substitutionX178 -> T454,\nX179 -> T453,\nT398 -> .(T454, T453),\nT399 -> T455,\nT423 -> T456,\nX180 -> .(T455, T456),\nT397 -> T452,\nX181 -> T452,\nT449 -> T453,\nT448 -> T454,\nT450 -> T455,\nT451 -> T456"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 321,
7.03/2.65	                "to": 335,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 324,
7.03/2.65	                "to": 326,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 334,
7.03/2.65	                "to": 313,
7.03/2.65	                "label": "INSTANCE with matching:\nT398 -> T453\nT399 -> T454\nT423 -> .(T455, T456)\nT397 -> T452"
7.03/2.65	            }
7.03/2.65	        ],
7.03/2.65	        "type": "Graph"
7.03/2.65	    }
7.03/2.65	}
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(36)
7.03/2.65	Obligation:
7.03/2.65	Q restricted rewrite system:
7.03/2.65	The TRS R consists of the following rules:
7.03/2.65	
7.03/2.65	   f2_in([]) -> f2_out1([])
7.03/2.65	   f2_in(.(T28, [])) -> f2_out1(.(T28, []))
7.03/2.65	   f2_in(.(T56, .(T57, []))) -> f2_out1(.(T57, .(T56, [])))
7.03/2.65	   f2_in(.(T95, .(T96, .(T97, [])))) -> f2_out1(.(T97, .(T96, .(T95, []))))
7.03/2.65	   f2_in(.(T145, .(T146, .(T147, .(T148, []))))) -> f2_out1(.(T148, .(T147, .(T146, .(T145, [])))))
7.03/2.65	   f2_in(.(T206, .(T207, .(T208, .(T209, .(T210, [])))))) -> f2_out1(.(T210, .(T209, .(T208, .(T207, .(T206, []))))))
7.03/2.65	   f2_in(.(T278, .(T279, .(T280, .(T281, .(T282, .(T283, []))))))) -> f2_out1(.(T283, .(T282, .(T281, .(T280, .(T279, .(T278, [])))))))
7.03/2.65	   f2_in(.(T361, .(T362, .(T363, .(T364, .(T365, .(T366, .(T367, [])))))))) -> f2_out1(.(T367, .(T366, .(T365, .(T364, .(T363, .(T362, .(T361, []))))))))
7.03/2.65	   f2_in(T397) -> U1(f313_in(T397), T397)
7.03/2.65	   U1(f313_out1(T398, T399, .(T400, .(T401, .(T402, .(T403, .(T404, .(T405, .(T406, [])))))))), T397) -> f2_out1(.(T406, .(T405, .(T404, .(T403, .(T402, .(T401, .(T400, .(T399, T398)))))))))
7.03/2.65	   f313_in(.(T436, T437)) -> f313_out1([], T436, T437)
7.03/2.65	   f313_in(T452) -> U2(f313_in(T452), T452)
7.03/2.65	   U2(f313_out1(T453, T454, .(T455, T456)), T452) -> f313_out1(.(T454, T453), T455, T456)
7.03/2.65	
7.03/2.65	Q is empty.
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(37) PrologToIRSwTTransformerProof (SOUND)
7.03/2.65	Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert
7.03/2.65	
7.03/2.65	{
7.03/2.65	    "root": 3,
7.03/2.65	    "program": {
7.03/2.65	        "directives": [],
7.03/2.65	        "clauses": [
7.03/2.65	            [
7.03/2.65	                "(reverse X1s X2s)",
7.03/2.65	                "(reverse X1s ([]) X2s)"
7.03/2.65	            ],
7.03/2.65	            [
7.03/2.65	                "(reverse ([]) Xs Xs)",
7.03/2.65	                null
7.03/2.65	            ],
7.03/2.65	            [
7.03/2.65	                "(reverse (. X X1s) X2s Ys)",
7.03/2.65	                "(reverse X1s (. X X2s) Ys)"
7.03/2.65	            ]
7.03/2.65	        ]
7.03/2.65	    },
7.03/2.65	    "graph": {
7.03/2.65	        "nodes": {
7.03/2.65	            "88": {
7.03/2.65	                "goal": [{
7.03/2.65	                    "clause": -1,
7.03/2.65	                    "scope": -1,
7.03/2.65	                    "term": "(reverse T20 (. T21 ([])) T19)"
7.03/2.65	                }],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": ["T19"],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "89": {
7.03/2.65	                "goal": [],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "type": "Nodes",
7.03/2.65	            "152": {
7.03/2.65	                "goal": [{
7.03/2.65	                    "clause": -1,
7.03/2.65	                    "scope": -1,
7.03/2.65	                    "term": "(true)"
7.03/2.65	                }],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "153": {
7.03/2.65	                "goal": [],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "274": {
7.03/2.65	                "goal": [{
7.03/2.65	                    "clause": 1,
7.03/2.65	                    "scope": 8,
7.03/2.65	                    "term": "(reverse T235 (. T236 (. T237 (. T238 (. T239 (. T240 (. T241 ([]))))))) T234)"
7.03/2.65	                }],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": ["T234"],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "154": {
7.03/2.65	                "goal": [],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "275": {
7.03/2.65	                "goal": [{
7.03/2.65	                    "clause": 2,
7.03/2.65	                    "scope": 8,
7.03/2.65	                    "term": "(reverse T235 (. T236 (. T237 (. T238 (. T239 (. T240 (. T241 ([]))))))) T234)"
7.03/2.65	                }],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": ["T234"],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "276": {
7.03/2.65	                "goal": [{
7.03/2.65	                    "clause": -1,
7.03/2.65	                    "scope": -1,
7.03/2.65	                    "term": "(true)"
7.03/2.65	                }],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "277": {
7.03/2.65	                "goal": [],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "278": {
7.03/2.65	                "goal": [],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
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7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": ["T9"],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "306": {
7.03/2.65	                "goal": [],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "82": {
7.03/2.65	                "goal": [
7.03/2.65	                    {
7.03/2.65	                        "clause": 1,
7.03/2.65	                        "scope": 2,
7.03/2.65	                        "term": "(reverse T10 ([]) T9)"
7.03/2.65	                    },
7.03/2.65	                    {
7.03/2.65	                        "clause": 2,
7.03/2.65	                        "scope": 2,
7.03/2.65	                        "term": "(reverse T10 ([]) T9)"
7.03/2.65	                    }
7.03/2.65	                ],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": ["T9"],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "307": {
7.03/2.65	                "goal": [],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "83": {
7.03/2.65	                "goal": [{
7.03/2.65	                    "clause": 1,
7.03/2.65	                    "scope": 2,
7.03/2.65	                    "term": "(reverse T10 ([]) T9)"
7.03/2.65	                }],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": ["T9"],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "84": {
7.03/2.65	                "goal": [{
7.03/2.65	                    "clause": 2,
7.03/2.65	                    "scope": 2,
7.03/2.65	                    "term": "(reverse T10 ([]) T9)"
7.03/2.65	                }],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": ["T9"],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "85": {
7.03/2.65	                "goal": [{
7.03/2.65	                    "clause": -1,
7.03/2.65	                    "scope": -1,
7.03/2.65	                    "term": "(true)"
7.03/2.65	                }],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "86": {
7.03/2.65	                "goal": [],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            },
7.03/2.65	            "87": {
7.03/2.65	                "goal": [],
7.03/2.65	                "kb": {
7.03/2.65	                    "nonunifying": [],
7.03/2.65	                    "intvars": {},
7.03/2.65	                    "arithmetic": {
7.03/2.65	                        "type": "PlainIntegerRelationState",
7.03/2.65	                        "relations": []
7.03/2.65	                    },
7.03/2.65	                    "ground": [],
7.03/2.65	                    "free": [],
7.03/2.65	                    "exprvars": []
7.03/2.65	                }
7.03/2.65	            }
7.03/2.65	        },
7.03/2.65	        "edges": [
7.03/2.65	            {
7.03/2.65	                "from": 3,
7.03/2.65	                "to": 5,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 5,
7.03/2.65	                "to": 81,
7.03/2.65	                "label": "ONLY EVAL with clause\nreverse(X7, X8) :- reverse(X7, [], X8).\nand substitutionT1 -> T10,\nX7 -> T10,\nT2 -> T9,\nX8 -> T9,\nT8 -> T10"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 81,
7.03/2.65	                "to": 82,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 82,
7.03/2.65	                "to": 83,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 82,
7.03/2.65	                "to": 84,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 83,
7.03/2.65	                "to": 85,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X15, X15).\nand substitutionT10 -> [],\nX15 -> [],\nT9 -> []"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 83,
7.03/2.65	                "to": 86,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 84,
7.03/2.65	                "to": 88,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X24, X25), X26, X27) :- reverse(X25, .(X24, X26), X27).\nand substitutionX24 -> T21,\nX25 -> T20,\nT10 -> .(T21, T20),\nX26 -> [],\nT9 -> T19,\nX27 -> T19,\nT18 -> T20,\nT17 -> T21"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 84,
7.03/2.65	                "to": 89,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 85,
7.03/2.65	                "to": 87,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 88,
7.03/2.65	                "to": 90,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 90,
7.03/2.65	                "to": 91,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 90,
7.03/2.65	                "to": 92,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 91,
7.03/2.65	                "to": 98,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X34, X34).\nand substitutionT20 -> [],\nT21 -> T28,\nX34 -> .(T28, []),\nT19 -> .(T28, [])"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 91,
7.03/2.65	                "to": 99,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 92,
7.03/2.65	                "to": 134,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X43, X44), X45, X46) :- reverse(X44, .(X43, X45), X46).\nand substitutionX43 -> T42,\nX44 -> T41,\nT20 -> .(T42, T41),\nT21 -> T43,\nX45 -> .(T43, []),\nT19 -> T40,\nX46 -> T40,\nT38 -> T41,\nT37 -> T42,\nT39 -> T43"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 92,
7.03/2.65	                "to": 139,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 98,
7.03/2.65	                "to": 100,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 134,
7.03/2.65	                "to": 143,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 143,
7.03/2.65	                "to": 146,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 143,
7.03/2.65	                "to": 147,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 146,
7.03/2.65	                "to": 152,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X53, X53).\nand substitutionT41 -> [],\nT42 -> T56,\nT43 -> T57,\nX53 -> .(T56, .(T57, [])),\nT40 -> .(T56, .(T57, []))"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 146,
7.03/2.65	                "to": 153,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 147,
7.03/2.65	                "to": 160,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X62, X63), X64, X65) :- reverse(X63, .(X62, X64), X65).\nand substitutionX62 -> T74,\nX63 -> T73,\nT41 -> .(T74, T73),\nT42 -> T75,\nT43 -> T76,\nX64 -> .(T75, .(T76, [])),\nT40 -> T72,\nX65 -> T72,\nT69 -> T73,\nT68 -> T74,\nT70 -> T75,\nT71 -> T76"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 147,
7.03/2.65	                "to": 161,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 152,
7.03/2.65	                "to": 154,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 160,
7.03/2.65	                "to": 165,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 165,
7.03/2.65	                "to": 169,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 165,
7.03/2.65	                "to": 170,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 169,
7.03/2.65	                "to": 173,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X72, X72).\nand substitutionT73 -> [],\nT74 -> T95,\nT75 -> T96,\nT76 -> T97,\nX72 -> .(T95, .(T96, .(T97, []))),\nT72 -> .(T95, .(T96, .(T97, [])))"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 169,
7.03/2.65	                "to": 174,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 170,
7.03/2.65	                "to": 182,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X81, X82), X83, X84) :- reverse(X82, .(X81, X83), X84).\nand substitutionX81 -> T117,\nX82 -> T116,\nT73 -> .(T117, T116),\nT74 -> T118,\nT75 -> T119,\nT76 -> T120,\nX83 -> .(T118, .(T119, .(T120, []))),\nT72 -> T115,\nX84 -> T115,\nT111 -> T116,\nT110 -> T117,\nT112 -> T118,\nT113 -> T119,\nT114 -> T120"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 170,
7.03/2.65	                "to": 183,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 173,
7.03/2.65	                "to": 175,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 182,
7.03/2.65	                "to": 186,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 186,
7.03/2.65	                "to": 188,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 186,
7.03/2.65	                "to": 200,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 188,
7.03/2.65	                "to": 201,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X91, X91).\nand substitutionT116 -> [],\nT117 -> T145,\nT118 -> T146,\nT119 -> T147,\nT120 -> T148,\nX91 -> .(T145, .(T146, .(T147, .(T148, [])))),\nT115 -> .(T145, .(T146, .(T147, .(T148, []))))"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 188,
7.03/2.65	                "to": 202,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 200,
7.03/2.65	                "to": 204,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X100, X101), X102, X103) :- reverse(X101, .(X100, X102), X103).\nand substitutionX100 -> T171,\nX101 -> T170,\nT116 -> .(T171, T170),\nT117 -> T172,\nT118 -> T173,\nT119 -> T174,\nT120 -> T175,\nX102 -> .(T172, .(T173, .(T174, .(T175, [])))),\nT115 -> T169,\nX103 -> T169,\nT164 -> T170,\nT163 -> T171,\nT165 -> T172,\nT166 -> T173,\nT167 -> T174,\nT168 -> T175"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 200,
7.03/2.65	                "to": 205,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 201,
7.03/2.65	                "to": 203,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 204,
7.03/2.65	                "to": 211,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 211,
7.03/2.65	                "to": 212,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 211,
7.03/2.65	                "to": 213,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 212,
7.03/2.65	                "to": 216,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X110, X110).\nand substitutionT170 -> [],\nT171 -> T206,\nT172 -> T207,\nT173 -> T208,\nT174 -> T209,\nT175 -> T210,\nX110 -> .(T206, .(T207, .(T208, .(T209, .(T210, []))))),\nT169 -> .(T206, .(T207, .(T208, .(T209, .(T210, [])))))"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 212,
7.03/2.65	                "to": 218,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 213,
7.03/2.65	                "to": 249,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X119, X120), X121, X122) :- reverse(X120, .(X119, X121), X122).\nand substitutionX119 -> T236,\nX120 -> T235,\nT170 -> .(T236, T235),\nT171 -> T237,\nT172 -> T238,\nT173 -> T239,\nT174 -> T240,\nT175 -> T241,\nX121 -> .(T237, .(T238, .(T239, .(T240, .(T241, []))))),\nT169 -> T234,\nX122 -> T234,\nT228 -> T235,\nT227 -> T236,\nT229 -> T237,\nT230 -> T238,\nT231 -> T239,\nT232 -> T240,\nT233 -> T241"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 213,
7.03/2.65	                "to": 250,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 216,
7.03/2.65	                "to": 219,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 249,
7.03/2.65	                "to": 269,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 269,
7.03/2.65	                "to": 274,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 269,
7.03/2.65	                "to": 275,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 274,
7.03/2.65	                "to": 276,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X129, X129).\nand substitutionT235 -> [],\nT236 -> T278,\nT237 -> T279,\nT238 -> T280,\nT239 -> T281,\nT240 -> T282,\nT241 -> T283,\nX129 -> .(T278, .(T279, .(T280, .(T281, .(T282, .(T283, [])))))),\nT234 -> .(T278, .(T279, .(T280, .(T281, .(T282, .(T283, []))))))"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 274,
7.03/2.65	                "to": 277,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 275,
7.03/2.65	                "to": 283,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X138, X139), X140, X141) :- reverse(X139, .(X138, X140), X141).\nand substitutionX138 -> T312,\nX139 -> T311,\nT235 -> .(T312, T311),\nT236 -> T313,\nT237 -> T314,\nT238 -> T315,\nT239 -> T316,\nT240 -> T317,\nT241 -> T318,\nX140 -> .(T313, .(T314, .(T315, .(T316, .(T317, .(T318, [])))))),\nT234 -> T310,\nX141 -> T310,\nT303 -> T311,\nT302 -> T312,\nT304 -> T313,\nT305 -> T314,\nT306 -> T315,\nT307 -> T316,\nT308 -> T317,\nT309 -> T318"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 275,
7.03/2.65	                "to": 284,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 276,
7.03/2.65	                "to": 278,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 283,
7.03/2.65	                "to": 287,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 287,
7.03/2.65	                "to": 288,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 287,
7.03/2.65	                "to": 289,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 288,
7.03/2.65	                "to": 290,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X148, X148).\nand substitutionT311 -> [],\nT312 -> T361,\nT313 -> T362,\nT314 -> T363,\nT315 -> T364,\nT316 -> T365,\nT317 -> T366,\nT318 -> T367,\nX148 -> .(T361, .(T362, .(T363, .(T364, .(T365, .(T366, .(T367, []))))))),\nT310 -> .(T361, .(T362, .(T363, .(T364, .(T365, .(T366, .(T367, [])))))))"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 288,
7.03/2.65	                "to": 291,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 289,
7.03/2.65	                "to": 293,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X157, X158), X159, X160) :- reverse(X158, .(X157, X159), X160).\nand substitutionX157 -> T399,\nX158 -> T398,\nT311 -> .(T399, T398),\nT312 -> T400,\nT313 -> T401,\nT314 -> T402,\nT315 -> T403,\nT316 -> T404,\nT317 -> T405,\nT318 -> T406,\nX159 -> .(T400, .(T401, .(T402, .(T403, .(T404, .(T405, .(T406, []))))))),\nT310 -> T397,\nX160 -> T397,\nT389 -> T398,\nT388 -> T399,\nT390 -> T400,\nT391 -> T401,\nT392 -> T402,\nT393 -> T403,\nT394 -> T404,\nT395 -> T405,\nT396 -> T406"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 289,
7.03/2.65	                "to": 294,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 290,
7.03/2.65	                "to": 292,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 293,
7.03/2.65	                "to": 298,
7.03/2.65	                "label": "GENERALIZATION\nT423 <-- .(T400, .(T401, .(T402, .(T403, .(T404, .(T405, .(T406, [])))))))"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 298,
7.03/2.65	                "to": 302,
7.03/2.65	                "label": "CASE"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 302,
7.03/2.65	                "to": 303,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 302,
7.03/2.65	                "to": 304,
7.03/2.65	                "label": "PARALLEL"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 303,
7.03/2.65	                "to": 305,
7.03/2.65	                "label": "EVAL with clause\nreverse([], X169, X169).\nand substitutionT398 -> [],\nT399 -> T436,\nT423 -> T437,\nX169 -> .(T436, T437),\nT397 -> .(T436, T437)"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 303,
7.03/2.65	                "to": 306,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 304,
7.03/2.65	                "to": 314,
7.03/2.65	                "label": "EVAL with clause\nreverse(.(X178, X179), X180, X181) :- reverse(X179, .(X178, X180), X181).\nand substitutionX178 -> T454,\nX179 -> T453,\nT398 -> .(T454, T453),\nT399 -> T455,\nT423 -> T456,\nX180 -> .(T455, T456),\nT397 -> T452,\nX181 -> T452,\nT449 -> T453,\nT448 -> T454,\nT450 -> T455,\nT451 -> T456"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 304,
7.03/2.65	                "to": 315,
7.03/2.65	                "label": "EVAL-BACKTRACK"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 305,
7.03/2.65	                "to": 307,
7.03/2.65	                "label": "SUCCESS"
7.03/2.65	            },
7.03/2.65	            {
7.03/2.65	                "from": 314,
7.03/2.65	                "to": 298,
7.03/2.65	                "label": "INSTANCE with matching:\nT398 -> T453\nT399 -> T454\nT423 -> .(T455, T456)\nT397 -> T452"
7.03/2.65	            }
7.03/2.65	        ],
7.03/2.65	        "type": "Graph"
7.03/2.65	    }
7.03/2.65	}
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(38)
7.03/2.65	Obligation:
7.03/2.65	Rules:
7.03/2.65	f298_out(T452) -> f314_out(T452) :|: TRUE
7.03/2.65	f314_in(x) -> f298_in(x) :|: TRUE
7.03/2.65	f298_in(T397) -> f302_in(T397) :|: TRUE
7.03/2.65	f302_out(x1) -> f298_out(x1) :|: TRUE
7.03/2.65	f304_in(x2) -> f314_in(x2) :|: TRUE
7.03/2.65	f314_out(x3) -> f304_out(x3) :|: TRUE
7.03/2.65	f315_out -> f304_out(x4) :|: TRUE
7.03/2.65	f304_in(x5) -> f315_in :|: TRUE
7.03/2.65	f303_out(x6) -> f302_out(x6) :|: TRUE
7.03/2.65	f304_out(x7) -> f302_out(x7) :|: TRUE
7.03/2.65	f302_in(x8) -> f303_in(x8) :|: TRUE
7.03/2.65	f302_in(x9) -> f304_in(x9) :|: TRUE
7.03/2.65	f5_out(T2) -> f3_out(T2) :|: TRUE
7.03/2.65	f3_in(x10) -> f5_in(x10) :|: TRUE
7.03/2.65	f5_in(T9) -> f81_in(T9) :|: TRUE
7.03/2.65	f81_out(x11) -> f5_out(x11) :|: TRUE
7.03/2.65	f82_out(x12) -> f81_out(x12) :|: TRUE
7.03/2.65	f81_in(x13) -> f82_in(x13) :|: TRUE
7.03/2.65	f84_out(x14) -> f82_out(x14) :|: TRUE
7.03/2.65	f82_in(x15) -> f83_in(x15) :|: TRUE
7.03/2.65	f83_out(x16) -> f82_out(x16) :|: TRUE
7.03/2.65	f82_in(x17) -> f84_in(x17) :|: TRUE
7.03/2.65	f84_in(x18) -> f89_in :|: TRUE
7.03/2.65	f88_out(T19) -> f84_out(T19) :|: TRUE
7.03/2.65	f89_out -> f84_out(x19) :|: TRUE
7.03/2.65	f84_in(x20) -> f88_in(x20) :|: TRUE
7.03/2.65	f88_in(x21) -> f90_in(x21) :|: TRUE
7.03/2.65	f90_out(x22) -> f88_out(x22) :|: TRUE
7.03/2.65	f91_out(x23) -> f90_out(x23) :|: TRUE
7.03/2.65	f92_out(x24) -> f90_out(x24) :|: TRUE
7.03/2.65	f90_in(x25) -> f92_in(x25) :|: TRUE
7.03/2.65	f90_in(x26) -> f91_in(x26) :|: TRUE
7.03/2.65	f92_in(x27) -> f139_in :|: TRUE
7.03/2.65	f92_in(T40) -> f134_in(T40) :|: TRUE
7.03/2.65	f134_out(x28) -> f92_out(x28) :|: TRUE
7.03/2.65	f139_out -> f92_out(x29) :|: TRUE
7.03/2.65	f134_in(x30) -> f143_in(x30) :|: TRUE
7.03/2.65	f143_out(x31) -> f134_out(x31) :|: TRUE
7.03/2.65	f146_out(x32) -> f143_out(x32) :|: TRUE
7.03/2.65	f143_in(x33) -> f147_in(x33) :|: TRUE
7.03/2.65	f143_in(x34) -> f146_in(x34) :|: TRUE
7.03/2.65	f147_out(x35) -> f143_out(x35) :|: TRUE
7.03/2.65	f147_in(x36) -> f161_in :|: TRUE
7.03/2.65	f147_in(T72) -> f160_in(T72) :|: TRUE
7.03/2.65	f161_out -> f147_out(x37) :|: TRUE
7.03/2.65	f160_out(x38) -> f147_out(x38) :|: TRUE
7.03/2.65	f165_out(x39) -> f160_out(x39) :|: TRUE
7.03/2.65	f160_in(x40) -> f165_in(x40) :|: TRUE
7.03/2.65	f169_out(x41) -> f165_out(x41) :|: TRUE
7.03/2.65	f165_in(x42) -> f170_in(x42) :|: TRUE
7.03/2.65	f170_out(x43) -> f165_out(x43) :|: TRUE
7.03/2.65	f165_in(x44) -> f169_in(x44) :|: TRUE
7.03/2.65	f182_out(T115) -> f170_out(T115) :|: TRUE
7.03/2.65	f170_in(x45) -> f183_in :|: TRUE
7.03/2.65	f170_in(x46) -> f182_in(x46) :|: TRUE
7.03/2.65	f183_out -> f170_out(x47) :|: TRUE
7.03/2.65	f182_in(x48) -> f186_in(x48) :|: TRUE
7.03/2.65	f186_out(x49) -> f182_out(x49) :|: TRUE
7.03/2.65	f186_in(x50) -> f188_in(x50) :|: TRUE
7.03/2.65	f186_in(x51) -> f200_in(x51) :|: TRUE
7.03/2.65	f188_out(x52) -> f186_out(x52) :|: TRUE
7.03/2.65	f200_out(x53) -> f186_out(x53) :|: TRUE
7.03/2.65	f200_in(T169) -> f204_in(T169) :|: TRUE
7.03/2.65	f204_out(x54) -> f200_out(x54) :|: TRUE
7.03/2.65	f200_in(x55) -> f205_in :|: TRUE
7.03/2.65	f205_out -> f200_out(x56) :|: TRUE
7.03/2.65	f204_in(x57) -> f211_in(x57) :|: TRUE
7.03/2.65	f211_out(x58) -> f204_out(x58) :|: TRUE
7.03/2.65	f212_out(x59) -> f211_out(x59) :|: TRUE
7.03/2.65	f211_in(x60) -> f213_in(x60) :|: TRUE
7.03/2.65	f213_out(x61) -> f211_out(x61) :|: TRUE
7.03/2.65	f211_in(x62) -> f212_in(x62) :|: TRUE
7.03/2.65	f250_out -> f213_out(x63) :|: TRUE
7.03/2.65	f213_in(x64) -> f250_in :|: TRUE
7.03/2.65	f213_in(T234) -> f249_in(T234) :|: TRUE
7.03/2.65	f249_out(x65) -> f213_out(x65) :|: TRUE
7.03/2.65	f269_out(x66) -> f249_out(x66) :|: TRUE
7.03/2.65	f249_in(x67) -> f269_in(x67) :|: TRUE
7.03/2.65	f269_in(x68) -> f274_in(x68) :|: TRUE
7.03/2.65	f274_out(x69) -> f269_out(x69) :|: TRUE
7.03/2.65	f275_out(x70) -> f269_out(x70) :|: TRUE
7.03/2.65	f269_in(x71) -> f275_in(x71) :|: TRUE
7.03/2.65	f275_in(x72) -> f284_in :|: TRUE
7.03/2.65	f275_in(T310) -> f283_in(T310) :|: TRUE
7.03/2.65	f283_out(x73) -> f275_out(x73) :|: TRUE
7.03/2.65	f284_out -> f275_out(x74) :|: TRUE
7.03/2.65	f287_out(x75) -> f283_out(x75) :|: TRUE
7.03/2.65	f283_in(x76) -> f287_in(x76) :|: TRUE
7.03/2.65	f287_in(x77) -> f288_in(x77) :|: TRUE
7.03/2.65	f288_out(x78) -> f287_out(x78) :|: TRUE
7.03/2.65	f289_out(x79) -> f287_out(x79) :|: TRUE
7.03/2.65	f287_in(x80) -> f289_in(x80) :|: TRUE
7.03/2.65	f289_in(x81) -> f294_in :|: TRUE
7.03/2.65	f294_out -> f289_out(x82) :|: TRUE
7.03/2.65	f289_in(x83) -> f293_in(x83) :|: TRUE
7.03/2.65	f293_out(x84) -> f289_out(x84) :|: TRUE
7.03/2.65	f298_out(x85) -> f293_out(x85) :|: TRUE
7.03/2.65	f293_in(x86) -> f298_in(x86) :|: TRUE
7.03/2.65	Start term: f3_in(T2)
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(39) IRSwTSimpleDependencyGraphProof (EQUIVALENT)
7.03/2.65	Constructed simple dependency graph.
7.03/2.65	
7.03/2.65	Simplified to the following IRSwTs:
7.03/2.65	
7.03/2.65	intTRSProblem:
7.03/2.65	f314_in(x) -> f298_in(x) :|: TRUE
7.03/2.65	f298_in(T397) -> f302_in(T397) :|: TRUE
7.03/2.65	f304_in(x2) -> f314_in(x2) :|: TRUE
7.03/2.65	f302_in(x9) -> f304_in(x9) :|: TRUE
7.03/2.65	
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(40)
7.03/2.65	Obligation:
7.03/2.65	Rules:
7.03/2.65	f314_in(x) -> f298_in(x) :|: TRUE
7.03/2.65	f298_in(T397) -> f302_in(T397) :|: TRUE
7.03/2.65	f304_in(x2) -> f314_in(x2) :|: TRUE
7.03/2.65	f302_in(x9) -> f304_in(x9) :|: TRUE
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(41) IntTRSCompressionProof (EQUIVALENT)
7.03/2.65	Compressed rules.
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(42)
7.03/2.65	Obligation:
7.03/2.65	Rules:
7.03/2.65	f304_in(x2:0) -> f304_in(x2:0) :|: TRUE
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(43) IRSFormatTransformerProof (EQUIVALENT)
7.03/2.65	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(44)
7.03/2.65	Obligation:
7.03/2.65	Rules:
7.03/2.65	f304_in(x2:0) -> f304_in(x2:0) :|: TRUE
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(45) IRSwTTerminationDigraphProof (EQUIVALENT)
7.03/2.65	Constructed termination digraph!
7.03/2.65	Nodes:
7.03/2.65	(1) f304_in(x2:0) -> f304_in(x2:0) :|: TRUE
7.03/2.65	
7.03/2.65	Arcs:
7.03/2.65	(1) -> (1)
7.03/2.65	
7.03/2.65	This digraph is fully evaluated!
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(46)
7.03/2.65	Obligation:
7.03/2.65	
7.03/2.65	Termination digraph:
7.03/2.65	Nodes:
7.03/2.65	(1) f304_in(x2:0) -> f304_in(x2:0) :|: TRUE
7.03/2.65	
7.03/2.65	Arcs:
7.03/2.65	(1) -> (1)
7.03/2.65	
7.03/2.65	This digraph is fully evaluated!
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(47) FilterProof (EQUIVALENT)
7.03/2.65	Used the following sort dictionary for filtering: 
7.03/2.65	f304_in(VARIABLE)
7.03/2.65	Replaced non-predefined constructor symbols by 0.
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(48)
7.03/2.65	Obligation:
7.03/2.65	Rules:
7.03/2.65	f304_in(x2:0) -> f304_in(x2:0) :|: TRUE
7.03/2.65	
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(49) IntTRSPeriodicNontermProof (COMPLETE)
7.03/2.65	Normalized system to the following form:
7.03/2.65	f(pc, x2:0) -> f(1, x2:0) :|: pc = 1 && TRUE
7.03/2.65	Witness term starting non-terminating reduction: f(1, -8)
7.03/2.65	----------------------------------------
7.03/2.65	
7.03/2.65	(50)
7.03/2.65	NO
7.03/2.68	EOF