details

property	value
status	complete
benchmark	fib_t.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	talp_mixed

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.70322489738 seconds
cpu usage	4.617207429
max memory	3.8254592E8

stage attributes

key	value
output-size	15478
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern fib(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0 ms] (2) PiTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 5 ms] (6) AND (7) PiDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) PiDP (10) PiDPToQDPProof [SOUND, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) PiDP (15) PiDPToQDPProof [SOUND, 1 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Clauses: add(0, 0, 0). add(s(X), Y, s(N)) :- add(X, Y, N). add(X, s(Y), s(N)) :- add(X, Y, N). fib(0, 0). fib(s(0), s(0)). fib(s(s(X)), N) :- ','(fib(s(X), N1), ','(fib(X, N2), add(N1, N2, N))). Query: fib(g,a) ---------------------------------------- (1) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: fib_in_2: (b,f) add_in_3: (b,b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: fib_in_ga(0, 0) -> fib_out_ga(0, 0) fib_in_ga(s(0), s(0)) -> fib_out_ga(s(0), s(0)) fib_in_ga(s(s(X)), N) -> U3_ga(X, N, fib_in_ga(s(X), N1)) U3_ga(X, N, fib_out_ga(s(X), N1)) -> U4_ga(X, N, N1, fib_in_ga(X, N2)) U4_ga(X, N, N1, fib_out_ga(X, N2)) -> U5_ga(X, N, add_in_gga(N1, N2, N)) add_in_gga(0, 0, 0) -> add_out_gga(0, 0, 0) add_in_gga(s(X), Y, s(N)) -> U1_gga(X, Y, N, add_in_gga(X, Y, N)) add_in_gga(X, s(Y), s(N)) -> U2_gga(X, Y, N, add_in_gga(X, Y, N)) U2_gga(X, Y, N, add_out_gga(X, Y, N)) -> add_out_gga(X, s(Y), s(N)) U1_gga(X, Y, N, add_out_gga(X, Y, N)) -> add_out_gga(s(X), Y, s(N)) U5_ga(X, N, add_out_gga(N1, N2, N)) -> fib_out_ga(s(s(X)), N) The argument filtering Pi contains the following mapping: fib_in_ga(x1, x2) = fib_in_ga(x1) 0 = 0 fib_out_ga(x1, x2) = fib_out_ga(x2) s(x1) = s(x1) U3_ga(x1, x2, x3) = U3_ga(x1, x3) U4_ga(x1, x2, x3, x4) = U4_ga(x3, x4) U5_ga(x1, x2, x3) = U5_ga(x3) add_in_gga(x1, x2, x3) = add_in_gga(x1, x2) add_out_gga(x1, x2, x3) = add_out_gga(x3) U1_gga(x1, x2, x3, x4) = U1_gga(x4) popout

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