details

property	value
status	complete
benchmark	ackermann.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n184.star.cs.uiowa.edu
space	SGST06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.94770789146 seconds
cpu usage	4.027479942
max memory	2.53083648E8

stage attributes

key	value
output-size	10501
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern ackermann(g,g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof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, 0 ms] (6) PiDP (7) PiDPToQDPProof [SOUND, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Clauses: ackermann(0, N, s(N)). ackermann(s(M), 0, Res) :- ackermann(M, s(0), Res). ackermann(s(M), s(N), Res) :- ','(ackermann(s(M), N, Res1), ackermann(M, Res1, Res)). Query: ackermann(g,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: ackermann_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: ackermann_in_gga(0, N, s(N)) -> ackermann_out_gga(0, N, s(N)) ackermann_in_gga(s(M), 0, Res) -> U1_gga(M, Res, ackermann_in_gga(M, s(0), Res)) ackermann_in_gga(s(M), s(N), Res) -> U2_gga(M, N, Res, ackermann_in_gga(s(M), N, Res1)) U2_gga(M, N, Res, ackermann_out_gga(s(M), N, Res1)) -> U3_gga(M, N, Res, ackermann_in_gga(M, Res1, Res)) U3_gga(M, N, Res, ackermann_out_gga(M, Res1, Res)) -> ackermann_out_gga(s(M), s(N), Res) U1_gga(M, Res, ackermann_out_gga(M, s(0), Res)) -> ackermann_out_gga(s(M), 0, Res) The argument filtering Pi contains the following mapping: ackermann_in_gga(x1, x2, x3) = ackermann_in_gga(x1, x2) 0 = 0 ackermann_out_gga(x1, x2, x3) = ackermann_out_gga(x3) s(x1) = s(x1) U1_gga(x1, x2, x3) = U1_gga(x3) U2_gga(x1, x2, x3, x4) = U2_gga(x1, x4) U3_gga(x1, x2, x3, x4) = U3_gga(x4) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (2) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: ackermann_in_gga(0, N, s(N)) -> ackermann_out_gga(0, N, s(N)) ackermann_in_gga(s(M), 0, Res) -> U1_gga(M, Res, ackermann_in_gga(M, s(0), Res)) ackermann_in_gga(s(M), s(N), Res) -> U2_gga(M, N, Res, ackermann_in_gga(s(M), N, Res1)) U2_gga(M, N, Res, ackermann_out_gga(s(M), N, Res1)) -> U3_gga(M, N, Res, ackermann_in_gga(M, Res1, Res)) U3_gga(M, N, Res, ackermann_out_gga(M, Res1, Res)) -> ackermann_out_gga(s(M), s(N), Res) U1_gga(M, Res, ackermann_out_gga(M, s(0), Res)) -> ackermann_out_gga(s(M), 0, Res) The argument filtering Pi contains the following mapping: ackermann_in_gga(x1, x2, x3) = ackermann_in_gga(x1, x2) popout

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