details

property	value
status	complete
benchmark	pl7.2.9.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	talp_plumer

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.98506307602 seconds
cpu usage	4.319783056
max memory	3.6818944E8

stage attributes

key	value
output-size	12402
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.pl # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern mult(g,g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND,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, 5 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 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) UsableRulesProof [EQUIVALENT, 0 ms] (16) PiDP (17) PiDPToQDPProof [SOUND, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Clauses: mult(0, Y, 0). mult(s(X), Y, Z) :- ','(mult(X, Y, Z1), add(Z1, Y, Z)). add(0, Y, Y). add(s(X), Y, s(Z)) :- add(X, Y, Z). Query: mult(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: mult_in_3: (b,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: mult_in_gga(0, Y, 0) -> mult_out_gga(0, Y, 0) mult_in_gga(s(X), Y, Z) -> U1_gga(X, Y, Z, mult_in_gga(X, Y, Z1)) U1_gga(X, Y, Z, mult_out_gga(X, Y, Z1)) -> U2_gga(X, Y, Z, add_in_gga(Z1, Y, Z)) add_in_gga(0, Y, Y) -> add_out_gga(0, Y, Y) add_in_gga(s(X), Y, s(Z)) -> U3_gga(X, Y, Z, add_in_gga(X, Y, Z)) U3_gga(X, Y, Z, add_out_gga(X, Y, Z)) -> add_out_gga(s(X), Y, s(Z)) U2_gga(X, Y, Z, add_out_gga(Z1, Y, Z)) -> mult_out_gga(s(X), Y, Z) The argument filtering Pi contains the following mapping: mult_in_gga(x1, x2, x3) = mult_in_gga(x1, x2) 0 = 0 mult_out_gga(x1, x2, x3) = mult_out_gga(x3) s(x1) = s(x1) U1_gga(x1, x2, x3, x4) = U1_gga(x2, x4) U2_gga(x1, x2, x3, x4) = U2_gga(x4) add_in_gga(x1, x2, x3) = add_in_gga(x1, x2) add_out_gga(x1, x2, x3) = add_out_gga(x3) U3_gga(x1, x2, x3, x4) = U3_gga(x4) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog popout

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