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Logic Progr 19030 pair #381919786
details
property
value
status
complete
benchmark
program-8-9.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n034.star.cs.uiowa.edu
space
Art-of-prolog
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.85106086731 seconds
cpu usage
4.33397359
max memory
3.3327104E8
stage attributes
key
value
output-size
16155
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern maximum(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) UndefinedPredicateHandlerProof [SOUND, 0 ms] (2) Prolog (3) PrologToPiTRSProof [SOUND, 0 ms] (4) PiTRS (5) DependencyPairsProof [EQUIVALENT, 1 ms] (6) PiDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) PiDP (9) UsableRulesProof [EQUIVALENT, 0 ms] (10) PiDP (11) PiDPToQDPProof [SOUND, 5 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Clauses: maximum(.(X, Xs), M) :- maximum(Xs, X, M). maximum(.(X, Xs), Y, M) :- ','(=<(X, Y), maximum(Xs, Y, M)). maximum(.(X, Xs), Y, M) :- ','(>(X, Y), maximum(Xs, X, M)). maximum([], M, M). Query: maximum(g,a) ---------------------------------------- (1) UndefinedPredicateHandlerProof (SOUND) Added facts for all undefined predicates [PROLOG]. ---------------------------------------- (2) Obligation: Clauses: maximum(.(X, Xs), M) :- maximum(Xs, X, M). maximum(.(X, Xs), Y, M) :- ','(=<(X, Y), maximum(Xs, Y, M)). maximum(.(X, Xs), Y, M) :- ','(>(X, Y), maximum(Xs, X, M)). maximum([], M, M). =<(X0, X1). >(X0, X1). Query: maximum(g,a) ---------------------------------------- (3) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: maximum_in_2: (b,f) maximum_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: maximum_in_ga(.(X, Xs), M) -> U1_ga(X, Xs, M, maximum_in_gga(Xs, X, M)) maximum_in_gga(.(X, Xs), Y, M) -> U2_gga(X, Xs, Y, M, =<_in_gg(X, Y)) =<_in_gg(X0, X1) -> =<_out_gg(X0, X1) U2_gga(X, Xs, Y, M, =<_out_gg(X, Y)) -> U3_gga(X, Xs, Y, M, maximum_in_gga(Xs, Y, M)) maximum_in_gga(.(X, Xs), Y, M) -> U4_gga(X, Xs, Y, M, >_in_gg(X, Y)) >_in_gg(X0, X1) -> >_out_gg(X0, X1) U4_gga(X, Xs, Y, M, >_out_gg(X, Y)) -> U5_gga(X, Xs, Y, M, maximum_in_gga(Xs, X, M)) maximum_in_gga([], M, M) -> maximum_out_gga([], M, M) U5_gga(X, Xs, Y, M, maximum_out_gga(Xs, X, M)) -> maximum_out_gga(.(X, Xs), Y, M) U3_gga(X, Xs, Y, M, maximum_out_gga(Xs, Y, M)) -> maximum_out_gga(.(X, Xs), Y, M) U1_ga(X, Xs, M, maximum_out_gga(Xs, X, M)) -> maximum_out_ga(.(X, Xs), M) The argument filtering Pi contains the following mapping: maximum_in_ga(x1, x2) = maximum_in_ga(x1) .(x1, x2) = .(x1, x2) U1_ga(x1, x2, x3, x4) = U1_ga(x1, x2, x4) maximum_in_gga(x1, x2, x3) = maximum_in_gga(x1, x2)
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