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Logic Progr 19030 pair #381919785
details
property
value
status
complete
benchmark
isort.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
Euler_queensu-cs260
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.92957496643 seconds
cpu usage
4.631683843
max memory
3.43085056E8
stage attributes
key
value
output-size
19545
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern isort(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1)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, 7 ms] (4) PiTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) PiDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) PiDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) PiDP (12) PiDPToQDPProof [SOUND, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 1 ms] (15) YES (16) PiDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) PiDP (19) PiDPToQDPProof [SOUND, 0 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Clauses: insert(X, [], .(X, [])). insert(X, .(Y, Ys), .(X, .(Y, Ys))) :- =<(X, Y). insert(X, .(Y, Ys), .(Y, Tail)) :- ','(>(X, Y), insert(X, Ys, Tail)). isort([], []). isort(.(X, Xs), Result) :- ','(isort(Xs, SortedTail), insert(X, SortedTail, Result)). Query: isort(g,a) ---------------------------------------- (1) UndefinedPredicateHandlerProof (SOUND) Added facts for all undefined predicates [PROLOG]. ---------------------------------------- (2) Obligation: Clauses: insert(X, [], .(X, [])). insert(X, .(Y, Ys), .(X, .(Y, Ys))) :- =<(X, Y). insert(X, .(Y, Ys), .(Y, Tail)) :- ','(>(X, Y), insert(X, Ys, Tail)). isort([], []). isort(.(X, Xs), Result) :- ','(isort(Xs, SortedTail), insert(X, SortedTail, Result)). =<(X0, X1). >(X0, X1). Query: isort(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: isort_in_2: (b,f) insert_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: isort_in_ga([], []) -> isort_out_ga([], []) isort_in_ga(.(X, Xs), Result) -> U4_ga(X, Xs, Result, isort_in_ga(Xs, SortedTail)) U4_ga(X, Xs, Result, isort_out_ga(Xs, SortedTail)) -> U5_ga(X, Xs, Result, insert_in_gga(X, SortedTail, Result)) insert_in_gga(X, [], .(X, [])) -> insert_out_gga(X, [], .(X, [])) insert_in_gga(X, .(Y, Ys), .(X, .(Y, Ys))) -> U1_gga(X, Y, Ys, =<_in_gg(X, Y)) =<_in_gg(X0, X1) -> =<_out_gg(X0, X1) U1_gga(X, Y, Ys, =<_out_gg(X, Y)) -> insert_out_gga(X, .(Y, Ys), .(X, .(Y, Ys))) insert_in_gga(X, .(Y, Ys), .(Y, Tail)) -> U2_gga(X, Y, Ys, Tail, >_in_gg(X, Y)) >_in_gg(X0, X1) -> >_out_gg(X0, X1) U2_gga(X, Y, Ys, Tail, >_out_gg(X, Y)) -> U3_gga(X, Y, Ys, Tail, insert_in_gga(X, Ys, Tail))
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