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Logic Progr 19030 pair #381919667
details
property
value
status
complete
benchmark
preorder_dl.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
terminweb_new
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.76005506516 seconds
cpu usage
3.945210976
max memory
2.079744E8
stage attributes
key
value
output-size
12628
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern preorder(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof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) UsableRulesProof [EQUIVALENT, 0 ms] (8) PiDP (9) PiDPToQDPProof [SOUND, 0 ms] (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Clauses: preorder(T, Xs) :- preorder_dl(T, -(Xs, [])). preorder_dl(nil, -(X, X)). preorder_dl(tree(L, X, R), -(.(X, Xs), Zs)) :- ','(preorder_dl(L, -(Xs, Ys)), preorder_dl(R, -(Ys, Zs))). Query: preorder(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: preorder_in_2: (b,f) preorder_dl_in_2: (b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: preorder_in_ga(T, Xs) -> U1_ga(T, Xs, preorder_dl_in_ga(T, -(Xs, []))) preorder_dl_in_ga(nil, -(X, X)) -> preorder_dl_out_ga(nil, -(X, X)) preorder_dl_in_ga(tree(L, X, R), -(.(X, Xs), Zs)) -> U2_ga(L, X, R, Xs, Zs, preorder_dl_in_ga(L, -(Xs, Ys))) U2_ga(L, X, R, Xs, Zs, preorder_dl_out_ga(L, -(Xs, Ys))) -> U3_ga(L, X, R, Xs, Zs, preorder_dl_in_ga(R, -(Ys, Zs))) U3_ga(L, X, R, Xs, Zs, preorder_dl_out_ga(R, -(Ys, Zs))) -> preorder_dl_out_ga(tree(L, X, R), -(.(X, Xs), Zs)) U1_ga(T, Xs, preorder_dl_out_ga(T, -(Xs, []))) -> preorder_out_ga(T, Xs) The argument filtering Pi contains the following mapping: preorder_in_ga(x1, x2) = preorder_in_ga(x1) U1_ga(x1, x2, x3) = U1_ga(x3) preorder_dl_in_ga(x1, x2) = preorder_dl_in_ga(x1) nil = nil preorder_dl_out_ga(x1, x2) = preorder_dl_out_ga tree(x1, x2, x3) = tree(x1, x2, x3) U2_ga(x1, x2, x3, x4, x5, x6) = U2_ga(x3, x6) U3_ga(x1, x2, x3, x4, x5, x6) = U3_ga(x6) preorder_out_ga(x1, x2) = preorder_out_ga Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (2) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: preorder_in_ga(T, Xs) -> U1_ga(T, Xs, preorder_dl_in_ga(T, -(Xs, [])))
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