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Logic Progr 19030 pair #381919977
details
property
value
status
complete
benchmark
perm.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
talp_mixed
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.13917207718 seconds
cpu usage
5.477517956
max memory
4.84954112E8
stage attributes
key
value
output-size
25104
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern perm(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0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, 10 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 (21) PiDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) PiDP (24) PiDPToQDPProof [SOUND, 0 ms] (25) QDP (26) MRRProof [EQUIVALENT, 2 ms] (27) QDP (28) PisEmptyProof [EQUIVALENT, 0 ms] (29) YES ---------------------------------------- (0) Obligation: Clauses: append(nil, XS, XS). append(cons(X, XS1), XS2, cons(X, YS)) :- append(XS1, XS2, YS). split(XS, nil, XS). split(cons(X, XS), cons(X, YS1), YS2) :- split(XS, YS1, YS2). perm(nil, nil). perm(XS, cons(Y, YS)) :- ','(split(XS, YS1, cons(Y, YS2)), ','(append(YS1, YS2, ZS), perm(ZS, YS))). Query: perm(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: perm_in_2: (b,f) split_in_3: (b,f,f) append_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: perm_in_ga(nil, nil) -> perm_out_ga(nil, nil) perm_in_ga(XS, cons(Y, YS)) -> U3_ga(XS, Y, YS, split_in_gaa(XS, YS1, cons(Y, YS2))) split_in_gaa(XS, nil, XS) -> split_out_gaa(XS, nil, XS) split_in_gaa(cons(X, XS), cons(X, YS1), YS2) -> U2_gaa(X, XS, YS1, YS2, split_in_gaa(XS, YS1, YS2)) U2_gaa(X, XS, YS1, YS2, split_out_gaa(XS, YS1, YS2)) -> split_out_gaa(cons(X, XS), cons(X, YS1), YS2) U3_ga(XS, Y, YS, split_out_gaa(XS, YS1, cons(Y, YS2))) -> U4_ga(XS, Y, YS, YS1, YS2, append_in_gga(YS1, YS2, ZS)) append_in_gga(nil, XS, XS) -> append_out_gga(nil, XS, XS) append_in_gga(cons(X, XS1), XS2, cons(X, YS)) -> U1_gga(X, XS1, XS2, YS, append_in_gga(XS1, XS2, YS)) U1_gga(X, XS1, XS2, YS, append_out_gga(XS1, XS2, YS)) -> append_out_gga(cons(X, XS1), XS2, cons(X, YS)) U4_ga(XS, Y, YS, YS1, YS2, append_out_gga(YS1, YS2, ZS)) -> U5_ga(XS, Y, YS, perm_in_ga(ZS, YS)) U5_ga(XS, Y, YS, perm_out_ga(ZS, YS)) -> perm_out_ga(XS, cons(Y, YS)) The argument filtering Pi contains the following mapping: perm_in_ga(x1, x2) = perm_in_ga(x1) nil = nil perm_out_ga(x1, x2) = perm_out_ga(x2) U3_ga(x1, x2, x3, x4) = U3_ga(x4)
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