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Logic Progr 19030 pair #381919978
details
property
value
status
complete
benchmark
gcd.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
talp_talp
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.62891197205 seconds
cpu usage
7.262514747
max memory
6.29723136E8
stage attributes
key
value
output-size
34729
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern gcd(g,g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND,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, 12 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) PiDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) PiDP (10) PiDPToQDPProof [EQUIVALENT, 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 [EQUIVALENT, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES (28) PiDP (29) UsableRulesProof [EQUIVALENT, 0 ms] (30) PiDP (31) PiDPToQDPProof [SOUND, 0 ms] (32) QDP (33) QDPQMonotonicMRRProof [EQUIVALENT, 43 ms] (34) QDP (35) DependencyGraphProof [EQUIVALENT, 0 ms] (36) TRUE ---------------------------------------- (0) Obligation: Clauses: gcd(X, Y, D) :- ','(le(X, Y), gcd_le(X, Y, D)). gcd(X, Y, D) :- ','(gt(X, Y), gcd_le(Y, X, D)). gcd_le(0, Y, Y). gcd_le(s(X), Y, D) :- ','(add(s(X), Z, Y), gcd(s(X), Z, D)). gt(s(X), s(Y)) :- gt(X, Y). gt(s(X), 0). le(s(X), s(Y)) :- le(X, Y). le(0, s(Y)). le(0, 0). add(s(X), Y, s(Z)) :- add(X, Y, Z). add(0, X, X). Query: gcd(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: gcd_in_3: (b,b,f) le_in_2: (b,b) gcd_le_in_3: (b,b,f) add_in_3: (b,f,b) gt_in_2: (b,b) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: gcd_in_gga(X, Y, D) -> U1_gga(X, Y, D, le_in_gg(X, Y)) le_in_gg(s(X), s(Y)) -> U8_gg(X, Y, le_in_gg(X, Y)) le_in_gg(0, s(Y)) -> le_out_gg(0, s(Y)) le_in_gg(0, 0) -> le_out_gg(0, 0)
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