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Logic Programming pair #487529625
details
property
value
status
complete
benchmark
nat.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
talp_talp
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.09014797211 seconds
cpu usage
4.722378831
max memory
3.872768E8
stage attributes
key
value
output-size
19510
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern factorial(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof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, 14 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) PiDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) PiDP (10) PiDPToQDPProof [SOUND, 4 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) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES ---------------------------------------- (0) Obligation: Clauses: isNat(s(X)) :- isNat(X). isNat(0). notEq(s(X), s(Y)) :- notEq(X, Y). notEq(s(X), 0). notEq(0, s(X)). lt(s(X), s(Y)) :- lt(X, Y). lt(0, s(Y)). 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). even(s(X)) :- odd(X). even(0). odd(s(X)) :- even(X). odd(s(0)). add(s(X), Y, s(Z)) :- add(X, Y, Z). add(0, X, X). mult(s(X), Y, R) :- ','(mult(X, Y, Z), add(Y, Z, R)). mult(0, Y, 0). factorial(s(X), R) :- ','(factorial(X, Y), mult(s(X), Y, R)). factorial(0, s(0)). Query: factorial(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: factorial_in_2: (b,f) mult_in_3: (b,b,f) add_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: factorial_in_ga(s(X), R) -> U11_ga(X, R, factorial_in_ga(X, Y)) factorial_in_ga(0, s(0)) -> factorial_out_ga(0, s(0)) U11_ga(X, R, factorial_out_ga(X, Y)) -> U12_ga(X, R, mult_in_gga(s(X), Y, R)) mult_in_gga(s(X), Y, R) -> U9_gga(X, Y, R, mult_in_gga(X, Y, Z)) mult_in_gga(0, Y, 0) -> mult_out_gga(0, Y, 0) U9_gga(X, Y, R, mult_out_gga(X, Y, Z)) -> U10_gga(X, Y, R, add_in_gga(Y, Z, R))
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