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Logic Programming pair #487529155
details
property
value
status
complete
benchmark
pl8.4.1.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
talp_plumer
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.75457406044 seconds
cpu usage
3.831659289
max memory
2.66534912E8
stage attributes
key
value
output-size
5318
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern even(g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0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 [EQUIVALENT, 0 ms] (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Clauses: even(0). even(s(X)) :- odd(X). odd(s(X)) :- even(X). Query: even(g) ---------------------------------------- (1) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: even_in_1: (b) odd_in_1: (b) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: even_in_g(0) -> even_out_g(0) even_in_g(s(X)) -> U1_g(X, odd_in_g(X)) odd_in_g(s(X)) -> U2_g(X, even_in_g(X)) U2_g(X, even_out_g(X)) -> odd_out_g(s(X)) U1_g(X, odd_out_g(X)) -> even_out_g(s(X)) Pi is empty. Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (2) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: even_in_g(0) -> even_out_g(0) even_in_g(s(X)) -> U1_g(X, odd_in_g(X)) odd_in_g(s(X)) -> U2_g(X, even_in_g(X)) U2_g(X, even_out_g(X)) -> odd_out_g(s(X)) U1_g(X, odd_out_g(X)) -> even_out_g(s(X)) Pi is empty. ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: Pi DP problem: The TRS P consists of the following rules: EVEN_IN_G(s(X)) -> U1_G(X, odd_in_g(X)) EVEN_IN_G(s(X)) -> ODD_IN_G(X) ODD_IN_G(s(X)) -> U2_G(X, even_in_g(X)) ODD_IN_G(s(X)) -> EVEN_IN_G(X) The TRS R consists of the following rules:
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