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Logic Programming pair #487529305
details
property
value
status
complete
benchmark
flatten_phd.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n022.star.cs.uiowa.edu
space
SGST06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.33077692986 seconds
cpu usage
5.845660762
max memory
5.16722688E8
stage attributes
key
value
output-size
21757
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern count(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND,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, 15 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) UsableRulesReductionPairsProof [EQUIVALENT, 20 ms] (13) QDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) PiDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) PiDP (19) PiDPToQDPProof [SOUND, 0 ms] (20) QDP (21) UsableRulesReductionPairsProof [EQUIVALENT, 32 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) TRUE ---------------------------------------- (0) Obligation: Clauses: flatten(atom(X), .(X, [])). flatten(cons(atom(X), U), .(X, Y)) :- flatten(U, Y). flatten(cons(cons(U, V), W), X) :- flatten(cons(U, cons(V, W)), X). count(atom(X), s(0)). count(cons(atom(X), Y), s(Z)) :- count(Y, Z). count(cons(cons(U, V), W), Z) :- ','(flatten(cons(cons(U, V), W), X), count(X, Z)). Query: count(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: count_in_2: (b,f) flatten_in_2: (b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: count_in_ga(atom(X), s(0)) -> count_out_ga(atom(X), s(0)) count_in_ga(cons(atom(X), Y), s(Z)) -> U3_ga(X, Y, Z, count_in_ga(Y, Z)) count_in_ga(cons(cons(U, V), W), Z) -> U4_ga(U, V, W, Z, flatten_in_ga(cons(cons(U, V), W), X)) flatten_in_ga(atom(X), .(X, [])) -> flatten_out_ga(atom(X), .(X, [])) flatten_in_ga(cons(atom(X), U), .(X, Y)) -> U1_ga(X, U, Y, flatten_in_ga(U, Y)) flatten_in_ga(cons(cons(U, V), W), X) -> U2_ga(U, V, W, X, flatten_in_ga(cons(U, cons(V, W)), X)) U2_ga(U, V, W, X, flatten_out_ga(cons(U, cons(V, W)), X)) -> flatten_out_ga(cons(cons(U, V), W), X) U1_ga(X, U, Y, flatten_out_ga(U, Y)) -> flatten_out_ga(cons(atom(X), U), .(X, Y)) U4_ga(U, V, W, Z, flatten_out_ga(cons(cons(U, V), W), X)) -> U5_ga(U, V, W, Z, count_in_ga(X, Z)) U5_ga(U, V, W, Z, count_out_ga(X, Z)) -> count_out_ga(cons(cons(U, V), W), Z) U3_ga(X, Y, Z, count_out_ga(Y, Z)) -> count_out_ga(cons(atom(X), Y), s(Z)) The argument filtering Pi contains the following mapping: count_in_ga(x1, x2) = count_in_ga(x1) atom(x1) = atom(x1) count_out_ga(x1, x2) = count_out_ga(x2) cons(x1, x2) = cons(x1, x2) U3_ga(x1, x2, x3, x4) = U3_ga(x4) U4_ga(x1, x2, x3, x4, x5) = U4_ga(x5) flatten_in_ga(x1, x2) = flatten_in_ga(x1)
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