details

property	value
status	complete
benchmark	totient.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	prolog_mixed

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.01214408875 seconds
cpu usage	8.836306462
max memory	9.8535424E8

stage attributes

key	value
output-size	62436
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern t_phi(g,a,g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 42 ms] (2) IRSwT (3) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 33 ms] (6) IRSwT (7) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 34 ms] (10) IRSwT (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 3 ms] (14) IRSwT (15) TempFilterProof [SOUND, 37 ms] (16) IntTRS (17) RankingReductionPairProof [EQUIVALENT, 19 ms] (18) YES ---------------------------------------- (0) Obligation: Clauses: totient_phi(1, 1) :- !. totient_phi(M, Phi) :- t_phi(M, Phi, 1, 0). t_phi(M, Phi, M, Phi) :- !. t_phi(M, Phi, K, C) :- ','(<(K, M), ','(coprime(K, M), ','(!, ','(is(C1, +(C, 1)), ','(is(K1, +(K, 1)), t_phi(M, Phi, K1, C1)))))). t_phi(M, Phi, K, C) :- ','(<(K, M), ','(is(K1, +(K, 1)), t_phi(M, Phi, K1, C))). coprime(X, Y) :- gcd(X, Y, 1). gcd(X, 0, X) :- >(X, 0). gcd(X, Y, G) :- ','(>(Y, 0), ','(is(Z, mod(X, Y)), gcd(Y, Z, G))). Query: t_phi(g,a,g,g) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 3, "program": { "directives": [], "clauses": [ [ "(totient_phi (1) (1))", "(!)" ], [ "(totient_phi M Phi)", "(t_phi M Phi (1) (0))" ], [ "(t_phi M Phi M Phi)", "(!)" ], [ "(t_phi M Phi K C)", "(',' (< K M) (',' (coprime K M) (',' (!) (',' (is C1 (+ C (1))) (',' (is K1 (+ K (1))) (t_phi M Phi K1 C1))))))" ], [ "(t_phi M Phi K C)", "(',' (< K M) (',' (is K1 (+ K (1))) (t_phi M Phi K1 C)))" ], [ "(coprime X Y)", "(gcd X Y (1))" ], [ "(gcd X (0) X)", "(> X (0))" ], [ "(gcd X Y G)", "(',' (> Y (0)) (',' (is Z (mod X Y)) (gcd Y Z G)))" ] ] }, "graph": { popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Logic Progr 19030