Logic Progr 19030 pair #381919971

details

property	value
status	complete
benchmark	p2_09.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	Hett

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.64884305 seconds
cpu usage	11.114072757
max memory	1.213956096E9

stage attributes

key	value
output-size	510650
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

totient_phi(g,a)

w.r.t. the given Prolog program could successfully be proven:

(0) Prolog
(1) PrologToIRSwTTransformerProof [SOUND, 134 ms]
(2) AND
    (3) IRSwT
        (4) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 1 ms]
        (5) TRUE
    (6) IRSwT
        (7) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms]
        (8) IRSwT
        (9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (10) IRSwT
        (11) IRSFormatTransformerProof [EQUIVALENT, 1 ms]
        (12) IRSwT
        (13) IRSwTTerminationDigraphProof [EQUIVALENT, 31 ms]
        (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) TempFilterProof [SOUND, 40 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (20) 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: totient_phi(g,a)
----------------------------------------

(1) PrologToIRSwTTransformerProof (SOUND)
Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert

{
    "root": 1,
    "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)))"
            ]
        ]

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