Logic Programming pair #487529333

details

property	value
status	complete
benchmark	ways.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	terminweb_new

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.80707502365 seconds
cpu usage	19.932140659
max memory	2.167595008E9

stage attributes

key	value
output-size	77922
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

ways(g,g,a)

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

(0) Prolog
(1) UnifyTransformerProof [EQUIVALENT, 0 ms]
(2) Prolog
(3) PrologToPiTRSProof [SOUND, 0 ms]
(4) PiTRS
(5) DependencyPairsProof [EQUIVALENT, 1 ms]
(6) PiDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) PiDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) PiDP
        (12) PiDPToQDPProof [EQUIVALENT, 3 ms]
        (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) PiDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) PiDP
        (19) PiDPToQDPProof [SOUND, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) PiDP
        (24) UsableRulesProof [EQUIVALENT, 0 ms]
        (25) PiDP
        (26) PiDPToQDPProof [SOUND, 0 ms]
        (27) QDP
        (28) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) PiDP
        (31) PiDPToQDPProof [SOUND, 4 ms]
        (32) QDP
        (33) TransformationProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) TransformationProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) TransformationProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) TransformationProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) TransformationProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) TransformationProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) QDPQMonotonicMRRProof [EQUIVALENT, 121 ms]
        (46) QDP
        (47) DependencyGraphProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) QDPOrderProof [EQUIVALENT, 395 ms]
        (50) QDP
        (51) DependencyGraphProof [EQUIVALENT, 0 ms]
        (52) TRUE


----------------------------------------

(0)
Obligation:
Clauses:

nat(0).
nat(s(X)) :- nat(X).
plus(0, X, X) :- nat(X).
plus(s(X), Y, s(Z)) :- plus(X, Y, Z).
ways(0, X1, s(0)).
ways(X2, [], 0).
ways(Amount, .(s(C), Coins), N) :- ','(=(Amount, s(X3)), ','(plus(s(C), NewAmount, Amount), ','(ways(Amount, Coins, N1), ','(ways(NewAmount, .(s(C), Coins), N2), plus(N1, N2, N))))).
ways(Amount, .(s(C), Coins), N) :- ','(=(Amount, s(X4)), ','(plus(Amount, s(X5), s(C)), ways(Amount, Coins, N))).


Query: ways(g,g,a)
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(1) UnifyTransformerProof (EQUIVALENT)
Added a fact for the built-in = predicate [PROLOG].
----------------------------------------

(2)
Obligation:
Clauses:

nat(0).

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