Logic Programming pair #487096356

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	n145.star.cs.uiowa.edu
space	terminweb_new

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.06019 seconds
cpu usage	16.6131
user time	15.6634
system time	0.949708
max virtual memory	8.131372E7
max residence set size	1855684.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 29 ms]
(4) PiTRS
(5) DependencyPairsProof [EQUIVALENT, 35 ms]
(6) PiDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) PiDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) PiDP
        (12) PiDPToQDPProof [EQUIVALENT, 8 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, 0 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) QDPOrderProof [EQUIVALENT, 186 ms]
        (46) QDP
        (47) DependencyGraphProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) QDPQMonotonicMRRProof [EQUIVALENT, 51 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)
----------------------------------------

(1) UnifyTransformerProof (EQUIVALENT)
Added a fact for the built-in = predicate [PROLOG].
----------------------------------------

(2)
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))))).

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