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Logic Programming pair #487529351
details
property
value
status
complete
benchmark
der.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
terminweb_new
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.02840614319 seconds
cpu usage
8.833632171
max memory
8.94009344E8
stage attributes
key
value
output-size
22278
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern der(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0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, 5 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) PiDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) PiDP (10) PiDPToQDPProof [SOUND, 2 ms] (11) QDP (12) QDPQMonotonicMRRProof [EQUIVALENT, 62 ms] (13) QDP (14) DependencyGraphProof [EQUIVALENT, 0 ms] (15) TRUE (16) PiDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) PiDP (19) PiDPToQDPProof [SOUND, 0 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Clauses: der(d(e(t)), const(1)). der(d(e(const(A))), const(0)). der(d(e(+(X, Y))), +(DX, DY)) :- ','(der(d(e(X)), DX), der(d(e(Y)), DY)). der(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) :- ','(der(d(e(X)), DX), der(d(e(Y)), DY)). der(d(d(X)), DDX) :- ','(der(d(X), DX), der(d(e(DX)), DDX)). Query: der(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: der_in_2: (b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: der_in_ga(d(e(t)), const(1)) -> der_out_ga(d(e(t)), const(1)) der_in_ga(d(e(const(A))), const(0)) -> der_out_ga(d(e(const(A))), const(0)) der_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, der_in_ga(d(e(X)), DX)) der_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, der_in_ga(d(e(X)), DX)) der_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, der_in_ga(d(X), DX)) U5_ga(X, DDX, der_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, der_in_ga(d(e(DX)), DDX)) U6_ga(X, DDX, DX, der_out_ga(d(e(DX)), DDX)) -> der_out_ga(d(d(X)), DDX) U3_ga(X, Y, DY, DX, der_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, der_in_ga(d(e(Y)), DY)) U4_ga(X, Y, DY, DX, der_out_ga(d(e(Y)), DY)) -> der_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) U1_ga(X, Y, DX, DY, der_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, der_in_ga(d(e(Y)), DY)) U2_ga(X, Y, DX, DY, der_out_ga(d(e(Y)), DY)) -> der_out_ga(d(e(+(X, Y))), +(DX, DY)) The argument filtering Pi contains the following mapping: der_in_ga(x1, x2) = der_in_ga(x1) d(x1) = d(x1) e(x1) = e(x1) t = t der_out_ga(x1, x2) = der_out_ga(x2) const(x1) = const(x1) +(x1, x2) = +(x1, x2) U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) *(x1, x2) = *(x1, x2) U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5)
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