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Logic Programming pair #487096234
details
property
value
status
complete
benchmark
cnfequiv.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
SGST06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.35159 seconds
cpu usage
9.28775
user time
8.80193
system time
0.485824
max virtual memory
1.9675028E7
max residence set size
861608.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern cnfequiv(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 24 ms] (2) PiTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) PiDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) PiDP (10) PiDPToQDPProof [SOUND, 9 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) PiDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) PiDP (17) PiDPToQDPProof [SOUND, 0 ms] (18) QDP (19) QDPOrderProof [EQUIVALENT, 176 ms] (20) QDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Clauses: cnfequiv(X, Y) :- ','(transform(X, Z), cnfequiv(Z, Y)). cnfequiv(X, X). transform(n(n(X)), X). transform(n(a(X, Y)), o(n(X), n(Y))). transform(n(o(X, Y)), a(n(X), n(Y))). transform(o(X, a(Y, Z)), a(o(X, Y), o(X, Z))). transform(o(a(X, Y), Z), a(o(X, Z), o(Y, Z))). transform(o(X1, Y), o(X2, Y)) :- transform(X1, X2). transform(o(X, Y1), o(X, Y2)) :- transform(Y1, Y2). transform(a(X1, Y), a(X2, Y)) :- transform(X1, X2). transform(a(X, Y1), a(X, Y2)) :- transform(Y1, Y2). transform(n(X1), n(X2)) :- transform(X1, X2). Query: cnfequiv(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: cnfequiv_in_2: (b,f) transform_in_2: (b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: cnfequiv_in_ga(X, Y) -> U1_ga(X, Y, transform_in_ga(X, Z)) transform_in_ga(n(n(X)), X) -> transform_out_ga(n(n(X)), X) transform_in_ga(n(a(X, Y)), o(n(X), n(Y))) -> transform_out_ga(n(a(X, Y)), o(n(X), n(Y))) transform_in_ga(n(o(X, Y)), a(n(X), n(Y))) -> transform_out_ga(n(o(X, Y)), a(n(X), n(Y))) transform_in_ga(o(X, a(Y, Z)), a(o(X, Y), o(X, Z))) -> transform_out_ga(o(X, a(Y, Z)), a(o(X, Y), o(X, Z))) transform_in_ga(o(a(X, Y), Z), a(o(X, Z), o(Y, Z))) -> transform_out_ga(o(a(X, Y), Z), a(o(X, Z), o(Y, Z))) transform_in_ga(o(X1, Y), o(X2, Y)) -> U3_ga(X1, Y, X2, transform_in_ga(X1, X2)) transform_in_ga(o(X, Y1), o(X, Y2)) -> U4_ga(X, Y1, Y2, transform_in_ga(Y1, Y2)) transform_in_ga(a(X1, Y), a(X2, Y)) -> U5_ga(X1, Y, X2, transform_in_ga(X1, X2)) transform_in_ga(a(X, Y1), a(X, Y2)) -> U6_ga(X, Y1, Y2, transform_in_ga(Y1, Y2)) transform_in_ga(n(X1), n(X2)) -> U7_ga(X1, X2, transform_in_ga(X1, X2)) U7_ga(X1, X2, transform_out_ga(X1, X2)) -> transform_out_ga(n(X1), n(X2)) U6_ga(X, Y1, Y2, transform_out_ga(Y1, Y2)) -> transform_out_ga(a(X, Y1), a(X, Y2)) U5_ga(X1, Y, X2, transform_out_ga(X1, X2)) -> transform_out_ga(a(X1, Y), a(X2, Y)) U4_ga(X, Y1, Y2, transform_out_ga(Y1, Y2)) -> transform_out_ga(o(X, Y1), o(X, Y2)) U3_ga(X1, Y, X2, transform_out_ga(X1, X2)) -> transform_out_ga(o(X1, Y), o(X2, Y)) U1_ga(X, Y, transform_out_ga(X, Z)) -> U2_ga(X, Y, cnfequiv_in_ga(Z, Y)) cnfequiv_in_ga(X, X) -> cnfequiv_out_ga(X, X) U2_ga(X, Y, cnfequiv_out_ga(Z, Y)) -> cnfequiv_out_ga(X, Y) The argument filtering Pi contains the following mapping: cnfequiv_in_ga(x1, x2) = cnfequiv_in_ga(x1) U1_ga(x1, x2, x3) = U1_ga(x3) transform_in_ga(x1, x2) = transform_in_ga(x1) n(x1) = n(x1)
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