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Logic Programming pair #487096494
details
property
value
status
complete
benchmark
delete-bfb.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
BCGGV05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.98618 seconds
cpu usage
4.70482
user time
4.51607
system time
0.18875
max virtual memory
1.874576E7
max residence set size
398268.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern delete(g,a,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0 ms] (2) PiTRS (3) DependencyPairsProof [EQUIVALENT, 4 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) PiDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) PiDP (10) PiDPToQDPProof [EQUIVALENT, 0 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) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) PiDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) PiDP (24) PiDPToQDPProof [SOUND, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES ---------------------------------------- (0) Obligation: Clauses: delete(X, tree(X, void, Right), Right). delete(X, tree(X, Left, void), Left). delete(X, tree(X, Left, Right), tree(Y, Left, Right1)) :- delmin(Right, Y, Right1). delete(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), delete(X, Left, Left1)). delete(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), delete(X, Right, Right1)). delmin(tree(Y, void, Right), Y, Right). delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1). less(0, s(X3)). less(s(X), s(Y)) :- less(X, Y). Query: delete(g,a,g) ---------------------------------------- (1) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: delete_in_3: (b,f,b) delmin_in_3: (f,b,b) less_in_2: (b,b) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: delete_in_gag(X, tree(X, void, Right), Right) -> delete_out_gag(X, tree(X, void, Right), Right) delete_in_gag(X, tree(X, Left, void), Left) -> delete_out_gag(X, tree(X, Left, void), Left) delete_in_gag(X, tree(X, Left, Right), tree(Y, Left, Right1)) -> U1_gag(X, Left, Right, Y, Right1, delmin_in_agg(Right, Y, Right1)) delmin_in_agg(tree(Y, void, Right), Y, Right) -> delmin_out_agg(tree(Y, void, Right), Y, Right) delmin_in_agg(tree(X, Left, X1), Y, tree(X, Left1, X2)) -> U6_agg(X, Left, X1, Y, Left1, X2, delmin_in_agg(Left, Y, Left1)) U6_agg(X, Left, X1, Y, Left1, X2, delmin_out_agg(Left, Y, Left1)) -> delmin_out_agg(tree(X, Left, X1), Y, tree(X, Left1, X2)) U1_gag(X, Left, Right, Y, Right1, delmin_out_agg(Right, Y, Right1)) -> delete_out_gag(X, tree(X, Left, Right), tree(Y, Left, Right1)) delete_in_gag(X, tree(Y, Left, Right), tree(Y, Left1, Right)) -> U2_gag(X, Y, Left, Right, Left1, less_in_gg(X, Y)) less_in_gg(0, s(X3)) -> less_out_gg(0, s(X3)) less_in_gg(s(X), s(Y)) -> U7_gg(X, Y, less_in_gg(X, Y)) U7_gg(X, Y, less_out_gg(X, Y)) -> less_out_gg(s(X), s(Y)) U2_gag(X, Y, Left, Right, Left1, less_out_gg(X, Y)) -> U3_gag(X, Y, Left, Right, Left1, delete_in_gag(X, Left, Left1)) delete_in_gag(X, tree(Y, Left, Right), tree(Y, Left, Right1)) -> U4_gag(X, Y, Left, Right, Right1, less_in_gg(Y, X)) U4_gag(X, Y, Left, Right, Right1, less_out_gg(Y, X)) -> U5_gag(X, Y, Left, Right, Right1, delete_in_gag(X, Right, Right1)) U5_gag(X, Y, Left, Right, Right1, delete_out_gag(X, Right, Right1)) -> delete_out_gag(X, tree(Y, Left, Right), tree(Y, Left, Right1)) U3_gag(X, Y, Left, Right, Left1, delete_out_gag(X, Left, Left1)) -> delete_out_gag(X, tree(Y, Left, Right), tree(Y, Left1, Right)) The argument filtering Pi contains the following mapping: delete_in_gag(x1, x2, x3) = delete_in_gag(x1, x3) delete_out_gag(x1, x2, x3) = delete_out_gag tree(x1, x2, x3) = tree(x1, x2, x3) U1_gag(x1, x2, x3, x4, x5, x6) = U1_gag(x6)
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