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Logic Progr 19030 pair #381919862
details
property
value
status
complete
benchmark
pl1.2_t.pl
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
talp_plumer
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.50277590752 seconds
cpu usage
6.603418472
max memory
3.58621184E8
stage attributes
key
value
output-size
28324
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern perm(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0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, 3 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) PiDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) PiDP (10) PiDPToQDPProof [SOUND, 0 ms] (11) QDP (12) UsableRulesReductionPairsProof [EQUIVALENT, 2 ms] (13) QDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) PiDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) PiDP (19) PiDPToQDPProof [SOUND, 0 ms] (20) QDP (21) UsableRulesReductionPairsProof [EQUIVALENT, 4 ms] (22) QDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES (25) PiDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) PiDP (28) PiDPToQDPProof [SOUND, 0 ms] (29) QDP (30) MRRProof [EQUIVALENT, 0 ms] (31) QDP (32) PisEmptyProof [EQUIVALENT, 0 ms] (33) YES ---------------------------------------- (0) Obligation: Clauses: append2(parts([], Y), is(sum(Y))). append2(parts(.(H, X), Y), is(sum(.(H, Z)))) :- append2(parts(X, Y), is(sum(Z))). append1(parts([], Y), is(sum(Y))). append1(parts(.(H, X), Y), is(sum(.(H, Z)))) :- append1(parts(X, Y), is(sum(Z))). perm([], []). perm(L, .(H, T)) :- ','(append2(parts(V, .(H, U)), is(sum(L))), ','(append1(parts(V, U), is(sum(W))), perm(W, T))). Query: perm(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: perm_in_2: (b,f) append2_in_2: (f,b) append1_in_2: (b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: perm_in_ga([], []) -> perm_out_ga([], []) perm_in_ga(L, .(H, T)) -> U3_ga(L, H, T, append2_in_ag(parts(V, .(H, U)), is(sum(L)))) append2_in_ag(parts([], Y), is(sum(Y))) -> append2_out_ag(parts([], Y), is(sum(Y))) append2_in_ag(parts(.(H, X), Y), is(sum(.(H, Z)))) -> U1_ag(H, X, Y, Z, append2_in_ag(parts(X, Y), is(sum(Z)))) U1_ag(H, X, Y, Z, append2_out_ag(parts(X, Y), is(sum(Z)))) -> append2_out_ag(parts(.(H, X), Y), is(sum(.(H, Z)))) U3_ga(L, H, T, append2_out_ag(parts(V, .(H, U)), is(sum(L)))) -> U4_ga(L, H, T, V, U, append1_in_ga(parts(V, U), is(sum(W)))) append1_in_ga(parts([], Y), is(sum(Y))) -> append1_out_ga(parts([], Y), is(sum(Y))) append1_in_ga(parts(.(H, X), Y), is(sum(.(H, Z)))) -> U2_ga(H, X, Y, Z, append1_in_ga(parts(X, Y), is(sum(Z)))) U2_ga(H, X, Y, Z, append1_out_ga(parts(X, Y), is(sum(Z)))) -> append1_out_ga(parts(.(H, X), Y), is(sum(.(H, Z)))) U4_ga(L, H, T, V, U, append1_out_ga(parts(V, U), is(sum(W)))) -> U5_ga(L, H, T, perm_in_ga(W, T)) U5_ga(L, H, T, perm_out_ga(W, T)) -> perm_out_ga(L, .(H, T)) The argument filtering Pi contains the following mapping: perm_in_ga(x1, x2) = perm_in_ga(x1) [] = []
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