details

property	value
status	complete
benchmark	balance_tree.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	terminweb_old

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.93317103386 seconds
cpu usage	4.508562517
max memory	3.62827776E8

stage attributes

key	value
output-size	21403
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern balance(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof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, 0 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) PiDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) PiDP (9) PiDPToQDPProof [SOUND, 0 ms] (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Clauses: balance(T, TB) :- balance(T, -(I, []), -(.(','(TB, -(I, [])), X), X), -(Rest, []), -(Rest, [])). balance(nil, -(X, X), -(A, B), -(A, B), -(.(','(nil, -(C, C)), T), T)). balance(tree(L, V, R), -(IH, IT), -(.(','(tree(LB, VB, RB), -(A, D)), H), .(','(LB, -(A, .(VB, X))), .(','(RB, -(X, D)), T))), -(HR, TR), -(NH, NT)) :- ','(balance(L, -(IH, .(V, IT1)), -(H, T), -(HR1, TR1), -(NH, NT1)), balance(R, -(IT1, IT), -(HR1, TR1), -(HR, TR), -(NT1, NT))). Query: balance(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: balance_in_2: (b,f) balance_in_5: (b,f,f,f,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: balance_in_ga(T, TB) -> U1_ga(T, TB, balance_in_gaaaa(T, -(I, []), -(.(','(TB, -(I, [])), X), X), -(Rest, []), -(Rest, []))) balance_in_gaaaa(nil, -(X, X), -(A, B), -(A, B), -(.(','(nil, -(C, C)), T), T)) -> balance_out_gaaaa(nil, -(X, X), -(A, B), -(A, B), -(.(','(nil, -(C, C)), T), T)) balance_in_gaaaa(tree(L, V, R), -(IH, IT), -(.(','(tree(LB, VB, RB), -(A, D)), H), .(','(LB, -(A, .(VB, X))), .(','(RB, -(X, D)), T))), -(HR, TR), -(NH, NT)) -> U2_gaaaa(L, V, R, IH, IT, LB, VB, RB, A, D, H, X, T, HR, TR, NH, NT, balance_in_gaaaa(L, -(IH, .(V, IT1)), -(H, T), -(HR1, TR1), -(NH, NT1))) U2_gaaaa(L, V, R, IH, IT, LB, VB, RB, A, D, H, X, T, HR, TR, NH, NT, balance_out_gaaaa(L, -(IH, .(V, IT1)), -(H, T), -(HR1, TR1), -(NH, NT1))) -> U3_gaaaa(L, V, R, IH, IT, LB, VB, RB, A, D, H, X, T, HR, TR, NH, NT, balance_in_gaaaa(R, -(IT1, IT), -(HR1, TR1), -(HR, TR), -(NT1, NT))) U3_gaaaa(L, V, R, IH, IT, LB, VB, RB, A, D, H, X, T, HR, TR, NH, NT, balance_out_gaaaa(R, -(IT1, IT), -(HR1, TR1), -(HR, TR), -(NT1, NT))) -> balance_out_gaaaa(tree(L, V, R), -(IH, IT), -(.(','(tree(LB, VB, RB), -(A, D)), H), .(','(LB, -(A, .(VB, X))), .(','(RB, -(X, D)), T))), -(HR, TR), -(NH, NT)) U1_ga(T, TB, balance_out_gaaaa(T, -(I, []), -(.(','(TB, -(I, [])), X), X), -(Rest, []), -(Rest, []))) -> balance_out_ga(T, TB) The argument filtering Pi contains the following mapping: balance_in_ga(x1, x2) = balance_in_ga(x1) U1_ga(x1, x2, x3) = U1_ga(x1, x3) balance_in_gaaaa(x1, x2, x3, x4, x5) = balance_in_gaaaa(x1) nil = nil balance_out_gaaaa(x1, x2, x3, x4, x5) = balance_out_gaaaa(x1) tree(x1, x2, x3) = tree(x1, x2, x3) U2_gaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) = U2_gaaaa(x1, x2, x3, x18) U3_gaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) = U3_gaaaa(x1, x2, x3, x18) balance_out_ga(x1, x2) = balance_out_ga(x1) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (2) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: balance_in_ga(T, TB) -> U1_ga(T, TB, balance_in_gaaaa(T, -(I, []), -(.(','(TB, -(I, [])), X), X), -(Rest, []), -(Rest, []))) popout

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