0 Prolog
↳1 PrologToPrologProblemTransformerProof (⇒, 383 ms)
↳2 Prolog
↳3 PrologToPiTRSProof (⇒, 0 ms)
↳4 PiTRS
↳5 DependencyPairsProof (⇔, 0 ms)
↳6 PiDP
↳7 PisEmptyProof (⇔, 0 ms)
↳8 YES
parseA_in_ga(.(a, .(book, .(falls, []))), s(s, book, fall)) → parseA_out_ga(.(a, .(book, .(falls, []))), s(s, book, fall))
parseA_in_ga(.(a, .(book, .(flies, []))), s(s, book, fly)) → parseA_out_ga(.(a, .(book, .(flies, []))), s(s, book, fly))
parseA_in_ga(.(a, .(box, .(falls, []))), s(s, box, fall)) → parseA_out_ga(.(a, .(box, .(falls, []))), s(s, box, fall))
parseA_in_ga(.(a, .(box, .(flies, []))), s(s, box, fly)) → parseA_out_ga(.(a, .(box, .(flies, []))), s(s, box, fly))
parseA_in_ga(.(the, .(book, .(falls, []))), s(s, book, fall)) → parseA_out_ga(.(the, .(book, .(falls, []))), s(s, book, fall))
parseA_in_ga(.(the, .(book, .(flies, []))), s(s, book, fly)) → parseA_out_ga(.(the, .(book, .(flies, []))), s(s, book, fly))
parseA_in_ga(.(the, .(books, .(fall, []))), s(p, book, fall)) → parseA_out_ga(.(the, .(books, .(fall, []))), s(p, book, fall))
parseA_in_ga(.(the, .(books, .(fly, []))), s(p, book, fly)) → parseA_out_ga(.(the, .(books, .(fly, []))), s(p, book, fly))
parseA_in_ga(.(the, .(box, .(falls, []))), s(s, box, fall)) → parseA_out_ga(.(the, .(box, .(falls, []))), s(s, box, fall))
parseA_in_ga(.(the, .(box, .(flies, []))), s(s, box, fly)) → parseA_out_ga(.(the, .(box, .(flies, []))), s(s, box, fly))
parseA_in_ga(.(the, .(boxes, .(fall, []))), s(p, box, fall)) → parseA_out_ga(.(the, .(boxes, .(fall, []))), s(p, box, fall))
parseA_in_ga(.(the, .(boxes, .(fly, []))), s(p, box, fly)) → parseA_out_ga(.(the, .(boxes, .(fly, []))), s(p, box, fly))
Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
parseA_in_ga(.(a, .(book, .(falls, []))), s(s, book, fall)) → parseA_out_ga(.(a, .(book, .(falls, []))), s(s, book, fall))
parseA_in_ga(.(a, .(book, .(flies, []))), s(s, book, fly)) → parseA_out_ga(.(a, .(book, .(flies, []))), s(s, book, fly))
parseA_in_ga(.(a, .(box, .(falls, []))), s(s, box, fall)) → parseA_out_ga(.(a, .(box, .(falls, []))), s(s, box, fall))
parseA_in_ga(.(a, .(box, .(flies, []))), s(s, box, fly)) → parseA_out_ga(.(a, .(box, .(flies, []))), s(s, box, fly))
parseA_in_ga(.(the, .(book, .(falls, []))), s(s, book, fall)) → parseA_out_ga(.(the, .(book, .(falls, []))), s(s, book, fall))
parseA_in_ga(.(the, .(book, .(flies, []))), s(s, book, fly)) → parseA_out_ga(.(the, .(book, .(flies, []))), s(s, book, fly))
parseA_in_ga(.(the, .(books, .(fall, []))), s(p, book, fall)) → parseA_out_ga(.(the, .(books, .(fall, []))), s(p, book, fall))
parseA_in_ga(.(the, .(books, .(fly, []))), s(p, book, fly)) → parseA_out_ga(.(the, .(books, .(fly, []))), s(p, book, fly))
parseA_in_ga(.(the, .(box, .(falls, []))), s(s, box, fall)) → parseA_out_ga(.(the, .(box, .(falls, []))), s(s, box, fall))
parseA_in_ga(.(the, .(box, .(flies, []))), s(s, box, fly)) → parseA_out_ga(.(the, .(box, .(flies, []))), s(s, box, fly))
parseA_in_ga(.(the, .(boxes, .(fall, []))), s(p, box, fall)) → parseA_out_ga(.(the, .(boxes, .(fall, []))), s(p, box, fall))
parseA_in_ga(.(the, .(boxes, .(fly, []))), s(p, box, fly)) → parseA_out_ga(.(the, .(boxes, .(fly, []))), s(p, box, fly))
parseA_in_ga(.(a, .(book, .(falls, []))), s(s, book, fall)) → parseA_out_ga(.(a, .(book, .(falls, []))), s(s, book, fall))
parseA_in_ga(.(a, .(book, .(flies, []))), s(s, book, fly)) → parseA_out_ga(.(a, .(book, .(flies, []))), s(s, book, fly))
parseA_in_ga(.(a, .(box, .(falls, []))), s(s, box, fall)) → parseA_out_ga(.(a, .(box, .(falls, []))), s(s, box, fall))
parseA_in_ga(.(a, .(box, .(flies, []))), s(s, box, fly)) → parseA_out_ga(.(a, .(box, .(flies, []))), s(s, box, fly))
parseA_in_ga(.(the, .(book, .(falls, []))), s(s, book, fall)) → parseA_out_ga(.(the, .(book, .(falls, []))), s(s, book, fall))
parseA_in_ga(.(the, .(book, .(flies, []))), s(s, book, fly)) → parseA_out_ga(.(the, .(book, .(flies, []))), s(s, book, fly))
parseA_in_ga(.(the, .(books, .(fall, []))), s(p, book, fall)) → parseA_out_ga(.(the, .(books, .(fall, []))), s(p, book, fall))
parseA_in_ga(.(the, .(books, .(fly, []))), s(p, book, fly)) → parseA_out_ga(.(the, .(books, .(fly, []))), s(p, book, fly))
parseA_in_ga(.(the, .(box, .(falls, []))), s(s, box, fall)) → parseA_out_ga(.(the, .(box, .(falls, []))), s(s, box, fall))
parseA_in_ga(.(the, .(box, .(flies, []))), s(s, box, fly)) → parseA_out_ga(.(the, .(box, .(flies, []))), s(s, box, fly))
parseA_in_ga(.(the, .(boxes, .(fall, []))), s(p, box, fall)) → parseA_out_ga(.(the, .(boxes, .(fall, []))), s(p, box, fall))
parseA_in_ga(.(the, .(boxes, .(fly, []))), s(p, box, fly)) → parseA_out_ga(.(the, .(boxes, .(fly, []))), s(p, box, fly))
parseA_in_ga(.(a, .(book, .(falls, []))), s(s, book, fall)) → parseA_out_ga(.(a, .(book, .(falls, []))), s(s, book, fall))
parseA_in_ga(.(a, .(book, .(flies, []))), s(s, book, fly)) → parseA_out_ga(.(a, .(book, .(flies, []))), s(s, book, fly))
parseA_in_ga(.(a, .(box, .(falls, []))), s(s, box, fall)) → parseA_out_ga(.(a, .(box, .(falls, []))), s(s, box, fall))
parseA_in_ga(.(a, .(box, .(flies, []))), s(s, box, fly)) → parseA_out_ga(.(a, .(box, .(flies, []))), s(s, box, fly))
parseA_in_ga(.(the, .(book, .(falls, []))), s(s, book, fall)) → parseA_out_ga(.(the, .(book, .(falls, []))), s(s, book, fall))
parseA_in_ga(.(the, .(book, .(flies, []))), s(s, book, fly)) → parseA_out_ga(.(the, .(book, .(flies, []))), s(s, book, fly))
parseA_in_ga(.(the, .(books, .(fall, []))), s(p, book, fall)) → parseA_out_ga(.(the, .(books, .(fall, []))), s(p, book, fall))
parseA_in_ga(.(the, .(books, .(fly, []))), s(p, book, fly)) → parseA_out_ga(.(the, .(books, .(fly, []))), s(p, book, fly))
parseA_in_ga(.(the, .(box, .(falls, []))), s(s, box, fall)) → parseA_out_ga(.(the, .(box, .(falls, []))), s(s, box, fall))
parseA_in_ga(.(the, .(box, .(flies, []))), s(s, box, fly)) → parseA_out_ga(.(the, .(box, .(flies, []))), s(s, box, fly))
parseA_in_ga(.(the, .(boxes, .(fall, []))), s(p, box, fall)) → parseA_out_ga(.(the, .(boxes, .(fall, []))), s(p, box, fall))
parseA_in_ga(.(the, .(boxes, .(fly, []))), s(p, box, fly)) → parseA_out_ga(.(the, .(boxes, .(fly, []))), s(p, box, fly))