0 Prolog
↳1 PrologToPiTRSViaGraphTransformerProof (⇒, 730 ms)
↳2 PiTRS
↳3 DependencyPairsProof (⇔, 16 ms)
↳4 PiDP
↳5 DependencyGraphProof (⇔, 0 ms)
↳6 PiDP
↳7 UsableRulesProof (⇔, 0 ms)
↳8 PiDP
↳9 PiDPToQDPProof (⇒, 20 ms)
↳10 QDP
↳11 QDPSizeChangeProof (⇔, 0 ms)
↳12 YES
revA_in_ga([], []) → revA_out_ga([], [])
revA_in_ga(.(T54, []), .(T54, [])) → revA_out_ga(.(T54, []), .(T54, []))
revA_in_ga(.(T125, .(T124, [])), .(T124, .(T125, []))) → revA_out_ga(.(T125, .(T124, [])), .(T124, .(T125, [])))
revA_in_ga(.(T220, .(T219, .(T218, []))), .(T218, .(T219, .(T220, [])))) → revA_out_ga(.(T220, .(T219, .(T218, []))), .(T218, .(T219, .(T220, []))))
revA_in_ga(.(T339, .(T338, .(T337, .(T336, [])))), .(T336, .(T337, .(T338, .(T339, []))))) → revA_out_ga(.(T339, .(T338, .(T337, .(T336, [])))), .(T336, .(T337, .(T338, .(T339, [])))))
revA_in_ga(.(T482, .(T481, .(T480, .(T479, .(T478, []))))), .(T478, .(T479, .(T480, .(T481, .(T482, [])))))) → revA_out_ga(.(T482, .(T481, .(T480, .(T479, .(T478, []))))), .(T478, .(T479, .(T480, .(T481, .(T482, []))))))
revA_in_ga(.(T649, .(T648, .(T647, .(T646, .(T645, .(T644, [])))))), .(T644, .(T645, .(T646, .(T647, .(T648, .(T649, []))))))) → revA_out_ga(.(T649, .(T648, .(T647, .(T646, .(T645, .(T644, [])))))), .(T644, .(T645, .(T646, .(T647, .(T648, .(T649, [])))))))
revA_in_ga(.(T840, .(T839, .(T838, .(T837, .(T836, .(T835, .(T834, []))))))), .(T834, .(T835, .(T836, .(T837, .(T838, .(T839, .(T840, [])))))))) → revA_out_ga(.(T840, .(T839, .(T838, .(T837, .(T836, .(T835, .(T834, []))))))), .(T834, .(T835, .(T836, .(T837, .(T838, .(T839, .(T840, []))))))))
revA_in_ga(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885) → U1_ga(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_in_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885))
revB_in_ggga([], T1029, T1030, .(T1029, T1030)) → revB_out_ggga([], T1029, T1030, .(T1029, T1030))
revB_in_ggga(.(T1103, T1104), T1047, T1048, T1050) → U2_ggga(T1103, T1104, T1047, T1048, T1050, revB_in_ggga(T1104, T1103, .(T1047, T1048), T1050))
U2_ggga(T1103, T1104, T1047, T1048, T1050, revB_out_ggga(T1104, T1103, .(T1047, T1048), T1050)) → revB_out_ggga(.(T1103, T1104), T1047, T1048, T1050)
U1_ga(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_out_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885)) → revA_out_ga(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885)
REVA_IN_GA(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885) → U1_GA(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_in_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885))
REVA_IN_GA(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885) → REVB_IN_GGGA(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885)
REVB_IN_GGGA(.(T1103, T1104), T1047, T1048, T1050) → U2_GGGA(T1103, T1104, T1047, T1048, T1050, revB_in_ggga(T1104, T1103, .(T1047, T1048), T1050))
REVB_IN_GGGA(.(T1103, T1104), T1047, T1048, T1050) → REVB_IN_GGGA(T1104, T1103, .(T1047, T1048), T1050)
revA_in_ga([], []) → revA_out_ga([], [])
revA_in_ga(.(T54, []), .(T54, [])) → revA_out_ga(.(T54, []), .(T54, []))
revA_in_ga(.(T125, .(T124, [])), .(T124, .(T125, []))) → revA_out_ga(.(T125, .(T124, [])), .(T124, .(T125, [])))
revA_in_ga(.(T220, .(T219, .(T218, []))), .(T218, .(T219, .(T220, [])))) → revA_out_ga(.(T220, .(T219, .(T218, []))), .(T218, .(T219, .(T220, []))))
revA_in_ga(.(T339, .(T338, .(T337, .(T336, [])))), .(T336, .(T337, .(T338, .(T339, []))))) → revA_out_ga(.(T339, .(T338, .(T337, .(T336, [])))), .(T336, .(T337, .(T338, .(T339, [])))))
revA_in_ga(.(T482, .(T481, .(T480, .(T479, .(T478, []))))), .(T478, .(T479, .(T480, .(T481, .(T482, [])))))) → revA_out_ga(.(T482, .(T481, .(T480, .(T479, .(T478, []))))), .(T478, .(T479, .(T480, .(T481, .(T482, []))))))
revA_in_ga(.(T649, .(T648, .(T647, .(T646, .(T645, .(T644, [])))))), .(T644, .(T645, .(T646, .(T647, .(T648, .(T649, []))))))) → revA_out_ga(.(T649, .(T648, .(T647, .(T646, .(T645, .(T644, [])))))), .(T644, .(T645, .(T646, .(T647, .(T648, .(T649, [])))))))
revA_in_ga(.(T840, .(T839, .(T838, .(T837, .(T836, .(T835, .(T834, []))))))), .(T834, .(T835, .(T836, .(T837, .(T838, .(T839, .(T840, [])))))))) → revA_out_ga(.(T840, .(T839, .(T838, .(T837, .(T836, .(T835, .(T834, []))))))), .(T834, .(T835, .(T836, .(T837, .(T838, .(T839, .(T840, []))))))))
revA_in_ga(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885) → U1_ga(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_in_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885))
revB_in_ggga([], T1029, T1030, .(T1029, T1030)) → revB_out_ggga([], T1029, T1030, .(T1029, T1030))
revB_in_ggga(.(T1103, T1104), T1047, T1048, T1050) → U2_ggga(T1103, T1104, T1047, T1048, T1050, revB_in_ggga(T1104, T1103, .(T1047, T1048), T1050))
U2_ggga(T1103, T1104, T1047, T1048, T1050, revB_out_ggga(T1104, T1103, .(T1047, T1048), T1050)) → revB_out_ggga(.(T1103, T1104), T1047, T1048, T1050)
U1_ga(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_out_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885)) → revA_out_ga(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885)
REVA_IN_GA(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885) → U1_GA(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_in_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885))
REVA_IN_GA(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885) → REVB_IN_GGGA(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885)
REVB_IN_GGGA(.(T1103, T1104), T1047, T1048, T1050) → U2_GGGA(T1103, T1104, T1047, T1048, T1050, revB_in_ggga(T1104, T1103, .(T1047, T1048), T1050))
REVB_IN_GGGA(.(T1103, T1104), T1047, T1048, T1050) → REVB_IN_GGGA(T1104, T1103, .(T1047, T1048), T1050)
revA_in_ga([], []) → revA_out_ga([], [])
revA_in_ga(.(T54, []), .(T54, [])) → revA_out_ga(.(T54, []), .(T54, []))
revA_in_ga(.(T125, .(T124, [])), .(T124, .(T125, []))) → revA_out_ga(.(T125, .(T124, [])), .(T124, .(T125, [])))
revA_in_ga(.(T220, .(T219, .(T218, []))), .(T218, .(T219, .(T220, [])))) → revA_out_ga(.(T220, .(T219, .(T218, []))), .(T218, .(T219, .(T220, []))))
revA_in_ga(.(T339, .(T338, .(T337, .(T336, [])))), .(T336, .(T337, .(T338, .(T339, []))))) → revA_out_ga(.(T339, .(T338, .(T337, .(T336, [])))), .(T336, .(T337, .(T338, .(T339, [])))))
revA_in_ga(.(T482, .(T481, .(T480, .(T479, .(T478, []))))), .(T478, .(T479, .(T480, .(T481, .(T482, [])))))) → revA_out_ga(.(T482, .(T481, .(T480, .(T479, .(T478, []))))), .(T478, .(T479, .(T480, .(T481, .(T482, []))))))
revA_in_ga(.(T649, .(T648, .(T647, .(T646, .(T645, .(T644, [])))))), .(T644, .(T645, .(T646, .(T647, .(T648, .(T649, []))))))) → revA_out_ga(.(T649, .(T648, .(T647, .(T646, .(T645, .(T644, [])))))), .(T644, .(T645, .(T646, .(T647, .(T648, .(T649, [])))))))
revA_in_ga(.(T840, .(T839, .(T838, .(T837, .(T836, .(T835, .(T834, []))))))), .(T834, .(T835, .(T836, .(T837, .(T838, .(T839, .(T840, [])))))))) → revA_out_ga(.(T840, .(T839, .(T838, .(T837, .(T836, .(T835, .(T834, []))))))), .(T834, .(T835, .(T836, .(T837, .(T838, .(T839, .(T840, []))))))))
revA_in_ga(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885) → U1_ga(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_in_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885))
revB_in_ggga([], T1029, T1030, .(T1029, T1030)) → revB_out_ggga([], T1029, T1030, .(T1029, T1030))
revB_in_ggga(.(T1103, T1104), T1047, T1048, T1050) → U2_ggga(T1103, T1104, T1047, T1048, T1050, revB_in_ggga(T1104, T1103, .(T1047, T1048), T1050))
U2_ggga(T1103, T1104, T1047, T1048, T1050, revB_out_ggga(T1104, T1103, .(T1047, T1048), T1050)) → revB_out_ggga(.(T1103, T1104), T1047, T1048, T1050)
U1_ga(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_out_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885)) → revA_out_ga(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885)
REVB_IN_GGGA(.(T1103, T1104), T1047, T1048, T1050) → REVB_IN_GGGA(T1104, T1103, .(T1047, T1048), T1050)
revA_in_ga([], []) → revA_out_ga([], [])
revA_in_ga(.(T54, []), .(T54, [])) → revA_out_ga(.(T54, []), .(T54, []))
revA_in_ga(.(T125, .(T124, [])), .(T124, .(T125, []))) → revA_out_ga(.(T125, .(T124, [])), .(T124, .(T125, [])))
revA_in_ga(.(T220, .(T219, .(T218, []))), .(T218, .(T219, .(T220, [])))) → revA_out_ga(.(T220, .(T219, .(T218, []))), .(T218, .(T219, .(T220, []))))
revA_in_ga(.(T339, .(T338, .(T337, .(T336, [])))), .(T336, .(T337, .(T338, .(T339, []))))) → revA_out_ga(.(T339, .(T338, .(T337, .(T336, [])))), .(T336, .(T337, .(T338, .(T339, [])))))
revA_in_ga(.(T482, .(T481, .(T480, .(T479, .(T478, []))))), .(T478, .(T479, .(T480, .(T481, .(T482, [])))))) → revA_out_ga(.(T482, .(T481, .(T480, .(T479, .(T478, []))))), .(T478, .(T479, .(T480, .(T481, .(T482, []))))))
revA_in_ga(.(T649, .(T648, .(T647, .(T646, .(T645, .(T644, [])))))), .(T644, .(T645, .(T646, .(T647, .(T648, .(T649, []))))))) → revA_out_ga(.(T649, .(T648, .(T647, .(T646, .(T645, .(T644, [])))))), .(T644, .(T645, .(T646, .(T647, .(T648, .(T649, [])))))))
revA_in_ga(.(T840, .(T839, .(T838, .(T837, .(T836, .(T835, .(T834, []))))))), .(T834, .(T835, .(T836, .(T837, .(T838, .(T839, .(T840, [])))))))) → revA_out_ga(.(T840, .(T839, .(T838, .(T837, .(T836, .(T835, .(T834, []))))))), .(T834, .(T835, .(T836, .(T837, .(T838, .(T839, .(T840, []))))))))
revA_in_ga(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885) → U1_ga(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_in_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885))
revB_in_ggga([], T1029, T1030, .(T1029, T1030)) → revB_out_ggga([], T1029, T1030, .(T1029, T1030))
revB_in_ggga(.(T1103, T1104), T1047, T1048, T1050) → U2_ggga(T1103, T1104, T1047, T1048, T1050, revB_in_ggga(T1104, T1103, .(T1047, T1048), T1050))
U2_ggga(T1103, T1104, T1047, T1048, T1050, revB_out_ggga(T1104, T1103, .(T1047, T1048), T1050)) → revB_out_ggga(.(T1103, T1104), T1047, T1048, T1050)
U1_ga(T883, T882, T881, T880, T879, T878, T877, T998, T999, T885, revB_out_ggga(T999, T998, .(T877, .(T878, .(T879, .(T880, .(T881, .(T882, .(T883, []))))))), T885)) → revA_out_ga(.(T883, .(T882, .(T881, .(T880, .(T879, .(T878, .(T877, .(T998, T999)))))))), T885)
REVB_IN_GGGA(.(T1103, T1104), T1047, T1048, T1050) → REVB_IN_GGGA(T1104, T1103, .(T1047, T1048), T1050)
REVB_IN_GGGA(.(T1103, T1104), T1047, T1048) → REVB_IN_GGGA(T1104, T1103, .(T1047, T1048))
From the DPs we obtained the following set of size-change graphs: