0 Prolog
↳1 PrologToPrologProblemTransformerProof (⇒, 373 ms)
↳2 Prolog
↳3 PrologToPiTRSProof (⇒, 179 ms)
↳4 PiTRS
↳5 DependencyPairsProof (⇔, 1285 ms)
↳6 PiDP
↳7 DependencyGraphProof (⇔, 7 ms)
↳8 AND
↳9 PiDP
↳10 UsableRulesProof (⇔, 0 ms)
↳11 PiDP
↳12 PiDPToQDPProof (⇔, 0 ms)
↳13 QDP
↳14 QDPSizeChangeProof (⇔, 0 ms)
↳15 YES
↳16 PiDP
↳17 UsableRulesProof (⇔, 0 ms)
↳18 PiDP
↳19 PiDPToQDPProof (⇒, 0 ms)
↳20 QDP
↳21 QDPSizeChangeProof (⇔, 0 ms)
↳22 YES
↳23 PiDP
↳24 UsableRulesProof (⇔, 0 ms)
↳25 PiDP
↳26 PiDPToQDPProof (⇒, 3 ms)
↳27 QDP
↳28 MRRProof (⇔, 99 ms)
↳29 QDP
↳30 DependencyGraphProof (⇔, 0 ms)
↳31 TRUE
log2D_in_ga(0, 0) → log2D_out_ga(0, 0)
log2D_in_ga(s(0), 0) → log2D_out_ga(s(0), 0)
log2D_in_ga(s(s(T12)), T14) → U8_ga(T12, T14, halfB_in_ga(T12, X26))
halfB_in_ga(T18, s(X35)) → U2_ga(T18, X35, halfA_in_ga(T18, X35))
halfA_in_ga(0, 0) → halfA_out_ga(0, 0)
halfA_in_ga(s(0), 0) → halfA_out_ga(s(0), 0)
halfA_in_ga(s(s(T21)), s(X44)) → U1_ga(T21, X44, halfA_in_ga(T21, X44))
U1_ga(T21, X44, halfA_out_ga(T21, X44)) → halfA_out_ga(s(s(T21)), s(X44))
U2_ga(T18, X35, halfA_out_ga(T18, X35)) → halfB_out_ga(T18, s(X35))
U8_ga(T12, T14, halfB_out_ga(T12, X26)) → log2D_out_ga(s(s(T12)), T14)
log2D_in_ga(s(s(T12)), s(0)) → U9_ga(T12, halfB_in_gg(T12, 0))
halfB_in_gg(T18, s(X35)) → U2_gg(T18, X35, halfA_in_gg(T18, X35))
halfA_in_gg(0, 0) → halfA_out_gg(0, 0)
halfA_in_gg(s(0), 0) → halfA_out_gg(s(0), 0)
halfA_in_gg(s(s(T21)), s(X44)) → U1_gg(T21, X44, halfA_in_gg(T21, X44))
U1_gg(T21, X44, halfA_out_gg(T21, X44)) → halfA_out_gg(s(s(T21)), s(X44))
U2_gg(T18, X35, halfA_out_gg(T18, X35)) → halfB_out_gg(T18, s(X35))
U9_ga(T12, halfB_out_gg(T12, 0)) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), s(0)) → U10_ga(T12, halfB_in_gg(T12, s(0)))
U10_ga(T12, halfB_out_gg(T12, s(0))) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), T28) → U11_ga(T12, T28, halfB_in_ga(T12, s(s(T26))))
U11_ga(T12, T28, halfB_out_ga(T12, s(s(T26)))) → U12_ga(T12, T28, halfB_in_ga(T26, X67))
U12_ga(T12, T28, halfB_out_ga(T26, X67)) → log2D_out_ga(s(s(T12)), T28)
log2D_in_ga(s(s(T12)), s(s(0))) → U13_ga(T12, halfB_in_ga(T12, s(s(T26))))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U14_ga(T12, halfB_in_gg(T26, 0))
U14_ga(T12, halfB_out_gg(T26, 0)) → log2D_out_ga(s(s(T12)), s(s(0)))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U15_ga(T12, halfB_in_gg(T26, s(0)))
U15_ga(T12, halfB_out_gg(T26, s(0))) → log2D_out_ga(s(s(T12)), s(s(0)))
log2D_in_ga(s(s(T12)), T36) → U16_ga(T12, T36, halfB_in_ga(T12, s(s(T26))))
U16_ga(T12, T36, halfB_out_ga(T12, s(s(T26)))) → U17_ga(T12, T36, halfB_in_ga(T26, s(s(T34))))
U17_ga(T12, T36, halfB_out_ga(T26, s(s(T34)))) → U18_ga(T12, T36, halfB_in_ga(T34, X90))
U18_ga(T12, T36, halfB_out_ga(T34, X90)) → log2D_out_ga(s(s(T12)), T36)
log2D_in_ga(s(s(T12)), s(s(s(0)))) → U19_ga(T12, halfB_in_ga(T12, s(s(T26))))
U19_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U20_ga(T12, halfB_in_ga(T26, s(s(T34))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U21_ga(T12, halfB_in_gg(T34, 0))
U21_ga(T12, halfB_out_gg(T34, 0)) → log2D_out_ga(s(s(T12)), s(s(s(0))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U22_ga(T12, halfB_in_gg(T34, s(0)))
U22_ga(T12, halfB_out_gg(T34, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(0))))
log2D_in_ga(s(s(T12)), T44) → U23_ga(T12, T44, halfB_in_ga(T12, s(s(T26))))
U23_ga(T12, T44, halfB_out_ga(T12, s(s(T26)))) → U24_ga(T12, T44, halfB_in_ga(T26, s(s(T34))))
U24_ga(T12, T44, halfB_out_ga(T26, s(s(T34)))) → U25_ga(T12, T44, halfB_in_ga(T34, s(s(T42))))
U25_ga(T12, T44, halfB_out_ga(T34, s(s(T42)))) → U26_ga(T12, T44, halfB_in_ga(T42, X113))
U26_ga(T12, T44, halfB_out_ga(T42, X113)) → log2D_out_ga(s(s(T12)), T44)
log2D_in_ga(s(s(T12)), s(s(s(s(0))))) → U27_ga(T12, halfB_in_ga(T12, s(s(T26))))
U27_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U28_ga(T12, halfB_in_ga(T26, s(s(T34))))
U28_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U29_ga(T12, halfB_in_ga(T34, s(s(T42))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U30_ga(T12, halfB_in_gg(T42, 0))
U30_ga(T12, halfB_out_gg(T42, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U31_ga(T12, halfB_in_gg(T42, s(0)))
U31_ga(T12, halfB_out_gg(T42, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
log2D_in_ga(s(s(T12)), T52) → U32_ga(T12, T52, halfB_in_ga(T12, s(s(T26))))
U32_ga(T12, T52, halfB_out_ga(T12, s(s(T26)))) → U33_ga(T12, T52, halfB_in_ga(T26, s(s(T34))))
U33_ga(T12, T52, halfB_out_ga(T26, s(s(T34)))) → U34_ga(T12, T52, halfB_in_ga(T34, s(s(T42))))
U34_ga(T12, T52, halfB_out_ga(T34, s(s(T42)))) → U35_ga(T12, T52, halfB_in_ga(T42, s(s(T50))))
U35_ga(T12, T52, halfB_out_ga(T42, s(s(T50)))) → U36_ga(T12, T52, halfB_in_ga(T50, X136))
U36_ga(T12, T52, halfB_out_ga(T50, X136)) → log2D_out_ga(s(s(T12)), T52)
log2D_in_ga(s(s(T12)), s(s(s(s(s(0)))))) → U37_ga(T12, halfB_in_ga(T12, s(s(T26))))
U37_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U38_ga(T12, halfB_in_ga(T26, s(s(T34))))
U38_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U39_ga(T12, halfB_in_ga(T34, s(s(T42))))
U39_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U40_ga(T12, halfB_in_ga(T42, s(s(T50))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U41_ga(T12, halfB_in_gg(T50, 0))
U41_ga(T12, halfB_out_gg(T50, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U42_ga(T12, halfB_in_gg(T50, s(0)))
U42_ga(T12, halfB_out_gg(T50, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
log2D_in_ga(s(s(T12)), T60) → U43_ga(T12, T60, halfB_in_ga(T12, s(s(T26))))
U43_ga(T12, T60, halfB_out_ga(T12, s(s(T26)))) → U44_ga(T12, T60, halfB_in_ga(T26, s(s(T34))))
U44_ga(T12, T60, halfB_out_ga(T26, s(s(T34)))) → U45_ga(T12, T60, halfB_in_ga(T34, s(s(T42))))
U45_ga(T12, T60, halfB_out_ga(T34, s(s(T42)))) → U46_ga(T12, T60, halfB_in_ga(T42, s(s(T50))))
U46_ga(T12, T60, halfB_out_ga(T42, s(s(T50)))) → U47_ga(T12, T60, halfB_in_ga(T50, s(s(T58))))
U47_ga(T12, T60, halfB_out_ga(T50, s(s(T58)))) → U48_ga(T12, T60, halfB_in_ga(T58, X159))
U48_ga(T12, T60, halfB_out_ga(T58, X159)) → log2D_out_ga(s(s(T12)), T60)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(0))))))) → U49_ga(T12, halfB_in_ga(T12, s(s(T26))))
U49_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U50_ga(T12, halfB_in_ga(T26, s(s(T34))))
U50_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U51_ga(T12, halfB_in_ga(T34, s(s(T42))))
U51_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U52_ga(T12, halfB_in_ga(T42, s(s(T50))))
U52_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U53_ga(T12, halfB_in_ga(T50, s(s(T58))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U54_ga(T12, halfB_in_gg(T58, 0))
U54_ga(T12, halfB_out_gg(T58, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U55_ga(T12, halfB_in_gg(T58, s(0)))
U55_ga(T12, halfB_out_gg(T58, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
log2D_in_ga(s(s(T12)), T68) → U56_ga(T12, T68, halfB_in_ga(T12, s(s(T26))))
U56_ga(T12, T68, halfB_out_ga(T12, s(s(T26)))) → U57_ga(T12, T68, halfB_in_ga(T26, s(s(T34))))
U57_ga(T12, T68, halfB_out_ga(T26, s(s(T34)))) → U58_ga(T12, T68, halfB_in_ga(T34, s(s(T42))))
U58_ga(T12, T68, halfB_out_ga(T34, s(s(T42)))) → U59_ga(T12, T68, halfB_in_ga(T42, s(s(T50))))
U59_ga(T12, T68, halfB_out_ga(T42, s(s(T50)))) → U60_ga(T12, T68, halfB_in_ga(T50, s(s(T58))))
U60_ga(T12, T68, halfB_out_ga(T50, s(s(T58)))) → U61_ga(T12, T68, halfB_in_ga(T58, s(s(T66))))
U61_ga(T12, T68, halfB_out_ga(T58, s(s(T66)))) → U62_ga(T12, T68, halfB_in_ga(T66, X182))
U62_ga(T12, T68, halfB_out_ga(T66, X182)) → log2D_out_ga(s(s(T12)), T68)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → U63_ga(T12, halfB_in_ga(T12, s(s(T26))))
U63_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U64_ga(T12, halfB_in_ga(T26, s(s(T34))))
U64_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U65_ga(T12, halfB_in_ga(T34, s(s(T42))))
U65_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U66_ga(T12, halfB_in_ga(T42, s(s(T50))))
U66_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U67_ga(T12, halfB_in_ga(T50, s(s(T58))))
U67_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U68_ga(T12, halfB_in_ga(T58, s(s(T66))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U69_ga(T12, halfB_in_gg(T66, 0))
U69_ga(T12, halfB_out_gg(T66, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U70_ga(T12, halfB_in_gg(T66, s(0)))
U70_ga(T12, halfB_out_gg(T66, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
log2D_in_ga(s(s(T12)), T76) → U71_ga(T12, T76, halfB_in_ga(T12, s(s(T26))))
U71_ga(T12, T76, halfB_out_ga(T12, s(s(T26)))) → U72_ga(T12, T76, halfB_in_ga(T26, s(s(T34))))
U72_ga(T12, T76, halfB_out_ga(T26, s(s(T34)))) → U73_ga(T12, T76, halfB_in_ga(T34, s(s(T42))))
U73_ga(T12, T76, halfB_out_ga(T34, s(s(T42)))) → U74_ga(T12, T76, halfB_in_ga(T42, s(s(T50))))
U74_ga(T12, T76, halfB_out_ga(T42, s(s(T50)))) → U75_ga(T12, T76, halfB_in_ga(T50, s(s(T58))))
U75_ga(T12, T76, halfB_out_ga(T50, s(s(T58)))) → U76_ga(T12, T76, halfB_in_ga(T58, s(s(T66))))
U76_ga(T12, T76, halfB_out_ga(T58, s(s(T66)))) → U77_ga(T12, T76, halfB_in_ga(T66, s(s(T74))))
U77_ga(T12, T76, halfB_out_ga(T66, s(s(T74)))) → U78_ga(T12, T76, pC_in_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76))
pC_in_gaga(T74, X205, T77, T76) → U3_gaga(T74, X205, T77, T76, halfB_in_ga(T74, X205))
U3_gaga(T74, X205, T77, T76, halfB_out_ga(T74, X205)) → pC_out_gaga(T74, X205, T77, T76)
pC_in_gaga(T74, 0, T85, s(T85)) → U4_gaga(T74, T85, halfB_in_gg(T74, 0))
U4_gaga(T74, T85, halfB_out_gg(T74, 0)) → pC_out_gaga(T74, 0, T85, s(T85))
pC_in_gaga(T74, s(0), T90, s(T90)) → U5_gaga(T74, T90, halfB_in_gg(T74, s(0)))
U5_gaga(T74, T90, halfB_out_gg(T74, s(0))) → pC_out_gaga(T74, s(0), T90, s(T90))
pC_in_gaga(T74, s(s(T97)), T98, T100) → U6_gaga(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
U6_gaga(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → U7_gaga(T74, T97, T98, T100, pC_in_gaga(T97, X228, s(T98), T100))
U7_gaga(T74, T97, T98, T100, pC_out_gaga(T97, X228, s(T98), T100)) → pC_out_gaga(T74, s(s(T97)), T98, T100)
U78_ga(T12, T76, pC_out_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76)) → log2D_out_ga(s(s(T12)), T76)
Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
log2D_in_ga(0, 0) → log2D_out_ga(0, 0)
log2D_in_ga(s(0), 0) → log2D_out_ga(s(0), 0)
log2D_in_ga(s(s(T12)), T14) → U8_ga(T12, T14, halfB_in_ga(T12, X26))
halfB_in_ga(T18, s(X35)) → U2_ga(T18, X35, halfA_in_ga(T18, X35))
halfA_in_ga(0, 0) → halfA_out_ga(0, 0)
halfA_in_ga(s(0), 0) → halfA_out_ga(s(0), 0)
halfA_in_ga(s(s(T21)), s(X44)) → U1_ga(T21, X44, halfA_in_ga(T21, X44))
U1_ga(T21, X44, halfA_out_ga(T21, X44)) → halfA_out_ga(s(s(T21)), s(X44))
U2_ga(T18, X35, halfA_out_ga(T18, X35)) → halfB_out_ga(T18, s(X35))
U8_ga(T12, T14, halfB_out_ga(T12, X26)) → log2D_out_ga(s(s(T12)), T14)
log2D_in_ga(s(s(T12)), s(0)) → U9_ga(T12, halfB_in_gg(T12, 0))
halfB_in_gg(T18, s(X35)) → U2_gg(T18, X35, halfA_in_gg(T18, X35))
halfA_in_gg(0, 0) → halfA_out_gg(0, 0)
halfA_in_gg(s(0), 0) → halfA_out_gg(s(0), 0)
halfA_in_gg(s(s(T21)), s(X44)) → U1_gg(T21, X44, halfA_in_gg(T21, X44))
U1_gg(T21, X44, halfA_out_gg(T21, X44)) → halfA_out_gg(s(s(T21)), s(X44))
U2_gg(T18, X35, halfA_out_gg(T18, X35)) → halfB_out_gg(T18, s(X35))
U9_ga(T12, halfB_out_gg(T12, 0)) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), s(0)) → U10_ga(T12, halfB_in_gg(T12, s(0)))
U10_ga(T12, halfB_out_gg(T12, s(0))) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), T28) → U11_ga(T12, T28, halfB_in_ga(T12, s(s(T26))))
U11_ga(T12, T28, halfB_out_ga(T12, s(s(T26)))) → U12_ga(T12, T28, halfB_in_ga(T26, X67))
U12_ga(T12, T28, halfB_out_ga(T26, X67)) → log2D_out_ga(s(s(T12)), T28)
log2D_in_ga(s(s(T12)), s(s(0))) → U13_ga(T12, halfB_in_ga(T12, s(s(T26))))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U14_ga(T12, halfB_in_gg(T26, 0))
U14_ga(T12, halfB_out_gg(T26, 0)) → log2D_out_ga(s(s(T12)), s(s(0)))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U15_ga(T12, halfB_in_gg(T26, s(0)))
U15_ga(T12, halfB_out_gg(T26, s(0))) → log2D_out_ga(s(s(T12)), s(s(0)))
log2D_in_ga(s(s(T12)), T36) → U16_ga(T12, T36, halfB_in_ga(T12, s(s(T26))))
U16_ga(T12, T36, halfB_out_ga(T12, s(s(T26)))) → U17_ga(T12, T36, halfB_in_ga(T26, s(s(T34))))
U17_ga(T12, T36, halfB_out_ga(T26, s(s(T34)))) → U18_ga(T12, T36, halfB_in_ga(T34, X90))
U18_ga(T12, T36, halfB_out_ga(T34, X90)) → log2D_out_ga(s(s(T12)), T36)
log2D_in_ga(s(s(T12)), s(s(s(0)))) → U19_ga(T12, halfB_in_ga(T12, s(s(T26))))
U19_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U20_ga(T12, halfB_in_ga(T26, s(s(T34))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U21_ga(T12, halfB_in_gg(T34, 0))
U21_ga(T12, halfB_out_gg(T34, 0)) → log2D_out_ga(s(s(T12)), s(s(s(0))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U22_ga(T12, halfB_in_gg(T34, s(0)))
U22_ga(T12, halfB_out_gg(T34, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(0))))
log2D_in_ga(s(s(T12)), T44) → U23_ga(T12, T44, halfB_in_ga(T12, s(s(T26))))
U23_ga(T12, T44, halfB_out_ga(T12, s(s(T26)))) → U24_ga(T12, T44, halfB_in_ga(T26, s(s(T34))))
U24_ga(T12, T44, halfB_out_ga(T26, s(s(T34)))) → U25_ga(T12, T44, halfB_in_ga(T34, s(s(T42))))
U25_ga(T12, T44, halfB_out_ga(T34, s(s(T42)))) → U26_ga(T12, T44, halfB_in_ga(T42, X113))
U26_ga(T12, T44, halfB_out_ga(T42, X113)) → log2D_out_ga(s(s(T12)), T44)
log2D_in_ga(s(s(T12)), s(s(s(s(0))))) → U27_ga(T12, halfB_in_ga(T12, s(s(T26))))
U27_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U28_ga(T12, halfB_in_ga(T26, s(s(T34))))
U28_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U29_ga(T12, halfB_in_ga(T34, s(s(T42))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U30_ga(T12, halfB_in_gg(T42, 0))
U30_ga(T12, halfB_out_gg(T42, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U31_ga(T12, halfB_in_gg(T42, s(0)))
U31_ga(T12, halfB_out_gg(T42, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
log2D_in_ga(s(s(T12)), T52) → U32_ga(T12, T52, halfB_in_ga(T12, s(s(T26))))
U32_ga(T12, T52, halfB_out_ga(T12, s(s(T26)))) → U33_ga(T12, T52, halfB_in_ga(T26, s(s(T34))))
U33_ga(T12, T52, halfB_out_ga(T26, s(s(T34)))) → U34_ga(T12, T52, halfB_in_ga(T34, s(s(T42))))
U34_ga(T12, T52, halfB_out_ga(T34, s(s(T42)))) → U35_ga(T12, T52, halfB_in_ga(T42, s(s(T50))))
U35_ga(T12, T52, halfB_out_ga(T42, s(s(T50)))) → U36_ga(T12, T52, halfB_in_ga(T50, X136))
U36_ga(T12, T52, halfB_out_ga(T50, X136)) → log2D_out_ga(s(s(T12)), T52)
log2D_in_ga(s(s(T12)), s(s(s(s(s(0)))))) → U37_ga(T12, halfB_in_ga(T12, s(s(T26))))
U37_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U38_ga(T12, halfB_in_ga(T26, s(s(T34))))
U38_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U39_ga(T12, halfB_in_ga(T34, s(s(T42))))
U39_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U40_ga(T12, halfB_in_ga(T42, s(s(T50))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U41_ga(T12, halfB_in_gg(T50, 0))
U41_ga(T12, halfB_out_gg(T50, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U42_ga(T12, halfB_in_gg(T50, s(0)))
U42_ga(T12, halfB_out_gg(T50, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
log2D_in_ga(s(s(T12)), T60) → U43_ga(T12, T60, halfB_in_ga(T12, s(s(T26))))
U43_ga(T12, T60, halfB_out_ga(T12, s(s(T26)))) → U44_ga(T12, T60, halfB_in_ga(T26, s(s(T34))))
U44_ga(T12, T60, halfB_out_ga(T26, s(s(T34)))) → U45_ga(T12, T60, halfB_in_ga(T34, s(s(T42))))
U45_ga(T12, T60, halfB_out_ga(T34, s(s(T42)))) → U46_ga(T12, T60, halfB_in_ga(T42, s(s(T50))))
U46_ga(T12, T60, halfB_out_ga(T42, s(s(T50)))) → U47_ga(T12, T60, halfB_in_ga(T50, s(s(T58))))
U47_ga(T12, T60, halfB_out_ga(T50, s(s(T58)))) → U48_ga(T12, T60, halfB_in_ga(T58, X159))
U48_ga(T12, T60, halfB_out_ga(T58, X159)) → log2D_out_ga(s(s(T12)), T60)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(0))))))) → U49_ga(T12, halfB_in_ga(T12, s(s(T26))))
U49_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U50_ga(T12, halfB_in_ga(T26, s(s(T34))))
U50_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U51_ga(T12, halfB_in_ga(T34, s(s(T42))))
U51_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U52_ga(T12, halfB_in_ga(T42, s(s(T50))))
U52_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U53_ga(T12, halfB_in_ga(T50, s(s(T58))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U54_ga(T12, halfB_in_gg(T58, 0))
U54_ga(T12, halfB_out_gg(T58, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U55_ga(T12, halfB_in_gg(T58, s(0)))
U55_ga(T12, halfB_out_gg(T58, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
log2D_in_ga(s(s(T12)), T68) → U56_ga(T12, T68, halfB_in_ga(T12, s(s(T26))))
U56_ga(T12, T68, halfB_out_ga(T12, s(s(T26)))) → U57_ga(T12, T68, halfB_in_ga(T26, s(s(T34))))
U57_ga(T12, T68, halfB_out_ga(T26, s(s(T34)))) → U58_ga(T12, T68, halfB_in_ga(T34, s(s(T42))))
U58_ga(T12, T68, halfB_out_ga(T34, s(s(T42)))) → U59_ga(T12, T68, halfB_in_ga(T42, s(s(T50))))
U59_ga(T12, T68, halfB_out_ga(T42, s(s(T50)))) → U60_ga(T12, T68, halfB_in_ga(T50, s(s(T58))))
U60_ga(T12, T68, halfB_out_ga(T50, s(s(T58)))) → U61_ga(T12, T68, halfB_in_ga(T58, s(s(T66))))
U61_ga(T12, T68, halfB_out_ga(T58, s(s(T66)))) → U62_ga(T12, T68, halfB_in_ga(T66, X182))
U62_ga(T12, T68, halfB_out_ga(T66, X182)) → log2D_out_ga(s(s(T12)), T68)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → U63_ga(T12, halfB_in_ga(T12, s(s(T26))))
U63_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U64_ga(T12, halfB_in_ga(T26, s(s(T34))))
U64_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U65_ga(T12, halfB_in_ga(T34, s(s(T42))))
U65_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U66_ga(T12, halfB_in_ga(T42, s(s(T50))))
U66_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U67_ga(T12, halfB_in_ga(T50, s(s(T58))))
U67_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U68_ga(T12, halfB_in_ga(T58, s(s(T66))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U69_ga(T12, halfB_in_gg(T66, 0))
U69_ga(T12, halfB_out_gg(T66, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U70_ga(T12, halfB_in_gg(T66, s(0)))
U70_ga(T12, halfB_out_gg(T66, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
log2D_in_ga(s(s(T12)), T76) → U71_ga(T12, T76, halfB_in_ga(T12, s(s(T26))))
U71_ga(T12, T76, halfB_out_ga(T12, s(s(T26)))) → U72_ga(T12, T76, halfB_in_ga(T26, s(s(T34))))
U72_ga(T12, T76, halfB_out_ga(T26, s(s(T34)))) → U73_ga(T12, T76, halfB_in_ga(T34, s(s(T42))))
U73_ga(T12, T76, halfB_out_ga(T34, s(s(T42)))) → U74_ga(T12, T76, halfB_in_ga(T42, s(s(T50))))
U74_ga(T12, T76, halfB_out_ga(T42, s(s(T50)))) → U75_ga(T12, T76, halfB_in_ga(T50, s(s(T58))))
U75_ga(T12, T76, halfB_out_ga(T50, s(s(T58)))) → U76_ga(T12, T76, halfB_in_ga(T58, s(s(T66))))
U76_ga(T12, T76, halfB_out_ga(T58, s(s(T66)))) → U77_ga(T12, T76, halfB_in_ga(T66, s(s(T74))))
U77_ga(T12, T76, halfB_out_ga(T66, s(s(T74)))) → U78_ga(T12, T76, pC_in_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76))
pC_in_gaga(T74, X205, T77, T76) → U3_gaga(T74, X205, T77, T76, halfB_in_ga(T74, X205))
U3_gaga(T74, X205, T77, T76, halfB_out_ga(T74, X205)) → pC_out_gaga(T74, X205, T77, T76)
pC_in_gaga(T74, 0, T85, s(T85)) → U4_gaga(T74, T85, halfB_in_gg(T74, 0))
U4_gaga(T74, T85, halfB_out_gg(T74, 0)) → pC_out_gaga(T74, 0, T85, s(T85))
pC_in_gaga(T74, s(0), T90, s(T90)) → U5_gaga(T74, T90, halfB_in_gg(T74, s(0)))
U5_gaga(T74, T90, halfB_out_gg(T74, s(0))) → pC_out_gaga(T74, s(0), T90, s(T90))
pC_in_gaga(T74, s(s(T97)), T98, T100) → U6_gaga(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
U6_gaga(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → U7_gaga(T74, T97, T98, T100, pC_in_gaga(T97, X228, s(T98), T100))
U7_gaga(T74, T97, T98, T100, pC_out_gaga(T97, X228, s(T98), T100)) → pC_out_gaga(T74, s(s(T97)), T98, T100)
U78_ga(T12, T76, pC_out_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76)) → log2D_out_ga(s(s(T12)), T76)
LOG2D_IN_GA(s(s(T12)), T14) → U8_GA(T12, T14, halfB_in_ga(T12, X26))
LOG2D_IN_GA(s(s(T12)), T14) → HALFB_IN_GA(T12, X26)
HALFB_IN_GA(T18, s(X35)) → U2_GA(T18, X35, halfA_in_ga(T18, X35))
HALFB_IN_GA(T18, s(X35)) → HALFA_IN_GA(T18, X35)
HALFA_IN_GA(s(s(T21)), s(X44)) → U1_GA(T21, X44, halfA_in_ga(T21, X44))
HALFA_IN_GA(s(s(T21)), s(X44)) → HALFA_IN_GA(T21, X44)
LOG2D_IN_GA(s(s(T12)), s(0)) → U9_GA(T12, halfB_in_gg(T12, 0))
LOG2D_IN_GA(s(s(T12)), s(0)) → HALFB_IN_GG(T12, 0)
HALFB_IN_GG(T18, s(X35)) → U2_GG(T18, X35, halfA_in_gg(T18, X35))
HALFB_IN_GG(T18, s(X35)) → HALFA_IN_GG(T18, X35)
HALFA_IN_GG(s(s(T21)), s(X44)) → U1_GG(T21, X44, halfA_in_gg(T21, X44))
HALFA_IN_GG(s(s(T21)), s(X44)) → HALFA_IN_GG(T21, X44)
LOG2D_IN_GA(s(s(T12)), s(0)) → U10_GA(T12, halfB_in_gg(T12, s(0)))
LOG2D_IN_GA(s(s(T12)), s(0)) → HALFB_IN_GG(T12, s(0))
LOG2D_IN_GA(s(s(T12)), T28) → U11_GA(T12, T28, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), T28) → HALFB_IN_GA(T12, s(s(T26)))
U11_GA(T12, T28, halfB_out_ga(T12, s(s(T26)))) → U12_GA(T12, T28, halfB_in_ga(T26, X67))
U11_GA(T12, T28, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, X67)
LOG2D_IN_GA(s(s(T12)), s(s(0))) → U13_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(0))) → HALFB_IN_GA(T12, s(s(T26)))
U13_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U14_GA(T12, halfB_in_gg(T26, 0))
U13_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GG(T26, 0)
U13_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U15_GA(T12, halfB_in_gg(T26, s(0)))
U13_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GG(T26, s(0))
LOG2D_IN_GA(s(s(T12)), T36) → U16_GA(T12, T36, halfB_in_ga(T12, s(s(T26))))
U16_GA(T12, T36, halfB_out_ga(T12, s(s(T26)))) → U17_GA(T12, T36, halfB_in_ga(T26, s(s(T34))))
U16_GA(T12, T36, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U17_GA(T12, T36, halfB_out_ga(T26, s(s(T34)))) → U18_GA(T12, T36, halfB_in_ga(T34, X90))
U17_GA(T12, T36, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, X90)
LOG2D_IN_GA(s(s(T12)), s(s(s(0)))) → U19_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(0)))) → HALFB_IN_GA(T12, s(s(T26)))
U19_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U20_GA(T12, halfB_in_ga(T26, s(s(T34))))
U19_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U20_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U21_GA(T12, halfB_in_gg(T34, 0))
U20_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GG(T34, 0)
U20_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U22_GA(T12, halfB_in_gg(T34, s(0)))
U20_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GG(T34, s(0))
LOG2D_IN_GA(s(s(T12)), T44) → U23_GA(T12, T44, halfB_in_ga(T12, s(s(T26))))
U23_GA(T12, T44, halfB_out_ga(T12, s(s(T26)))) → U24_GA(T12, T44, halfB_in_ga(T26, s(s(T34))))
U23_GA(T12, T44, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U24_GA(T12, T44, halfB_out_ga(T26, s(s(T34)))) → U25_GA(T12, T44, halfB_in_ga(T34, s(s(T42))))
U24_GA(T12, T44, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U25_GA(T12, T44, halfB_out_ga(T34, s(s(T42)))) → U26_GA(T12, T44, halfB_in_ga(T42, X113))
U25_GA(T12, T44, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, X113)
LOG2D_IN_GA(s(s(T12)), s(s(s(s(0))))) → U27_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(s(0))))) → HALFB_IN_GA(T12, s(s(T26)))
U27_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U28_GA(T12, halfB_in_ga(T26, s(s(T34))))
U27_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U28_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U29_GA(T12, halfB_in_ga(T34, s(s(T42))))
U28_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U29_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U30_GA(T12, halfB_in_gg(T42, 0))
U29_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GG(T42, 0)
U29_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U31_GA(T12, halfB_in_gg(T42, s(0)))
U29_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GG(T42, s(0))
LOG2D_IN_GA(s(s(T12)), T52) → U32_GA(T12, T52, halfB_in_ga(T12, s(s(T26))))
U32_GA(T12, T52, halfB_out_ga(T12, s(s(T26)))) → U33_GA(T12, T52, halfB_in_ga(T26, s(s(T34))))
U32_GA(T12, T52, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U33_GA(T12, T52, halfB_out_ga(T26, s(s(T34)))) → U34_GA(T12, T52, halfB_in_ga(T34, s(s(T42))))
U33_GA(T12, T52, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U34_GA(T12, T52, halfB_out_ga(T34, s(s(T42)))) → U35_GA(T12, T52, halfB_in_ga(T42, s(s(T50))))
U34_GA(T12, T52, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U35_GA(T12, T52, halfB_out_ga(T42, s(s(T50)))) → U36_GA(T12, T52, halfB_in_ga(T50, X136))
U35_GA(T12, T52, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, X136)
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(0)))))) → U37_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(0)))))) → HALFB_IN_GA(T12, s(s(T26)))
U37_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U38_GA(T12, halfB_in_ga(T26, s(s(T34))))
U37_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U38_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U39_GA(T12, halfB_in_ga(T34, s(s(T42))))
U38_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U39_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U40_GA(T12, halfB_in_ga(T42, s(s(T50))))
U39_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U40_GA(T12, halfB_out_ga(T42, s(s(T50)))) → U41_GA(T12, halfB_in_gg(T50, 0))
U40_GA(T12, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GG(T50, 0)
U40_GA(T12, halfB_out_ga(T42, s(s(T50)))) → U42_GA(T12, halfB_in_gg(T50, s(0)))
U40_GA(T12, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GG(T50, s(0))
LOG2D_IN_GA(s(s(T12)), T60) → U43_GA(T12, T60, halfB_in_ga(T12, s(s(T26))))
U43_GA(T12, T60, halfB_out_ga(T12, s(s(T26)))) → U44_GA(T12, T60, halfB_in_ga(T26, s(s(T34))))
U43_GA(T12, T60, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U44_GA(T12, T60, halfB_out_ga(T26, s(s(T34)))) → U45_GA(T12, T60, halfB_in_ga(T34, s(s(T42))))
U44_GA(T12, T60, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U45_GA(T12, T60, halfB_out_ga(T34, s(s(T42)))) → U46_GA(T12, T60, halfB_in_ga(T42, s(s(T50))))
U45_GA(T12, T60, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U46_GA(T12, T60, halfB_out_ga(T42, s(s(T50)))) → U47_GA(T12, T60, halfB_in_ga(T50, s(s(T58))))
U46_GA(T12, T60, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U47_GA(T12, T60, halfB_out_ga(T50, s(s(T58)))) → U48_GA(T12, T60, halfB_in_ga(T58, X159))
U47_GA(T12, T60, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GA(T58, X159)
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(s(0))))))) → U49_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(s(0))))))) → HALFB_IN_GA(T12, s(s(T26)))
U49_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U50_GA(T12, halfB_in_ga(T26, s(s(T34))))
U49_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U50_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U51_GA(T12, halfB_in_ga(T34, s(s(T42))))
U50_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U51_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U52_GA(T12, halfB_in_ga(T42, s(s(T50))))
U51_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U52_GA(T12, halfB_out_ga(T42, s(s(T50)))) → U53_GA(T12, halfB_in_ga(T50, s(s(T58))))
U52_GA(T12, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U53_GA(T12, halfB_out_ga(T50, s(s(T58)))) → U54_GA(T12, halfB_in_gg(T58, 0))
U53_GA(T12, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GG(T58, 0)
U53_GA(T12, halfB_out_ga(T50, s(s(T58)))) → U55_GA(T12, halfB_in_gg(T58, s(0)))
U53_GA(T12, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GG(T58, s(0))
LOG2D_IN_GA(s(s(T12)), T68) → U56_GA(T12, T68, halfB_in_ga(T12, s(s(T26))))
U56_GA(T12, T68, halfB_out_ga(T12, s(s(T26)))) → U57_GA(T12, T68, halfB_in_ga(T26, s(s(T34))))
U56_GA(T12, T68, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U57_GA(T12, T68, halfB_out_ga(T26, s(s(T34)))) → U58_GA(T12, T68, halfB_in_ga(T34, s(s(T42))))
U57_GA(T12, T68, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U58_GA(T12, T68, halfB_out_ga(T34, s(s(T42)))) → U59_GA(T12, T68, halfB_in_ga(T42, s(s(T50))))
U58_GA(T12, T68, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U59_GA(T12, T68, halfB_out_ga(T42, s(s(T50)))) → U60_GA(T12, T68, halfB_in_ga(T50, s(s(T58))))
U59_GA(T12, T68, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U60_GA(T12, T68, halfB_out_ga(T50, s(s(T58)))) → U61_GA(T12, T68, halfB_in_ga(T58, s(s(T66))))
U60_GA(T12, T68, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GA(T58, s(s(T66)))
U61_GA(T12, T68, halfB_out_ga(T58, s(s(T66)))) → U62_GA(T12, T68, halfB_in_ga(T66, X182))
U61_GA(T12, T68, halfB_out_ga(T58, s(s(T66)))) → HALFB_IN_GA(T66, X182)
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → U63_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → HALFB_IN_GA(T12, s(s(T26)))
U63_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U64_GA(T12, halfB_in_ga(T26, s(s(T34))))
U63_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U64_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U65_GA(T12, halfB_in_ga(T34, s(s(T42))))
U64_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U65_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U66_GA(T12, halfB_in_ga(T42, s(s(T50))))
U65_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U66_GA(T12, halfB_out_ga(T42, s(s(T50)))) → U67_GA(T12, halfB_in_ga(T50, s(s(T58))))
U66_GA(T12, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U67_GA(T12, halfB_out_ga(T50, s(s(T58)))) → U68_GA(T12, halfB_in_ga(T58, s(s(T66))))
U67_GA(T12, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GA(T58, s(s(T66)))
U68_GA(T12, halfB_out_ga(T58, s(s(T66)))) → U69_GA(T12, halfB_in_gg(T66, 0))
U68_GA(T12, halfB_out_ga(T58, s(s(T66)))) → HALFB_IN_GG(T66, 0)
U68_GA(T12, halfB_out_ga(T58, s(s(T66)))) → U70_GA(T12, halfB_in_gg(T66, s(0)))
U68_GA(T12, halfB_out_ga(T58, s(s(T66)))) → HALFB_IN_GG(T66, s(0))
LOG2D_IN_GA(s(s(T12)), T76) → U71_GA(T12, T76, halfB_in_ga(T12, s(s(T26))))
U71_GA(T12, T76, halfB_out_ga(T12, s(s(T26)))) → U72_GA(T12, T76, halfB_in_ga(T26, s(s(T34))))
U71_GA(T12, T76, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U72_GA(T12, T76, halfB_out_ga(T26, s(s(T34)))) → U73_GA(T12, T76, halfB_in_ga(T34, s(s(T42))))
U72_GA(T12, T76, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U73_GA(T12, T76, halfB_out_ga(T34, s(s(T42)))) → U74_GA(T12, T76, halfB_in_ga(T42, s(s(T50))))
U73_GA(T12, T76, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U74_GA(T12, T76, halfB_out_ga(T42, s(s(T50)))) → U75_GA(T12, T76, halfB_in_ga(T50, s(s(T58))))
U74_GA(T12, T76, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U75_GA(T12, T76, halfB_out_ga(T50, s(s(T58)))) → U76_GA(T12, T76, halfB_in_ga(T58, s(s(T66))))
U75_GA(T12, T76, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GA(T58, s(s(T66)))
U76_GA(T12, T76, halfB_out_ga(T58, s(s(T66)))) → U77_GA(T12, T76, halfB_in_ga(T66, s(s(T74))))
U76_GA(T12, T76, halfB_out_ga(T58, s(s(T66)))) → HALFB_IN_GA(T66, s(s(T74)))
U77_GA(T12, T76, halfB_out_ga(T66, s(s(T74)))) → U78_GA(T12, T76, pC_in_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76))
U77_GA(T12, T76, halfB_out_ga(T66, s(s(T74)))) → PC_IN_GAGA(T74, X205, s(s(s(s(s(s(s(0))))))), T76)
PC_IN_GAGA(T74, X205, T77, T76) → U3_GAGA(T74, X205, T77, T76, halfB_in_ga(T74, X205))
PC_IN_GAGA(T74, X205, T77, T76) → HALFB_IN_GA(T74, X205)
PC_IN_GAGA(T74, 0, T85, s(T85)) → U4_GAGA(T74, T85, halfB_in_gg(T74, 0))
PC_IN_GAGA(T74, 0, T85, s(T85)) → HALFB_IN_GG(T74, 0)
PC_IN_GAGA(T74, s(0), T90, s(T90)) → U5_GAGA(T74, T90, halfB_in_gg(T74, s(0)))
PC_IN_GAGA(T74, s(0), T90, s(T90)) → HALFB_IN_GG(T74, s(0))
PC_IN_GAGA(T74, s(s(T97)), T98, T100) → U6_GAGA(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
PC_IN_GAGA(T74, s(s(T97)), T98, T100) → HALFB_IN_GA(T74, s(s(T97)))
U6_GAGA(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → U7_GAGA(T74, T97, T98, T100, pC_in_gaga(T97, X228, s(T98), T100))
U6_GAGA(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → PC_IN_GAGA(T97, X228, s(T98), T100)
log2D_in_ga(0, 0) → log2D_out_ga(0, 0)
log2D_in_ga(s(0), 0) → log2D_out_ga(s(0), 0)
log2D_in_ga(s(s(T12)), T14) → U8_ga(T12, T14, halfB_in_ga(T12, X26))
halfB_in_ga(T18, s(X35)) → U2_ga(T18, X35, halfA_in_ga(T18, X35))
halfA_in_ga(0, 0) → halfA_out_ga(0, 0)
halfA_in_ga(s(0), 0) → halfA_out_ga(s(0), 0)
halfA_in_ga(s(s(T21)), s(X44)) → U1_ga(T21, X44, halfA_in_ga(T21, X44))
U1_ga(T21, X44, halfA_out_ga(T21, X44)) → halfA_out_ga(s(s(T21)), s(X44))
U2_ga(T18, X35, halfA_out_ga(T18, X35)) → halfB_out_ga(T18, s(X35))
U8_ga(T12, T14, halfB_out_ga(T12, X26)) → log2D_out_ga(s(s(T12)), T14)
log2D_in_ga(s(s(T12)), s(0)) → U9_ga(T12, halfB_in_gg(T12, 0))
halfB_in_gg(T18, s(X35)) → U2_gg(T18, X35, halfA_in_gg(T18, X35))
halfA_in_gg(0, 0) → halfA_out_gg(0, 0)
halfA_in_gg(s(0), 0) → halfA_out_gg(s(0), 0)
halfA_in_gg(s(s(T21)), s(X44)) → U1_gg(T21, X44, halfA_in_gg(T21, X44))
U1_gg(T21, X44, halfA_out_gg(T21, X44)) → halfA_out_gg(s(s(T21)), s(X44))
U2_gg(T18, X35, halfA_out_gg(T18, X35)) → halfB_out_gg(T18, s(X35))
U9_ga(T12, halfB_out_gg(T12, 0)) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), s(0)) → U10_ga(T12, halfB_in_gg(T12, s(0)))
U10_ga(T12, halfB_out_gg(T12, s(0))) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), T28) → U11_ga(T12, T28, halfB_in_ga(T12, s(s(T26))))
U11_ga(T12, T28, halfB_out_ga(T12, s(s(T26)))) → U12_ga(T12, T28, halfB_in_ga(T26, X67))
U12_ga(T12, T28, halfB_out_ga(T26, X67)) → log2D_out_ga(s(s(T12)), T28)
log2D_in_ga(s(s(T12)), s(s(0))) → U13_ga(T12, halfB_in_ga(T12, s(s(T26))))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U14_ga(T12, halfB_in_gg(T26, 0))
U14_ga(T12, halfB_out_gg(T26, 0)) → log2D_out_ga(s(s(T12)), s(s(0)))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U15_ga(T12, halfB_in_gg(T26, s(0)))
U15_ga(T12, halfB_out_gg(T26, s(0))) → log2D_out_ga(s(s(T12)), s(s(0)))
log2D_in_ga(s(s(T12)), T36) → U16_ga(T12, T36, halfB_in_ga(T12, s(s(T26))))
U16_ga(T12, T36, halfB_out_ga(T12, s(s(T26)))) → U17_ga(T12, T36, halfB_in_ga(T26, s(s(T34))))
U17_ga(T12, T36, halfB_out_ga(T26, s(s(T34)))) → U18_ga(T12, T36, halfB_in_ga(T34, X90))
U18_ga(T12, T36, halfB_out_ga(T34, X90)) → log2D_out_ga(s(s(T12)), T36)
log2D_in_ga(s(s(T12)), s(s(s(0)))) → U19_ga(T12, halfB_in_ga(T12, s(s(T26))))
U19_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U20_ga(T12, halfB_in_ga(T26, s(s(T34))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U21_ga(T12, halfB_in_gg(T34, 0))
U21_ga(T12, halfB_out_gg(T34, 0)) → log2D_out_ga(s(s(T12)), s(s(s(0))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U22_ga(T12, halfB_in_gg(T34, s(0)))
U22_ga(T12, halfB_out_gg(T34, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(0))))
log2D_in_ga(s(s(T12)), T44) → U23_ga(T12, T44, halfB_in_ga(T12, s(s(T26))))
U23_ga(T12, T44, halfB_out_ga(T12, s(s(T26)))) → U24_ga(T12, T44, halfB_in_ga(T26, s(s(T34))))
U24_ga(T12, T44, halfB_out_ga(T26, s(s(T34)))) → U25_ga(T12, T44, halfB_in_ga(T34, s(s(T42))))
U25_ga(T12, T44, halfB_out_ga(T34, s(s(T42)))) → U26_ga(T12, T44, halfB_in_ga(T42, X113))
U26_ga(T12, T44, halfB_out_ga(T42, X113)) → log2D_out_ga(s(s(T12)), T44)
log2D_in_ga(s(s(T12)), s(s(s(s(0))))) → U27_ga(T12, halfB_in_ga(T12, s(s(T26))))
U27_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U28_ga(T12, halfB_in_ga(T26, s(s(T34))))
U28_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U29_ga(T12, halfB_in_ga(T34, s(s(T42))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U30_ga(T12, halfB_in_gg(T42, 0))
U30_ga(T12, halfB_out_gg(T42, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U31_ga(T12, halfB_in_gg(T42, s(0)))
U31_ga(T12, halfB_out_gg(T42, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
log2D_in_ga(s(s(T12)), T52) → U32_ga(T12, T52, halfB_in_ga(T12, s(s(T26))))
U32_ga(T12, T52, halfB_out_ga(T12, s(s(T26)))) → U33_ga(T12, T52, halfB_in_ga(T26, s(s(T34))))
U33_ga(T12, T52, halfB_out_ga(T26, s(s(T34)))) → U34_ga(T12, T52, halfB_in_ga(T34, s(s(T42))))
U34_ga(T12, T52, halfB_out_ga(T34, s(s(T42)))) → U35_ga(T12, T52, halfB_in_ga(T42, s(s(T50))))
U35_ga(T12, T52, halfB_out_ga(T42, s(s(T50)))) → U36_ga(T12, T52, halfB_in_ga(T50, X136))
U36_ga(T12, T52, halfB_out_ga(T50, X136)) → log2D_out_ga(s(s(T12)), T52)
log2D_in_ga(s(s(T12)), s(s(s(s(s(0)))))) → U37_ga(T12, halfB_in_ga(T12, s(s(T26))))
U37_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U38_ga(T12, halfB_in_ga(T26, s(s(T34))))
U38_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U39_ga(T12, halfB_in_ga(T34, s(s(T42))))
U39_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U40_ga(T12, halfB_in_ga(T42, s(s(T50))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U41_ga(T12, halfB_in_gg(T50, 0))
U41_ga(T12, halfB_out_gg(T50, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U42_ga(T12, halfB_in_gg(T50, s(0)))
U42_ga(T12, halfB_out_gg(T50, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
log2D_in_ga(s(s(T12)), T60) → U43_ga(T12, T60, halfB_in_ga(T12, s(s(T26))))
U43_ga(T12, T60, halfB_out_ga(T12, s(s(T26)))) → U44_ga(T12, T60, halfB_in_ga(T26, s(s(T34))))
U44_ga(T12, T60, halfB_out_ga(T26, s(s(T34)))) → U45_ga(T12, T60, halfB_in_ga(T34, s(s(T42))))
U45_ga(T12, T60, halfB_out_ga(T34, s(s(T42)))) → U46_ga(T12, T60, halfB_in_ga(T42, s(s(T50))))
U46_ga(T12, T60, halfB_out_ga(T42, s(s(T50)))) → U47_ga(T12, T60, halfB_in_ga(T50, s(s(T58))))
U47_ga(T12, T60, halfB_out_ga(T50, s(s(T58)))) → U48_ga(T12, T60, halfB_in_ga(T58, X159))
U48_ga(T12, T60, halfB_out_ga(T58, X159)) → log2D_out_ga(s(s(T12)), T60)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(0))))))) → U49_ga(T12, halfB_in_ga(T12, s(s(T26))))
U49_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U50_ga(T12, halfB_in_ga(T26, s(s(T34))))
U50_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U51_ga(T12, halfB_in_ga(T34, s(s(T42))))
U51_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U52_ga(T12, halfB_in_ga(T42, s(s(T50))))
U52_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U53_ga(T12, halfB_in_ga(T50, s(s(T58))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U54_ga(T12, halfB_in_gg(T58, 0))
U54_ga(T12, halfB_out_gg(T58, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U55_ga(T12, halfB_in_gg(T58, s(0)))
U55_ga(T12, halfB_out_gg(T58, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
log2D_in_ga(s(s(T12)), T68) → U56_ga(T12, T68, halfB_in_ga(T12, s(s(T26))))
U56_ga(T12, T68, halfB_out_ga(T12, s(s(T26)))) → U57_ga(T12, T68, halfB_in_ga(T26, s(s(T34))))
U57_ga(T12, T68, halfB_out_ga(T26, s(s(T34)))) → U58_ga(T12, T68, halfB_in_ga(T34, s(s(T42))))
U58_ga(T12, T68, halfB_out_ga(T34, s(s(T42)))) → U59_ga(T12, T68, halfB_in_ga(T42, s(s(T50))))
U59_ga(T12, T68, halfB_out_ga(T42, s(s(T50)))) → U60_ga(T12, T68, halfB_in_ga(T50, s(s(T58))))
U60_ga(T12, T68, halfB_out_ga(T50, s(s(T58)))) → U61_ga(T12, T68, halfB_in_ga(T58, s(s(T66))))
U61_ga(T12, T68, halfB_out_ga(T58, s(s(T66)))) → U62_ga(T12, T68, halfB_in_ga(T66, X182))
U62_ga(T12, T68, halfB_out_ga(T66, X182)) → log2D_out_ga(s(s(T12)), T68)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → U63_ga(T12, halfB_in_ga(T12, s(s(T26))))
U63_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U64_ga(T12, halfB_in_ga(T26, s(s(T34))))
U64_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U65_ga(T12, halfB_in_ga(T34, s(s(T42))))
U65_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U66_ga(T12, halfB_in_ga(T42, s(s(T50))))
U66_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U67_ga(T12, halfB_in_ga(T50, s(s(T58))))
U67_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U68_ga(T12, halfB_in_ga(T58, s(s(T66))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U69_ga(T12, halfB_in_gg(T66, 0))
U69_ga(T12, halfB_out_gg(T66, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U70_ga(T12, halfB_in_gg(T66, s(0)))
U70_ga(T12, halfB_out_gg(T66, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
log2D_in_ga(s(s(T12)), T76) → U71_ga(T12, T76, halfB_in_ga(T12, s(s(T26))))
U71_ga(T12, T76, halfB_out_ga(T12, s(s(T26)))) → U72_ga(T12, T76, halfB_in_ga(T26, s(s(T34))))
U72_ga(T12, T76, halfB_out_ga(T26, s(s(T34)))) → U73_ga(T12, T76, halfB_in_ga(T34, s(s(T42))))
U73_ga(T12, T76, halfB_out_ga(T34, s(s(T42)))) → U74_ga(T12, T76, halfB_in_ga(T42, s(s(T50))))
U74_ga(T12, T76, halfB_out_ga(T42, s(s(T50)))) → U75_ga(T12, T76, halfB_in_ga(T50, s(s(T58))))
U75_ga(T12, T76, halfB_out_ga(T50, s(s(T58)))) → U76_ga(T12, T76, halfB_in_ga(T58, s(s(T66))))
U76_ga(T12, T76, halfB_out_ga(T58, s(s(T66)))) → U77_ga(T12, T76, halfB_in_ga(T66, s(s(T74))))
U77_ga(T12, T76, halfB_out_ga(T66, s(s(T74)))) → U78_ga(T12, T76, pC_in_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76))
pC_in_gaga(T74, X205, T77, T76) → U3_gaga(T74, X205, T77, T76, halfB_in_ga(T74, X205))
U3_gaga(T74, X205, T77, T76, halfB_out_ga(T74, X205)) → pC_out_gaga(T74, X205, T77, T76)
pC_in_gaga(T74, 0, T85, s(T85)) → U4_gaga(T74, T85, halfB_in_gg(T74, 0))
U4_gaga(T74, T85, halfB_out_gg(T74, 0)) → pC_out_gaga(T74, 0, T85, s(T85))
pC_in_gaga(T74, s(0), T90, s(T90)) → U5_gaga(T74, T90, halfB_in_gg(T74, s(0)))
U5_gaga(T74, T90, halfB_out_gg(T74, s(0))) → pC_out_gaga(T74, s(0), T90, s(T90))
pC_in_gaga(T74, s(s(T97)), T98, T100) → U6_gaga(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
U6_gaga(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → U7_gaga(T74, T97, T98, T100, pC_in_gaga(T97, X228, s(T98), T100))
U7_gaga(T74, T97, T98, T100, pC_out_gaga(T97, X228, s(T98), T100)) → pC_out_gaga(T74, s(s(T97)), T98, T100)
U78_ga(T12, T76, pC_out_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76)) → log2D_out_ga(s(s(T12)), T76)
LOG2D_IN_GA(s(s(T12)), T14) → U8_GA(T12, T14, halfB_in_ga(T12, X26))
LOG2D_IN_GA(s(s(T12)), T14) → HALFB_IN_GA(T12, X26)
HALFB_IN_GA(T18, s(X35)) → U2_GA(T18, X35, halfA_in_ga(T18, X35))
HALFB_IN_GA(T18, s(X35)) → HALFA_IN_GA(T18, X35)
HALFA_IN_GA(s(s(T21)), s(X44)) → U1_GA(T21, X44, halfA_in_ga(T21, X44))
HALFA_IN_GA(s(s(T21)), s(X44)) → HALFA_IN_GA(T21, X44)
LOG2D_IN_GA(s(s(T12)), s(0)) → U9_GA(T12, halfB_in_gg(T12, 0))
LOG2D_IN_GA(s(s(T12)), s(0)) → HALFB_IN_GG(T12, 0)
HALFB_IN_GG(T18, s(X35)) → U2_GG(T18, X35, halfA_in_gg(T18, X35))
HALFB_IN_GG(T18, s(X35)) → HALFA_IN_GG(T18, X35)
HALFA_IN_GG(s(s(T21)), s(X44)) → U1_GG(T21, X44, halfA_in_gg(T21, X44))
HALFA_IN_GG(s(s(T21)), s(X44)) → HALFA_IN_GG(T21, X44)
LOG2D_IN_GA(s(s(T12)), s(0)) → U10_GA(T12, halfB_in_gg(T12, s(0)))
LOG2D_IN_GA(s(s(T12)), s(0)) → HALFB_IN_GG(T12, s(0))
LOG2D_IN_GA(s(s(T12)), T28) → U11_GA(T12, T28, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), T28) → HALFB_IN_GA(T12, s(s(T26)))
U11_GA(T12, T28, halfB_out_ga(T12, s(s(T26)))) → U12_GA(T12, T28, halfB_in_ga(T26, X67))
U11_GA(T12, T28, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, X67)
LOG2D_IN_GA(s(s(T12)), s(s(0))) → U13_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(0))) → HALFB_IN_GA(T12, s(s(T26)))
U13_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U14_GA(T12, halfB_in_gg(T26, 0))
U13_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GG(T26, 0)
U13_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U15_GA(T12, halfB_in_gg(T26, s(0)))
U13_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GG(T26, s(0))
LOG2D_IN_GA(s(s(T12)), T36) → U16_GA(T12, T36, halfB_in_ga(T12, s(s(T26))))
U16_GA(T12, T36, halfB_out_ga(T12, s(s(T26)))) → U17_GA(T12, T36, halfB_in_ga(T26, s(s(T34))))
U16_GA(T12, T36, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U17_GA(T12, T36, halfB_out_ga(T26, s(s(T34)))) → U18_GA(T12, T36, halfB_in_ga(T34, X90))
U17_GA(T12, T36, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, X90)
LOG2D_IN_GA(s(s(T12)), s(s(s(0)))) → U19_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(0)))) → HALFB_IN_GA(T12, s(s(T26)))
U19_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U20_GA(T12, halfB_in_ga(T26, s(s(T34))))
U19_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U20_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U21_GA(T12, halfB_in_gg(T34, 0))
U20_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GG(T34, 0)
U20_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U22_GA(T12, halfB_in_gg(T34, s(0)))
U20_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GG(T34, s(0))
LOG2D_IN_GA(s(s(T12)), T44) → U23_GA(T12, T44, halfB_in_ga(T12, s(s(T26))))
U23_GA(T12, T44, halfB_out_ga(T12, s(s(T26)))) → U24_GA(T12, T44, halfB_in_ga(T26, s(s(T34))))
U23_GA(T12, T44, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U24_GA(T12, T44, halfB_out_ga(T26, s(s(T34)))) → U25_GA(T12, T44, halfB_in_ga(T34, s(s(T42))))
U24_GA(T12, T44, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U25_GA(T12, T44, halfB_out_ga(T34, s(s(T42)))) → U26_GA(T12, T44, halfB_in_ga(T42, X113))
U25_GA(T12, T44, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, X113)
LOG2D_IN_GA(s(s(T12)), s(s(s(s(0))))) → U27_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(s(0))))) → HALFB_IN_GA(T12, s(s(T26)))
U27_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U28_GA(T12, halfB_in_ga(T26, s(s(T34))))
U27_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U28_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U29_GA(T12, halfB_in_ga(T34, s(s(T42))))
U28_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U29_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U30_GA(T12, halfB_in_gg(T42, 0))
U29_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GG(T42, 0)
U29_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U31_GA(T12, halfB_in_gg(T42, s(0)))
U29_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GG(T42, s(0))
LOG2D_IN_GA(s(s(T12)), T52) → U32_GA(T12, T52, halfB_in_ga(T12, s(s(T26))))
U32_GA(T12, T52, halfB_out_ga(T12, s(s(T26)))) → U33_GA(T12, T52, halfB_in_ga(T26, s(s(T34))))
U32_GA(T12, T52, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U33_GA(T12, T52, halfB_out_ga(T26, s(s(T34)))) → U34_GA(T12, T52, halfB_in_ga(T34, s(s(T42))))
U33_GA(T12, T52, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U34_GA(T12, T52, halfB_out_ga(T34, s(s(T42)))) → U35_GA(T12, T52, halfB_in_ga(T42, s(s(T50))))
U34_GA(T12, T52, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U35_GA(T12, T52, halfB_out_ga(T42, s(s(T50)))) → U36_GA(T12, T52, halfB_in_ga(T50, X136))
U35_GA(T12, T52, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, X136)
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(0)))))) → U37_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(0)))))) → HALFB_IN_GA(T12, s(s(T26)))
U37_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U38_GA(T12, halfB_in_ga(T26, s(s(T34))))
U37_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U38_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U39_GA(T12, halfB_in_ga(T34, s(s(T42))))
U38_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U39_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U40_GA(T12, halfB_in_ga(T42, s(s(T50))))
U39_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U40_GA(T12, halfB_out_ga(T42, s(s(T50)))) → U41_GA(T12, halfB_in_gg(T50, 0))
U40_GA(T12, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GG(T50, 0)
U40_GA(T12, halfB_out_ga(T42, s(s(T50)))) → U42_GA(T12, halfB_in_gg(T50, s(0)))
U40_GA(T12, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GG(T50, s(0))
LOG2D_IN_GA(s(s(T12)), T60) → U43_GA(T12, T60, halfB_in_ga(T12, s(s(T26))))
U43_GA(T12, T60, halfB_out_ga(T12, s(s(T26)))) → U44_GA(T12, T60, halfB_in_ga(T26, s(s(T34))))
U43_GA(T12, T60, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U44_GA(T12, T60, halfB_out_ga(T26, s(s(T34)))) → U45_GA(T12, T60, halfB_in_ga(T34, s(s(T42))))
U44_GA(T12, T60, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U45_GA(T12, T60, halfB_out_ga(T34, s(s(T42)))) → U46_GA(T12, T60, halfB_in_ga(T42, s(s(T50))))
U45_GA(T12, T60, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U46_GA(T12, T60, halfB_out_ga(T42, s(s(T50)))) → U47_GA(T12, T60, halfB_in_ga(T50, s(s(T58))))
U46_GA(T12, T60, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U47_GA(T12, T60, halfB_out_ga(T50, s(s(T58)))) → U48_GA(T12, T60, halfB_in_ga(T58, X159))
U47_GA(T12, T60, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GA(T58, X159)
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(s(0))))))) → U49_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(s(0))))))) → HALFB_IN_GA(T12, s(s(T26)))
U49_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U50_GA(T12, halfB_in_ga(T26, s(s(T34))))
U49_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U50_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U51_GA(T12, halfB_in_ga(T34, s(s(T42))))
U50_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U51_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U52_GA(T12, halfB_in_ga(T42, s(s(T50))))
U51_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U52_GA(T12, halfB_out_ga(T42, s(s(T50)))) → U53_GA(T12, halfB_in_ga(T50, s(s(T58))))
U52_GA(T12, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U53_GA(T12, halfB_out_ga(T50, s(s(T58)))) → U54_GA(T12, halfB_in_gg(T58, 0))
U53_GA(T12, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GG(T58, 0)
U53_GA(T12, halfB_out_ga(T50, s(s(T58)))) → U55_GA(T12, halfB_in_gg(T58, s(0)))
U53_GA(T12, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GG(T58, s(0))
LOG2D_IN_GA(s(s(T12)), T68) → U56_GA(T12, T68, halfB_in_ga(T12, s(s(T26))))
U56_GA(T12, T68, halfB_out_ga(T12, s(s(T26)))) → U57_GA(T12, T68, halfB_in_ga(T26, s(s(T34))))
U56_GA(T12, T68, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U57_GA(T12, T68, halfB_out_ga(T26, s(s(T34)))) → U58_GA(T12, T68, halfB_in_ga(T34, s(s(T42))))
U57_GA(T12, T68, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U58_GA(T12, T68, halfB_out_ga(T34, s(s(T42)))) → U59_GA(T12, T68, halfB_in_ga(T42, s(s(T50))))
U58_GA(T12, T68, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U59_GA(T12, T68, halfB_out_ga(T42, s(s(T50)))) → U60_GA(T12, T68, halfB_in_ga(T50, s(s(T58))))
U59_GA(T12, T68, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U60_GA(T12, T68, halfB_out_ga(T50, s(s(T58)))) → U61_GA(T12, T68, halfB_in_ga(T58, s(s(T66))))
U60_GA(T12, T68, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GA(T58, s(s(T66)))
U61_GA(T12, T68, halfB_out_ga(T58, s(s(T66)))) → U62_GA(T12, T68, halfB_in_ga(T66, X182))
U61_GA(T12, T68, halfB_out_ga(T58, s(s(T66)))) → HALFB_IN_GA(T66, X182)
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → U63_GA(T12, halfB_in_ga(T12, s(s(T26))))
LOG2D_IN_GA(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → HALFB_IN_GA(T12, s(s(T26)))
U63_GA(T12, halfB_out_ga(T12, s(s(T26)))) → U64_GA(T12, halfB_in_ga(T26, s(s(T34))))
U63_GA(T12, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U64_GA(T12, halfB_out_ga(T26, s(s(T34)))) → U65_GA(T12, halfB_in_ga(T34, s(s(T42))))
U64_GA(T12, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U65_GA(T12, halfB_out_ga(T34, s(s(T42)))) → U66_GA(T12, halfB_in_ga(T42, s(s(T50))))
U65_GA(T12, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U66_GA(T12, halfB_out_ga(T42, s(s(T50)))) → U67_GA(T12, halfB_in_ga(T50, s(s(T58))))
U66_GA(T12, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U67_GA(T12, halfB_out_ga(T50, s(s(T58)))) → U68_GA(T12, halfB_in_ga(T58, s(s(T66))))
U67_GA(T12, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GA(T58, s(s(T66)))
U68_GA(T12, halfB_out_ga(T58, s(s(T66)))) → U69_GA(T12, halfB_in_gg(T66, 0))
U68_GA(T12, halfB_out_ga(T58, s(s(T66)))) → HALFB_IN_GG(T66, 0)
U68_GA(T12, halfB_out_ga(T58, s(s(T66)))) → U70_GA(T12, halfB_in_gg(T66, s(0)))
U68_GA(T12, halfB_out_ga(T58, s(s(T66)))) → HALFB_IN_GG(T66, s(0))
LOG2D_IN_GA(s(s(T12)), T76) → U71_GA(T12, T76, halfB_in_ga(T12, s(s(T26))))
U71_GA(T12, T76, halfB_out_ga(T12, s(s(T26)))) → U72_GA(T12, T76, halfB_in_ga(T26, s(s(T34))))
U71_GA(T12, T76, halfB_out_ga(T12, s(s(T26)))) → HALFB_IN_GA(T26, s(s(T34)))
U72_GA(T12, T76, halfB_out_ga(T26, s(s(T34)))) → U73_GA(T12, T76, halfB_in_ga(T34, s(s(T42))))
U72_GA(T12, T76, halfB_out_ga(T26, s(s(T34)))) → HALFB_IN_GA(T34, s(s(T42)))
U73_GA(T12, T76, halfB_out_ga(T34, s(s(T42)))) → U74_GA(T12, T76, halfB_in_ga(T42, s(s(T50))))
U73_GA(T12, T76, halfB_out_ga(T34, s(s(T42)))) → HALFB_IN_GA(T42, s(s(T50)))
U74_GA(T12, T76, halfB_out_ga(T42, s(s(T50)))) → U75_GA(T12, T76, halfB_in_ga(T50, s(s(T58))))
U74_GA(T12, T76, halfB_out_ga(T42, s(s(T50)))) → HALFB_IN_GA(T50, s(s(T58)))
U75_GA(T12, T76, halfB_out_ga(T50, s(s(T58)))) → U76_GA(T12, T76, halfB_in_ga(T58, s(s(T66))))
U75_GA(T12, T76, halfB_out_ga(T50, s(s(T58)))) → HALFB_IN_GA(T58, s(s(T66)))
U76_GA(T12, T76, halfB_out_ga(T58, s(s(T66)))) → U77_GA(T12, T76, halfB_in_ga(T66, s(s(T74))))
U76_GA(T12, T76, halfB_out_ga(T58, s(s(T66)))) → HALFB_IN_GA(T66, s(s(T74)))
U77_GA(T12, T76, halfB_out_ga(T66, s(s(T74)))) → U78_GA(T12, T76, pC_in_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76))
U77_GA(T12, T76, halfB_out_ga(T66, s(s(T74)))) → PC_IN_GAGA(T74, X205, s(s(s(s(s(s(s(0))))))), T76)
PC_IN_GAGA(T74, X205, T77, T76) → U3_GAGA(T74, X205, T77, T76, halfB_in_ga(T74, X205))
PC_IN_GAGA(T74, X205, T77, T76) → HALFB_IN_GA(T74, X205)
PC_IN_GAGA(T74, 0, T85, s(T85)) → U4_GAGA(T74, T85, halfB_in_gg(T74, 0))
PC_IN_GAGA(T74, 0, T85, s(T85)) → HALFB_IN_GG(T74, 0)
PC_IN_GAGA(T74, s(0), T90, s(T90)) → U5_GAGA(T74, T90, halfB_in_gg(T74, s(0)))
PC_IN_GAGA(T74, s(0), T90, s(T90)) → HALFB_IN_GG(T74, s(0))
PC_IN_GAGA(T74, s(s(T97)), T98, T100) → U6_GAGA(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
PC_IN_GAGA(T74, s(s(T97)), T98, T100) → HALFB_IN_GA(T74, s(s(T97)))
U6_GAGA(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → U7_GAGA(T74, T97, T98, T100, pC_in_gaga(T97, X228, s(T98), T100))
U6_GAGA(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → PC_IN_GAGA(T97, X228, s(T98), T100)
log2D_in_ga(0, 0) → log2D_out_ga(0, 0)
log2D_in_ga(s(0), 0) → log2D_out_ga(s(0), 0)
log2D_in_ga(s(s(T12)), T14) → U8_ga(T12, T14, halfB_in_ga(T12, X26))
halfB_in_ga(T18, s(X35)) → U2_ga(T18, X35, halfA_in_ga(T18, X35))
halfA_in_ga(0, 0) → halfA_out_ga(0, 0)
halfA_in_ga(s(0), 0) → halfA_out_ga(s(0), 0)
halfA_in_ga(s(s(T21)), s(X44)) → U1_ga(T21, X44, halfA_in_ga(T21, X44))
U1_ga(T21, X44, halfA_out_ga(T21, X44)) → halfA_out_ga(s(s(T21)), s(X44))
U2_ga(T18, X35, halfA_out_ga(T18, X35)) → halfB_out_ga(T18, s(X35))
U8_ga(T12, T14, halfB_out_ga(T12, X26)) → log2D_out_ga(s(s(T12)), T14)
log2D_in_ga(s(s(T12)), s(0)) → U9_ga(T12, halfB_in_gg(T12, 0))
halfB_in_gg(T18, s(X35)) → U2_gg(T18, X35, halfA_in_gg(T18, X35))
halfA_in_gg(0, 0) → halfA_out_gg(0, 0)
halfA_in_gg(s(0), 0) → halfA_out_gg(s(0), 0)
halfA_in_gg(s(s(T21)), s(X44)) → U1_gg(T21, X44, halfA_in_gg(T21, X44))
U1_gg(T21, X44, halfA_out_gg(T21, X44)) → halfA_out_gg(s(s(T21)), s(X44))
U2_gg(T18, X35, halfA_out_gg(T18, X35)) → halfB_out_gg(T18, s(X35))
U9_ga(T12, halfB_out_gg(T12, 0)) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), s(0)) → U10_ga(T12, halfB_in_gg(T12, s(0)))
U10_ga(T12, halfB_out_gg(T12, s(0))) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), T28) → U11_ga(T12, T28, halfB_in_ga(T12, s(s(T26))))
U11_ga(T12, T28, halfB_out_ga(T12, s(s(T26)))) → U12_ga(T12, T28, halfB_in_ga(T26, X67))
U12_ga(T12, T28, halfB_out_ga(T26, X67)) → log2D_out_ga(s(s(T12)), T28)
log2D_in_ga(s(s(T12)), s(s(0))) → U13_ga(T12, halfB_in_ga(T12, s(s(T26))))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U14_ga(T12, halfB_in_gg(T26, 0))
U14_ga(T12, halfB_out_gg(T26, 0)) → log2D_out_ga(s(s(T12)), s(s(0)))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U15_ga(T12, halfB_in_gg(T26, s(0)))
U15_ga(T12, halfB_out_gg(T26, s(0))) → log2D_out_ga(s(s(T12)), s(s(0)))
log2D_in_ga(s(s(T12)), T36) → U16_ga(T12, T36, halfB_in_ga(T12, s(s(T26))))
U16_ga(T12, T36, halfB_out_ga(T12, s(s(T26)))) → U17_ga(T12, T36, halfB_in_ga(T26, s(s(T34))))
U17_ga(T12, T36, halfB_out_ga(T26, s(s(T34)))) → U18_ga(T12, T36, halfB_in_ga(T34, X90))
U18_ga(T12, T36, halfB_out_ga(T34, X90)) → log2D_out_ga(s(s(T12)), T36)
log2D_in_ga(s(s(T12)), s(s(s(0)))) → U19_ga(T12, halfB_in_ga(T12, s(s(T26))))
U19_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U20_ga(T12, halfB_in_ga(T26, s(s(T34))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U21_ga(T12, halfB_in_gg(T34, 0))
U21_ga(T12, halfB_out_gg(T34, 0)) → log2D_out_ga(s(s(T12)), s(s(s(0))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U22_ga(T12, halfB_in_gg(T34, s(0)))
U22_ga(T12, halfB_out_gg(T34, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(0))))
log2D_in_ga(s(s(T12)), T44) → U23_ga(T12, T44, halfB_in_ga(T12, s(s(T26))))
U23_ga(T12, T44, halfB_out_ga(T12, s(s(T26)))) → U24_ga(T12, T44, halfB_in_ga(T26, s(s(T34))))
U24_ga(T12, T44, halfB_out_ga(T26, s(s(T34)))) → U25_ga(T12, T44, halfB_in_ga(T34, s(s(T42))))
U25_ga(T12, T44, halfB_out_ga(T34, s(s(T42)))) → U26_ga(T12, T44, halfB_in_ga(T42, X113))
U26_ga(T12, T44, halfB_out_ga(T42, X113)) → log2D_out_ga(s(s(T12)), T44)
log2D_in_ga(s(s(T12)), s(s(s(s(0))))) → U27_ga(T12, halfB_in_ga(T12, s(s(T26))))
U27_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U28_ga(T12, halfB_in_ga(T26, s(s(T34))))
U28_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U29_ga(T12, halfB_in_ga(T34, s(s(T42))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U30_ga(T12, halfB_in_gg(T42, 0))
U30_ga(T12, halfB_out_gg(T42, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U31_ga(T12, halfB_in_gg(T42, s(0)))
U31_ga(T12, halfB_out_gg(T42, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
log2D_in_ga(s(s(T12)), T52) → U32_ga(T12, T52, halfB_in_ga(T12, s(s(T26))))
U32_ga(T12, T52, halfB_out_ga(T12, s(s(T26)))) → U33_ga(T12, T52, halfB_in_ga(T26, s(s(T34))))
U33_ga(T12, T52, halfB_out_ga(T26, s(s(T34)))) → U34_ga(T12, T52, halfB_in_ga(T34, s(s(T42))))
U34_ga(T12, T52, halfB_out_ga(T34, s(s(T42)))) → U35_ga(T12, T52, halfB_in_ga(T42, s(s(T50))))
U35_ga(T12, T52, halfB_out_ga(T42, s(s(T50)))) → U36_ga(T12, T52, halfB_in_ga(T50, X136))
U36_ga(T12, T52, halfB_out_ga(T50, X136)) → log2D_out_ga(s(s(T12)), T52)
log2D_in_ga(s(s(T12)), s(s(s(s(s(0)))))) → U37_ga(T12, halfB_in_ga(T12, s(s(T26))))
U37_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U38_ga(T12, halfB_in_ga(T26, s(s(T34))))
U38_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U39_ga(T12, halfB_in_ga(T34, s(s(T42))))
U39_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U40_ga(T12, halfB_in_ga(T42, s(s(T50))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U41_ga(T12, halfB_in_gg(T50, 0))
U41_ga(T12, halfB_out_gg(T50, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U42_ga(T12, halfB_in_gg(T50, s(0)))
U42_ga(T12, halfB_out_gg(T50, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
log2D_in_ga(s(s(T12)), T60) → U43_ga(T12, T60, halfB_in_ga(T12, s(s(T26))))
U43_ga(T12, T60, halfB_out_ga(T12, s(s(T26)))) → U44_ga(T12, T60, halfB_in_ga(T26, s(s(T34))))
U44_ga(T12, T60, halfB_out_ga(T26, s(s(T34)))) → U45_ga(T12, T60, halfB_in_ga(T34, s(s(T42))))
U45_ga(T12, T60, halfB_out_ga(T34, s(s(T42)))) → U46_ga(T12, T60, halfB_in_ga(T42, s(s(T50))))
U46_ga(T12, T60, halfB_out_ga(T42, s(s(T50)))) → U47_ga(T12, T60, halfB_in_ga(T50, s(s(T58))))
U47_ga(T12, T60, halfB_out_ga(T50, s(s(T58)))) → U48_ga(T12, T60, halfB_in_ga(T58, X159))
U48_ga(T12, T60, halfB_out_ga(T58, X159)) → log2D_out_ga(s(s(T12)), T60)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(0))))))) → U49_ga(T12, halfB_in_ga(T12, s(s(T26))))
U49_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U50_ga(T12, halfB_in_ga(T26, s(s(T34))))
U50_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U51_ga(T12, halfB_in_ga(T34, s(s(T42))))
U51_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U52_ga(T12, halfB_in_ga(T42, s(s(T50))))
U52_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U53_ga(T12, halfB_in_ga(T50, s(s(T58))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U54_ga(T12, halfB_in_gg(T58, 0))
U54_ga(T12, halfB_out_gg(T58, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U55_ga(T12, halfB_in_gg(T58, s(0)))
U55_ga(T12, halfB_out_gg(T58, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
log2D_in_ga(s(s(T12)), T68) → U56_ga(T12, T68, halfB_in_ga(T12, s(s(T26))))
U56_ga(T12, T68, halfB_out_ga(T12, s(s(T26)))) → U57_ga(T12, T68, halfB_in_ga(T26, s(s(T34))))
U57_ga(T12, T68, halfB_out_ga(T26, s(s(T34)))) → U58_ga(T12, T68, halfB_in_ga(T34, s(s(T42))))
U58_ga(T12, T68, halfB_out_ga(T34, s(s(T42)))) → U59_ga(T12, T68, halfB_in_ga(T42, s(s(T50))))
U59_ga(T12, T68, halfB_out_ga(T42, s(s(T50)))) → U60_ga(T12, T68, halfB_in_ga(T50, s(s(T58))))
U60_ga(T12, T68, halfB_out_ga(T50, s(s(T58)))) → U61_ga(T12, T68, halfB_in_ga(T58, s(s(T66))))
U61_ga(T12, T68, halfB_out_ga(T58, s(s(T66)))) → U62_ga(T12, T68, halfB_in_ga(T66, X182))
U62_ga(T12, T68, halfB_out_ga(T66, X182)) → log2D_out_ga(s(s(T12)), T68)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → U63_ga(T12, halfB_in_ga(T12, s(s(T26))))
U63_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U64_ga(T12, halfB_in_ga(T26, s(s(T34))))
U64_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U65_ga(T12, halfB_in_ga(T34, s(s(T42))))
U65_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U66_ga(T12, halfB_in_ga(T42, s(s(T50))))
U66_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U67_ga(T12, halfB_in_ga(T50, s(s(T58))))
U67_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U68_ga(T12, halfB_in_ga(T58, s(s(T66))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U69_ga(T12, halfB_in_gg(T66, 0))
U69_ga(T12, halfB_out_gg(T66, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U70_ga(T12, halfB_in_gg(T66, s(0)))
U70_ga(T12, halfB_out_gg(T66, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
log2D_in_ga(s(s(T12)), T76) → U71_ga(T12, T76, halfB_in_ga(T12, s(s(T26))))
U71_ga(T12, T76, halfB_out_ga(T12, s(s(T26)))) → U72_ga(T12, T76, halfB_in_ga(T26, s(s(T34))))
U72_ga(T12, T76, halfB_out_ga(T26, s(s(T34)))) → U73_ga(T12, T76, halfB_in_ga(T34, s(s(T42))))
U73_ga(T12, T76, halfB_out_ga(T34, s(s(T42)))) → U74_ga(T12, T76, halfB_in_ga(T42, s(s(T50))))
U74_ga(T12, T76, halfB_out_ga(T42, s(s(T50)))) → U75_ga(T12, T76, halfB_in_ga(T50, s(s(T58))))
U75_ga(T12, T76, halfB_out_ga(T50, s(s(T58)))) → U76_ga(T12, T76, halfB_in_ga(T58, s(s(T66))))
U76_ga(T12, T76, halfB_out_ga(T58, s(s(T66)))) → U77_ga(T12, T76, halfB_in_ga(T66, s(s(T74))))
U77_ga(T12, T76, halfB_out_ga(T66, s(s(T74)))) → U78_ga(T12, T76, pC_in_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76))
pC_in_gaga(T74, X205, T77, T76) → U3_gaga(T74, X205, T77, T76, halfB_in_ga(T74, X205))
U3_gaga(T74, X205, T77, T76, halfB_out_ga(T74, X205)) → pC_out_gaga(T74, X205, T77, T76)
pC_in_gaga(T74, 0, T85, s(T85)) → U4_gaga(T74, T85, halfB_in_gg(T74, 0))
U4_gaga(T74, T85, halfB_out_gg(T74, 0)) → pC_out_gaga(T74, 0, T85, s(T85))
pC_in_gaga(T74, s(0), T90, s(T90)) → U5_gaga(T74, T90, halfB_in_gg(T74, s(0)))
U5_gaga(T74, T90, halfB_out_gg(T74, s(0))) → pC_out_gaga(T74, s(0), T90, s(T90))
pC_in_gaga(T74, s(s(T97)), T98, T100) → U6_gaga(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
U6_gaga(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → U7_gaga(T74, T97, T98, T100, pC_in_gaga(T97, X228, s(T98), T100))
U7_gaga(T74, T97, T98, T100, pC_out_gaga(T97, X228, s(T98), T100)) → pC_out_gaga(T74, s(s(T97)), T98, T100)
U78_ga(T12, T76, pC_out_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76)) → log2D_out_ga(s(s(T12)), T76)
HALFA_IN_GG(s(s(T21)), s(X44)) → HALFA_IN_GG(T21, X44)
log2D_in_ga(0, 0) → log2D_out_ga(0, 0)
log2D_in_ga(s(0), 0) → log2D_out_ga(s(0), 0)
log2D_in_ga(s(s(T12)), T14) → U8_ga(T12, T14, halfB_in_ga(T12, X26))
halfB_in_ga(T18, s(X35)) → U2_ga(T18, X35, halfA_in_ga(T18, X35))
halfA_in_ga(0, 0) → halfA_out_ga(0, 0)
halfA_in_ga(s(0), 0) → halfA_out_ga(s(0), 0)
halfA_in_ga(s(s(T21)), s(X44)) → U1_ga(T21, X44, halfA_in_ga(T21, X44))
U1_ga(T21, X44, halfA_out_ga(T21, X44)) → halfA_out_ga(s(s(T21)), s(X44))
U2_ga(T18, X35, halfA_out_ga(T18, X35)) → halfB_out_ga(T18, s(X35))
U8_ga(T12, T14, halfB_out_ga(T12, X26)) → log2D_out_ga(s(s(T12)), T14)
log2D_in_ga(s(s(T12)), s(0)) → U9_ga(T12, halfB_in_gg(T12, 0))
halfB_in_gg(T18, s(X35)) → U2_gg(T18, X35, halfA_in_gg(T18, X35))
halfA_in_gg(0, 0) → halfA_out_gg(0, 0)
halfA_in_gg(s(0), 0) → halfA_out_gg(s(0), 0)
halfA_in_gg(s(s(T21)), s(X44)) → U1_gg(T21, X44, halfA_in_gg(T21, X44))
U1_gg(T21, X44, halfA_out_gg(T21, X44)) → halfA_out_gg(s(s(T21)), s(X44))
U2_gg(T18, X35, halfA_out_gg(T18, X35)) → halfB_out_gg(T18, s(X35))
U9_ga(T12, halfB_out_gg(T12, 0)) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), s(0)) → U10_ga(T12, halfB_in_gg(T12, s(0)))
U10_ga(T12, halfB_out_gg(T12, s(0))) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), T28) → U11_ga(T12, T28, halfB_in_ga(T12, s(s(T26))))
U11_ga(T12, T28, halfB_out_ga(T12, s(s(T26)))) → U12_ga(T12, T28, halfB_in_ga(T26, X67))
U12_ga(T12, T28, halfB_out_ga(T26, X67)) → log2D_out_ga(s(s(T12)), T28)
log2D_in_ga(s(s(T12)), s(s(0))) → U13_ga(T12, halfB_in_ga(T12, s(s(T26))))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U14_ga(T12, halfB_in_gg(T26, 0))
U14_ga(T12, halfB_out_gg(T26, 0)) → log2D_out_ga(s(s(T12)), s(s(0)))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U15_ga(T12, halfB_in_gg(T26, s(0)))
U15_ga(T12, halfB_out_gg(T26, s(0))) → log2D_out_ga(s(s(T12)), s(s(0)))
log2D_in_ga(s(s(T12)), T36) → U16_ga(T12, T36, halfB_in_ga(T12, s(s(T26))))
U16_ga(T12, T36, halfB_out_ga(T12, s(s(T26)))) → U17_ga(T12, T36, halfB_in_ga(T26, s(s(T34))))
U17_ga(T12, T36, halfB_out_ga(T26, s(s(T34)))) → U18_ga(T12, T36, halfB_in_ga(T34, X90))
U18_ga(T12, T36, halfB_out_ga(T34, X90)) → log2D_out_ga(s(s(T12)), T36)
log2D_in_ga(s(s(T12)), s(s(s(0)))) → U19_ga(T12, halfB_in_ga(T12, s(s(T26))))
U19_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U20_ga(T12, halfB_in_ga(T26, s(s(T34))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U21_ga(T12, halfB_in_gg(T34, 0))
U21_ga(T12, halfB_out_gg(T34, 0)) → log2D_out_ga(s(s(T12)), s(s(s(0))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U22_ga(T12, halfB_in_gg(T34, s(0)))
U22_ga(T12, halfB_out_gg(T34, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(0))))
log2D_in_ga(s(s(T12)), T44) → U23_ga(T12, T44, halfB_in_ga(T12, s(s(T26))))
U23_ga(T12, T44, halfB_out_ga(T12, s(s(T26)))) → U24_ga(T12, T44, halfB_in_ga(T26, s(s(T34))))
U24_ga(T12, T44, halfB_out_ga(T26, s(s(T34)))) → U25_ga(T12, T44, halfB_in_ga(T34, s(s(T42))))
U25_ga(T12, T44, halfB_out_ga(T34, s(s(T42)))) → U26_ga(T12, T44, halfB_in_ga(T42, X113))
U26_ga(T12, T44, halfB_out_ga(T42, X113)) → log2D_out_ga(s(s(T12)), T44)
log2D_in_ga(s(s(T12)), s(s(s(s(0))))) → U27_ga(T12, halfB_in_ga(T12, s(s(T26))))
U27_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U28_ga(T12, halfB_in_ga(T26, s(s(T34))))
U28_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U29_ga(T12, halfB_in_ga(T34, s(s(T42))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U30_ga(T12, halfB_in_gg(T42, 0))
U30_ga(T12, halfB_out_gg(T42, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U31_ga(T12, halfB_in_gg(T42, s(0)))
U31_ga(T12, halfB_out_gg(T42, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
log2D_in_ga(s(s(T12)), T52) → U32_ga(T12, T52, halfB_in_ga(T12, s(s(T26))))
U32_ga(T12, T52, halfB_out_ga(T12, s(s(T26)))) → U33_ga(T12, T52, halfB_in_ga(T26, s(s(T34))))
U33_ga(T12, T52, halfB_out_ga(T26, s(s(T34)))) → U34_ga(T12, T52, halfB_in_ga(T34, s(s(T42))))
U34_ga(T12, T52, halfB_out_ga(T34, s(s(T42)))) → U35_ga(T12, T52, halfB_in_ga(T42, s(s(T50))))
U35_ga(T12, T52, halfB_out_ga(T42, s(s(T50)))) → U36_ga(T12, T52, halfB_in_ga(T50, X136))
U36_ga(T12, T52, halfB_out_ga(T50, X136)) → log2D_out_ga(s(s(T12)), T52)
log2D_in_ga(s(s(T12)), s(s(s(s(s(0)))))) → U37_ga(T12, halfB_in_ga(T12, s(s(T26))))
U37_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U38_ga(T12, halfB_in_ga(T26, s(s(T34))))
U38_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U39_ga(T12, halfB_in_ga(T34, s(s(T42))))
U39_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U40_ga(T12, halfB_in_ga(T42, s(s(T50))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U41_ga(T12, halfB_in_gg(T50, 0))
U41_ga(T12, halfB_out_gg(T50, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U42_ga(T12, halfB_in_gg(T50, s(0)))
U42_ga(T12, halfB_out_gg(T50, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
log2D_in_ga(s(s(T12)), T60) → U43_ga(T12, T60, halfB_in_ga(T12, s(s(T26))))
U43_ga(T12, T60, halfB_out_ga(T12, s(s(T26)))) → U44_ga(T12, T60, halfB_in_ga(T26, s(s(T34))))
U44_ga(T12, T60, halfB_out_ga(T26, s(s(T34)))) → U45_ga(T12, T60, halfB_in_ga(T34, s(s(T42))))
U45_ga(T12, T60, halfB_out_ga(T34, s(s(T42)))) → U46_ga(T12, T60, halfB_in_ga(T42, s(s(T50))))
U46_ga(T12, T60, halfB_out_ga(T42, s(s(T50)))) → U47_ga(T12, T60, halfB_in_ga(T50, s(s(T58))))
U47_ga(T12, T60, halfB_out_ga(T50, s(s(T58)))) → U48_ga(T12, T60, halfB_in_ga(T58, X159))
U48_ga(T12, T60, halfB_out_ga(T58, X159)) → log2D_out_ga(s(s(T12)), T60)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(0))))))) → U49_ga(T12, halfB_in_ga(T12, s(s(T26))))
U49_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U50_ga(T12, halfB_in_ga(T26, s(s(T34))))
U50_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U51_ga(T12, halfB_in_ga(T34, s(s(T42))))
U51_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U52_ga(T12, halfB_in_ga(T42, s(s(T50))))
U52_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U53_ga(T12, halfB_in_ga(T50, s(s(T58))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U54_ga(T12, halfB_in_gg(T58, 0))
U54_ga(T12, halfB_out_gg(T58, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U55_ga(T12, halfB_in_gg(T58, s(0)))
U55_ga(T12, halfB_out_gg(T58, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
log2D_in_ga(s(s(T12)), T68) → U56_ga(T12, T68, halfB_in_ga(T12, s(s(T26))))
U56_ga(T12, T68, halfB_out_ga(T12, s(s(T26)))) → U57_ga(T12, T68, halfB_in_ga(T26, s(s(T34))))
U57_ga(T12, T68, halfB_out_ga(T26, s(s(T34)))) → U58_ga(T12, T68, halfB_in_ga(T34, s(s(T42))))
U58_ga(T12, T68, halfB_out_ga(T34, s(s(T42)))) → U59_ga(T12, T68, halfB_in_ga(T42, s(s(T50))))
U59_ga(T12, T68, halfB_out_ga(T42, s(s(T50)))) → U60_ga(T12, T68, halfB_in_ga(T50, s(s(T58))))
U60_ga(T12, T68, halfB_out_ga(T50, s(s(T58)))) → U61_ga(T12, T68, halfB_in_ga(T58, s(s(T66))))
U61_ga(T12, T68, halfB_out_ga(T58, s(s(T66)))) → U62_ga(T12, T68, halfB_in_ga(T66, X182))
U62_ga(T12, T68, halfB_out_ga(T66, X182)) → log2D_out_ga(s(s(T12)), T68)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → U63_ga(T12, halfB_in_ga(T12, s(s(T26))))
U63_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U64_ga(T12, halfB_in_ga(T26, s(s(T34))))
U64_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U65_ga(T12, halfB_in_ga(T34, s(s(T42))))
U65_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U66_ga(T12, halfB_in_ga(T42, s(s(T50))))
U66_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U67_ga(T12, halfB_in_ga(T50, s(s(T58))))
U67_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U68_ga(T12, halfB_in_ga(T58, s(s(T66))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U69_ga(T12, halfB_in_gg(T66, 0))
U69_ga(T12, halfB_out_gg(T66, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U70_ga(T12, halfB_in_gg(T66, s(0)))
U70_ga(T12, halfB_out_gg(T66, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
log2D_in_ga(s(s(T12)), T76) → U71_ga(T12, T76, halfB_in_ga(T12, s(s(T26))))
U71_ga(T12, T76, halfB_out_ga(T12, s(s(T26)))) → U72_ga(T12, T76, halfB_in_ga(T26, s(s(T34))))
U72_ga(T12, T76, halfB_out_ga(T26, s(s(T34)))) → U73_ga(T12, T76, halfB_in_ga(T34, s(s(T42))))
U73_ga(T12, T76, halfB_out_ga(T34, s(s(T42)))) → U74_ga(T12, T76, halfB_in_ga(T42, s(s(T50))))
U74_ga(T12, T76, halfB_out_ga(T42, s(s(T50)))) → U75_ga(T12, T76, halfB_in_ga(T50, s(s(T58))))
U75_ga(T12, T76, halfB_out_ga(T50, s(s(T58)))) → U76_ga(T12, T76, halfB_in_ga(T58, s(s(T66))))
U76_ga(T12, T76, halfB_out_ga(T58, s(s(T66)))) → U77_ga(T12, T76, halfB_in_ga(T66, s(s(T74))))
U77_ga(T12, T76, halfB_out_ga(T66, s(s(T74)))) → U78_ga(T12, T76, pC_in_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76))
pC_in_gaga(T74, X205, T77, T76) → U3_gaga(T74, X205, T77, T76, halfB_in_ga(T74, X205))
U3_gaga(T74, X205, T77, T76, halfB_out_ga(T74, X205)) → pC_out_gaga(T74, X205, T77, T76)
pC_in_gaga(T74, 0, T85, s(T85)) → U4_gaga(T74, T85, halfB_in_gg(T74, 0))
U4_gaga(T74, T85, halfB_out_gg(T74, 0)) → pC_out_gaga(T74, 0, T85, s(T85))
pC_in_gaga(T74, s(0), T90, s(T90)) → U5_gaga(T74, T90, halfB_in_gg(T74, s(0)))
U5_gaga(T74, T90, halfB_out_gg(T74, s(0))) → pC_out_gaga(T74, s(0), T90, s(T90))
pC_in_gaga(T74, s(s(T97)), T98, T100) → U6_gaga(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
U6_gaga(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → U7_gaga(T74, T97, T98, T100, pC_in_gaga(T97, X228, s(T98), T100))
U7_gaga(T74, T97, T98, T100, pC_out_gaga(T97, X228, s(T98), T100)) → pC_out_gaga(T74, s(s(T97)), T98, T100)
U78_ga(T12, T76, pC_out_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76)) → log2D_out_ga(s(s(T12)), T76)
HALFA_IN_GG(s(s(T21)), s(X44)) → HALFA_IN_GG(T21, X44)
HALFA_IN_GG(s(s(T21)), s(X44)) → HALFA_IN_GG(T21, X44)
From the DPs we obtained the following set of size-change graphs:
HALFA_IN_GA(s(s(T21)), s(X44)) → HALFA_IN_GA(T21, X44)
log2D_in_ga(0, 0) → log2D_out_ga(0, 0)
log2D_in_ga(s(0), 0) → log2D_out_ga(s(0), 0)
log2D_in_ga(s(s(T12)), T14) → U8_ga(T12, T14, halfB_in_ga(T12, X26))
halfB_in_ga(T18, s(X35)) → U2_ga(T18, X35, halfA_in_ga(T18, X35))
halfA_in_ga(0, 0) → halfA_out_ga(0, 0)
halfA_in_ga(s(0), 0) → halfA_out_ga(s(0), 0)
halfA_in_ga(s(s(T21)), s(X44)) → U1_ga(T21, X44, halfA_in_ga(T21, X44))
U1_ga(T21, X44, halfA_out_ga(T21, X44)) → halfA_out_ga(s(s(T21)), s(X44))
U2_ga(T18, X35, halfA_out_ga(T18, X35)) → halfB_out_ga(T18, s(X35))
U8_ga(T12, T14, halfB_out_ga(T12, X26)) → log2D_out_ga(s(s(T12)), T14)
log2D_in_ga(s(s(T12)), s(0)) → U9_ga(T12, halfB_in_gg(T12, 0))
halfB_in_gg(T18, s(X35)) → U2_gg(T18, X35, halfA_in_gg(T18, X35))
halfA_in_gg(0, 0) → halfA_out_gg(0, 0)
halfA_in_gg(s(0), 0) → halfA_out_gg(s(0), 0)
halfA_in_gg(s(s(T21)), s(X44)) → U1_gg(T21, X44, halfA_in_gg(T21, X44))
U1_gg(T21, X44, halfA_out_gg(T21, X44)) → halfA_out_gg(s(s(T21)), s(X44))
U2_gg(T18, X35, halfA_out_gg(T18, X35)) → halfB_out_gg(T18, s(X35))
U9_ga(T12, halfB_out_gg(T12, 0)) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), s(0)) → U10_ga(T12, halfB_in_gg(T12, s(0)))
U10_ga(T12, halfB_out_gg(T12, s(0))) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), T28) → U11_ga(T12, T28, halfB_in_ga(T12, s(s(T26))))
U11_ga(T12, T28, halfB_out_ga(T12, s(s(T26)))) → U12_ga(T12, T28, halfB_in_ga(T26, X67))
U12_ga(T12, T28, halfB_out_ga(T26, X67)) → log2D_out_ga(s(s(T12)), T28)
log2D_in_ga(s(s(T12)), s(s(0))) → U13_ga(T12, halfB_in_ga(T12, s(s(T26))))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U14_ga(T12, halfB_in_gg(T26, 0))
U14_ga(T12, halfB_out_gg(T26, 0)) → log2D_out_ga(s(s(T12)), s(s(0)))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U15_ga(T12, halfB_in_gg(T26, s(0)))
U15_ga(T12, halfB_out_gg(T26, s(0))) → log2D_out_ga(s(s(T12)), s(s(0)))
log2D_in_ga(s(s(T12)), T36) → U16_ga(T12, T36, halfB_in_ga(T12, s(s(T26))))
U16_ga(T12, T36, halfB_out_ga(T12, s(s(T26)))) → U17_ga(T12, T36, halfB_in_ga(T26, s(s(T34))))
U17_ga(T12, T36, halfB_out_ga(T26, s(s(T34)))) → U18_ga(T12, T36, halfB_in_ga(T34, X90))
U18_ga(T12, T36, halfB_out_ga(T34, X90)) → log2D_out_ga(s(s(T12)), T36)
log2D_in_ga(s(s(T12)), s(s(s(0)))) → U19_ga(T12, halfB_in_ga(T12, s(s(T26))))
U19_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U20_ga(T12, halfB_in_ga(T26, s(s(T34))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U21_ga(T12, halfB_in_gg(T34, 0))
U21_ga(T12, halfB_out_gg(T34, 0)) → log2D_out_ga(s(s(T12)), s(s(s(0))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U22_ga(T12, halfB_in_gg(T34, s(0)))
U22_ga(T12, halfB_out_gg(T34, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(0))))
log2D_in_ga(s(s(T12)), T44) → U23_ga(T12, T44, halfB_in_ga(T12, s(s(T26))))
U23_ga(T12, T44, halfB_out_ga(T12, s(s(T26)))) → U24_ga(T12, T44, halfB_in_ga(T26, s(s(T34))))
U24_ga(T12, T44, halfB_out_ga(T26, s(s(T34)))) → U25_ga(T12, T44, halfB_in_ga(T34, s(s(T42))))
U25_ga(T12, T44, halfB_out_ga(T34, s(s(T42)))) → U26_ga(T12, T44, halfB_in_ga(T42, X113))
U26_ga(T12, T44, halfB_out_ga(T42, X113)) → log2D_out_ga(s(s(T12)), T44)
log2D_in_ga(s(s(T12)), s(s(s(s(0))))) → U27_ga(T12, halfB_in_ga(T12, s(s(T26))))
U27_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U28_ga(T12, halfB_in_ga(T26, s(s(T34))))
U28_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U29_ga(T12, halfB_in_ga(T34, s(s(T42))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U30_ga(T12, halfB_in_gg(T42, 0))
U30_ga(T12, halfB_out_gg(T42, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U31_ga(T12, halfB_in_gg(T42, s(0)))
U31_ga(T12, halfB_out_gg(T42, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
log2D_in_ga(s(s(T12)), T52) → U32_ga(T12, T52, halfB_in_ga(T12, s(s(T26))))
U32_ga(T12, T52, halfB_out_ga(T12, s(s(T26)))) → U33_ga(T12, T52, halfB_in_ga(T26, s(s(T34))))
U33_ga(T12, T52, halfB_out_ga(T26, s(s(T34)))) → U34_ga(T12, T52, halfB_in_ga(T34, s(s(T42))))
U34_ga(T12, T52, halfB_out_ga(T34, s(s(T42)))) → U35_ga(T12, T52, halfB_in_ga(T42, s(s(T50))))
U35_ga(T12, T52, halfB_out_ga(T42, s(s(T50)))) → U36_ga(T12, T52, halfB_in_ga(T50, X136))
U36_ga(T12, T52, halfB_out_ga(T50, X136)) → log2D_out_ga(s(s(T12)), T52)
log2D_in_ga(s(s(T12)), s(s(s(s(s(0)))))) → U37_ga(T12, halfB_in_ga(T12, s(s(T26))))
U37_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U38_ga(T12, halfB_in_ga(T26, s(s(T34))))
U38_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U39_ga(T12, halfB_in_ga(T34, s(s(T42))))
U39_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U40_ga(T12, halfB_in_ga(T42, s(s(T50))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U41_ga(T12, halfB_in_gg(T50, 0))
U41_ga(T12, halfB_out_gg(T50, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U42_ga(T12, halfB_in_gg(T50, s(0)))
U42_ga(T12, halfB_out_gg(T50, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
log2D_in_ga(s(s(T12)), T60) → U43_ga(T12, T60, halfB_in_ga(T12, s(s(T26))))
U43_ga(T12, T60, halfB_out_ga(T12, s(s(T26)))) → U44_ga(T12, T60, halfB_in_ga(T26, s(s(T34))))
U44_ga(T12, T60, halfB_out_ga(T26, s(s(T34)))) → U45_ga(T12, T60, halfB_in_ga(T34, s(s(T42))))
U45_ga(T12, T60, halfB_out_ga(T34, s(s(T42)))) → U46_ga(T12, T60, halfB_in_ga(T42, s(s(T50))))
U46_ga(T12, T60, halfB_out_ga(T42, s(s(T50)))) → U47_ga(T12, T60, halfB_in_ga(T50, s(s(T58))))
U47_ga(T12, T60, halfB_out_ga(T50, s(s(T58)))) → U48_ga(T12, T60, halfB_in_ga(T58, X159))
U48_ga(T12, T60, halfB_out_ga(T58, X159)) → log2D_out_ga(s(s(T12)), T60)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(0))))))) → U49_ga(T12, halfB_in_ga(T12, s(s(T26))))
U49_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U50_ga(T12, halfB_in_ga(T26, s(s(T34))))
U50_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U51_ga(T12, halfB_in_ga(T34, s(s(T42))))
U51_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U52_ga(T12, halfB_in_ga(T42, s(s(T50))))
U52_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U53_ga(T12, halfB_in_ga(T50, s(s(T58))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U54_ga(T12, halfB_in_gg(T58, 0))
U54_ga(T12, halfB_out_gg(T58, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U55_ga(T12, halfB_in_gg(T58, s(0)))
U55_ga(T12, halfB_out_gg(T58, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
log2D_in_ga(s(s(T12)), T68) → U56_ga(T12, T68, halfB_in_ga(T12, s(s(T26))))
U56_ga(T12, T68, halfB_out_ga(T12, s(s(T26)))) → U57_ga(T12, T68, halfB_in_ga(T26, s(s(T34))))
U57_ga(T12, T68, halfB_out_ga(T26, s(s(T34)))) → U58_ga(T12, T68, halfB_in_ga(T34, s(s(T42))))
U58_ga(T12, T68, halfB_out_ga(T34, s(s(T42)))) → U59_ga(T12, T68, halfB_in_ga(T42, s(s(T50))))
U59_ga(T12, T68, halfB_out_ga(T42, s(s(T50)))) → U60_ga(T12, T68, halfB_in_ga(T50, s(s(T58))))
U60_ga(T12, T68, halfB_out_ga(T50, s(s(T58)))) → U61_ga(T12, T68, halfB_in_ga(T58, s(s(T66))))
U61_ga(T12, T68, halfB_out_ga(T58, s(s(T66)))) → U62_ga(T12, T68, halfB_in_ga(T66, X182))
U62_ga(T12, T68, halfB_out_ga(T66, X182)) → log2D_out_ga(s(s(T12)), T68)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → U63_ga(T12, halfB_in_ga(T12, s(s(T26))))
U63_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U64_ga(T12, halfB_in_ga(T26, s(s(T34))))
U64_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U65_ga(T12, halfB_in_ga(T34, s(s(T42))))
U65_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U66_ga(T12, halfB_in_ga(T42, s(s(T50))))
U66_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U67_ga(T12, halfB_in_ga(T50, s(s(T58))))
U67_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U68_ga(T12, halfB_in_ga(T58, s(s(T66))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U69_ga(T12, halfB_in_gg(T66, 0))
U69_ga(T12, halfB_out_gg(T66, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U70_ga(T12, halfB_in_gg(T66, s(0)))
U70_ga(T12, halfB_out_gg(T66, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
log2D_in_ga(s(s(T12)), T76) → U71_ga(T12, T76, halfB_in_ga(T12, s(s(T26))))
U71_ga(T12, T76, halfB_out_ga(T12, s(s(T26)))) → U72_ga(T12, T76, halfB_in_ga(T26, s(s(T34))))
U72_ga(T12, T76, halfB_out_ga(T26, s(s(T34)))) → U73_ga(T12, T76, halfB_in_ga(T34, s(s(T42))))
U73_ga(T12, T76, halfB_out_ga(T34, s(s(T42)))) → U74_ga(T12, T76, halfB_in_ga(T42, s(s(T50))))
U74_ga(T12, T76, halfB_out_ga(T42, s(s(T50)))) → U75_ga(T12, T76, halfB_in_ga(T50, s(s(T58))))
U75_ga(T12, T76, halfB_out_ga(T50, s(s(T58)))) → U76_ga(T12, T76, halfB_in_ga(T58, s(s(T66))))
U76_ga(T12, T76, halfB_out_ga(T58, s(s(T66)))) → U77_ga(T12, T76, halfB_in_ga(T66, s(s(T74))))
U77_ga(T12, T76, halfB_out_ga(T66, s(s(T74)))) → U78_ga(T12, T76, pC_in_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76))
pC_in_gaga(T74, X205, T77, T76) → U3_gaga(T74, X205, T77, T76, halfB_in_ga(T74, X205))
U3_gaga(T74, X205, T77, T76, halfB_out_ga(T74, X205)) → pC_out_gaga(T74, X205, T77, T76)
pC_in_gaga(T74, 0, T85, s(T85)) → U4_gaga(T74, T85, halfB_in_gg(T74, 0))
U4_gaga(T74, T85, halfB_out_gg(T74, 0)) → pC_out_gaga(T74, 0, T85, s(T85))
pC_in_gaga(T74, s(0), T90, s(T90)) → U5_gaga(T74, T90, halfB_in_gg(T74, s(0)))
U5_gaga(T74, T90, halfB_out_gg(T74, s(0))) → pC_out_gaga(T74, s(0), T90, s(T90))
pC_in_gaga(T74, s(s(T97)), T98, T100) → U6_gaga(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
U6_gaga(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → U7_gaga(T74, T97, T98, T100, pC_in_gaga(T97, X228, s(T98), T100))
U7_gaga(T74, T97, T98, T100, pC_out_gaga(T97, X228, s(T98), T100)) → pC_out_gaga(T74, s(s(T97)), T98, T100)
U78_ga(T12, T76, pC_out_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76)) → log2D_out_ga(s(s(T12)), T76)
HALFA_IN_GA(s(s(T21)), s(X44)) → HALFA_IN_GA(T21, X44)
HALFA_IN_GA(s(s(T21))) → HALFA_IN_GA(T21)
From the DPs we obtained the following set of size-change graphs:
PC_IN_GAGA(T74, s(s(T97)), T98, T100) → U6_GAGA(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
U6_GAGA(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → PC_IN_GAGA(T97, X228, s(T98), T100)
log2D_in_ga(0, 0) → log2D_out_ga(0, 0)
log2D_in_ga(s(0), 0) → log2D_out_ga(s(0), 0)
log2D_in_ga(s(s(T12)), T14) → U8_ga(T12, T14, halfB_in_ga(T12, X26))
halfB_in_ga(T18, s(X35)) → U2_ga(T18, X35, halfA_in_ga(T18, X35))
halfA_in_ga(0, 0) → halfA_out_ga(0, 0)
halfA_in_ga(s(0), 0) → halfA_out_ga(s(0), 0)
halfA_in_ga(s(s(T21)), s(X44)) → U1_ga(T21, X44, halfA_in_ga(T21, X44))
U1_ga(T21, X44, halfA_out_ga(T21, X44)) → halfA_out_ga(s(s(T21)), s(X44))
U2_ga(T18, X35, halfA_out_ga(T18, X35)) → halfB_out_ga(T18, s(X35))
U8_ga(T12, T14, halfB_out_ga(T12, X26)) → log2D_out_ga(s(s(T12)), T14)
log2D_in_ga(s(s(T12)), s(0)) → U9_ga(T12, halfB_in_gg(T12, 0))
halfB_in_gg(T18, s(X35)) → U2_gg(T18, X35, halfA_in_gg(T18, X35))
halfA_in_gg(0, 0) → halfA_out_gg(0, 0)
halfA_in_gg(s(0), 0) → halfA_out_gg(s(0), 0)
halfA_in_gg(s(s(T21)), s(X44)) → U1_gg(T21, X44, halfA_in_gg(T21, X44))
U1_gg(T21, X44, halfA_out_gg(T21, X44)) → halfA_out_gg(s(s(T21)), s(X44))
U2_gg(T18, X35, halfA_out_gg(T18, X35)) → halfB_out_gg(T18, s(X35))
U9_ga(T12, halfB_out_gg(T12, 0)) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), s(0)) → U10_ga(T12, halfB_in_gg(T12, s(0)))
U10_ga(T12, halfB_out_gg(T12, s(0))) → log2D_out_ga(s(s(T12)), s(0))
log2D_in_ga(s(s(T12)), T28) → U11_ga(T12, T28, halfB_in_ga(T12, s(s(T26))))
U11_ga(T12, T28, halfB_out_ga(T12, s(s(T26)))) → U12_ga(T12, T28, halfB_in_ga(T26, X67))
U12_ga(T12, T28, halfB_out_ga(T26, X67)) → log2D_out_ga(s(s(T12)), T28)
log2D_in_ga(s(s(T12)), s(s(0))) → U13_ga(T12, halfB_in_ga(T12, s(s(T26))))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U14_ga(T12, halfB_in_gg(T26, 0))
U14_ga(T12, halfB_out_gg(T26, 0)) → log2D_out_ga(s(s(T12)), s(s(0)))
U13_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U15_ga(T12, halfB_in_gg(T26, s(0)))
U15_ga(T12, halfB_out_gg(T26, s(0))) → log2D_out_ga(s(s(T12)), s(s(0)))
log2D_in_ga(s(s(T12)), T36) → U16_ga(T12, T36, halfB_in_ga(T12, s(s(T26))))
U16_ga(T12, T36, halfB_out_ga(T12, s(s(T26)))) → U17_ga(T12, T36, halfB_in_ga(T26, s(s(T34))))
U17_ga(T12, T36, halfB_out_ga(T26, s(s(T34)))) → U18_ga(T12, T36, halfB_in_ga(T34, X90))
U18_ga(T12, T36, halfB_out_ga(T34, X90)) → log2D_out_ga(s(s(T12)), T36)
log2D_in_ga(s(s(T12)), s(s(s(0)))) → U19_ga(T12, halfB_in_ga(T12, s(s(T26))))
U19_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U20_ga(T12, halfB_in_ga(T26, s(s(T34))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U21_ga(T12, halfB_in_gg(T34, 0))
U21_ga(T12, halfB_out_gg(T34, 0)) → log2D_out_ga(s(s(T12)), s(s(s(0))))
U20_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U22_ga(T12, halfB_in_gg(T34, s(0)))
U22_ga(T12, halfB_out_gg(T34, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(0))))
log2D_in_ga(s(s(T12)), T44) → U23_ga(T12, T44, halfB_in_ga(T12, s(s(T26))))
U23_ga(T12, T44, halfB_out_ga(T12, s(s(T26)))) → U24_ga(T12, T44, halfB_in_ga(T26, s(s(T34))))
U24_ga(T12, T44, halfB_out_ga(T26, s(s(T34)))) → U25_ga(T12, T44, halfB_in_ga(T34, s(s(T42))))
U25_ga(T12, T44, halfB_out_ga(T34, s(s(T42)))) → U26_ga(T12, T44, halfB_in_ga(T42, X113))
U26_ga(T12, T44, halfB_out_ga(T42, X113)) → log2D_out_ga(s(s(T12)), T44)
log2D_in_ga(s(s(T12)), s(s(s(s(0))))) → U27_ga(T12, halfB_in_ga(T12, s(s(T26))))
U27_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U28_ga(T12, halfB_in_ga(T26, s(s(T34))))
U28_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U29_ga(T12, halfB_in_ga(T34, s(s(T42))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U30_ga(T12, halfB_in_gg(T42, 0))
U30_ga(T12, halfB_out_gg(T42, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
U29_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U31_ga(T12, halfB_in_gg(T42, s(0)))
U31_ga(T12, halfB_out_gg(T42, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(0)))))
log2D_in_ga(s(s(T12)), T52) → U32_ga(T12, T52, halfB_in_ga(T12, s(s(T26))))
U32_ga(T12, T52, halfB_out_ga(T12, s(s(T26)))) → U33_ga(T12, T52, halfB_in_ga(T26, s(s(T34))))
U33_ga(T12, T52, halfB_out_ga(T26, s(s(T34)))) → U34_ga(T12, T52, halfB_in_ga(T34, s(s(T42))))
U34_ga(T12, T52, halfB_out_ga(T34, s(s(T42)))) → U35_ga(T12, T52, halfB_in_ga(T42, s(s(T50))))
U35_ga(T12, T52, halfB_out_ga(T42, s(s(T50)))) → U36_ga(T12, T52, halfB_in_ga(T50, X136))
U36_ga(T12, T52, halfB_out_ga(T50, X136)) → log2D_out_ga(s(s(T12)), T52)
log2D_in_ga(s(s(T12)), s(s(s(s(s(0)))))) → U37_ga(T12, halfB_in_ga(T12, s(s(T26))))
U37_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U38_ga(T12, halfB_in_ga(T26, s(s(T34))))
U38_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U39_ga(T12, halfB_in_ga(T34, s(s(T42))))
U39_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U40_ga(T12, halfB_in_ga(T42, s(s(T50))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U41_ga(T12, halfB_in_gg(T50, 0))
U41_ga(T12, halfB_out_gg(T50, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
U40_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U42_ga(T12, halfB_in_gg(T50, s(0)))
U42_ga(T12, halfB_out_gg(T50, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(0))))))
log2D_in_ga(s(s(T12)), T60) → U43_ga(T12, T60, halfB_in_ga(T12, s(s(T26))))
U43_ga(T12, T60, halfB_out_ga(T12, s(s(T26)))) → U44_ga(T12, T60, halfB_in_ga(T26, s(s(T34))))
U44_ga(T12, T60, halfB_out_ga(T26, s(s(T34)))) → U45_ga(T12, T60, halfB_in_ga(T34, s(s(T42))))
U45_ga(T12, T60, halfB_out_ga(T34, s(s(T42)))) → U46_ga(T12, T60, halfB_in_ga(T42, s(s(T50))))
U46_ga(T12, T60, halfB_out_ga(T42, s(s(T50)))) → U47_ga(T12, T60, halfB_in_ga(T50, s(s(T58))))
U47_ga(T12, T60, halfB_out_ga(T50, s(s(T58)))) → U48_ga(T12, T60, halfB_in_ga(T58, X159))
U48_ga(T12, T60, halfB_out_ga(T58, X159)) → log2D_out_ga(s(s(T12)), T60)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(0))))))) → U49_ga(T12, halfB_in_ga(T12, s(s(T26))))
U49_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U50_ga(T12, halfB_in_ga(T26, s(s(T34))))
U50_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U51_ga(T12, halfB_in_ga(T34, s(s(T42))))
U51_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U52_ga(T12, halfB_in_ga(T42, s(s(T50))))
U52_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U53_ga(T12, halfB_in_ga(T50, s(s(T58))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U54_ga(T12, halfB_in_gg(T58, 0))
U54_ga(T12, halfB_out_gg(T58, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
U53_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U55_ga(T12, halfB_in_gg(T58, s(0)))
U55_ga(T12, halfB_out_gg(T58, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(0)))))))
log2D_in_ga(s(s(T12)), T68) → U56_ga(T12, T68, halfB_in_ga(T12, s(s(T26))))
U56_ga(T12, T68, halfB_out_ga(T12, s(s(T26)))) → U57_ga(T12, T68, halfB_in_ga(T26, s(s(T34))))
U57_ga(T12, T68, halfB_out_ga(T26, s(s(T34)))) → U58_ga(T12, T68, halfB_in_ga(T34, s(s(T42))))
U58_ga(T12, T68, halfB_out_ga(T34, s(s(T42)))) → U59_ga(T12, T68, halfB_in_ga(T42, s(s(T50))))
U59_ga(T12, T68, halfB_out_ga(T42, s(s(T50)))) → U60_ga(T12, T68, halfB_in_ga(T50, s(s(T58))))
U60_ga(T12, T68, halfB_out_ga(T50, s(s(T58)))) → U61_ga(T12, T68, halfB_in_ga(T58, s(s(T66))))
U61_ga(T12, T68, halfB_out_ga(T58, s(s(T66)))) → U62_ga(T12, T68, halfB_in_ga(T66, X182))
U62_ga(T12, T68, halfB_out_ga(T66, X182)) → log2D_out_ga(s(s(T12)), T68)
log2D_in_ga(s(s(T12)), s(s(s(s(s(s(s(0)))))))) → U63_ga(T12, halfB_in_ga(T12, s(s(T26))))
U63_ga(T12, halfB_out_ga(T12, s(s(T26)))) → U64_ga(T12, halfB_in_ga(T26, s(s(T34))))
U64_ga(T12, halfB_out_ga(T26, s(s(T34)))) → U65_ga(T12, halfB_in_ga(T34, s(s(T42))))
U65_ga(T12, halfB_out_ga(T34, s(s(T42)))) → U66_ga(T12, halfB_in_ga(T42, s(s(T50))))
U66_ga(T12, halfB_out_ga(T42, s(s(T50)))) → U67_ga(T12, halfB_in_ga(T50, s(s(T58))))
U67_ga(T12, halfB_out_ga(T50, s(s(T58)))) → U68_ga(T12, halfB_in_ga(T58, s(s(T66))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U69_ga(T12, halfB_in_gg(T66, 0))
U69_ga(T12, halfB_out_gg(T66, 0)) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
U68_ga(T12, halfB_out_ga(T58, s(s(T66)))) → U70_ga(T12, halfB_in_gg(T66, s(0)))
U70_ga(T12, halfB_out_gg(T66, s(0))) → log2D_out_ga(s(s(T12)), s(s(s(s(s(s(s(0))))))))
log2D_in_ga(s(s(T12)), T76) → U71_ga(T12, T76, halfB_in_ga(T12, s(s(T26))))
U71_ga(T12, T76, halfB_out_ga(T12, s(s(T26)))) → U72_ga(T12, T76, halfB_in_ga(T26, s(s(T34))))
U72_ga(T12, T76, halfB_out_ga(T26, s(s(T34)))) → U73_ga(T12, T76, halfB_in_ga(T34, s(s(T42))))
U73_ga(T12, T76, halfB_out_ga(T34, s(s(T42)))) → U74_ga(T12, T76, halfB_in_ga(T42, s(s(T50))))
U74_ga(T12, T76, halfB_out_ga(T42, s(s(T50)))) → U75_ga(T12, T76, halfB_in_ga(T50, s(s(T58))))
U75_ga(T12, T76, halfB_out_ga(T50, s(s(T58)))) → U76_ga(T12, T76, halfB_in_ga(T58, s(s(T66))))
U76_ga(T12, T76, halfB_out_ga(T58, s(s(T66)))) → U77_ga(T12, T76, halfB_in_ga(T66, s(s(T74))))
U77_ga(T12, T76, halfB_out_ga(T66, s(s(T74)))) → U78_ga(T12, T76, pC_in_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76))
pC_in_gaga(T74, X205, T77, T76) → U3_gaga(T74, X205, T77, T76, halfB_in_ga(T74, X205))
U3_gaga(T74, X205, T77, T76, halfB_out_ga(T74, X205)) → pC_out_gaga(T74, X205, T77, T76)
pC_in_gaga(T74, 0, T85, s(T85)) → U4_gaga(T74, T85, halfB_in_gg(T74, 0))
U4_gaga(T74, T85, halfB_out_gg(T74, 0)) → pC_out_gaga(T74, 0, T85, s(T85))
pC_in_gaga(T74, s(0), T90, s(T90)) → U5_gaga(T74, T90, halfB_in_gg(T74, s(0)))
U5_gaga(T74, T90, halfB_out_gg(T74, s(0))) → pC_out_gaga(T74, s(0), T90, s(T90))
pC_in_gaga(T74, s(s(T97)), T98, T100) → U6_gaga(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
U6_gaga(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → U7_gaga(T74, T97, T98, T100, pC_in_gaga(T97, X228, s(T98), T100))
U7_gaga(T74, T97, T98, T100, pC_out_gaga(T97, X228, s(T98), T100)) → pC_out_gaga(T74, s(s(T97)), T98, T100)
U78_ga(T12, T76, pC_out_gaga(T74, X205, s(s(s(s(s(s(s(0))))))), T76)) → log2D_out_ga(s(s(T12)), T76)
PC_IN_GAGA(T74, s(s(T97)), T98, T100) → U6_GAGA(T74, T97, T98, T100, halfB_in_ga(T74, s(s(T97))))
U6_GAGA(T74, T97, T98, T100, halfB_out_ga(T74, s(s(T97)))) → PC_IN_GAGA(T97, X228, s(T98), T100)
halfB_in_ga(T18, s(X35)) → U2_ga(T18, X35, halfA_in_ga(T18, X35))
U2_ga(T18, X35, halfA_out_ga(T18, X35)) → halfB_out_ga(T18, s(X35))
halfA_in_ga(0, 0) → halfA_out_ga(0, 0)
halfA_in_ga(s(0), 0) → halfA_out_ga(s(0), 0)
halfA_in_ga(s(s(T21)), s(X44)) → U1_ga(T21, X44, halfA_in_ga(T21, X44))
U1_ga(T21, X44, halfA_out_ga(T21, X44)) → halfA_out_ga(s(s(T21)), s(X44))
PC_IN_GAGA(T74, T98) → U6_GAGA(T98, halfB_in_ga(T74))
U6_GAGA(T98, halfB_out_ga(s(s(T97)))) → PC_IN_GAGA(T97, s(T98))
halfB_in_ga(T18) → U2_ga(halfA_in_ga(T18))
U2_ga(halfA_out_ga(X35)) → halfB_out_ga(s(X35))
halfA_in_ga(0) → halfA_out_ga(0)
halfA_in_ga(s(0)) → halfA_out_ga(0)
halfA_in_ga(s(s(T21))) → U1_ga(halfA_in_ga(T21))
U1_ga(halfA_out_ga(X44)) → halfA_out_ga(s(X44))
halfB_in_ga(x0)
U2_ga(x0)
halfA_in_ga(x0)
U1_ga(x0)
U6_GAGA(T98, halfB_out_ga(s(s(T97)))) → PC_IN_GAGA(T97, s(T98))
halfA_in_ga(s(0)) → halfA_out_ga(0)
POL(0) = 0
POL(PC_IN_GAGA(x1, x2)) = 2 + 2·x1 + x2
POL(U1_ga(x1)) = 2 + x1
POL(U2_ga(x1)) = 1 + x1
POL(U6_GAGA(x1, x2)) = x1 + 2·x2
POL(halfA_in_ga(x1)) = x1
POL(halfA_out_ga(x1)) = 2·x1
POL(halfB_in_ga(x1)) = 1 + x1
POL(halfB_out_ga(x1)) = x1
POL(s(x1)) = 1 + x1
PC_IN_GAGA(T74, T98) → U6_GAGA(T98, halfB_in_ga(T74))
halfB_in_ga(T18) → U2_ga(halfA_in_ga(T18))
U2_ga(halfA_out_ga(X35)) → halfB_out_ga(s(X35))
halfA_in_ga(0) → halfA_out_ga(0)
halfA_in_ga(s(s(T21))) → U1_ga(halfA_in_ga(T21))
U1_ga(halfA_out_ga(X44)) → halfA_out_ga(s(X44))
halfB_in_ga(x0)
U2_ga(x0)
halfA_in_ga(x0)
U1_ga(x0)