(0) Obligation:

Clauses:

log2(X, Y) :- log2(X, 0, s(0), Y).
log2(s(s(X)), Half, Acc, Y) :- log2(X, s(Half), Acc, Y).
log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y)).
log2(X, Half, Y, Y) :- ','(small(X), small(Half)).
small(0).
small(s(0)).

Query: log2(g,a)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

(2) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)

(3) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_GA(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → LOG2B_IN_GGA(T107, s(s(s(s(s(s(s(0))))))), T109)
LOG2B_IN_GGA(s(s(T128)), T129, T131) → U14_GGA(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
LOG2B_IN_GGA(s(s(T128)), T129, T131) → LOG2B_IN_GGA(T128, s(T129), T131)
LOG2B_IN_GGA(0, s(T148), T150) → U15_GGA(T148, T150, log2I_in_ga(T148, T150))
LOG2B_IN_GGA(0, s(T148), T150) → LOG2I_IN_GA(T148, T150)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_GA(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → LOG2J_IN_GGA(T241, s(s(s(s(s(s(s(0))))))), T243)
LOG2J_IN_GGA(s(s(T262)), T263, T265) → U17_GGA(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
LOG2J_IN_GGA(s(s(T262)), T263, T265) → LOG2J_IN_GGA(T262, s(T263), T265)
LOG2J_IN_GGA(0, s(T282), T284) → U18_GGA(T282, T284, log2K_in_ga(T282, T284))
LOG2J_IN_GGA(0, s(T282), T284) → LOG2K_IN_GA(T282, T284)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_GA(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → LOG2L_IN_GGA(T375, s(s(s(s(s(s(s(0))))))), T377)
LOG2L_IN_GGA(s(s(T396)), T397, T399) → U20_GGA(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
LOG2L_IN_GGA(s(s(T396)), T397, T399) → LOG2L_IN_GGA(T396, s(T397), T399)
LOG2L_IN_GGA(0, s(T416), T418) → U21_GGA(T416, T418, log2M_in_ga(T416, T418))
LOG2L_IN_GGA(0, s(T416), T418) → LOG2M_IN_GA(T416, T418)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_GA(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → LOG2N_IN_GGA(T509, s(s(s(s(s(s(s(0))))))), T511)
LOG2N_IN_GGA(s(s(T530)), T531, T533) → U23_GGA(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
LOG2N_IN_GGA(s(s(T530)), T531, T533) → LOG2N_IN_GGA(T530, s(T531), T533)
LOG2N_IN_GGA(0, s(T550), T552) → U24_GGA(T550, T552, log2O_in_ga(T550, T552))
LOG2N_IN_GGA(0, s(T550), T552) → LOG2O_IN_GA(T550, T552)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_GA(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → LOG2P_IN_GGA(T643, s(s(s(s(s(s(s(0))))))), T645)
LOG2P_IN_GGA(s(s(T664)), T665, T667) → U26_GGA(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
LOG2P_IN_GGA(s(s(T664)), T665, T667) → LOG2P_IN_GGA(T664, s(T665), T667)
LOG2P_IN_GGA(0, s(T684), T686) → U27_GGA(T684, T686, log2Q_in_ga(T684, T686))
LOG2P_IN_GGA(0, s(T684), T686) → LOG2Q_IN_GA(T684, T686)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_GA(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → LOG2R_IN_GGA(T777, s(s(s(s(s(s(s(0))))))), T779)
LOG2R_IN_GGA(s(s(T798)), T799, T801) → U29_GGA(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
LOG2R_IN_GGA(s(s(T798)), T799, T801) → LOG2R_IN_GGA(T798, s(T799), T801)
LOG2R_IN_GGA(0, s(T818), T820) → U30_GGA(T818, T820, log2S_in_ga(T818, T820))
LOG2R_IN_GGA(0, s(T818), T820) → LOG2S_IN_GA(T818, T820)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_GA(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → LOG2T_IN_GGA(T911, s(s(s(s(s(s(s(0))))))), T913)
LOG2T_IN_GGA(s(s(T932)), T933, T935) → U32_GGA(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
LOG2T_IN_GGA(s(s(T932)), T933, T935) → LOG2T_IN_GGA(T932, s(T933), T935)
LOG2T_IN_GGA(0, s(T952), T954) → U33_GGA(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
LOG2T_IN_GGA(0, s(T952), T954) → LOG2U_IN_GGA(T952, s(s(s(s(s(s(s(0))))))), T954)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_GGA(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → LOG2V_IN_GGGA(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)
LOG2V_IN_GGGA(s(s(T1117)), T1118, T1119, T1121) → U48_GGGA(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
LOG2V_IN_GGGA(s(s(T1117)), T1118, T1119, T1121) → LOG2V_IN_GGGA(T1117, s(T1118), T1119, T1121)
LOG2V_IN_GGGA(0, s(T1143), T1144, T1146) → U49_GGGA(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
LOG2V_IN_GGGA(0, s(T1143), T1144, T1146) → LOG2U_IN_GGA(T1143, s(T1144), T1146)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_GGA(T1184, T1186, log2W_in_ga(T1184, T1186))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → LOG2W_IN_GA(T1184, T1186)
LOG2W_IN_GA(T1233, T1235) → U51_GA(T1233, T1235, log2N3_in_ga(T1233, T1235))
LOG2W_IN_GA(T1233, T1235) → LOG2N3_IN_GA(T1233, T1235)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_GGA(T1184, T1186, log2W_in_ga(T1184, T1186))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → LOG2W_IN_GA(T1184, T1186)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_GGA(T1288, T1290, log2X_in_ga(T1288, T1290))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → LOG2X_IN_GA(T1288, T1290)
LOG2X_IN_GA(T1337, T1339) → U52_GA(T1337, T1339, log2N3_in_ga(T1337, T1339))
LOG2X_IN_GA(T1337, T1339) → LOG2N3_IN_GA(T1337, T1339)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_GGA(T1288, T1290, log2X_in_ga(T1288, T1290))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → LOG2X_IN_GA(T1288, T1290)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_GGA(T1389, T1391, log2Y_in_ga(T1389, T1391))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → LOG2Y_IN_GA(T1389, T1391)
LOG2Y_IN_GA(T1419, T1421) → U53_GA(T1419, T1421, log2N4_in_ga(T1419, T1421))
LOG2Y_IN_GA(T1419, T1421) → LOG2N4_IN_GA(T1419, T1421)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_GGA(T1389, T1391, log2Y_in_ga(T1389, T1391))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → LOG2Y_IN_GA(T1389, T1391)
LOG2U_IN_GGA(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_GGA(T1458, T1460, log2Z_in_ga(T1458, T1460))
LOG2U_IN_GGA(s(s(s(s(s(s(0)))))), T1458, T1460) → LOG2Z_IN_GA(T1458, T1460)
LOG2Z_IN_GA(T1488, T1490) → U54_GA(T1488, T1490, log2N4_in_ga(T1488, T1490))
LOG2Z_IN_GA(T1488, T1490) → LOG2N4_IN_GA(T1488, T1490)
LOG2U_IN_GGA(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_GGA(T1458, T1460, log2Z_in_ga(T1458, T1460))
LOG2U_IN_GGA(s(s(s(s(s(s(s(0))))))), T1458, T1460) → LOG2Z_IN_GA(T1458, T1460)
LOG2U_IN_GGA(s(s(s(s(0)))), T1520, T1522) → U44_GGA(T1520, T1522, log2N1_in_ga(T1520, T1522))
LOG2U_IN_GGA(s(s(s(s(0)))), T1520, T1522) → LOG2N1_IN_GA(T1520, T1522)
LOG2U_IN_GGA(s(s(s(s(s(0))))), T1520, T1522) → U45_GGA(T1520, T1522, log2N1_in_ga(T1520, T1522))
LOG2U_IN_GGA(s(s(s(s(s(0))))), T1520, T1522) → LOG2N1_IN_GA(T1520, T1522)
LOG2U_IN_GGA(s(s(0)), T1547, T1549) → U46_GGA(T1547, T1549, log2N2_in_ga(T1547, T1549))
LOG2U_IN_GGA(s(s(0)), T1547, T1549) → LOG2N2_IN_GA(T1547, T1549)
LOG2U_IN_GGA(s(s(s(0))), T1547, T1549) → U47_GGA(T1547, T1549, log2N2_in_ga(T1547, T1549))
LOG2U_IN_GGA(s(s(s(0))), T1547, T1549) → LOG2N2_IN_GA(T1547, T1549)
LOG2V_IN_GGGA(s(0), s(T1143), T1144, T1146) → U50_GGGA(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
LOG2V_IN_GGGA(s(0), s(T1143), T1144, T1146) → LOG2U_IN_GGA(T1143, s(T1144), T1146)
LOG2T_IN_GGA(s(0), s(T952), T954) → U34_GGA(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
LOG2T_IN_GGA(s(0), s(T952), T954) → LOG2U_IN_GGA(T952, s(s(s(s(s(s(s(0))))))), T954)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_GA(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → LOG2N5_IN_GA(s(s(s(s(s(s(s(0))))))), T1592)
LOG2N5_IN_GA(T1640, T1642) → U55_GA(T1640, T1642, log2N1_in_ga(T1640, T1642))
LOG2N5_IN_GA(T1640, T1642) → LOG2N1_IN_GA(T1640, T1642)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_GA(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → LOG2N5_IN_GA(s(s(s(s(s(s(s(0))))))), T1592)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_GA(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → LOG2N6_IN_GA(s(s(s(s(s(s(s(0))))))), T1686)
LOG2N6_IN_GA(T1734, T1736) → U56_GA(T1734, T1736, log2N1_in_ga(T1734, T1736))
LOG2N6_IN_GA(T1734, T1736) → LOG2N1_IN_GA(T1734, T1736)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_GA(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → LOG2N6_IN_GA(s(s(s(s(s(s(s(0))))))), T1686)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_GA(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T1780) → LOG2N7_IN_GA(s(s(s(s(s(s(s(0))))))), T1780)
LOG2N7_IN_GA(T1809, T1811) → U57_GA(T1809, T1811, log2N2_in_ga(T1809, T1811))
LOG2N7_IN_GA(T1809, T1811) → LOG2N2_IN_GA(T1809, T1811)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_GA(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → LOG2N7_IN_GA(s(s(s(s(s(s(s(0))))))), T1780)
LOG2S_IN_GA(s(s(s(s(s(s(0)))))), T1839) → U66_GA(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
LOG2S_IN_GA(s(s(s(s(s(s(0)))))), T1839) → LOG2N8_IN_GA(s(s(s(s(s(s(s(0))))))), T1839)
LOG2N8_IN_GA(T1868, T1870) → U58_GA(T1868, T1870, log2N2_in_ga(T1868, T1870))
LOG2N8_IN_GA(T1868, T1870) → LOG2N2_IN_GA(T1868, T1870)
LOG2S_IN_GA(s(s(s(s(s(s(s(0))))))), T1839) → U67_GA(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
LOG2S_IN_GA(s(s(s(s(s(s(s(0))))))), T1839) → LOG2N8_IN_GA(s(s(s(s(s(s(s(0))))))), T1839)
LOG2S_IN_GA(s(s(s(s(0)))), T1896) → U68_GA(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
LOG2S_IN_GA(s(s(s(s(0)))), T1896) → LOG2N9_IN_GA(s(s(s(s(s(s(s(0))))))), T1896)
LOG2S_IN_GA(s(s(s(s(s(0))))), T1896) → U69_GA(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
LOG2S_IN_GA(s(s(s(s(s(0))))), T1896) → LOG2N9_IN_GA(s(s(s(s(s(s(s(0))))))), T1896)
LOG2S_IN_GA(s(s(0)), T1917) → U70_GA(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
LOG2S_IN_GA(s(s(0)), T1917) → LOG2N10_IN_GA(s(s(s(s(s(s(s(0))))))), T1917)
LOG2S_IN_GA(s(s(s(0))), T1917) → U71_GA(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
LOG2S_IN_GA(s(s(s(0))), T1917) → LOG2N10_IN_GA(s(s(s(s(s(s(s(0))))))), T1917)
LOG2R_IN_GGA(s(0), s(T818), T820) → U31_GGA(T818, T820, log2S_in_ga(T818, T820))
LOG2R_IN_GGA(s(0), s(T818), T820) → LOG2S_IN_GA(T818, T820)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_GA(T1952, log2N11_in_a(T1952))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → LOG2N11_IN_A(T1952)
LOG2N11_IN_A(T1981) → U72_A(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
LOG2N11_IN_A(T1981) → LOG2N9_IN_GA(s(s(s(s(s(s(s(0))))))), T1981)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_GA(T1952, log2N11_in_a(T1952))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → LOG2N11_IN_A(T1952)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_GA(T2009, log2N12_in_a(T2009))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → LOG2N12_IN_A(T2009)
LOG2N12_IN_A(T2038) → U73_A(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
LOG2N12_IN_A(T2038) → LOG2N9_IN_GA(s(s(s(s(s(s(s(0))))))), T2038)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_GA(T2009, log2N12_in_a(T2009))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → LOG2N12_IN_A(T2009)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_GA(T2066, log2N13_in_a(T2066))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2066) → LOG2N13_IN_A(T2066)
LOG2N13_IN_A(T2084) → U74_A(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
LOG2N13_IN_A(T2084) → LOG2N10_IN_GA(s(s(s(s(s(s(s(0))))))), T2084)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_GA(T2066, log2N13_in_a(T2066))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → LOG2N13_IN_A(T2066)
LOG2Q_IN_GA(s(s(s(s(s(s(0)))))), T2104) → U83_GA(T2104, log2N14_in_a(T2104))
LOG2Q_IN_GA(s(s(s(s(s(s(0)))))), T2104) → LOG2N14_IN_A(T2104)
LOG2N14_IN_A(T2122) → U75_A(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
LOG2N14_IN_A(T2122) → LOG2N10_IN_GA(s(s(s(s(s(s(s(0))))))), T2122)
LOG2Q_IN_GA(s(s(s(s(s(s(s(0))))))), T2104) → U84_GA(T2104, log2N14_in_a(T2104))
LOG2Q_IN_GA(s(s(s(s(s(s(s(0))))))), T2104) → LOG2N14_IN_A(T2104)
LOG2Q_IN_GA(s(s(s(s(0)))), T2140) → U85_GA(T2140, log2N15_in_a(T2140))
LOG2Q_IN_GA(s(s(s(s(0)))), T2140) → LOG2N15_IN_A(T2140)
LOG2Q_IN_GA(s(s(s(s(s(0))))), T2140) → U86_GA(T2140, log2N15_in_a(T2140))
LOG2Q_IN_GA(s(s(s(s(s(0))))), T2140) → LOG2N15_IN_A(T2140)
LOG2Q_IN_GA(s(s(0)), T2156) → U87_GA(T2156, log2N16_in_a(T2156))
LOG2Q_IN_GA(s(s(0)), T2156) → LOG2N16_IN_A(T2156)
LOG2Q_IN_GA(s(s(s(0))), T2156) → U88_GA(T2156, log2N16_in_a(T2156))
LOG2Q_IN_GA(s(s(s(0))), T2156) → LOG2N16_IN_A(T2156)
LOG2P_IN_GGA(s(0), s(T684), T686) → U28_GGA(T684, T686, log2Q_in_ga(T684, T686))
LOG2P_IN_GGA(s(0), s(T684), T686) → LOG2Q_IN_GA(T684, T686)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_GA(T2186, log2N17_in_a(T2186))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → LOG2N17_IN_A(T2186)
LOG2N17_IN_A(T2215) → U89_A(T2215, log2N15_in_a(T2215))
LOG2N17_IN_A(T2215) → LOG2N15_IN_A(T2215)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_GA(T2186, log2N17_in_a(T2186))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → LOG2N17_IN_A(T2186)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_GA(T2242, log2N18_in_a(T2242))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → LOG2N18_IN_A(T2242)
LOG2N18_IN_A(T2271) → U90_A(T2271, log2N15_in_a(T2271))
LOG2N18_IN_A(T2271) → LOG2N15_IN_A(T2271)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_GA(T2242, log2N18_in_a(T2242))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → LOG2N18_IN_A(T2242)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_GA(T2298, log2N19_in_a(T2298))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2298) → LOG2N19_IN_A(T2298)
LOG2N19_IN_A(T2316) → U91_A(T2316, log2N16_in_a(T2316))
LOG2N19_IN_A(T2316) → LOG2N16_IN_A(T2316)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_GA(T2298, log2N19_in_a(T2298))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → LOG2N19_IN_A(T2298)
LOG2O_IN_GA(s(s(s(s(s(s(0)))))), T2335) → U100_GA(T2335, log2N20_in_a(T2335))
LOG2O_IN_GA(s(s(s(s(s(s(0)))))), T2335) → LOG2N20_IN_A(T2335)
LOG2N20_IN_A(T2353) → U92_A(T2353, log2N16_in_a(T2353))
LOG2N20_IN_A(T2353) → LOG2N16_IN_A(T2353)
LOG2O_IN_GA(s(s(s(s(s(s(s(0))))))), T2335) → U101_GA(T2335, log2N20_in_a(T2335))
LOG2O_IN_GA(s(s(s(s(s(s(s(0))))))), T2335) → LOG2N20_IN_A(T2335)
LOG2O_IN_GA(s(s(s(s(0)))), T2370) → U102_GA(T2370, log2N21_in_a(T2370))
LOG2O_IN_GA(s(s(s(s(0)))), T2370) → LOG2N21_IN_A(T2370)
LOG2O_IN_GA(s(s(s(s(s(0))))), T2370) → U103_GA(T2370, log2N21_in_a(T2370))
LOG2O_IN_GA(s(s(s(s(s(0))))), T2370) → LOG2N21_IN_A(T2370)
LOG2O_IN_GA(s(s(0)), T2386) → U104_GA(T2386, log2N22_in_a(T2386))
LOG2O_IN_GA(s(s(0)), T2386) → LOG2N22_IN_A(T2386)
LOG2O_IN_GA(s(s(s(0))), T2386) → U105_GA(T2386, log2N22_in_a(T2386))
LOG2O_IN_GA(s(s(s(0))), T2386) → LOG2N22_IN_A(T2386)
LOG2N_IN_GGA(s(0), s(T550), T552) → U25_GGA(T550, T552, log2O_in_ga(T550, T552))
LOG2N_IN_GGA(s(0), s(T550), T552) → LOG2O_IN_GA(T550, T552)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_GA(T2416, log2N23_in_a(T2416))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → LOG2N23_IN_A(T2416)
LOG2N23_IN_A(T2445) → U106_A(T2445, log2N21_in_a(T2445))
LOG2N23_IN_A(T2445) → LOG2N21_IN_A(T2445)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_GA(T2416, log2N23_in_a(T2416))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → LOG2N23_IN_A(T2416)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_GA(T2472, log2N24_in_a(T2472))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → LOG2N24_IN_A(T2472)
LOG2N24_IN_A(T2501) → U107_A(T2501, log2N21_in_a(T2501))
LOG2N24_IN_A(T2501) → LOG2N21_IN_A(T2501)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_GA(T2472, log2N24_in_a(T2472))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → LOG2N24_IN_A(T2472)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_GA(T2528, log2N25_in_a(T2528))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2528) → LOG2N25_IN_A(T2528)
LOG2N25_IN_A(T2546) → U108_A(T2546, log2N22_in_a(T2546))
LOG2N25_IN_A(T2546) → LOG2N22_IN_A(T2546)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_GA(T2528, log2N25_in_a(T2528))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → LOG2N25_IN_A(T2528)
LOG2M_IN_GA(s(s(s(s(s(s(0)))))), T2565) → U117_GA(T2565, log2N26_in_a(T2565))
LOG2M_IN_GA(s(s(s(s(s(s(0)))))), T2565) → LOG2N26_IN_A(T2565)
LOG2N26_IN_A(T2583) → U109_A(T2583, log2N22_in_a(T2583))
LOG2N26_IN_A(T2583) → LOG2N22_IN_A(T2583)
LOG2M_IN_GA(s(s(s(s(s(s(s(0))))))), T2565) → U118_GA(T2565, log2N26_in_a(T2565))
LOG2M_IN_GA(s(s(s(s(s(s(s(0))))))), T2565) → LOG2N26_IN_A(T2565)
LOG2M_IN_GA(s(s(s(s(0)))), T2600) → U119_GA(T2600, log2N27_in_a(T2600))
LOG2M_IN_GA(s(s(s(s(0)))), T2600) → LOG2N27_IN_A(T2600)
LOG2M_IN_GA(s(s(s(s(s(0))))), T2600) → U120_GA(T2600, log2N27_in_a(T2600))
LOG2M_IN_GA(s(s(s(s(s(0))))), T2600) → LOG2N27_IN_A(T2600)
LOG2M_IN_GA(s(s(0)), T2616) → U121_GA(T2616, log2N28_in_a(T2616))
LOG2M_IN_GA(s(s(0)), T2616) → LOG2N28_IN_A(T2616)
LOG2M_IN_GA(s(s(s(0))), T2616) → U122_GA(T2616, log2N28_in_a(T2616))
LOG2M_IN_GA(s(s(s(0))), T2616) → LOG2N28_IN_A(T2616)
LOG2L_IN_GGA(s(0), s(T416), T418) → U22_GGA(T416, T418, log2M_in_ga(T416, T418))
LOG2L_IN_GGA(s(0), s(T416), T418) → LOG2M_IN_GA(T416, T418)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_GA(T2646, log2N29_in_a(T2646))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → LOG2N29_IN_A(T2646)
LOG2N29_IN_A(T2675) → U123_A(T2675, log2N27_in_a(T2675))
LOG2N29_IN_A(T2675) → LOG2N27_IN_A(T2675)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_GA(T2646, log2N29_in_a(T2646))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → LOG2N29_IN_A(T2646)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_GA(T2702, log2N30_in_a(T2702))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → LOG2N30_IN_A(T2702)
LOG2N30_IN_A(T2731) → U124_A(T2731, log2N27_in_a(T2731))
LOG2N30_IN_A(T2731) → LOG2N27_IN_A(T2731)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_GA(T2702, log2N30_in_a(T2702))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → LOG2N30_IN_A(T2702)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_GA(T2758, log2N31_in_a(T2758))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2758) → LOG2N31_IN_A(T2758)
LOG2N31_IN_A(T2776) → U125_A(T2776, log2N28_in_a(T2776))
LOG2N31_IN_A(T2776) → LOG2N28_IN_A(T2776)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_GA(T2758, log2N31_in_a(T2758))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → LOG2N31_IN_A(T2758)
LOG2K_IN_GA(s(s(s(s(s(s(0)))))), T2795) → U134_GA(T2795, log2N32_in_a(T2795))
LOG2K_IN_GA(s(s(s(s(s(s(0)))))), T2795) → LOG2N32_IN_A(T2795)
LOG2N32_IN_A(T2813) → U126_A(T2813, log2N28_in_a(T2813))
LOG2N32_IN_A(T2813) → LOG2N28_IN_A(T2813)
LOG2K_IN_GA(s(s(s(s(s(s(s(0))))))), T2795) → U135_GA(T2795, log2N32_in_a(T2795))
LOG2K_IN_GA(s(s(s(s(s(s(s(0))))))), T2795) → LOG2N32_IN_A(T2795)
LOG2K_IN_GA(s(s(s(s(0)))), T2830) → U136_GA(T2830, log2N33_in_a(T2830))
LOG2K_IN_GA(s(s(s(s(0)))), T2830) → LOG2N33_IN_A(T2830)
LOG2K_IN_GA(s(s(s(s(s(0))))), T2830) → U137_GA(T2830, log2N33_in_a(T2830))
LOG2K_IN_GA(s(s(s(s(s(0))))), T2830) → LOG2N33_IN_A(T2830)
LOG2K_IN_GA(s(s(0)), T2846) → U138_GA(T2846, log2N34_in_a(T2846))
LOG2K_IN_GA(s(s(0)), T2846) → LOG2N34_IN_A(T2846)
LOG2K_IN_GA(s(s(s(0))), T2846) → U139_GA(T2846, log2N34_in_a(T2846))
LOG2K_IN_GA(s(s(s(0))), T2846) → LOG2N34_IN_A(T2846)
LOG2J_IN_GGA(s(0), s(T282), T284) → U19_GGA(T282, T284, log2K_in_ga(T282, T284))
LOG2J_IN_GGA(s(0), s(T282), T284) → LOG2K_IN_GA(T282, T284)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_GA(T2876, log2N35_in_a(T2876))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → LOG2N35_IN_A(T2876)
LOG2N35_IN_A(T2905) → U140_A(T2905, log2N33_in_a(T2905))
LOG2N35_IN_A(T2905) → LOG2N33_IN_A(T2905)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_GA(T2876, log2N35_in_a(T2876))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → LOG2N35_IN_A(T2876)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_GA(T2932, log2N36_in_a(T2932))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → LOG2N36_IN_A(T2932)
LOG2N36_IN_A(T2961) → U141_A(T2961, log2N33_in_a(T2961))
LOG2N36_IN_A(T2961) → LOG2N33_IN_A(T2961)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_GA(T2932, log2N36_in_a(T2932))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → LOG2N36_IN_A(T2932)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_GA(T2988, log2N37_in_a(T2988))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2988) → LOG2N37_IN_A(T2988)
LOG2N37_IN_A(T3006) → U142_A(T3006, log2N34_in_a(T3006))
LOG2N37_IN_A(T3006) → LOG2N34_IN_A(T3006)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_GA(T2988, log2N37_in_a(T2988))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → LOG2N37_IN_A(T2988)
LOG2I_IN_GA(s(s(s(s(s(s(0)))))), T3025) → U151_GA(T3025, log2N38_in_a(T3025))
LOG2I_IN_GA(s(s(s(s(s(s(0)))))), T3025) → LOG2N38_IN_A(T3025)
LOG2N38_IN_A(T3043) → U143_A(T3043, log2N34_in_a(T3043))
LOG2N38_IN_A(T3043) → LOG2N34_IN_A(T3043)
LOG2I_IN_GA(s(s(s(s(s(s(s(0))))))), T3025) → U152_GA(T3025, log2N38_in_a(T3025))
LOG2I_IN_GA(s(s(s(s(s(s(s(0))))))), T3025) → LOG2N38_IN_A(T3025)
LOG2I_IN_GA(s(s(s(s(0)))), T3060) → U153_GA(T3060, log2N39_in_a(T3060))
LOG2I_IN_GA(s(s(s(s(0)))), T3060) → LOG2N39_IN_A(T3060)
LOG2I_IN_GA(s(s(s(s(s(0))))), T3060) → U154_GA(T3060, log2N39_in_a(T3060))
LOG2I_IN_GA(s(s(s(s(s(0))))), T3060) → LOG2N39_IN_A(T3060)
LOG2I_IN_GA(s(s(0)), T3076) → U155_GA(T3076, log2N40_in_a(T3076))
LOG2I_IN_GA(s(s(0)), T3076) → LOG2N40_IN_A(T3076)
LOG2I_IN_GA(s(s(s(0))), T3076) → U156_GA(T3076, log2N40_in_a(T3076))
LOG2I_IN_GA(s(s(s(0))), T3076) → LOG2N40_IN_A(T3076)
LOG2B_IN_GGA(s(0), s(T148), T150) → U16_GGA(T148, T150, log2I_in_ga(T148, T150))
LOG2B_IN_GGA(s(0), s(T148), T150) → LOG2I_IN_GA(T148, T150)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_GA(T3106, log2C_in_a(T3106))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → LOG2C_IN_A(T3106)
LOG2C_IN_A(T3135) → U157_A(T3135, log2N39_in_a(T3135))
LOG2C_IN_A(T3135) → LOG2N39_IN_A(T3135)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_GA(T3106, log2C_in_a(T3106))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → LOG2C_IN_A(T3106)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_GA(T3162, log2D_in_a(T3162))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → LOG2D_IN_A(T3162)
LOG2D_IN_A(T3191) → U158_A(T3191, log2N39_in_a(T3191))
LOG2D_IN_A(T3191) → LOG2N39_IN_A(T3191)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_GA(T3162, log2D_in_a(T3162))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → LOG2D_IN_A(T3162)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_GA(T3218, log2E_in_a(T3218))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → LOG2E_IN_A(T3218)
LOG2E_IN_A(T3236) → U159_A(T3236, log2N40_in_a(T3236))
LOG2E_IN_A(T3236) → LOG2N40_IN_A(T3236)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_GA(T3218, log2E_in_a(T3218))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → LOG2E_IN_A(T3218)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_GA(T3255, log2F_in_a(T3255))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T3255) → LOG2F_IN_A(T3255)
LOG2F_IN_A(T3273) → U160_A(T3273, log2N40_in_a(T3273))
LOG2F_IN_A(T3273) → LOG2N40_IN_A(T3273)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_GA(T3255, log2F_in_a(T3255))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → LOG2F_IN_A(T3255)
LOG2A_IN_GA(s(s(s(s(s(s(0)))))), T3290) → U10_GA(T3290, log2G_in_a(T3290))
LOG2A_IN_GA(s(s(s(s(s(s(0)))))), T3290) → LOG2G_IN_A(T3290)
LOG2A_IN_GA(s(s(s(s(s(s(s(0))))))), T3290) → U11_GA(T3290, log2G_in_a(T3290))
LOG2A_IN_GA(s(s(s(s(s(s(s(0))))))), T3290) → LOG2G_IN_A(T3290)
LOG2A_IN_GA(s(s(s(s(0)))), T3306) → U12_GA(T3306, log2H_in_a(T3306))
LOG2A_IN_GA(s(s(s(s(0)))), T3306) → LOG2H_IN_A(T3306)
LOG2A_IN_GA(s(s(s(s(s(0))))), T3306) → U13_GA(T3306, log2H_in_a(T3306))
LOG2A_IN_GA(s(s(s(s(s(0))))), T3306) → LOG2H_IN_A(T3306)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2A_IN_GA(x1, x2)  =  LOG2A_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x1, x3)
LOG2B_IN_GGA(x1, x2, x3)  =  LOG2B_IN_GGA(x1, x2)
U14_GGA(x1, x2, x3, x4)  =  U14_GGA(x1, x2, x4)
U15_GGA(x1, x2, x3)  =  U15_GGA(x1, x3)
LOG2I_IN_GA(x1, x2)  =  LOG2I_IN_GA(x1)
U144_GA(x1, x2, x3)  =  U144_GA(x1, x3)
LOG2J_IN_GGA(x1, x2, x3)  =  LOG2J_IN_GGA(x1, x2)
U17_GGA(x1, x2, x3, x4)  =  U17_GGA(x1, x2, x4)
U18_GGA(x1, x2, x3)  =  U18_GGA(x1, x3)
LOG2K_IN_GA(x1, x2)  =  LOG2K_IN_GA(x1)
U127_GA(x1, x2, x3)  =  U127_GA(x1, x3)
LOG2L_IN_GGA(x1, x2, x3)  =  LOG2L_IN_GGA(x1, x2)
U20_GGA(x1, x2, x3, x4)  =  U20_GGA(x1, x2, x4)
U21_GGA(x1, x2, x3)  =  U21_GGA(x1, x3)
LOG2M_IN_GA(x1, x2)  =  LOG2M_IN_GA(x1)
U110_GA(x1, x2, x3)  =  U110_GA(x1, x3)
LOG2N_IN_GGA(x1, x2, x3)  =  LOG2N_IN_GGA(x1, x2)
U23_GGA(x1, x2, x3, x4)  =  U23_GGA(x1, x2, x4)
U24_GGA(x1, x2, x3)  =  U24_GGA(x1, x3)
LOG2O_IN_GA(x1, x2)  =  LOG2O_IN_GA(x1)
U93_GA(x1, x2, x3)  =  U93_GA(x1, x3)
LOG2P_IN_GGA(x1, x2, x3)  =  LOG2P_IN_GGA(x1, x2)
U26_GGA(x1, x2, x3, x4)  =  U26_GGA(x1, x2, x4)
U27_GGA(x1, x2, x3)  =  U27_GGA(x1, x3)
LOG2Q_IN_GA(x1, x2)  =  LOG2Q_IN_GA(x1)
U76_GA(x1, x2, x3)  =  U76_GA(x1, x3)
LOG2R_IN_GGA(x1, x2, x3)  =  LOG2R_IN_GGA(x1, x2)
U29_GGA(x1, x2, x3, x4)  =  U29_GGA(x1, x2, x4)
U30_GGA(x1, x2, x3)  =  U30_GGA(x1, x3)
LOG2S_IN_GA(x1, x2)  =  LOG2S_IN_GA(x1)
U59_GA(x1, x2, x3)  =  U59_GA(x1, x3)
LOG2T_IN_GGA(x1, x2, x3)  =  LOG2T_IN_GGA(x1, x2)
U32_GGA(x1, x2, x3, x4)  =  U32_GGA(x1, x2, x4)
U33_GGA(x1, x2, x3)  =  U33_GGA(x1, x3)
LOG2U_IN_GGA(x1, x2, x3)  =  LOG2U_IN_GGA(x1, x2)
U35_GGA(x1, x2, x3, x4)  =  U35_GGA(x1, x2, x4)
LOG2V_IN_GGGA(x1, x2, x3, x4)  =  LOG2V_IN_GGGA(x1, x2, x3)
U48_GGGA(x1, x2, x3, x4, x5)  =  U48_GGGA(x1, x2, x3, x5)
U49_GGGA(x1, x2, x3, x4)  =  U49_GGGA(x1, x2, x4)
U36_GGA(x1, x2, x3)  =  U36_GGA(x1, x3)
LOG2W_IN_GA(x1, x2)  =  LOG2W_IN_GA(x1)
U51_GA(x1, x2, x3)  =  U51_GA(x1, x3)
LOG2N3_IN_GA(x1, x2)  =  LOG2N3_IN_GA(x1)
U37_GGA(x1, x2, x3)  =  U37_GGA(x1, x3)
U38_GGA(x1, x2, x3)  =  U38_GGA(x1, x3)
LOG2X_IN_GA(x1, x2)  =  LOG2X_IN_GA(x1)
U52_GA(x1, x2, x3)  =  U52_GA(x1, x3)
U39_GGA(x1, x2, x3)  =  U39_GGA(x1, x3)
U40_GGA(x1, x2, x3)  =  U40_GGA(x1, x3)
LOG2Y_IN_GA(x1, x2)  =  LOG2Y_IN_GA(x1)
U53_GA(x1, x2, x3)  =  U53_GA(x1, x3)
LOG2N4_IN_GA(x1, x2)  =  LOG2N4_IN_GA(x1)
U41_GGA(x1, x2, x3)  =  U41_GGA(x1, x3)
U42_GGA(x1, x2, x3)  =  U42_GGA(x1, x3)
LOG2Z_IN_GA(x1, x2)  =  LOG2Z_IN_GA(x1)
U54_GA(x1, x2, x3)  =  U54_GA(x1, x3)
U43_GGA(x1, x2, x3)  =  U43_GGA(x1, x3)
U44_GGA(x1, x2, x3)  =  U44_GGA(x1, x3)
LOG2N1_IN_GA(x1, x2)  =  LOG2N1_IN_GA(x1)
U45_GGA(x1, x2, x3)  =  U45_GGA(x1, x3)
U46_GGA(x1, x2, x3)  =  U46_GGA(x1, x3)
LOG2N2_IN_GA(x1, x2)  =  LOG2N2_IN_GA(x1)
U47_GGA(x1, x2, x3)  =  U47_GGA(x1, x3)
U50_GGGA(x1, x2, x3, x4)  =  U50_GGGA(x1, x2, x4)
U34_GGA(x1, x2, x3)  =  U34_GGA(x1, x3)
U60_GA(x1, x2)  =  U60_GA(x2)
LOG2N5_IN_GA(x1, x2)  =  LOG2N5_IN_GA(x1)
U55_GA(x1, x2, x3)  =  U55_GA(x1, x3)
U61_GA(x1, x2)  =  U61_GA(x2)
U62_GA(x1, x2)  =  U62_GA(x2)
LOG2N6_IN_GA(x1, x2)  =  LOG2N6_IN_GA(x1)
U56_GA(x1, x2, x3)  =  U56_GA(x1, x3)
U63_GA(x1, x2)  =  U63_GA(x2)
U64_GA(x1, x2)  =  U64_GA(x2)
LOG2N7_IN_GA(x1, x2)  =  LOG2N7_IN_GA(x1)
U57_GA(x1, x2, x3)  =  U57_GA(x1, x3)
U65_GA(x1, x2)  =  U65_GA(x2)
U66_GA(x1, x2)  =  U66_GA(x2)
LOG2N8_IN_GA(x1, x2)  =  LOG2N8_IN_GA(x1)
U58_GA(x1, x2, x3)  =  U58_GA(x1, x3)
U67_GA(x1, x2)  =  U67_GA(x2)
U68_GA(x1, x2)  =  U68_GA(x2)
LOG2N9_IN_GA(x1, x2)  =  LOG2N9_IN_GA(x1)
U69_GA(x1, x2)  =  U69_GA(x2)
U70_GA(x1, x2)  =  U70_GA(x2)
LOG2N10_IN_GA(x1, x2)  =  LOG2N10_IN_GA(x1)
U71_GA(x1, x2)  =  U71_GA(x2)
U31_GGA(x1, x2, x3)  =  U31_GGA(x1, x3)
U77_GA(x1, x2)  =  U77_GA(x2)
LOG2N11_IN_A(x1)  =  LOG2N11_IN_A
U72_A(x1, x2)  =  U72_A(x2)
U78_GA(x1, x2)  =  U78_GA(x2)
U79_GA(x1, x2)  =  U79_GA(x2)
LOG2N12_IN_A(x1)  =  LOG2N12_IN_A
U73_A(x1, x2)  =  U73_A(x2)
U80_GA(x1, x2)  =  U80_GA(x2)
U81_GA(x1, x2)  =  U81_GA(x2)
LOG2N13_IN_A(x1)  =  LOG2N13_IN_A
U74_A(x1, x2)  =  U74_A(x2)
U82_GA(x1, x2)  =  U82_GA(x2)
U83_GA(x1, x2)  =  U83_GA(x2)
LOG2N14_IN_A(x1)  =  LOG2N14_IN_A
U75_A(x1, x2)  =  U75_A(x2)
U84_GA(x1, x2)  =  U84_GA(x2)
U85_GA(x1, x2)  =  U85_GA(x2)
LOG2N15_IN_A(x1)  =  LOG2N15_IN_A
U86_GA(x1, x2)  =  U86_GA(x2)
U87_GA(x1, x2)  =  U87_GA(x2)
LOG2N16_IN_A(x1)  =  LOG2N16_IN_A
U88_GA(x1, x2)  =  U88_GA(x2)
U28_GGA(x1, x2, x3)  =  U28_GGA(x1, x3)
U94_GA(x1, x2)  =  U94_GA(x2)
LOG2N17_IN_A(x1)  =  LOG2N17_IN_A
U89_A(x1, x2)  =  U89_A(x2)
U95_GA(x1, x2)  =  U95_GA(x2)
U96_GA(x1, x2)  =  U96_GA(x2)
LOG2N18_IN_A(x1)  =  LOG2N18_IN_A
U90_A(x1, x2)  =  U90_A(x2)
U97_GA(x1, x2)  =  U97_GA(x2)
U98_GA(x1, x2)  =  U98_GA(x2)
LOG2N19_IN_A(x1)  =  LOG2N19_IN_A
U91_A(x1, x2)  =  U91_A(x2)
U99_GA(x1, x2)  =  U99_GA(x2)
U100_GA(x1, x2)  =  U100_GA(x2)
LOG2N20_IN_A(x1)  =  LOG2N20_IN_A
U92_A(x1, x2)  =  U92_A(x2)
U101_GA(x1, x2)  =  U101_GA(x2)
U102_GA(x1, x2)  =  U102_GA(x2)
LOG2N21_IN_A(x1)  =  LOG2N21_IN_A
U103_GA(x1, x2)  =  U103_GA(x2)
U104_GA(x1, x2)  =  U104_GA(x2)
LOG2N22_IN_A(x1)  =  LOG2N22_IN_A
U105_GA(x1, x2)  =  U105_GA(x2)
U25_GGA(x1, x2, x3)  =  U25_GGA(x1, x3)
U111_GA(x1, x2)  =  U111_GA(x2)
LOG2N23_IN_A(x1)  =  LOG2N23_IN_A
U106_A(x1, x2)  =  U106_A(x2)
U112_GA(x1, x2)  =  U112_GA(x2)
U113_GA(x1, x2)  =  U113_GA(x2)
LOG2N24_IN_A(x1)  =  LOG2N24_IN_A
U107_A(x1, x2)  =  U107_A(x2)
U114_GA(x1, x2)  =  U114_GA(x2)
U115_GA(x1, x2)  =  U115_GA(x2)
LOG2N25_IN_A(x1)  =  LOG2N25_IN_A
U108_A(x1, x2)  =  U108_A(x2)
U116_GA(x1, x2)  =  U116_GA(x2)
U117_GA(x1, x2)  =  U117_GA(x2)
LOG2N26_IN_A(x1)  =  LOG2N26_IN_A
U109_A(x1, x2)  =  U109_A(x2)
U118_GA(x1, x2)  =  U118_GA(x2)
U119_GA(x1, x2)  =  U119_GA(x2)
LOG2N27_IN_A(x1)  =  LOG2N27_IN_A
U120_GA(x1, x2)  =  U120_GA(x2)
U121_GA(x1, x2)  =  U121_GA(x2)
LOG2N28_IN_A(x1)  =  LOG2N28_IN_A
U122_GA(x1, x2)  =  U122_GA(x2)
U22_GGA(x1, x2, x3)  =  U22_GGA(x1, x3)
U128_GA(x1, x2)  =  U128_GA(x2)
LOG2N29_IN_A(x1)  =  LOG2N29_IN_A
U123_A(x1, x2)  =  U123_A(x2)
U129_GA(x1, x2)  =  U129_GA(x2)
U130_GA(x1, x2)  =  U130_GA(x2)
LOG2N30_IN_A(x1)  =  LOG2N30_IN_A
U124_A(x1, x2)  =  U124_A(x2)
U131_GA(x1, x2)  =  U131_GA(x2)
U132_GA(x1, x2)  =  U132_GA(x2)
LOG2N31_IN_A(x1)  =  LOG2N31_IN_A
U125_A(x1, x2)  =  U125_A(x2)
U133_GA(x1, x2)  =  U133_GA(x2)
U134_GA(x1, x2)  =  U134_GA(x2)
LOG2N32_IN_A(x1)  =  LOG2N32_IN_A
U126_A(x1, x2)  =  U126_A(x2)
U135_GA(x1, x2)  =  U135_GA(x2)
U136_GA(x1, x2)  =  U136_GA(x2)
LOG2N33_IN_A(x1)  =  LOG2N33_IN_A
U137_GA(x1, x2)  =  U137_GA(x2)
U138_GA(x1, x2)  =  U138_GA(x2)
LOG2N34_IN_A(x1)  =  LOG2N34_IN_A
U139_GA(x1, x2)  =  U139_GA(x2)
U19_GGA(x1, x2, x3)  =  U19_GGA(x1, x3)
U145_GA(x1, x2)  =  U145_GA(x2)
LOG2N35_IN_A(x1)  =  LOG2N35_IN_A
U140_A(x1, x2)  =  U140_A(x2)
U146_GA(x1, x2)  =  U146_GA(x2)
U147_GA(x1, x2)  =  U147_GA(x2)
LOG2N36_IN_A(x1)  =  LOG2N36_IN_A
U141_A(x1, x2)  =  U141_A(x2)
U148_GA(x1, x2)  =  U148_GA(x2)
U149_GA(x1, x2)  =  U149_GA(x2)
LOG2N37_IN_A(x1)  =  LOG2N37_IN_A
U142_A(x1, x2)  =  U142_A(x2)
U150_GA(x1, x2)  =  U150_GA(x2)
U151_GA(x1, x2)  =  U151_GA(x2)
LOG2N38_IN_A(x1)  =  LOG2N38_IN_A
U143_A(x1, x2)  =  U143_A(x2)
U152_GA(x1, x2)  =  U152_GA(x2)
U153_GA(x1, x2)  =  U153_GA(x2)
LOG2N39_IN_A(x1)  =  LOG2N39_IN_A
U154_GA(x1, x2)  =  U154_GA(x2)
U155_GA(x1, x2)  =  U155_GA(x2)
LOG2N40_IN_A(x1)  =  LOG2N40_IN_A
U156_GA(x1, x2)  =  U156_GA(x2)
U16_GGA(x1, x2, x3)  =  U16_GGA(x1, x3)
U2_GA(x1, x2)  =  U2_GA(x2)
LOG2C_IN_A(x1)  =  LOG2C_IN_A
U157_A(x1, x2)  =  U157_A(x2)
U3_GA(x1, x2)  =  U3_GA(x2)
U4_GA(x1, x2)  =  U4_GA(x2)
LOG2D_IN_A(x1)  =  LOG2D_IN_A
U158_A(x1, x2)  =  U158_A(x2)
U5_GA(x1, x2)  =  U5_GA(x2)
U6_GA(x1, x2)  =  U6_GA(x2)
LOG2E_IN_A(x1)  =  LOG2E_IN_A
U159_A(x1, x2)  =  U159_A(x2)
U7_GA(x1, x2)  =  U7_GA(x2)
U8_GA(x1, x2)  =  U8_GA(x2)
LOG2F_IN_A(x1)  =  LOG2F_IN_A
U160_A(x1, x2)  =  U160_A(x2)
U9_GA(x1, x2)  =  U9_GA(x2)
U10_GA(x1, x2)  =  U10_GA(x2)
LOG2G_IN_A(x1)  =  LOG2G_IN_A
U11_GA(x1, x2)  =  U11_GA(x2)
U12_GA(x1, x2)  =  U12_GA(x2)
LOG2H_IN_A(x1)  =  LOG2H_IN_A
U13_GA(x1, x2)  =  U13_GA(x2)

We have to consider all (P,R,Pi)-chains

(4) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_GA(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → LOG2B_IN_GGA(T107, s(s(s(s(s(s(s(0))))))), T109)
LOG2B_IN_GGA(s(s(T128)), T129, T131) → U14_GGA(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
LOG2B_IN_GGA(s(s(T128)), T129, T131) → LOG2B_IN_GGA(T128, s(T129), T131)
LOG2B_IN_GGA(0, s(T148), T150) → U15_GGA(T148, T150, log2I_in_ga(T148, T150))
LOG2B_IN_GGA(0, s(T148), T150) → LOG2I_IN_GA(T148, T150)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_GA(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → LOG2J_IN_GGA(T241, s(s(s(s(s(s(s(0))))))), T243)
LOG2J_IN_GGA(s(s(T262)), T263, T265) → U17_GGA(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
LOG2J_IN_GGA(s(s(T262)), T263, T265) → LOG2J_IN_GGA(T262, s(T263), T265)
LOG2J_IN_GGA(0, s(T282), T284) → U18_GGA(T282, T284, log2K_in_ga(T282, T284))
LOG2J_IN_GGA(0, s(T282), T284) → LOG2K_IN_GA(T282, T284)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_GA(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → LOG2L_IN_GGA(T375, s(s(s(s(s(s(s(0))))))), T377)
LOG2L_IN_GGA(s(s(T396)), T397, T399) → U20_GGA(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
LOG2L_IN_GGA(s(s(T396)), T397, T399) → LOG2L_IN_GGA(T396, s(T397), T399)
LOG2L_IN_GGA(0, s(T416), T418) → U21_GGA(T416, T418, log2M_in_ga(T416, T418))
LOG2L_IN_GGA(0, s(T416), T418) → LOG2M_IN_GA(T416, T418)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_GA(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → LOG2N_IN_GGA(T509, s(s(s(s(s(s(s(0))))))), T511)
LOG2N_IN_GGA(s(s(T530)), T531, T533) → U23_GGA(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
LOG2N_IN_GGA(s(s(T530)), T531, T533) → LOG2N_IN_GGA(T530, s(T531), T533)
LOG2N_IN_GGA(0, s(T550), T552) → U24_GGA(T550, T552, log2O_in_ga(T550, T552))
LOG2N_IN_GGA(0, s(T550), T552) → LOG2O_IN_GA(T550, T552)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_GA(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → LOG2P_IN_GGA(T643, s(s(s(s(s(s(s(0))))))), T645)
LOG2P_IN_GGA(s(s(T664)), T665, T667) → U26_GGA(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
LOG2P_IN_GGA(s(s(T664)), T665, T667) → LOG2P_IN_GGA(T664, s(T665), T667)
LOG2P_IN_GGA(0, s(T684), T686) → U27_GGA(T684, T686, log2Q_in_ga(T684, T686))
LOG2P_IN_GGA(0, s(T684), T686) → LOG2Q_IN_GA(T684, T686)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_GA(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → LOG2R_IN_GGA(T777, s(s(s(s(s(s(s(0))))))), T779)
LOG2R_IN_GGA(s(s(T798)), T799, T801) → U29_GGA(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
LOG2R_IN_GGA(s(s(T798)), T799, T801) → LOG2R_IN_GGA(T798, s(T799), T801)
LOG2R_IN_GGA(0, s(T818), T820) → U30_GGA(T818, T820, log2S_in_ga(T818, T820))
LOG2R_IN_GGA(0, s(T818), T820) → LOG2S_IN_GA(T818, T820)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_GA(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → LOG2T_IN_GGA(T911, s(s(s(s(s(s(s(0))))))), T913)
LOG2T_IN_GGA(s(s(T932)), T933, T935) → U32_GGA(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
LOG2T_IN_GGA(s(s(T932)), T933, T935) → LOG2T_IN_GGA(T932, s(T933), T935)
LOG2T_IN_GGA(0, s(T952), T954) → U33_GGA(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
LOG2T_IN_GGA(0, s(T952), T954) → LOG2U_IN_GGA(T952, s(s(s(s(s(s(s(0))))))), T954)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_GGA(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → LOG2V_IN_GGGA(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)
LOG2V_IN_GGGA(s(s(T1117)), T1118, T1119, T1121) → U48_GGGA(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
LOG2V_IN_GGGA(s(s(T1117)), T1118, T1119, T1121) → LOG2V_IN_GGGA(T1117, s(T1118), T1119, T1121)
LOG2V_IN_GGGA(0, s(T1143), T1144, T1146) → U49_GGGA(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
LOG2V_IN_GGGA(0, s(T1143), T1144, T1146) → LOG2U_IN_GGA(T1143, s(T1144), T1146)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_GGA(T1184, T1186, log2W_in_ga(T1184, T1186))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → LOG2W_IN_GA(T1184, T1186)
LOG2W_IN_GA(T1233, T1235) → U51_GA(T1233, T1235, log2N3_in_ga(T1233, T1235))
LOG2W_IN_GA(T1233, T1235) → LOG2N3_IN_GA(T1233, T1235)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_GGA(T1184, T1186, log2W_in_ga(T1184, T1186))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → LOG2W_IN_GA(T1184, T1186)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_GGA(T1288, T1290, log2X_in_ga(T1288, T1290))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → LOG2X_IN_GA(T1288, T1290)
LOG2X_IN_GA(T1337, T1339) → U52_GA(T1337, T1339, log2N3_in_ga(T1337, T1339))
LOG2X_IN_GA(T1337, T1339) → LOG2N3_IN_GA(T1337, T1339)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_GGA(T1288, T1290, log2X_in_ga(T1288, T1290))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → LOG2X_IN_GA(T1288, T1290)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_GGA(T1389, T1391, log2Y_in_ga(T1389, T1391))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → LOG2Y_IN_GA(T1389, T1391)
LOG2Y_IN_GA(T1419, T1421) → U53_GA(T1419, T1421, log2N4_in_ga(T1419, T1421))
LOG2Y_IN_GA(T1419, T1421) → LOG2N4_IN_GA(T1419, T1421)
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_GGA(T1389, T1391, log2Y_in_ga(T1389, T1391))
LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → LOG2Y_IN_GA(T1389, T1391)
LOG2U_IN_GGA(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_GGA(T1458, T1460, log2Z_in_ga(T1458, T1460))
LOG2U_IN_GGA(s(s(s(s(s(s(0)))))), T1458, T1460) → LOG2Z_IN_GA(T1458, T1460)
LOG2Z_IN_GA(T1488, T1490) → U54_GA(T1488, T1490, log2N4_in_ga(T1488, T1490))
LOG2Z_IN_GA(T1488, T1490) → LOG2N4_IN_GA(T1488, T1490)
LOG2U_IN_GGA(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_GGA(T1458, T1460, log2Z_in_ga(T1458, T1460))
LOG2U_IN_GGA(s(s(s(s(s(s(s(0))))))), T1458, T1460) → LOG2Z_IN_GA(T1458, T1460)
LOG2U_IN_GGA(s(s(s(s(0)))), T1520, T1522) → U44_GGA(T1520, T1522, log2N1_in_ga(T1520, T1522))
LOG2U_IN_GGA(s(s(s(s(0)))), T1520, T1522) → LOG2N1_IN_GA(T1520, T1522)
LOG2U_IN_GGA(s(s(s(s(s(0))))), T1520, T1522) → U45_GGA(T1520, T1522, log2N1_in_ga(T1520, T1522))
LOG2U_IN_GGA(s(s(s(s(s(0))))), T1520, T1522) → LOG2N1_IN_GA(T1520, T1522)
LOG2U_IN_GGA(s(s(0)), T1547, T1549) → U46_GGA(T1547, T1549, log2N2_in_ga(T1547, T1549))
LOG2U_IN_GGA(s(s(0)), T1547, T1549) → LOG2N2_IN_GA(T1547, T1549)
LOG2U_IN_GGA(s(s(s(0))), T1547, T1549) → U47_GGA(T1547, T1549, log2N2_in_ga(T1547, T1549))
LOG2U_IN_GGA(s(s(s(0))), T1547, T1549) → LOG2N2_IN_GA(T1547, T1549)
LOG2V_IN_GGGA(s(0), s(T1143), T1144, T1146) → U50_GGGA(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
LOG2V_IN_GGGA(s(0), s(T1143), T1144, T1146) → LOG2U_IN_GGA(T1143, s(T1144), T1146)
LOG2T_IN_GGA(s(0), s(T952), T954) → U34_GGA(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
LOG2T_IN_GGA(s(0), s(T952), T954) → LOG2U_IN_GGA(T952, s(s(s(s(s(s(s(0))))))), T954)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_GA(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → LOG2N5_IN_GA(s(s(s(s(s(s(s(0))))))), T1592)
LOG2N5_IN_GA(T1640, T1642) → U55_GA(T1640, T1642, log2N1_in_ga(T1640, T1642))
LOG2N5_IN_GA(T1640, T1642) → LOG2N1_IN_GA(T1640, T1642)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_GA(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → LOG2N5_IN_GA(s(s(s(s(s(s(s(0))))))), T1592)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_GA(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → LOG2N6_IN_GA(s(s(s(s(s(s(s(0))))))), T1686)
LOG2N6_IN_GA(T1734, T1736) → U56_GA(T1734, T1736, log2N1_in_ga(T1734, T1736))
LOG2N6_IN_GA(T1734, T1736) → LOG2N1_IN_GA(T1734, T1736)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_GA(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → LOG2N6_IN_GA(s(s(s(s(s(s(s(0))))))), T1686)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_GA(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T1780) → LOG2N7_IN_GA(s(s(s(s(s(s(s(0))))))), T1780)
LOG2N7_IN_GA(T1809, T1811) → U57_GA(T1809, T1811, log2N2_in_ga(T1809, T1811))
LOG2N7_IN_GA(T1809, T1811) → LOG2N2_IN_GA(T1809, T1811)
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_GA(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
LOG2S_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → LOG2N7_IN_GA(s(s(s(s(s(s(s(0))))))), T1780)
LOG2S_IN_GA(s(s(s(s(s(s(0)))))), T1839) → U66_GA(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
LOG2S_IN_GA(s(s(s(s(s(s(0)))))), T1839) → LOG2N8_IN_GA(s(s(s(s(s(s(s(0))))))), T1839)
LOG2N8_IN_GA(T1868, T1870) → U58_GA(T1868, T1870, log2N2_in_ga(T1868, T1870))
LOG2N8_IN_GA(T1868, T1870) → LOG2N2_IN_GA(T1868, T1870)
LOG2S_IN_GA(s(s(s(s(s(s(s(0))))))), T1839) → U67_GA(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
LOG2S_IN_GA(s(s(s(s(s(s(s(0))))))), T1839) → LOG2N8_IN_GA(s(s(s(s(s(s(s(0))))))), T1839)
LOG2S_IN_GA(s(s(s(s(0)))), T1896) → U68_GA(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
LOG2S_IN_GA(s(s(s(s(0)))), T1896) → LOG2N9_IN_GA(s(s(s(s(s(s(s(0))))))), T1896)
LOG2S_IN_GA(s(s(s(s(s(0))))), T1896) → U69_GA(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
LOG2S_IN_GA(s(s(s(s(s(0))))), T1896) → LOG2N9_IN_GA(s(s(s(s(s(s(s(0))))))), T1896)
LOG2S_IN_GA(s(s(0)), T1917) → U70_GA(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
LOG2S_IN_GA(s(s(0)), T1917) → LOG2N10_IN_GA(s(s(s(s(s(s(s(0))))))), T1917)
LOG2S_IN_GA(s(s(s(0))), T1917) → U71_GA(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
LOG2S_IN_GA(s(s(s(0))), T1917) → LOG2N10_IN_GA(s(s(s(s(s(s(s(0))))))), T1917)
LOG2R_IN_GGA(s(0), s(T818), T820) → U31_GGA(T818, T820, log2S_in_ga(T818, T820))
LOG2R_IN_GGA(s(0), s(T818), T820) → LOG2S_IN_GA(T818, T820)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_GA(T1952, log2N11_in_a(T1952))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → LOG2N11_IN_A(T1952)
LOG2N11_IN_A(T1981) → U72_A(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
LOG2N11_IN_A(T1981) → LOG2N9_IN_GA(s(s(s(s(s(s(s(0))))))), T1981)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_GA(T1952, log2N11_in_a(T1952))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → LOG2N11_IN_A(T1952)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_GA(T2009, log2N12_in_a(T2009))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → LOG2N12_IN_A(T2009)
LOG2N12_IN_A(T2038) → U73_A(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
LOG2N12_IN_A(T2038) → LOG2N9_IN_GA(s(s(s(s(s(s(s(0))))))), T2038)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_GA(T2009, log2N12_in_a(T2009))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → LOG2N12_IN_A(T2009)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_GA(T2066, log2N13_in_a(T2066))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2066) → LOG2N13_IN_A(T2066)
LOG2N13_IN_A(T2084) → U74_A(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
LOG2N13_IN_A(T2084) → LOG2N10_IN_GA(s(s(s(s(s(s(s(0))))))), T2084)
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_GA(T2066, log2N13_in_a(T2066))
LOG2Q_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → LOG2N13_IN_A(T2066)
LOG2Q_IN_GA(s(s(s(s(s(s(0)))))), T2104) → U83_GA(T2104, log2N14_in_a(T2104))
LOG2Q_IN_GA(s(s(s(s(s(s(0)))))), T2104) → LOG2N14_IN_A(T2104)
LOG2N14_IN_A(T2122) → U75_A(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
LOG2N14_IN_A(T2122) → LOG2N10_IN_GA(s(s(s(s(s(s(s(0))))))), T2122)
LOG2Q_IN_GA(s(s(s(s(s(s(s(0))))))), T2104) → U84_GA(T2104, log2N14_in_a(T2104))
LOG2Q_IN_GA(s(s(s(s(s(s(s(0))))))), T2104) → LOG2N14_IN_A(T2104)
LOG2Q_IN_GA(s(s(s(s(0)))), T2140) → U85_GA(T2140, log2N15_in_a(T2140))
LOG2Q_IN_GA(s(s(s(s(0)))), T2140) → LOG2N15_IN_A(T2140)
LOG2Q_IN_GA(s(s(s(s(s(0))))), T2140) → U86_GA(T2140, log2N15_in_a(T2140))
LOG2Q_IN_GA(s(s(s(s(s(0))))), T2140) → LOG2N15_IN_A(T2140)
LOG2Q_IN_GA(s(s(0)), T2156) → U87_GA(T2156, log2N16_in_a(T2156))
LOG2Q_IN_GA(s(s(0)), T2156) → LOG2N16_IN_A(T2156)
LOG2Q_IN_GA(s(s(s(0))), T2156) → U88_GA(T2156, log2N16_in_a(T2156))
LOG2Q_IN_GA(s(s(s(0))), T2156) → LOG2N16_IN_A(T2156)
LOG2P_IN_GGA(s(0), s(T684), T686) → U28_GGA(T684, T686, log2Q_in_ga(T684, T686))
LOG2P_IN_GGA(s(0), s(T684), T686) → LOG2Q_IN_GA(T684, T686)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_GA(T2186, log2N17_in_a(T2186))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → LOG2N17_IN_A(T2186)
LOG2N17_IN_A(T2215) → U89_A(T2215, log2N15_in_a(T2215))
LOG2N17_IN_A(T2215) → LOG2N15_IN_A(T2215)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_GA(T2186, log2N17_in_a(T2186))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → LOG2N17_IN_A(T2186)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_GA(T2242, log2N18_in_a(T2242))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → LOG2N18_IN_A(T2242)
LOG2N18_IN_A(T2271) → U90_A(T2271, log2N15_in_a(T2271))
LOG2N18_IN_A(T2271) → LOG2N15_IN_A(T2271)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_GA(T2242, log2N18_in_a(T2242))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → LOG2N18_IN_A(T2242)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_GA(T2298, log2N19_in_a(T2298))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2298) → LOG2N19_IN_A(T2298)
LOG2N19_IN_A(T2316) → U91_A(T2316, log2N16_in_a(T2316))
LOG2N19_IN_A(T2316) → LOG2N16_IN_A(T2316)
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_GA(T2298, log2N19_in_a(T2298))
LOG2O_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → LOG2N19_IN_A(T2298)
LOG2O_IN_GA(s(s(s(s(s(s(0)))))), T2335) → U100_GA(T2335, log2N20_in_a(T2335))
LOG2O_IN_GA(s(s(s(s(s(s(0)))))), T2335) → LOG2N20_IN_A(T2335)
LOG2N20_IN_A(T2353) → U92_A(T2353, log2N16_in_a(T2353))
LOG2N20_IN_A(T2353) → LOG2N16_IN_A(T2353)
LOG2O_IN_GA(s(s(s(s(s(s(s(0))))))), T2335) → U101_GA(T2335, log2N20_in_a(T2335))
LOG2O_IN_GA(s(s(s(s(s(s(s(0))))))), T2335) → LOG2N20_IN_A(T2335)
LOG2O_IN_GA(s(s(s(s(0)))), T2370) → U102_GA(T2370, log2N21_in_a(T2370))
LOG2O_IN_GA(s(s(s(s(0)))), T2370) → LOG2N21_IN_A(T2370)
LOG2O_IN_GA(s(s(s(s(s(0))))), T2370) → U103_GA(T2370, log2N21_in_a(T2370))
LOG2O_IN_GA(s(s(s(s(s(0))))), T2370) → LOG2N21_IN_A(T2370)
LOG2O_IN_GA(s(s(0)), T2386) → U104_GA(T2386, log2N22_in_a(T2386))
LOG2O_IN_GA(s(s(0)), T2386) → LOG2N22_IN_A(T2386)
LOG2O_IN_GA(s(s(s(0))), T2386) → U105_GA(T2386, log2N22_in_a(T2386))
LOG2O_IN_GA(s(s(s(0))), T2386) → LOG2N22_IN_A(T2386)
LOG2N_IN_GGA(s(0), s(T550), T552) → U25_GGA(T550, T552, log2O_in_ga(T550, T552))
LOG2N_IN_GGA(s(0), s(T550), T552) → LOG2O_IN_GA(T550, T552)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_GA(T2416, log2N23_in_a(T2416))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → LOG2N23_IN_A(T2416)
LOG2N23_IN_A(T2445) → U106_A(T2445, log2N21_in_a(T2445))
LOG2N23_IN_A(T2445) → LOG2N21_IN_A(T2445)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_GA(T2416, log2N23_in_a(T2416))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → LOG2N23_IN_A(T2416)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_GA(T2472, log2N24_in_a(T2472))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → LOG2N24_IN_A(T2472)
LOG2N24_IN_A(T2501) → U107_A(T2501, log2N21_in_a(T2501))
LOG2N24_IN_A(T2501) → LOG2N21_IN_A(T2501)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_GA(T2472, log2N24_in_a(T2472))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → LOG2N24_IN_A(T2472)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_GA(T2528, log2N25_in_a(T2528))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2528) → LOG2N25_IN_A(T2528)
LOG2N25_IN_A(T2546) → U108_A(T2546, log2N22_in_a(T2546))
LOG2N25_IN_A(T2546) → LOG2N22_IN_A(T2546)
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_GA(T2528, log2N25_in_a(T2528))
LOG2M_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → LOG2N25_IN_A(T2528)
LOG2M_IN_GA(s(s(s(s(s(s(0)))))), T2565) → U117_GA(T2565, log2N26_in_a(T2565))
LOG2M_IN_GA(s(s(s(s(s(s(0)))))), T2565) → LOG2N26_IN_A(T2565)
LOG2N26_IN_A(T2583) → U109_A(T2583, log2N22_in_a(T2583))
LOG2N26_IN_A(T2583) → LOG2N22_IN_A(T2583)
LOG2M_IN_GA(s(s(s(s(s(s(s(0))))))), T2565) → U118_GA(T2565, log2N26_in_a(T2565))
LOG2M_IN_GA(s(s(s(s(s(s(s(0))))))), T2565) → LOG2N26_IN_A(T2565)
LOG2M_IN_GA(s(s(s(s(0)))), T2600) → U119_GA(T2600, log2N27_in_a(T2600))
LOG2M_IN_GA(s(s(s(s(0)))), T2600) → LOG2N27_IN_A(T2600)
LOG2M_IN_GA(s(s(s(s(s(0))))), T2600) → U120_GA(T2600, log2N27_in_a(T2600))
LOG2M_IN_GA(s(s(s(s(s(0))))), T2600) → LOG2N27_IN_A(T2600)
LOG2M_IN_GA(s(s(0)), T2616) → U121_GA(T2616, log2N28_in_a(T2616))
LOG2M_IN_GA(s(s(0)), T2616) → LOG2N28_IN_A(T2616)
LOG2M_IN_GA(s(s(s(0))), T2616) → U122_GA(T2616, log2N28_in_a(T2616))
LOG2M_IN_GA(s(s(s(0))), T2616) → LOG2N28_IN_A(T2616)
LOG2L_IN_GGA(s(0), s(T416), T418) → U22_GGA(T416, T418, log2M_in_ga(T416, T418))
LOG2L_IN_GGA(s(0), s(T416), T418) → LOG2M_IN_GA(T416, T418)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_GA(T2646, log2N29_in_a(T2646))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → LOG2N29_IN_A(T2646)
LOG2N29_IN_A(T2675) → U123_A(T2675, log2N27_in_a(T2675))
LOG2N29_IN_A(T2675) → LOG2N27_IN_A(T2675)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_GA(T2646, log2N29_in_a(T2646))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → LOG2N29_IN_A(T2646)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_GA(T2702, log2N30_in_a(T2702))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → LOG2N30_IN_A(T2702)
LOG2N30_IN_A(T2731) → U124_A(T2731, log2N27_in_a(T2731))
LOG2N30_IN_A(T2731) → LOG2N27_IN_A(T2731)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_GA(T2702, log2N30_in_a(T2702))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → LOG2N30_IN_A(T2702)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_GA(T2758, log2N31_in_a(T2758))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2758) → LOG2N31_IN_A(T2758)
LOG2N31_IN_A(T2776) → U125_A(T2776, log2N28_in_a(T2776))
LOG2N31_IN_A(T2776) → LOG2N28_IN_A(T2776)
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_GA(T2758, log2N31_in_a(T2758))
LOG2K_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → LOG2N31_IN_A(T2758)
LOG2K_IN_GA(s(s(s(s(s(s(0)))))), T2795) → U134_GA(T2795, log2N32_in_a(T2795))
LOG2K_IN_GA(s(s(s(s(s(s(0)))))), T2795) → LOG2N32_IN_A(T2795)
LOG2N32_IN_A(T2813) → U126_A(T2813, log2N28_in_a(T2813))
LOG2N32_IN_A(T2813) → LOG2N28_IN_A(T2813)
LOG2K_IN_GA(s(s(s(s(s(s(s(0))))))), T2795) → U135_GA(T2795, log2N32_in_a(T2795))
LOG2K_IN_GA(s(s(s(s(s(s(s(0))))))), T2795) → LOG2N32_IN_A(T2795)
LOG2K_IN_GA(s(s(s(s(0)))), T2830) → U136_GA(T2830, log2N33_in_a(T2830))
LOG2K_IN_GA(s(s(s(s(0)))), T2830) → LOG2N33_IN_A(T2830)
LOG2K_IN_GA(s(s(s(s(s(0))))), T2830) → U137_GA(T2830, log2N33_in_a(T2830))
LOG2K_IN_GA(s(s(s(s(s(0))))), T2830) → LOG2N33_IN_A(T2830)
LOG2K_IN_GA(s(s(0)), T2846) → U138_GA(T2846, log2N34_in_a(T2846))
LOG2K_IN_GA(s(s(0)), T2846) → LOG2N34_IN_A(T2846)
LOG2K_IN_GA(s(s(s(0))), T2846) → U139_GA(T2846, log2N34_in_a(T2846))
LOG2K_IN_GA(s(s(s(0))), T2846) → LOG2N34_IN_A(T2846)
LOG2J_IN_GGA(s(0), s(T282), T284) → U19_GGA(T282, T284, log2K_in_ga(T282, T284))
LOG2J_IN_GGA(s(0), s(T282), T284) → LOG2K_IN_GA(T282, T284)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_GA(T2876, log2N35_in_a(T2876))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → LOG2N35_IN_A(T2876)
LOG2N35_IN_A(T2905) → U140_A(T2905, log2N33_in_a(T2905))
LOG2N35_IN_A(T2905) → LOG2N33_IN_A(T2905)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_GA(T2876, log2N35_in_a(T2876))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → LOG2N35_IN_A(T2876)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_GA(T2932, log2N36_in_a(T2932))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → LOG2N36_IN_A(T2932)
LOG2N36_IN_A(T2961) → U141_A(T2961, log2N33_in_a(T2961))
LOG2N36_IN_A(T2961) → LOG2N33_IN_A(T2961)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_GA(T2932, log2N36_in_a(T2932))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → LOG2N36_IN_A(T2932)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_GA(T2988, log2N37_in_a(T2988))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T2988) → LOG2N37_IN_A(T2988)
LOG2N37_IN_A(T3006) → U142_A(T3006, log2N34_in_a(T3006))
LOG2N37_IN_A(T3006) → LOG2N34_IN_A(T3006)
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_GA(T2988, log2N37_in_a(T2988))
LOG2I_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → LOG2N37_IN_A(T2988)
LOG2I_IN_GA(s(s(s(s(s(s(0)))))), T3025) → U151_GA(T3025, log2N38_in_a(T3025))
LOG2I_IN_GA(s(s(s(s(s(s(0)))))), T3025) → LOG2N38_IN_A(T3025)
LOG2N38_IN_A(T3043) → U143_A(T3043, log2N34_in_a(T3043))
LOG2N38_IN_A(T3043) → LOG2N34_IN_A(T3043)
LOG2I_IN_GA(s(s(s(s(s(s(s(0))))))), T3025) → U152_GA(T3025, log2N38_in_a(T3025))
LOG2I_IN_GA(s(s(s(s(s(s(s(0))))))), T3025) → LOG2N38_IN_A(T3025)
LOG2I_IN_GA(s(s(s(s(0)))), T3060) → U153_GA(T3060, log2N39_in_a(T3060))
LOG2I_IN_GA(s(s(s(s(0)))), T3060) → LOG2N39_IN_A(T3060)
LOG2I_IN_GA(s(s(s(s(s(0))))), T3060) → U154_GA(T3060, log2N39_in_a(T3060))
LOG2I_IN_GA(s(s(s(s(s(0))))), T3060) → LOG2N39_IN_A(T3060)
LOG2I_IN_GA(s(s(0)), T3076) → U155_GA(T3076, log2N40_in_a(T3076))
LOG2I_IN_GA(s(s(0)), T3076) → LOG2N40_IN_A(T3076)
LOG2I_IN_GA(s(s(s(0))), T3076) → U156_GA(T3076, log2N40_in_a(T3076))
LOG2I_IN_GA(s(s(s(0))), T3076) → LOG2N40_IN_A(T3076)
LOG2B_IN_GGA(s(0), s(T148), T150) → U16_GGA(T148, T150, log2I_in_ga(T148, T150))
LOG2B_IN_GGA(s(0), s(T148), T150) → LOG2I_IN_GA(T148, T150)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_GA(T3106, log2C_in_a(T3106))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → LOG2C_IN_A(T3106)
LOG2C_IN_A(T3135) → U157_A(T3135, log2N39_in_a(T3135))
LOG2C_IN_A(T3135) → LOG2N39_IN_A(T3135)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_GA(T3106, log2C_in_a(T3106))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → LOG2C_IN_A(T3106)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_GA(T3162, log2D_in_a(T3162))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → LOG2D_IN_A(T3162)
LOG2D_IN_A(T3191) → U158_A(T3191, log2N39_in_a(T3191))
LOG2D_IN_A(T3191) → LOG2N39_IN_A(T3191)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_GA(T3162, log2D_in_a(T3162))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → LOG2D_IN_A(T3162)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_GA(T3218, log2E_in_a(T3218))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → LOG2E_IN_A(T3218)
LOG2E_IN_A(T3236) → U159_A(T3236, log2N40_in_a(T3236))
LOG2E_IN_A(T3236) → LOG2N40_IN_A(T3236)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_GA(T3218, log2E_in_a(T3218))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → LOG2E_IN_A(T3218)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_GA(T3255, log2F_in_a(T3255))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(0)))))))), T3255) → LOG2F_IN_A(T3255)
LOG2F_IN_A(T3273) → U160_A(T3273, log2N40_in_a(T3273))
LOG2F_IN_A(T3273) → LOG2N40_IN_A(T3273)
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_GA(T3255, log2F_in_a(T3255))
LOG2A_IN_GA(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → LOG2F_IN_A(T3255)
LOG2A_IN_GA(s(s(s(s(s(s(0)))))), T3290) → U10_GA(T3290, log2G_in_a(T3290))
LOG2A_IN_GA(s(s(s(s(s(s(0)))))), T3290) → LOG2G_IN_A(T3290)
LOG2A_IN_GA(s(s(s(s(s(s(s(0))))))), T3290) → U11_GA(T3290, log2G_in_a(T3290))
LOG2A_IN_GA(s(s(s(s(s(s(s(0))))))), T3290) → LOG2G_IN_A(T3290)
LOG2A_IN_GA(s(s(s(s(0)))), T3306) → U12_GA(T3306, log2H_in_a(T3306))
LOG2A_IN_GA(s(s(s(s(0)))), T3306) → LOG2H_IN_A(T3306)
LOG2A_IN_GA(s(s(s(s(s(0))))), T3306) → U13_GA(T3306, log2H_in_a(T3306))
LOG2A_IN_GA(s(s(s(s(s(0))))), T3306) → LOG2H_IN_A(T3306)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2A_IN_GA(x1, x2)  =  LOG2A_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x1, x3)
LOG2B_IN_GGA(x1, x2, x3)  =  LOG2B_IN_GGA(x1, x2)
U14_GGA(x1, x2, x3, x4)  =  U14_GGA(x1, x2, x4)
U15_GGA(x1, x2, x3)  =  U15_GGA(x1, x3)
LOG2I_IN_GA(x1, x2)  =  LOG2I_IN_GA(x1)
U144_GA(x1, x2, x3)  =  U144_GA(x1, x3)
LOG2J_IN_GGA(x1, x2, x3)  =  LOG2J_IN_GGA(x1, x2)
U17_GGA(x1, x2, x3, x4)  =  U17_GGA(x1, x2, x4)
U18_GGA(x1, x2, x3)  =  U18_GGA(x1, x3)
LOG2K_IN_GA(x1, x2)  =  LOG2K_IN_GA(x1)
U127_GA(x1, x2, x3)  =  U127_GA(x1, x3)
LOG2L_IN_GGA(x1, x2, x3)  =  LOG2L_IN_GGA(x1, x2)
U20_GGA(x1, x2, x3, x4)  =  U20_GGA(x1, x2, x4)
U21_GGA(x1, x2, x3)  =  U21_GGA(x1, x3)
LOG2M_IN_GA(x1, x2)  =  LOG2M_IN_GA(x1)
U110_GA(x1, x2, x3)  =  U110_GA(x1, x3)
LOG2N_IN_GGA(x1, x2, x3)  =  LOG2N_IN_GGA(x1, x2)
U23_GGA(x1, x2, x3, x4)  =  U23_GGA(x1, x2, x4)
U24_GGA(x1, x2, x3)  =  U24_GGA(x1, x3)
LOG2O_IN_GA(x1, x2)  =  LOG2O_IN_GA(x1)
U93_GA(x1, x2, x3)  =  U93_GA(x1, x3)
LOG2P_IN_GGA(x1, x2, x3)  =  LOG2P_IN_GGA(x1, x2)
U26_GGA(x1, x2, x3, x4)  =  U26_GGA(x1, x2, x4)
U27_GGA(x1, x2, x3)  =  U27_GGA(x1, x3)
LOG2Q_IN_GA(x1, x2)  =  LOG2Q_IN_GA(x1)
U76_GA(x1, x2, x3)  =  U76_GA(x1, x3)
LOG2R_IN_GGA(x1, x2, x3)  =  LOG2R_IN_GGA(x1, x2)
U29_GGA(x1, x2, x3, x4)  =  U29_GGA(x1, x2, x4)
U30_GGA(x1, x2, x3)  =  U30_GGA(x1, x3)
LOG2S_IN_GA(x1, x2)  =  LOG2S_IN_GA(x1)
U59_GA(x1, x2, x3)  =  U59_GA(x1, x3)
LOG2T_IN_GGA(x1, x2, x3)  =  LOG2T_IN_GGA(x1, x2)
U32_GGA(x1, x2, x3, x4)  =  U32_GGA(x1, x2, x4)
U33_GGA(x1, x2, x3)  =  U33_GGA(x1, x3)
LOG2U_IN_GGA(x1, x2, x3)  =  LOG2U_IN_GGA(x1, x2)
U35_GGA(x1, x2, x3, x4)  =  U35_GGA(x1, x2, x4)
LOG2V_IN_GGGA(x1, x2, x3, x4)  =  LOG2V_IN_GGGA(x1, x2, x3)
U48_GGGA(x1, x2, x3, x4, x5)  =  U48_GGGA(x1, x2, x3, x5)
U49_GGGA(x1, x2, x3, x4)  =  U49_GGGA(x1, x2, x4)
U36_GGA(x1, x2, x3)  =  U36_GGA(x1, x3)
LOG2W_IN_GA(x1, x2)  =  LOG2W_IN_GA(x1)
U51_GA(x1, x2, x3)  =  U51_GA(x1, x3)
LOG2N3_IN_GA(x1, x2)  =  LOG2N3_IN_GA(x1)
U37_GGA(x1, x2, x3)  =  U37_GGA(x1, x3)
U38_GGA(x1, x2, x3)  =  U38_GGA(x1, x3)
LOG2X_IN_GA(x1, x2)  =  LOG2X_IN_GA(x1)
U52_GA(x1, x2, x3)  =  U52_GA(x1, x3)
U39_GGA(x1, x2, x3)  =  U39_GGA(x1, x3)
U40_GGA(x1, x2, x3)  =  U40_GGA(x1, x3)
LOG2Y_IN_GA(x1, x2)  =  LOG2Y_IN_GA(x1)
U53_GA(x1, x2, x3)  =  U53_GA(x1, x3)
LOG2N4_IN_GA(x1, x2)  =  LOG2N4_IN_GA(x1)
U41_GGA(x1, x2, x3)  =  U41_GGA(x1, x3)
U42_GGA(x1, x2, x3)  =  U42_GGA(x1, x3)
LOG2Z_IN_GA(x1, x2)  =  LOG2Z_IN_GA(x1)
U54_GA(x1, x2, x3)  =  U54_GA(x1, x3)
U43_GGA(x1, x2, x3)  =  U43_GGA(x1, x3)
U44_GGA(x1, x2, x3)  =  U44_GGA(x1, x3)
LOG2N1_IN_GA(x1, x2)  =  LOG2N1_IN_GA(x1)
U45_GGA(x1, x2, x3)  =  U45_GGA(x1, x3)
U46_GGA(x1, x2, x3)  =  U46_GGA(x1, x3)
LOG2N2_IN_GA(x1, x2)  =  LOG2N2_IN_GA(x1)
U47_GGA(x1, x2, x3)  =  U47_GGA(x1, x3)
U50_GGGA(x1, x2, x3, x4)  =  U50_GGGA(x1, x2, x4)
U34_GGA(x1, x2, x3)  =  U34_GGA(x1, x3)
U60_GA(x1, x2)  =  U60_GA(x2)
LOG2N5_IN_GA(x1, x2)  =  LOG2N5_IN_GA(x1)
U55_GA(x1, x2, x3)  =  U55_GA(x1, x3)
U61_GA(x1, x2)  =  U61_GA(x2)
U62_GA(x1, x2)  =  U62_GA(x2)
LOG2N6_IN_GA(x1, x2)  =  LOG2N6_IN_GA(x1)
U56_GA(x1, x2, x3)  =  U56_GA(x1, x3)
U63_GA(x1, x2)  =  U63_GA(x2)
U64_GA(x1, x2)  =  U64_GA(x2)
LOG2N7_IN_GA(x1, x2)  =  LOG2N7_IN_GA(x1)
U57_GA(x1, x2, x3)  =  U57_GA(x1, x3)
U65_GA(x1, x2)  =  U65_GA(x2)
U66_GA(x1, x2)  =  U66_GA(x2)
LOG2N8_IN_GA(x1, x2)  =  LOG2N8_IN_GA(x1)
U58_GA(x1, x2, x3)  =  U58_GA(x1, x3)
U67_GA(x1, x2)  =  U67_GA(x2)
U68_GA(x1, x2)  =  U68_GA(x2)
LOG2N9_IN_GA(x1, x2)  =  LOG2N9_IN_GA(x1)
U69_GA(x1, x2)  =  U69_GA(x2)
U70_GA(x1, x2)  =  U70_GA(x2)
LOG2N10_IN_GA(x1, x2)  =  LOG2N10_IN_GA(x1)
U71_GA(x1, x2)  =  U71_GA(x2)
U31_GGA(x1, x2, x3)  =  U31_GGA(x1, x3)
U77_GA(x1, x2)  =  U77_GA(x2)
LOG2N11_IN_A(x1)  =  LOG2N11_IN_A
U72_A(x1, x2)  =  U72_A(x2)
U78_GA(x1, x2)  =  U78_GA(x2)
U79_GA(x1, x2)  =  U79_GA(x2)
LOG2N12_IN_A(x1)  =  LOG2N12_IN_A
U73_A(x1, x2)  =  U73_A(x2)
U80_GA(x1, x2)  =  U80_GA(x2)
U81_GA(x1, x2)  =  U81_GA(x2)
LOG2N13_IN_A(x1)  =  LOG2N13_IN_A
U74_A(x1, x2)  =  U74_A(x2)
U82_GA(x1, x2)  =  U82_GA(x2)
U83_GA(x1, x2)  =  U83_GA(x2)
LOG2N14_IN_A(x1)  =  LOG2N14_IN_A
U75_A(x1, x2)  =  U75_A(x2)
U84_GA(x1, x2)  =  U84_GA(x2)
U85_GA(x1, x2)  =  U85_GA(x2)
LOG2N15_IN_A(x1)  =  LOG2N15_IN_A
U86_GA(x1, x2)  =  U86_GA(x2)
U87_GA(x1, x2)  =  U87_GA(x2)
LOG2N16_IN_A(x1)  =  LOG2N16_IN_A
U88_GA(x1, x2)  =  U88_GA(x2)
U28_GGA(x1, x2, x3)  =  U28_GGA(x1, x3)
U94_GA(x1, x2)  =  U94_GA(x2)
LOG2N17_IN_A(x1)  =  LOG2N17_IN_A
U89_A(x1, x2)  =  U89_A(x2)
U95_GA(x1, x2)  =  U95_GA(x2)
U96_GA(x1, x2)  =  U96_GA(x2)
LOG2N18_IN_A(x1)  =  LOG2N18_IN_A
U90_A(x1, x2)  =  U90_A(x2)
U97_GA(x1, x2)  =  U97_GA(x2)
U98_GA(x1, x2)  =  U98_GA(x2)
LOG2N19_IN_A(x1)  =  LOG2N19_IN_A
U91_A(x1, x2)  =  U91_A(x2)
U99_GA(x1, x2)  =  U99_GA(x2)
U100_GA(x1, x2)  =  U100_GA(x2)
LOG2N20_IN_A(x1)  =  LOG2N20_IN_A
U92_A(x1, x2)  =  U92_A(x2)
U101_GA(x1, x2)  =  U101_GA(x2)
U102_GA(x1, x2)  =  U102_GA(x2)
LOG2N21_IN_A(x1)  =  LOG2N21_IN_A
U103_GA(x1, x2)  =  U103_GA(x2)
U104_GA(x1, x2)  =  U104_GA(x2)
LOG2N22_IN_A(x1)  =  LOG2N22_IN_A
U105_GA(x1, x2)  =  U105_GA(x2)
U25_GGA(x1, x2, x3)  =  U25_GGA(x1, x3)
U111_GA(x1, x2)  =  U111_GA(x2)
LOG2N23_IN_A(x1)  =  LOG2N23_IN_A
U106_A(x1, x2)  =  U106_A(x2)
U112_GA(x1, x2)  =  U112_GA(x2)
U113_GA(x1, x2)  =  U113_GA(x2)
LOG2N24_IN_A(x1)  =  LOG2N24_IN_A
U107_A(x1, x2)  =  U107_A(x2)
U114_GA(x1, x2)  =  U114_GA(x2)
U115_GA(x1, x2)  =  U115_GA(x2)
LOG2N25_IN_A(x1)  =  LOG2N25_IN_A
U108_A(x1, x2)  =  U108_A(x2)
U116_GA(x1, x2)  =  U116_GA(x2)
U117_GA(x1, x2)  =  U117_GA(x2)
LOG2N26_IN_A(x1)  =  LOG2N26_IN_A
U109_A(x1, x2)  =  U109_A(x2)
U118_GA(x1, x2)  =  U118_GA(x2)
U119_GA(x1, x2)  =  U119_GA(x2)
LOG2N27_IN_A(x1)  =  LOG2N27_IN_A
U120_GA(x1, x2)  =  U120_GA(x2)
U121_GA(x1, x2)  =  U121_GA(x2)
LOG2N28_IN_A(x1)  =  LOG2N28_IN_A
U122_GA(x1, x2)  =  U122_GA(x2)
U22_GGA(x1, x2, x3)  =  U22_GGA(x1, x3)
U128_GA(x1, x2)  =  U128_GA(x2)
LOG2N29_IN_A(x1)  =  LOG2N29_IN_A
U123_A(x1, x2)  =  U123_A(x2)
U129_GA(x1, x2)  =  U129_GA(x2)
U130_GA(x1, x2)  =  U130_GA(x2)
LOG2N30_IN_A(x1)  =  LOG2N30_IN_A
U124_A(x1, x2)  =  U124_A(x2)
U131_GA(x1, x2)  =  U131_GA(x2)
U132_GA(x1, x2)  =  U132_GA(x2)
LOG2N31_IN_A(x1)  =  LOG2N31_IN_A
U125_A(x1, x2)  =  U125_A(x2)
U133_GA(x1, x2)  =  U133_GA(x2)
U134_GA(x1, x2)  =  U134_GA(x2)
LOG2N32_IN_A(x1)  =  LOG2N32_IN_A
U126_A(x1, x2)  =  U126_A(x2)
U135_GA(x1, x2)  =  U135_GA(x2)
U136_GA(x1, x2)  =  U136_GA(x2)
LOG2N33_IN_A(x1)  =  LOG2N33_IN_A
U137_GA(x1, x2)  =  U137_GA(x2)
U138_GA(x1, x2)  =  U138_GA(x2)
LOG2N34_IN_A(x1)  =  LOG2N34_IN_A
U139_GA(x1, x2)  =  U139_GA(x2)
U19_GGA(x1, x2, x3)  =  U19_GGA(x1, x3)
U145_GA(x1, x2)  =  U145_GA(x2)
LOG2N35_IN_A(x1)  =  LOG2N35_IN_A
U140_A(x1, x2)  =  U140_A(x2)
U146_GA(x1, x2)  =  U146_GA(x2)
U147_GA(x1, x2)  =  U147_GA(x2)
LOG2N36_IN_A(x1)  =  LOG2N36_IN_A
U141_A(x1, x2)  =  U141_A(x2)
U148_GA(x1, x2)  =  U148_GA(x2)
U149_GA(x1, x2)  =  U149_GA(x2)
LOG2N37_IN_A(x1)  =  LOG2N37_IN_A
U142_A(x1, x2)  =  U142_A(x2)
U150_GA(x1, x2)  =  U150_GA(x2)
U151_GA(x1, x2)  =  U151_GA(x2)
LOG2N38_IN_A(x1)  =  LOG2N38_IN_A
U143_A(x1, x2)  =  U143_A(x2)
U152_GA(x1, x2)  =  U152_GA(x2)
U153_GA(x1, x2)  =  U153_GA(x2)
LOG2N39_IN_A(x1)  =  LOG2N39_IN_A
U154_GA(x1, x2)  =  U154_GA(x2)
U155_GA(x1, x2)  =  U155_GA(x2)
LOG2N40_IN_A(x1)  =  LOG2N40_IN_A
U156_GA(x1, x2)  =  U156_GA(x2)
U16_GGA(x1, x2, x3)  =  U16_GGA(x1, x3)
U2_GA(x1, x2)  =  U2_GA(x2)
LOG2C_IN_A(x1)  =  LOG2C_IN_A
U157_A(x1, x2)  =  U157_A(x2)
U3_GA(x1, x2)  =  U3_GA(x2)
U4_GA(x1, x2)  =  U4_GA(x2)
LOG2D_IN_A(x1)  =  LOG2D_IN_A
U158_A(x1, x2)  =  U158_A(x2)
U5_GA(x1, x2)  =  U5_GA(x2)
U6_GA(x1, x2)  =  U6_GA(x2)
LOG2E_IN_A(x1)  =  LOG2E_IN_A
U159_A(x1, x2)  =  U159_A(x2)
U7_GA(x1, x2)  =  U7_GA(x2)
U8_GA(x1, x2)  =  U8_GA(x2)
LOG2F_IN_A(x1)  =  LOG2F_IN_A
U160_A(x1, x2)  =  U160_A(x2)
U9_GA(x1, x2)  =  U9_GA(x2)
U10_GA(x1, x2)  =  U10_GA(x2)
LOG2G_IN_A(x1)  =  LOG2G_IN_A
U11_GA(x1, x2)  =  U11_GA(x2)
U12_GA(x1, x2)  =  U12_GA(x2)
LOG2H_IN_A(x1)  =  LOG2H_IN_A
U13_GA(x1, x2)  =  U13_GA(x2)

We have to consider all (P,R,Pi)-chains

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 309 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → LOG2V_IN_GGGA(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)
LOG2V_IN_GGGA(s(s(T1117)), T1118, T1119, T1121) → LOG2V_IN_GGGA(T1117, s(T1118), T1119, T1121)
LOG2V_IN_GGGA(0, s(T1143), T1144, T1146) → LOG2U_IN_GGA(T1143, s(T1144), T1146)
LOG2V_IN_GGGA(s(0), s(T1143), T1144, T1146) → LOG2U_IN_GGA(T1143, s(T1144), T1146)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2U_IN_GGA(x1, x2, x3)  =  LOG2U_IN_GGA(x1, x2)
LOG2V_IN_GGGA(x1, x2, x3, x4)  =  LOG2V_IN_GGGA(x1, x2, x3)

We have to consider all (P,R,Pi)-chains

(8) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(9) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → LOG2V_IN_GGGA(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)
LOG2V_IN_GGGA(s(s(T1117)), T1118, T1119, T1121) → LOG2V_IN_GGGA(T1117, s(T1118), T1119, T1121)
LOG2V_IN_GGGA(0, s(T1143), T1144, T1146) → LOG2U_IN_GGA(T1143, s(T1144), T1146)
LOG2V_IN_GGGA(s(0), s(T1143), T1144, T1146) → LOG2U_IN_GGA(T1143, s(T1144), T1146)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
0  =  0
LOG2U_IN_GGA(x1, x2, x3)  =  LOG2U_IN_GGA(x1, x2)
LOG2V_IN_GGGA(x1, x2, x3, x4)  =  LOG2V_IN_GGGA(x1, x2, x3)

We have to consider all (P,R,Pi)-chains

(10) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(11) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090) → LOG2V_IN_GGGA(T1089, s(s(s(s(s(s(s(0))))))), T1090)
LOG2V_IN_GGGA(s(s(T1117)), T1118, T1119) → LOG2V_IN_GGGA(T1117, s(T1118), T1119)
LOG2V_IN_GGGA(0, s(T1143), T1144) → LOG2U_IN_GGA(T1143, s(T1144))
LOG2V_IN_GGGA(s(0), s(T1143), T1144) → LOG2U_IN_GGA(T1143, s(T1144))

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(12) MRRProof (EQUIVALENT transformation)

By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.
Strictly oriented dependency pairs:

LOG2U_IN_GGA(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090) → LOG2V_IN_GGGA(T1089, s(s(s(s(s(s(s(0))))))), T1090)
LOG2V_IN_GGGA(s(s(T1117)), T1118, T1119) → LOG2V_IN_GGGA(T1117, s(T1118), T1119)
LOG2V_IN_GGGA(0, s(T1143), T1144) → LOG2U_IN_GGA(T1143, s(T1144))
LOG2V_IN_GGGA(s(0), s(T1143), T1144) → LOG2U_IN_GGA(T1143, s(T1144))


Used ordering: Knuth-Bendix order [KBO] with precedence:
0 > s1 > LOG2UINGGA2 > LOG2VINGGGA3

and weight map:

0=1
s_1=1
LOG2U_IN_GGA_2=0
LOG2V_IN_GGGA_3=6

The variable weight is 1

(13) Obligation:

Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(14) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(15) YES

(16) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2T_IN_GGA(s(s(T932)), T933, T935) → LOG2T_IN_GGA(T932, s(T933), T935)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2T_IN_GGA(x1, x2, x3)  =  LOG2T_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(17) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(18) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2T_IN_GGA(s(s(T932)), T933, T935) → LOG2T_IN_GGA(T932, s(T933), T935)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LOG2T_IN_GGA(x1, x2, x3)  =  LOG2T_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(19) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(20) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOG2T_IN_GGA(s(s(T932)), T933) → LOG2T_IN_GGA(T932, s(T933))

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(21) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

  • LOG2T_IN_GGA(s(s(T932)), T933) → LOG2T_IN_GGA(T932, s(T933))
    The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2R_IN_GGA(s(s(T798)), T799, T801) → LOG2R_IN_GGA(T798, s(T799), T801)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2R_IN_GGA(x1, x2, x3)  =  LOG2R_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(24) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(25) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2R_IN_GGA(s(s(T798)), T799, T801) → LOG2R_IN_GGA(T798, s(T799), T801)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LOG2R_IN_GGA(x1, x2, x3)  =  LOG2R_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(26) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(27) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOG2R_IN_GGA(s(s(T798)), T799) → LOG2R_IN_GGA(T798, s(T799))

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(28) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

  • LOG2R_IN_GGA(s(s(T798)), T799) → LOG2R_IN_GGA(T798, s(T799))
    The graph contains the following edges 1 > 1

(29) YES

(30) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2P_IN_GGA(s(s(T664)), T665, T667) → LOG2P_IN_GGA(T664, s(T665), T667)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2P_IN_GGA(x1, x2, x3)  =  LOG2P_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(31) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(32) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2P_IN_GGA(s(s(T664)), T665, T667) → LOG2P_IN_GGA(T664, s(T665), T667)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LOG2P_IN_GGA(x1, x2, x3)  =  LOG2P_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(33) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(34) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOG2P_IN_GGA(s(s(T664)), T665) → LOG2P_IN_GGA(T664, s(T665))

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(35) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

  • LOG2P_IN_GGA(s(s(T664)), T665) → LOG2P_IN_GGA(T664, s(T665))
    The graph contains the following edges 1 > 1

(36) YES

(37) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2N_IN_GGA(s(s(T530)), T531, T533) → LOG2N_IN_GGA(T530, s(T531), T533)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2N_IN_GGA(x1, x2, x3)  =  LOG2N_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(38) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(39) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2N_IN_GGA(s(s(T530)), T531, T533) → LOG2N_IN_GGA(T530, s(T531), T533)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LOG2N_IN_GGA(x1, x2, x3)  =  LOG2N_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(40) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(41) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOG2N_IN_GGA(s(s(T530)), T531) → LOG2N_IN_GGA(T530, s(T531))

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(42) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

  • LOG2N_IN_GGA(s(s(T530)), T531) → LOG2N_IN_GGA(T530, s(T531))
    The graph contains the following edges 1 > 1

(43) YES

(44) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2L_IN_GGA(s(s(T396)), T397, T399) → LOG2L_IN_GGA(T396, s(T397), T399)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2L_IN_GGA(x1, x2, x3)  =  LOG2L_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(45) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(46) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2L_IN_GGA(s(s(T396)), T397, T399) → LOG2L_IN_GGA(T396, s(T397), T399)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LOG2L_IN_GGA(x1, x2, x3)  =  LOG2L_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(47) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(48) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOG2L_IN_GGA(s(s(T396)), T397) → LOG2L_IN_GGA(T396, s(T397))

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(49) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

  • LOG2L_IN_GGA(s(s(T396)), T397) → LOG2L_IN_GGA(T396, s(T397))
    The graph contains the following edges 1 > 1

(50) YES

(51) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2J_IN_GGA(s(s(T262)), T263, T265) → LOG2J_IN_GGA(T262, s(T263), T265)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2J_IN_GGA(x1, x2, x3)  =  LOG2J_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(52) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(53) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2J_IN_GGA(s(s(T262)), T263, T265) → LOG2J_IN_GGA(T262, s(T263), T265)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LOG2J_IN_GGA(x1, x2, x3)  =  LOG2J_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(54) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(55) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOG2J_IN_GGA(s(s(T262)), T263) → LOG2J_IN_GGA(T262, s(T263))

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(56) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

  • LOG2J_IN_GGA(s(s(T262)), T263) → LOG2J_IN_GGA(T262, s(T263))
    The graph contains the following edges 1 > 1

(57) YES

(58) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2B_IN_GGA(s(s(T128)), T129, T131) → LOG2B_IN_GGA(T128, s(T129), T131)

The TRS R consists of the following rules:

log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109) → U1_ga(T107, T109, log2B_in_gga(T107, s(s(s(s(s(s(s(0))))))), T109))
log2B_in_gga(s(s(T128)), T129, T131) → U14_gga(T128, T129, T131, log2B_in_gga(T128, s(T129), T131))
log2B_in_gga(0, s(T148), T150) → U15_gga(T148, T150, log2I_in_ga(T148, T150))
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243) → U144_ga(T241, T243, log2J_in_gga(T241, s(s(s(s(s(s(s(0))))))), T243))
log2J_in_gga(s(s(T262)), T263, T265) → U17_gga(T262, T263, T265, log2J_in_gga(T262, s(T263), T265))
log2J_in_gga(0, s(T282), T284) → U18_gga(T282, T284, log2K_in_ga(T282, T284))
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377) → U127_ga(T375, T377, log2L_in_gga(T375, s(s(s(s(s(s(s(0))))))), T377))
log2L_in_gga(s(s(T396)), T397, T399) → U20_gga(T396, T397, T399, log2L_in_gga(T396, s(T397), T399))
log2L_in_gga(0, s(T416), T418) → U21_gga(T416, T418, log2M_in_ga(T416, T418))
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511) → U110_ga(T509, T511, log2N_in_gga(T509, s(s(s(s(s(s(s(0))))))), T511))
log2N_in_gga(s(s(T530)), T531, T533) → U23_gga(T530, T531, T533, log2N_in_gga(T530, s(T531), T533))
log2N_in_gga(0, s(T550), T552) → U24_gga(T550, T552, log2O_in_ga(T550, T552))
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645) → U93_ga(T643, T645, log2P_in_gga(T643, s(s(s(s(s(s(s(0))))))), T645))
log2P_in_gga(s(s(T664)), T665, T667) → U26_gga(T664, T665, T667, log2P_in_gga(T664, s(T665), T667))
log2P_in_gga(0, s(T684), T686) → U27_gga(T684, T686, log2Q_in_ga(T684, T686))
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779) → U76_ga(T777, T779, log2R_in_gga(T777, s(s(s(s(s(s(s(0))))))), T779))
log2R_in_gga(s(s(T798)), T799, T801) → U29_gga(T798, T799, T801, log2R_in_gga(T798, s(T799), T801))
log2R_in_gga(0, s(T818), T820) → U30_gga(T818, T820, log2S_in_ga(T818, T820))
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913) → U59_ga(T911, T913, log2T_in_gga(T911, s(s(s(s(s(s(s(0))))))), T913))
log2T_in_gga(s(s(T932)), T933, T935) → U32_gga(T932, T933, T935, log2T_in_gga(T932, s(T933), T935))
log2T_in_gga(0, s(T952), T954) → U33_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092) → U35_gga(T1089, T1090, T1092, log2V_in_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092))
log2V_in_ggga(s(s(T1117)), T1118, T1119, T1121) → U48_ggga(T1117, T1118, T1119, T1121, log2V_in_ggga(T1117, s(T1118), T1119, T1121))
log2V_in_ggga(0, s(T1143), T1144, T1146) → U49_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186) → U36_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
log2W_in_ga(T1233, T1235) → U51_ga(T1233, T1235, log2N3_in_ga(T1233, T1235))
log2N3_in_ga(T1238, s(s(s(T1238)))) → log2N3_out_ga(T1238, s(s(s(T1238))))
U51_ga(T1233, T1235, log2N3_out_ga(T1233, T1235)) → log2W_out_ga(T1233, T1235)
U36_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186) → U37_gga(T1184, T1186, log2W_in_ga(T1184, T1186))
U37_gga(T1184, T1186, log2W_out_ga(T1184, T1186)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1184, T1186)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290) → U38_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
log2X_in_ga(T1337, T1339) → U52_ga(T1337, T1339, log2N3_in_ga(T1337, T1339))
U52_ga(T1337, T1339, log2N3_out_ga(T1337, T1339)) → log2X_out_ga(T1337, T1339)
U38_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290) → U39_gga(T1288, T1290, log2X_in_ga(T1288, T1290))
U39_gga(T1288, T1290, log2X_out_ga(T1288, T1290)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1288, T1290)
log2U_in_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391) → U40_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
log2Y_in_ga(T1419, T1421) → U53_ga(T1419, T1421, log2N4_in_ga(T1419, T1421))
log2N4_in_ga(T1424, s(s(s(T1424)))) → log2N4_out_ga(T1424, s(s(s(T1424))))
U53_ga(T1419, T1421, log2N4_out_ga(T1419, T1421)) → log2Y_out_ga(T1419, T1421)
U40_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(0)))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391) → U41_gga(T1389, T1391, log2Y_in_ga(T1389, T1391))
U41_gga(T1389, T1391, log2Y_out_ga(T1389, T1391)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(0))))))))), T1389, T1391)
log2U_in_gga(s(s(s(s(s(s(0)))))), T1458, T1460) → U42_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
log2Z_in_ga(T1488, T1490) → U54_ga(T1488, T1490, log2N4_in_ga(T1488, T1490))
U54_ga(T1488, T1490, log2N4_out_ga(T1488, T1490)) → log2Z_out_ga(T1488, T1490)
U42_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(0)))))), T1458, T1460)
log2U_in_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460) → U43_gga(T1458, T1460, log2Z_in_ga(T1458, T1460))
U43_gga(T1458, T1460, log2Z_out_ga(T1458, T1460)) → log2U_out_gga(s(s(s(s(s(s(s(0))))))), T1458, T1460)
log2U_in_gga(s(s(s(s(0)))), T1520, T1522) → U44_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
log2N1_in_ga(T1525, s(s(T1525))) → log2N1_out_ga(T1525, s(s(T1525)))
U44_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(0)))), T1520, T1522)
log2U_in_gga(s(s(s(s(s(0))))), T1520, T1522) → U45_gga(T1520, T1522, log2N1_in_ga(T1520, T1522))
U45_gga(T1520, T1522, log2N1_out_ga(T1520, T1522)) → log2U_out_gga(s(s(s(s(s(0))))), T1520, T1522)
log2U_in_gga(s(s(0)), T1547, T1549) → U46_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
log2N2_in_ga(T1552, s(s(T1552))) → log2N2_out_ga(T1552, s(s(T1552)))
U46_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(0)), T1547, T1549)
log2U_in_gga(s(s(s(0))), T1547, T1549) → U47_gga(T1547, T1549, log2N2_in_ga(T1547, T1549))
U47_gga(T1547, T1549, log2N2_out_ga(T1547, T1549)) → log2U_out_gga(s(s(s(0))), T1547, T1549)
log2U_in_gga(0, T1565, s(T1565)) → log2U_out_gga(0, T1565, s(T1565))
log2U_in_gga(s(0), T1565, s(T1565)) → log2U_out_gga(s(0), T1565, s(T1565))
U49_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(0, s(T1143), T1144, T1146)
log2V_in_ggga(s(0), s(T1143), T1144, T1146) → U50_ggga(T1143, T1144, T1146, log2U_in_gga(T1143, s(T1144), T1146))
U50_ggga(T1143, T1144, T1146, log2U_out_gga(T1143, s(T1144), T1146)) → log2V_out_ggga(s(0), s(T1143), T1144, T1146)
log2V_in_ggga(0, 0, T1164, s(T1164)) → log2V_out_ggga(0, 0, T1164, s(T1164))
log2V_in_ggga(s(0), 0, T1164, s(T1164)) → log2V_out_ggga(s(0), 0, T1164, s(T1164))
U48_ggga(T1117, T1118, T1119, T1121, log2V_out_ggga(T1117, s(T1118), T1119, T1121)) → log2V_out_ggga(s(s(T1117)), T1118, T1119, T1121)
U35_gga(T1089, T1090, T1092, log2V_out_ggga(T1089, s(s(s(s(s(s(s(0))))))), T1090, T1092)) → log2U_out_gga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1089)))))))))))))), T1090, T1092)
U33_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(0, s(T952), T954)
log2T_in_gga(s(0), s(T952), T954) → U34_gga(T952, T954, log2U_in_gga(T952, s(s(s(s(s(s(s(0))))))), T954))
U34_gga(T952, T954, log2U_out_gga(T952, s(s(s(s(s(s(s(0))))))), T954)) → log2T_out_gga(s(0), s(T952), T954)
log2T_in_gga(0, 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(0, 0, s(s(s(s(s(s(s(0))))))))
log2T_in_gga(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2T_out_gga(s(0), 0, s(s(s(s(s(s(s(0))))))))
U32_gga(T932, T933, T935, log2T_out_gga(T932, s(T933), T935)) → log2T_out_gga(s(s(T932)), T933, T935)
U59_ga(T911, T913, log2T_out_gga(T911, s(s(s(s(s(s(s(0))))))), T913)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T911)))))))))))))), T913)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592) → U60_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
log2N5_in_ga(T1640, T1642) → U55_ga(T1640, T1642, log2N1_in_ga(T1640, T1642))
U55_ga(T1640, T1642, log2N1_out_ga(T1640, T1642)) → log2N5_out_ga(T1640, T1642)
U60_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592) → U61_ga(T1592, log2N5_in_ga(s(s(s(s(s(s(s(0))))))), T1592))
U61_ga(T1592, log2N5_out_ga(s(s(s(s(s(s(s(0))))))), T1592)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1592)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686) → U62_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
log2N6_in_ga(T1734, T1736) → U56_ga(T1734, T1736, log2N1_in_ga(T1734, T1736))
U56_ga(T1734, T1736, log2N1_out_ga(T1734, T1736)) → log2N6_out_ga(T1734, T1736)
U62_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686) → U63_ga(T1686, log2N6_in_ga(s(s(s(s(s(s(s(0))))))), T1686))
U63_ga(T1686, log2N6_out_ga(s(s(s(s(s(s(s(0))))))), T1686)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1686)
log2S_in_ga(s(s(s(s(s(s(s(s(0)))))))), T1780) → U64_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
log2N7_in_ga(T1809, T1811) → U57_ga(T1809, T1811, log2N2_in_ga(T1809, T1811))
U57_ga(T1809, T1811, log2N2_out_ga(T1809, T1811)) → log2N7_out_ga(T1809, T1811)
U64_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(0)))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780) → U65_ga(T1780, log2N7_in_ga(s(s(s(s(s(s(s(0))))))), T1780))
U65_ga(T1780, log2N7_out_ga(s(s(s(s(s(s(s(0))))))), T1780)) → log2S_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T1780)
log2S_in_ga(s(s(s(s(s(s(0)))))), T1839) → U66_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
log2N8_in_ga(T1868, T1870) → U58_ga(T1868, T1870, log2N2_in_ga(T1868, T1870))
U58_ga(T1868, T1870, log2N2_out_ga(T1868, T1870)) → log2N8_out_ga(T1868, T1870)
U66_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(0)))))), T1839)
log2S_in_ga(s(s(s(s(s(s(s(0))))))), T1839) → U67_ga(T1839, log2N8_in_ga(s(s(s(s(s(s(s(0))))))), T1839))
U67_ga(T1839, log2N8_out_ga(s(s(s(s(s(s(s(0))))))), T1839)) → log2S_out_ga(s(s(s(s(s(s(s(0))))))), T1839)
log2S_in_ga(s(s(s(s(0)))), T1896) → U68_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
log2N9_in_ga(T1900, s(T1900)) → log2N9_out_ga(T1900, s(T1900))
U68_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(0)))), T1896)
log2S_in_ga(s(s(s(s(s(0))))), T1896) → U69_ga(T1896, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1896))
U69_ga(T1896, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1896)) → log2S_out_ga(s(s(s(s(s(0))))), T1896)
log2S_in_ga(s(s(0)), T1917) → U70_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
log2N10_in_ga(T1921, s(T1921)) → log2N10_out_ga(T1921, s(T1921))
U70_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(0)), T1917)
log2S_in_ga(s(s(s(0))), T1917) → U71_ga(T1917, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T1917))
U71_ga(T1917, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T1917)) → log2S_out_ga(s(s(s(0))), T1917)
log2S_in_ga(0, s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(0, s(s(s(s(s(s(s(0))))))))
log2S_in_ga(s(0), s(s(s(s(s(s(s(0)))))))) → log2S_out_ga(s(0), s(s(s(s(s(s(s(0))))))))
U30_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(0, s(T818), T820)
log2R_in_gga(s(0), s(T818), T820) → U31_gga(T818, T820, log2S_in_ga(T818, T820))
U31_gga(T818, T820, log2S_out_ga(T818, T820)) → log2R_out_gga(s(0), s(T818), T820)
log2R_in_gga(0, 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(0, 0, s(s(s(s(s(s(0)))))))
log2R_in_gga(s(0), 0, s(s(s(s(s(s(0))))))) → log2R_out_gga(s(0), 0, s(s(s(s(s(s(0)))))))
U29_gga(T798, T799, T801, log2R_out_gga(T798, s(T799), T801)) → log2R_out_gga(s(s(T798)), T799, T801)
U76_ga(T777, T779, log2R_out_gga(T777, s(s(s(s(s(s(s(0))))))), T779)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T777)))))))))))))), T779)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952) → U77_ga(T1952, log2N11_in_a(T1952))
log2N11_in_a(T1981) → U72_a(T1981, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T1981))
U72_a(T1981, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T1981)) → log2N11_out_a(T1981)
U77_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952) → U78_ga(T1952, log2N11_in_a(T1952))
U78_ga(T1952, log2N11_out_a(T1952)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1952)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009) → U79_ga(T2009, log2N12_in_a(T2009))
log2N12_in_a(T2038) → U73_a(T2038, log2N9_in_ga(s(s(s(s(s(s(s(0))))))), T2038))
U73_a(T2038, log2N9_out_ga(s(s(s(s(s(s(s(0))))))), T2038)) → log2N12_out_a(T2038)
U79_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009) → U80_ga(T2009, log2N12_in_a(T2009))
U80_ga(T2009, log2N12_out_a(T2009)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2009)
log2Q_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2066) → U81_ga(T2066, log2N13_in_a(T2066))
log2N13_in_a(T2084) → U74_a(T2084, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2084))
U74_a(T2084, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2084)) → log2N13_out_a(T2084)
U81_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066) → U82_ga(T2066, log2N13_in_a(T2066))
U82_ga(T2066, log2N13_out_a(T2066)) → log2Q_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2066)
log2Q_in_ga(s(s(s(s(s(s(0)))))), T2104) → U83_ga(T2104, log2N14_in_a(T2104))
log2N14_in_a(T2122) → U75_a(T2122, log2N10_in_ga(s(s(s(s(s(s(s(0))))))), T2122))
U75_a(T2122, log2N10_out_ga(s(s(s(s(s(s(s(0))))))), T2122)) → log2N14_out_a(T2122)
U83_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(0)))))), T2104)
log2Q_in_ga(s(s(s(s(s(s(s(0))))))), T2104) → U84_ga(T2104, log2N14_in_a(T2104))
U84_ga(T2104, log2N14_out_a(T2104)) → log2Q_out_ga(s(s(s(s(s(s(s(0))))))), T2104)
log2Q_in_ga(s(s(s(s(0)))), T2140) → U85_ga(T2140, log2N15_in_a(T2140))
log2N15_in_a(s(s(s(s(s(s(s(0)))))))) → log2N15_out_a(s(s(s(s(s(s(s(0))))))))
U85_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(0)))), T2140)
log2Q_in_ga(s(s(s(s(s(0))))), T2140) → U86_ga(T2140, log2N15_in_a(T2140))
U86_ga(T2140, log2N15_out_a(T2140)) → log2Q_out_ga(s(s(s(s(s(0))))), T2140)
log2Q_in_ga(s(s(0)), T2156) → U87_ga(T2156, log2N16_in_a(T2156))
log2N16_in_a(s(s(s(s(s(s(s(0)))))))) → log2N16_out_a(s(s(s(s(s(s(s(0))))))))
U87_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(0)), T2156)
log2Q_in_ga(s(s(s(0))), T2156) → U88_ga(T2156, log2N16_in_a(T2156))
U88_ga(T2156, log2N16_out_a(T2156)) → log2Q_out_ga(s(s(s(0))), T2156)
log2Q_in_ga(0, s(s(s(s(s(s(0))))))) → log2Q_out_ga(0, s(s(s(s(s(s(0)))))))
log2Q_in_ga(s(0), s(s(s(s(s(s(0))))))) → log2Q_out_ga(s(0), s(s(s(s(s(s(0)))))))
U27_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(0, s(T684), T686)
log2P_in_gga(s(0), s(T684), T686) → U28_gga(T684, T686, log2Q_in_ga(T684, T686))
U28_gga(T684, T686, log2Q_out_ga(T684, T686)) → log2P_out_gga(s(0), s(T684), T686)
log2P_in_gga(0, 0, s(s(s(s(s(0)))))) → log2P_out_gga(0, 0, s(s(s(s(s(0))))))
log2P_in_gga(s(0), 0, s(s(s(s(s(0)))))) → log2P_out_gga(s(0), 0, s(s(s(s(s(0))))))
U26_gga(T664, T665, T667, log2P_out_gga(T664, s(T665), T667)) → log2P_out_gga(s(s(T664)), T665, T667)
U93_ga(T643, T645, log2P_out_gga(T643, s(s(s(s(s(s(s(0))))))), T645)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T643)))))))))))))), T645)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186) → U94_ga(T2186, log2N17_in_a(T2186))
log2N17_in_a(T2215) → U89_a(T2215, log2N15_in_a(T2215))
U89_a(T2215, log2N15_out_a(T2215)) → log2N17_out_a(T2215)
U94_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186) → U95_ga(T2186, log2N17_in_a(T2186))
U95_ga(T2186, log2N17_out_a(T2186)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2186)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242) → U96_ga(T2242, log2N18_in_a(T2242))
log2N18_in_a(T2271) → U90_a(T2271, log2N15_in_a(T2271))
U90_a(T2271, log2N15_out_a(T2271)) → log2N18_out_a(T2271)
U96_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242) → U97_ga(T2242, log2N18_in_a(T2242))
U97_ga(T2242, log2N18_out_a(T2242)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2242)
log2O_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2298) → U98_ga(T2298, log2N19_in_a(T2298))
log2N19_in_a(T2316) → U91_a(T2316, log2N16_in_a(T2316))
U91_a(T2316, log2N16_out_a(T2316)) → log2N19_out_a(T2316)
U98_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298) → U99_ga(T2298, log2N19_in_a(T2298))
U99_ga(T2298, log2N19_out_a(T2298)) → log2O_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2298)
log2O_in_ga(s(s(s(s(s(s(0)))))), T2335) → U100_ga(T2335, log2N20_in_a(T2335))
log2N20_in_a(T2353) → U92_a(T2353, log2N16_in_a(T2353))
U92_a(T2353, log2N16_out_a(T2353)) → log2N20_out_a(T2353)
U100_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(0)))))), T2335)
log2O_in_ga(s(s(s(s(s(s(s(0))))))), T2335) → U101_ga(T2335, log2N20_in_a(T2335))
U101_ga(T2335, log2N20_out_a(T2335)) → log2O_out_ga(s(s(s(s(s(s(s(0))))))), T2335)
log2O_in_ga(s(s(s(s(0)))), T2370) → U102_ga(T2370, log2N21_in_a(T2370))
log2N21_in_a(s(s(s(s(s(s(0))))))) → log2N21_out_a(s(s(s(s(s(s(0)))))))
U102_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(0)))), T2370)
log2O_in_ga(s(s(s(s(s(0))))), T2370) → U103_ga(T2370, log2N21_in_a(T2370))
U103_ga(T2370, log2N21_out_a(T2370)) → log2O_out_ga(s(s(s(s(s(0))))), T2370)
log2O_in_ga(s(s(0)), T2386) → U104_ga(T2386, log2N22_in_a(T2386))
log2N22_in_a(s(s(s(s(s(s(0))))))) → log2N22_out_a(s(s(s(s(s(s(0)))))))
U104_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(0)), T2386)
log2O_in_ga(s(s(s(0))), T2386) → U105_ga(T2386, log2N22_in_a(T2386))
U105_ga(T2386, log2N22_out_a(T2386)) → log2O_out_ga(s(s(s(0))), T2386)
log2O_in_ga(0, s(s(s(s(s(0)))))) → log2O_out_ga(0, s(s(s(s(s(0))))))
log2O_in_ga(s(0), s(s(s(s(s(0)))))) → log2O_out_ga(s(0), s(s(s(s(s(0))))))
U24_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(0, s(T550), T552)
log2N_in_gga(s(0), s(T550), T552) → U25_gga(T550, T552, log2O_in_ga(T550, T552))
U25_gga(T550, T552, log2O_out_ga(T550, T552)) → log2N_out_gga(s(0), s(T550), T552)
log2N_in_gga(0, 0, s(s(s(s(0))))) → log2N_out_gga(0, 0, s(s(s(s(0)))))
log2N_in_gga(s(0), 0, s(s(s(s(0))))) → log2N_out_gga(s(0), 0, s(s(s(s(0)))))
U23_gga(T530, T531, T533, log2N_out_gga(T530, s(T531), T533)) → log2N_out_gga(s(s(T530)), T531, T533)
U110_ga(T509, T511, log2N_out_gga(T509, s(s(s(s(s(s(s(0))))))), T511)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T509)))))))))))))), T511)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416) → U111_ga(T2416, log2N23_in_a(T2416))
log2N23_in_a(T2445) → U106_a(T2445, log2N21_in_a(T2445))
U106_a(T2445, log2N21_out_a(T2445)) → log2N23_out_a(T2445)
U111_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416) → U112_ga(T2416, log2N23_in_a(T2416))
U112_ga(T2416, log2N23_out_a(T2416)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2416)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472) → U113_ga(T2472, log2N24_in_a(T2472))
log2N24_in_a(T2501) → U107_a(T2501, log2N21_in_a(T2501))
U107_a(T2501, log2N21_out_a(T2501)) → log2N24_out_a(T2501)
U113_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472) → U114_ga(T2472, log2N24_in_a(T2472))
U114_ga(T2472, log2N24_out_a(T2472)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2472)
log2M_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_ga(T2528, log2N25_in_a(T2528))
log2N25_in_a(T2546) → U108_a(T2546, log2N22_in_a(T2546))
U108_a(T2546, log2N22_out_a(T2546)) → log2N25_out_a(T2546)
U115_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_ga(T2528, log2N25_in_a(T2528))
U116_ga(T2528, log2N25_out_a(T2528)) → log2M_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2M_in_ga(s(s(s(s(s(s(0)))))), T2565) → U117_ga(T2565, log2N26_in_a(T2565))
log2N26_in_a(T2583) → U109_a(T2583, log2N22_in_a(T2583))
U109_a(T2583, log2N22_out_a(T2583)) → log2N26_out_a(T2583)
U117_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(0)))))), T2565)
log2M_in_ga(s(s(s(s(s(s(s(0))))))), T2565) → U118_ga(T2565, log2N26_in_a(T2565))
U118_ga(T2565, log2N26_out_a(T2565)) → log2M_out_ga(s(s(s(s(s(s(s(0))))))), T2565)
log2M_in_ga(s(s(s(s(0)))), T2600) → U119_ga(T2600, log2N27_in_a(T2600))
log2N27_in_a(s(s(s(s(s(0)))))) → log2N27_out_a(s(s(s(s(s(0))))))
U119_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(0)))), T2600)
log2M_in_ga(s(s(s(s(s(0))))), T2600) → U120_ga(T2600, log2N27_in_a(T2600))
U120_ga(T2600, log2N27_out_a(T2600)) → log2M_out_ga(s(s(s(s(s(0))))), T2600)
log2M_in_ga(s(s(0)), T2616) → U121_ga(T2616, log2N28_in_a(T2616))
log2N28_in_a(s(s(s(s(s(0)))))) → log2N28_out_a(s(s(s(s(s(0))))))
U121_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(0)), T2616)
log2M_in_ga(s(s(s(0))), T2616) → U122_ga(T2616, log2N28_in_a(T2616))
U122_ga(T2616, log2N28_out_a(T2616)) → log2M_out_ga(s(s(s(0))), T2616)
log2M_in_ga(0, s(s(s(s(0))))) → log2M_out_ga(0, s(s(s(s(0)))))
log2M_in_ga(s(0), s(s(s(s(0))))) → log2M_out_ga(s(0), s(s(s(s(0)))))
U21_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(0, s(T416), T418)
log2L_in_gga(s(0), s(T416), T418) → U22_gga(T416, T418, log2M_in_ga(T416, T418))
U22_gga(T416, T418, log2M_out_ga(T416, T418)) → log2L_out_gga(s(0), s(T416), T418)
log2L_in_gga(0, 0, s(s(s(0)))) → log2L_out_gga(0, 0, s(s(s(0))))
log2L_in_gga(s(0), 0, s(s(s(0)))) → log2L_out_gga(s(0), 0, s(s(s(0))))
U20_gga(T396, T397, T399, log2L_out_gga(T396, s(T397), T399)) → log2L_out_gga(s(s(T396)), T397, T399)
U127_ga(T375, T377, log2L_out_gga(T375, s(s(s(s(s(s(s(0))))))), T377)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T375)))))))))))))), T377)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646) → U128_ga(T2646, log2N29_in_a(T2646))
log2N29_in_a(T2675) → U123_a(T2675, log2N27_in_a(T2675))
U123_a(T2675, log2N27_out_a(T2675)) → log2N29_out_a(T2675)
U128_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646) → U129_ga(T2646, log2N29_in_a(T2646))
U129_ga(T2646, log2N29_out_a(T2646)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2646)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702) → U130_ga(T2702, log2N30_in_a(T2702))
log2N30_in_a(T2731) → U124_a(T2731, log2N27_in_a(T2731))
U124_a(T2731, log2N27_out_a(T2731)) → log2N30_out_a(T2731)
U130_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702) → U131_ga(T2702, log2N30_in_a(T2702))
U131_ga(T2702, log2N30_out_a(T2702)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2702)
log2K_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2758) → U132_ga(T2758, log2N31_in_a(T2758))
log2N31_in_a(T2776) → U125_a(T2776, log2N28_in_a(T2776))
U125_a(T2776, log2N28_out_a(T2776)) → log2N31_out_a(T2776)
U132_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758) → U133_ga(T2758, log2N31_in_a(T2758))
U133_ga(T2758, log2N31_out_a(T2758)) → log2K_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2758)
log2K_in_ga(s(s(s(s(s(s(0)))))), T2795) → U134_ga(T2795, log2N32_in_a(T2795))
log2N32_in_a(T2813) → U126_a(T2813, log2N28_in_a(T2813))
U126_a(T2813, log2N28_out_a(T2813)) → log2N32_out_a(T2813)
U134_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(0)))))), T2795)
log2K_in_ga(s(s(s(s(s(s(s(0))))))), T2795) → U135_ga(T2795, log2N32_in_a(T2795))
U135_ga(T2795, log2N32_out_a(T2795)) → log2K_out_ga(s(s(s(s(s(s(s(0))))))), T2795)
log2K_in_ga(s(s(s(s(0)))), T2830) → U136_ga(T2830, log2N33_in_a(T2830))
log2N33_in_a(s(s(s(s(0))))) → log2N33_out_a(s(s(s(s(0)))))
U136_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(0)))), T2830)
log2K_in_ga(s(s(s(s(s(0))))), T2830) → U137_ga(T2830, log2N33_in_a(T2830))
U137_ga(T2830, log2N33_out_a(T2830)) → log2K_out_ga(s(s(s(s(s(0))))), T2830)
log2K_in_ga(s(s(0)), T2846) → U138_ga(T2846, log2N34_in_a(T2846))
log2N34_in_a(s(s(s(s(0))))) → log2N34_out_a(s(s(s(s(0)))))
U138_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(0)), T2846)
log2K_in_ga(s(s(s(0))), T2846) → U139_ga(T2846, log2N34_in_a(T2846))
U139_ga(T2846, log2N34_out_a(T2846)) → log2K_out_ga(s(s(s(0))), T2846)
log2K_in_ga(0, s(s(s(0)))) → log2K_out_ga(0, s(s(s(0))))
log2K_in_ga(s(0), s(s(s(0)))) → log2K_out_ga(s(0), s(s(s(0))))
U18_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(0, s(T282), T284)
log2J_in_gga(s(0), s(T282), T284) → U19_gga(T282, T284, log2K_in_ga(T282, T284))
U19_gga(T282, T284, log2K_out_ga(T282, T284)) → log2J_out_gga(s(0), s(T282), T284)
log2J_in_gga(0, 0, s(s(0))) → log2J_out_gga(0, 0, s(s(0)))
log2J_in_gga(s(0), 0, s(s(0))) → log2J_out_gga(s(0), 0, s(s(0)))
U17_gga(T262, T263, T265, log2J_out_gga(T262, s(T263), T265)) → log2J_out_gga(s(s(T262)), T263, T265)
U144_ga(T241, T243, log2J_out_gga(T241, s(s(s(s(s(s(s(0))))))), T243)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T241)))))))))))))), T243)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876) → U145_ga(T2876, log2N35_in_a(T2876))
log2N35_in_a(T2905) → U140_a(T2905, log2N33_in_a(T2905))
U140_a(T2905, log2N33_out_a(T2905)) → log2N35_out_a(T2905)
U145_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876) → U146_ga(T2876, log2N35_in_a(T2876))
U146_ga(T2876, log2N35_out_a(T2876)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2876)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932) → U147_ga(T2932, log2N36_in_a(T2932))
log2N36_in_a(T2961) → U141_a(T2961, log2N33_in_a(T2961))
U141_a(T2961, log2N33_out_a(T2961)) → log2N36_out_a(T2961)
U147_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932) → U148_ga(T2932, log2N36_in_a(T2932))
U148_ga(T2932, log2N36_out_a(T2932)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2932)
log2I_in_ga(s(s(s(s(s(s(s(s(0)))))))), T2988) → U149_ga(T2988, log2N37_in_a(T2988))
log2N37_in_a(T3006) → U142_a(T3006, log2N34_in_a(T3006))
U142_a(T3006, log2N34_out_a(T3006)) → log2N37_out_a(T3006)
U149_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(0)))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988) → U150_ga(T2988, log2N37_in_a(T2988))
U150_ga(T2988, log2N37_out_a(T2988)) → log2I_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T2988)
log2I_in_ga(s(s(s(s(s(s(0)))))), T3025) → U151_ga(T3025, log2N38_in_a(T3025))
log2N38_in_a(T3043) → U143_a(T3043, log2N34_in_a(T3043))
U143_a(T3043, log2N34_out_a(T3043)) → log2N38_out_a(T3043)
U151_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(0)))))), T3025)
log2I_in_ga(s(s(s(s(s(s(s(0))))))), T3025) → U152_ga(T3025, log2N38_in_a(T3025))
U152_ga(T3025, log2N38_out_a(T3025)) → log2I_out_ga(s(s(s(s(s(s(s(0))))))), T3025)
log2I_in_ga(s(s(s(s(0)))), T3060) → U153_ga(T3060, log2N39_in_a(T3060))
log2N39_in_a(s(s(s(0)))) → log2N39_out_a(s(s(s(0))))
U153_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(0)))), T3060)
log2I_in_ga(s(s(s(s(s(0))))), T3060) → U154_ga(T3060, log2N39_in_a(T3060))
U154_ga(T3060, log2N39_out_a(T3060)) → log2I_out_ga(s(s(s(s(s(0))))), T3060)
log2I_in_ga(s(s(0)), T3076) → U155_ga(T3076, log2N40_in_a(T3076))
log2N40_in_a(s(s(s(0)))) → log2N40_out_a(s(s(s(0))))
U155_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(0)), T3076)
log2I_in_ga(s(s(s(0))), T3076) → U156_ga(T3076, log2N40_in_a(T3076))
U156_ga(T3076, log2N40_out_a(T3076)) → log2I_out_ga(s(s(s(0))), T3076)
log2I_in_ga(0, s(s(0))) → log2I_out_ga(0, s(s(0)))
log2I_in_ga(s(0), s(s(0))) → log2I_out_ga(s(0), s(s(0)))
U15_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(0, s(T148), T150)
log2B_in_gga(s(0), s(T148), T150) → U16_gga(T148, T150, log2I_in_ga(T148, T150))
U16_gga(T148, T150, log2I_out_ga(T148, T150)) → log2B_out_gga(s(0), s(T148), T150)
log2B_in_gga(0, 0, s(0)) → log2B_out_gga(0, 0, s(0))
log2B_in_gga(s(0), 0, s(0)) → log2B_out_gga(s(0), 0, s(0))
U14_gga(T128, T129, T131, log2B_out_gga(T128, s(T129), T131)) → log2B_out_gga(s(s(T128)), T129, T131)
U1_ga(T107, T109, log2B_out_gga(T107, s(s(s(s(s(s(s(0))))))), T109)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T107)))))))))))))))), T109)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106) → U2_ga(T3106, log2C_in_a(T3106))
log2C_in_a(T3135) → U157_a(T3135, log2N39_in_a(T3135))
U157_a(T3135, log2N39_out_a(T3135)) → log2C_out_a(T3135)
U2_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106) → U3_ga(T3106, log2C_in_a(T3106))
U3_ga(T3106, log2C_out_a(T3106)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T3106)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162) → U4_ga(T3162, log2D_in_a(T3162))
log2D_in_a(T3191) → U158_a(T3191, log2N39_in_a(T3191))
U158_a(T3191, log2N39_out_a(T3191)) → log2D_out_a(T3191)
U4_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162) → U5_ga(T3162, log2D_in_a(T3162))
U5_ga(T3162, log2D_out_a(T3162)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T3162)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218) → U6_ga(T3218, log2E_in_a(T3218))
log2E_in_a(T3236) → U159_a(T3236, log2N40_in_a(T3236))
U159_a(T3236, log2N40_out_a(T3236)) → log2E_out_a(T3236)
U6_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(0)))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218) → U7_ga(T3218, log2E_in_a(T3218))
U7_ga(T3218, log2E_out_a(T3218)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T3218)
log2A_in_ga(s(s(s(s(s(s(s(s(0)))))))), T3255) → U8_ga(T3255, log2F_in_a(T3255))
log2F_in_a(T3273) → U160_a(T3273, log2N40_in_a(T3273))
U160_a(T3273, log2N40_out_a(T3273)) → log2F_out_a(T3273)
U8_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(0)))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255) → U9_ga(T3255, log2F_in_a(T3255))
U9_ga(T3255, log2F_out_a(T3255)) → log2A_out_ga(s(s(s(s(s(s(s(s(s(0))))))))), T3255)
log2A_in_ga(s(s(s(s(s(s(0)))))), T3290) → U10_ga(T3290, log2G_in_a(T3290))
log2G_in_a(s(s(0))) → log2G_out_a(s(s(0)))
U10_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(0)))))), T3290)
log2A_in_ga(s(s(s(s(s(s(s(0))))))), T3290) → U11_ga(T3290, log2G_in_a(T3290))
U11_ga(T3290, log2G_out_a(T3290)) → log2A_out_ga(s(s(s(s(s(s(s(0))))))), T3290)
log2A_in_ga(s(s(s(s(0)))), T3306) → U12_ga(T3306, log2H_in_a(T3306))
log2H_in_a(s(s(0))) → log2H_out_a(s(s(0)))
U12_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(0)))), T3306)
log2A_in_ga(s(s(s(s(s(0))))), T3306) → U13_ga(T3306, log2H_in_a(T3306))
U13_ga(T3306, log2H_out_a(T3306)) → log2A_out_ga(s(s(s(s(s(0))))), T3306)
log2A_in_ga(s(s(0)), s(0)) → log2A_out_ga(s(s(0)), s(0))
log2A_in_ga(s(s(s(0))), s(0)) → log2A_out_ga(s(s(s(0))), s(0))
log2A_in_ga(0, s(0)) → log2A_out_ga(0, s(0))
log2A_in_ga(s(0), s(0)) → log2A_out_ga(s(0), s(0))

The argument filtering Pi contains the following mapping:
log2A_in_ga(x1, x2)  =  log2A_in_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
log2B_in_gga(x1, x2, x3)  =  log2B_in_gga(x1, x2)
U14_gga(x1, x2, x3, x4)  =  U14_gga(x1, x2, x4)
0  =  0
U15_gga(x1, x2, x3)  =  U15_gga(x1, x3)
log2I_in_ga(x1, x2)  =  log2I_in_ga(x1)
U144_ga(x1, x2, x3)  =  U144_ga(x1, x3)
log2J_in_gga(x1, x2, x3)  =  log2J_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
U18_gga(x1, x2, x3)  =  U18_gga(x1, x3)
log2K_in_ga(x1, x2)  =  log2K_in_ga(x1)
U127_ga(x1, x2, x3)  =  U127_ga(x1, x3)
log2L_in_gga(x1, x2, x3)  =  log2L_in_gga(x1, x2)
U20_gga(x1, x2, x3, x4)  =  U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3)  =  U21_gga(x1, x3)
log2M_in_ga(x1, x2)  =  log2M_in_ga(x1)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
log2N_in_gga(x1, x2, x3)  =  log2N_in_gga(x1, x2)
U23_gga(x1, x2, x3, x4)  =  U23_gga(x1, x2, x4)
U24_gga(x1, x2, x3)  =  U24_gga(x1, x3)
log2O_in_ga(x1, x2)  =  log2O_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
log2P_in_gga(x1, x2, x3)  =  log2P_in_gga(x1, x2)
U26_gga(x1, x2, x3, x4)  =  U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3)  =  U27_gga(x1, x3)
log2Q_in_ga(x1, x2)  =  log2Q_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
log2R_in_gga(x1, x2, x3)  =  log2R_in_gga(x1, x2)
U29_gga(x1, x2, x3, x4)  =  U29_gga(x1, x2, x4)
U30_gga(x1, x2, x3)  =  U30_gga(x1, x3)
log2S_in_ga(x1, x2)  =  log2S_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
log2T_in_gga(x1, x2, x3)  =  log2T_in_gga(x1, x2)
U32_gga(x1, x2, x3, x4)  =  U32_gga(x1, x2, x4)
U33_gga(x1, x2, x3)  =  U33_gga(x1, x3)
log2U_in_gga(x1, x2, x3)  =  log2U_in_gga(x1, x2)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
log2V_in_ggga(x1, x2, x3, x4)  =  log2V_in_ggga(x1, x2, x3)
U48_ggga(x1, x2, x3, x4, x5)  =  U48_ggga(x1, x2, x3, x5)
U49_ggga(x1, x2, x3, x4)  =  U49_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
log2W_in_ga(x1, x2)  =  log2W_in_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
log2N3_in_ga(x1, x2)  =  log2N3_in_ga(x1)
log2N3_out_ga(x1, x2)  =  log2N3_out_ga(x1, x2)
log2W_out_ga(x1, x2)  =  log2W_out_ga(x1, x2)
log2U_out_gga(x1, x2, x3)  =  log2U_out_gga(x1, x2, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
log2X_in_ga(x1, x2)  =  log2X_in_ga(x1)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
log2X_out_ga(x1, x2)  =  log2X_out_ga(x1, x2)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
log2Y_in_ga(x1, x2)  =  log2Y_in_ga(x1)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
log2N4_in_ga(x1, x2)  =  log2N4_in_ga(x1)
log2N4_out_ga(x1, x2)  =  log2N4_out_ga(x1, x2)
log2Y_out_ga(x1, x2)  =  log2Y_out_ga(x1, x2)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
U42_gga(x1, x2, x3)  =  U42_gga(x1, x3)
log2Z_in_ga(x1, x2)  =  log2Z_in_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
log2Z_out_ga(x1, x2)  =  log2Z_out_ga(x1, x2)
U43_gga(x1, x2, x3)  =  U43_gga(x1, x3)
U44_gga(x1, x2, x3)  =  U44_gga(x1, x3)
log2N1_in_ga(x1, x2)  =  log2N1_in_ga(x1)
log2N1_out_ga(x1, x2)  =  log2N1_out_ga(x1, x2)
U45_gga(x1, x2, x3)  =  U45_gga(x1, x3)
U46_gga(x1, x2, x3)  =  U46_gga(x1, x3)
log2N2_in_ga(x1, x2)  =  log2N2_in_ga(x1)
log2N2_out_ga(x1, x2)  =  log2N2_out_ga(x1, x2)
U47_gga(x1, x2, x3)  =  U47_gga(x1, x3)
log2V_out_ggga(x1, x2, x3, x4)  =  log2V_out_ggga(x1, x2, x3, x4)
U50_ggga(x1, x2, x3, x4)  =  U50_ggga(x1, x2, x4)
log2T_out_gga(x1, x2, x3)  =  log2T_out_gga(x1, x2, x3)
U34_gga(x1, x2, x3)  =  U34_gga(x1, x3)
log2S_out_ga(x1, x2)  =  log2S_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
log2N5_in_ga(x1, x2)  =  log2N5_in_ga(x1)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
log2N5_out_ga(x1, x2)  =  log2N5_out_ga(x1, x2)
U61_ga(x1, x2)  =  U61_ga(x2)
U62_ga(x1, x2)  =  U62_ga(x2)
log2N6_in_ga(x1, x2)  =  log2N6_in_ga(x1)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
log2N6_out_ga(x1, x2)  =  log2N6_out_ga(x1, x2)
U63_ga(x1, x2)  =  U63_ga(x2)
U64_ga(x1, x2)  =  U64_ga(x2)
log2N7_in_ga(x1, x2)  =  log2N7_in_ga(x1)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
log2N7_out_ga(x1, x2)  =  log2N7_out_ga(x1, x2)
U65_ga(x1, x2)  =  U65_ga(x2)
U66_ga(x1, x2)  =  U66_ga(x2)
log2N8_in_ga(x1, x2)  =  log2N8_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
log2N8_out_ga(x1, x2)  =  log2N8_out_ga(x1, x2)
U67_ga(x1, x2)  =  U67_ga(x2)
U68_ga(x1, x2)  =  U68_ga(x2)
log2N9_in_ga(x1, x2)  =  log2N9_in_ga(x1)
log2N9_out_ga(x1, x2)  =  log2N9_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
U70_ga(x1, x2)  =  U70_ga(x2)
log2N10_in_ga(x1, x2)  =  log2N10_in_ga(x1)
log2N10_out_ga(x1, x2)  =  log2N10_out_ga(x1, x2)
U71_ga(x1, x2)  =  U71_ga(x2)
log2R_out_gga(x1, x2, x3)  =  log2R_out_gga(x1, x2, x3)
U31_gga(x1, x2, x3)  =  U31_gga(x1, x3)
log2Q_out_ga(x1, x2)  =  log2Q_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
log2N11_in_a(x1)  =  log2N11_in_a
U72_a(x1, x2)  =  U72_a(x2)
log2N11_out_a(x1)  =  log2N11_out_a(x1)
U78_ga(x1, x2)  =  U78_ga(x2)
U79_ga(x1, x2)  =  U79_ga(x2)
log2N12_in_a(x1)  =  log2N12_in_a
U73_a(x1, x2)  =  U73_a(x2)
log2N12_out_a(x1)  =  log2N12_out_a(x1)
U80_ga(x1, x2)  =  U80_ga(x2)
U81_ga(x1, x2)  =  U81_ga(x2)
log2N13_in_a(x1)  =  log2N13_in_a
U74_a(x1, x2)  =  U74_a(x2)
log2N13_out_a(x1)  =  log2N13_out_a(x1)
U82_ga(x1, x2)  =  U82_ga(x2)
U83_ga(x1, x2)  =  U83_ga(x2)
log2N14_in_a(x1)  =  log2N14_in_a
U75_a(x1, x2)  =  U75_a(x2)
log2N14_out_a(x1)  =  log2N14_out_a(x1)
U84_ga(x1, x2)  =  U84_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
log2N15_in_a(x1)  =  log2N15_in_a
log2N15_out_a(x1)  =  log2N15_out_a(x1)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
log2N16_in_a(x1)  =  log2N16_in_a
log2N16_out_a(x1)  =  log2N16_out_a(x1)
U88_ga(x1, x2)  =  U88_ga(x2)
log2P_out_gga(x1, x2, x3)  =  log2P_out_gga(x1, x2, x3)
U28_gga(x1, x2, x3)  =  U28_gga(x1, x3)
log2O_out_ga(x1, x2)  =  log2O_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
log2N17_in_a(x1)  =  log2N17_in_a
U89_a(x1, x2)  =  U89_a(x2)
log2N17_out_a(x1)  =  log2N17_out_a(x1)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
log2N18_in_a(x1)  =  log2N18_in_a
U90_a(x1, x2)  =  U90_a(x2)
log2N18_out_a(x1)  =  log2N18_out_a(x1)
U97_ga(x1, x2)  =  U97_ga(x2)
U98_ga(x1, x2)  =  U98_ga(x2)
log2N19_in_a(x1)  =  log2N19_in_a
U91_a(x1, x2)  =  U91_a(x2)
log2N19_out_a(x1)  =  log2N19_out_a(x1)
U99_ga(x1, x2)  =  U99_ga(x2)
U100_ga(x1, x2)  =  U100_ga(x2)
log2N20_in_a(x1)  =  log2N20_in_a
U92_a(x1, x2)  =  U92_a(x2)
log2N20_out_a(x1)  =  log2N20_out_a(x1)
U101_ga(x1, x2)  =  U101_ga(x2)
U102_ga(x1, x2)  =  U102_ga(x2)
log2N21_in_a(x1)  =  log2N21_in_a
log2N21_out_a(x1)  =  log2N21_out_a(x1)
U103_ga(x1, x2)  =  U103_ga(x2)
U104_ga(x1, x2)  =  U104_ga(x2)
log2N22_in_a(x1)  =  log2N22_in_a
log2N22_out_a(x1)  =  log2N22_out_a(x1)
U105_ga(x1, x2)  =  U105_ga(x2)
log2N_out_gga(x1, x2, x3)  =  log2N_out_gga(x1, x2, x3)
U25_gga(x1, x2, x3)  =  U25_gga(x1, x3)
log2M_out_ga(x1, x2)  =  log2M_out_ga(x1, x2)
U111_ga(x1, x2)  =  U111_ga(x2)
log2N23_in_a(x1)  =  log2N23_in_a
U106_a(x1, x2)  =  U106_a(x2)
log2N23_out_a(x1)  =  log2N23_out_a(x1)
U112_ga(x1, x2)  =  U112_ga(x2)
U113_ga(x1, x2)  =  U113_ga(x2)
log2N24_in_a(x1)  =  log2N24_in_a
U107_a(x1, x2)  =  U107_a(x2)
log2N24_out_a(x1)  =  log2N24_out_a(x1)
U114_ga(x1, x2)  =  U114_ga(x2)
U115_ga(x1, x2)  =  U115_ga(x2)
log2N25_in_a(x1)  =  log2N25_in_a
U108_a(x1, x2)  =  U108_a(x2)
log2N25_out_a(x1)  =  log2N25_out_a(x1)
U116_ga(x1, x2)  =  U116_ga(x2)
U117_ga(x1, x2)  =  U117_ga(x2)
log2N26_in_a(x1)  =  log2N26_in_a
U109_a(x1, x2)  =  U109_a(x2)
log2N26_out_a(x1)  =  log2N26_out_a(x1)
U118_ga(x1, x2)  =  U118_ga(x2)
U119_ga(x1, x2)  =  U119_ga(x2)
log2N27_in_a(x1)  =  log2N27_in_a
log2N27_out_a(x1)  =  log2N27_out_a(x1)
U120_ga(x1, x2)  =  U120_ga(x2)
U121_ga(x1, x2)  =  U121_ga(x2)
log2N28_in_a(x1)  =  log2N28_in_a
log2N28_out_a(x1)  =  log2N28_out_a(x1)
U122_ga(x1, x2)  =  U122_ga(x2)
log2L_out_gga(x1, x2, x3)  =  log2L_out_gga(x1, x2, x3)
U22_gga(x1, x2, x3)  =  U22_gga(x1, x3)
log2K_out_ga(x1, x2)  =  log2K_out_ga(x1, x2)
U128_ga(x1, x2)  =  U128_ga(x2)
log2N29_in_a(x1)  =  log2N29_in_a
U123_a(x1, x2)  =  U123_a(x2)
log2N29_out_a(x1)  =  log2N29_out_a(x1)
U129_ga(x1, x2)  =  U129_ga(x2)
U130_ga(x1, x2)  =  U130_ga(x2)
log2N30_in_a(x1)  =  log2N30_in_a
U124_a(x1, x2)  =  U124_a(x2)
log2N30_out_a(x1)  =  log2N30_out_a(x1)
U131_ga(x1, x2)  =  U131_ga(x2)
U132_ga(x1, x2)  =  U132_ga(x2)
log2N31_in_a(x1)  =  log2N31_in_a
U125_a(x1, x2)  =  U125_a(x2)
log2N31_out_a(x1)  =  log2N31_out_a(x1)
U133_ga(x1, x2)  =  U133_ga(x2)
U134_ga(x1, x2)  =  U134_ga(x2)
log2N32_in_a(x1)  =  log2N32_in_a
U126_a(x1, x2)  =  U126_a(x2)
log2N32_out_a(x1)  =  log2N32_out_a(x1)
U135_ga(x1, x2)  =  U135_ga(x2)
U136_ga(x1, x2)  =  U136_ga(x2)
log2N33_in_a(x1)  =  log2N33_in_a
log2N33_out_a(x1)  =  log2N33_out_a(x1)
U137_ga(x1, x2)  =  U137_ga(x2)
U138_ga(x1, x2)  =  U138_ga(x2)
log2N34_in_a(x1)  =  log2N34_in_a
log2N34_out_a(x1)  =  log2N34_out_a(x1)
U139_ga(x1, x2)  =  U139_ga(x2)
log2J_out_gga(x1, x2, x3)  =  log2J_out_gga(x1, x2, x3)
U19_gga(x1, x2, x3)  =  U19_gga(x1, x3)
log2I_out_ga(x1, x2)  =  log2I_out_ga(x1, x2)
U145_ga(x1, x2)  =  U145_ga(x2)
log2N35_in_a(x1)  =  log2N35_in_a
U140_a(x1, x2)  =  U140_a(x2)
log2N35_out_a(x1)  =  log2N35_out_a(x1)
U146_ga(x1, x2)  =  U146_ga(x2)
U147_ga(x1, x2)  =  U147_ga(x2)
log2N36_in_a(x1)  =  log2N36_in_a
U141_a(x1, x2)  =  U141_a(x2)
log2N36_out_a(x1)  =  log2N36_out_a(x1)
U148_ga(x1, x2)  =  U148_ga(x2)
U149_ga(x1, x2)  =  U149_ga(x2)
log2N37_in_a(x1)  =  log2N37_in_a
U142_a(x1, x2)  =  U142_a(x2)
log2N37_out_a(x1)  =  log2N37_out_a(x1)
U150_ga(x1, x2)  =  U150_ga(x2)
U151_ga(x1, x2)  =  U151_ga(x2)
log2N38_in_a(x1)  =  log2N38_in_a
U143_a(x1, x2)  =  U143_a(x2)
log2N38_out_a(x1)  =  log2N38_out_a(x1)
U152_ga(x1, x2)  =  U152_ga(x2)
U153_ga(x1, x2)  =  U153_ga(x2)
log2N39_in_a(x1)  =  log2N39_in_a
log2N39_out_a(x1)  =  log2N39_out_a(x1)
U154_ga(x1, x2)  =  U154_ga(x2)
U155_ga(x1, x2)  =  U155_ga(x2)
log2N40_in_a(x1)  =  log2N40_in_a
log2N40_out_a(x1)  =  log2N40_out_a(x1)
U156_ga(x1, x2)  =  U156_ga(x2)
log2B_out_gga(x1, x2, x3)  =  log2B_out_gga(x1, x2, x3)
U16_gga(x1, x2, x3)  =  U16_gga(x1, x3)
log2A_out_ga(x1, x2)  =  log2A_out_ga(x1, x2)
U2_ga(x1, x2)  =  U2_ga(x2)
log2C_in_a(x1)  =  log2C_in_a
U157_a(x1, x2)  =  U157_a(x2)
log2C_out_a(x1)  =  log2C_out_a(x1)
U3_ga(x1, x2)  =  U3_ga(x2)
U4_ga(x1, x2)  =  U4_ga(x2)
log2D_in_a(x1)  =  log2D_in_a
U158_a(x1, x2)  =  U158_a(x2)
log2D_out_a(x1)  =  log2D_out_a(x1)
U5_ga(x1, x2)  =  U5_ga(x2)
U6_ga(x1, x2)  =  U6_ga(x2)
log2E_in_a(x1)  =  log2E_in_a
U159_a(x1, x2)  =  U159_a(x2)
log2E_out_a(x1)  =  log2E_out_a(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2)  =  U8_ga(x2)
log2F_in_a(x1)  =  log2F_in_a
U160_a(x1, x2)  =  U160_a(x2)
log2F_out_a(x1)  =  log2F_out_a(x1)
U9_ga(x1, x2)  =  U9_ga(x2)
U10_ga(x1, x2)  =  U10_ga(x2)
log2G_in_a(x1)  =  log2G_in_a
log2G_out_a(x1)  =  log2G_out_a(x1)
U11_ga(x1, x2)  =  U11_ga(x2)
U12_ga(x1, x2)  =  U12_ga(x2)
log2H_in_a(x1)  =  log2H_in_a
log2H_out_a(x1)  =  log2H_out_a(x1)
U13_ga(x1, x2)  =  U13_ga(x2)
LOG2B_IN_GGA(x1, x2, x3)  =  LOG2B_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(59) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(60) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LOG2B_IN_GGA(s(s(T128)), T129, T131) → LOG2B_IN_GGA(T128, s(T129), T131)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LOG2B_IN_GGA(x1, x2, x3)  =  LOG2B_IN_GGA(x1, x2)

We have to consider all (P,R,Pi)-chains

(61) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(62) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LOG2B_IN_GGA(s(s(T128)), T129) → LOG2B_IN_GGA(T128, s(T129))

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(63) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

  • LOG2B_IN_GGA(s(s(T128)), T129) → LOG2B_IN_GGA(T128, s(T129))
    The graph contains the following edges 1 > 1

(64) YES