(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)).

Queries:

log2(a,g).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

(2) Obligation:

Clauses:

log244(s(s(T131)), T129, T130) :- log244(T131, s(T129), T130).
log244(0, s(T148), T149) :- log257(T148, T149).
log244(s(0), s(T148), T149) :- log257(T148, T149).
log244(0, 0, s(0)).
log244(s(0), 0, s(0)).
log294(s(s(T255)), T256, T257) :- log294(T255, s(T256), T257).
log294(0, s(T274), T275) :- log2107(T274, T275).
log294(s(0), s(T274), T275) :- log2107(T274, T275).
log294(0, 0, s(s(0))).
log294(s(0), 0, s(s(0))).
log2144(s(s(T380)), T381, T382) :- log2144(T380, s(T381), T382).
log2144(0, s(T399), T400) :- log2157(T399, T400).
log2144(s(0), s(T399), T400) :- log2157(T399, T400).
log2144(0, 0, s(s(s(0)))).
log2144(s(0), 0, s(s(s(0)))).
log2194(s(s(T505)), T506, T507) :- log2194(T505, s(T506), T507).
log2194(0, s(T524), T525) :- log2207(T524, T525).
log2194(s(0), s(T524), T525) :- log2207(T524, T525).
log2194(0, 0, s(s(s(s(0))))).
log2194(s(0), 0, s(s(s(s(0))))).
log2244(s(s(T630)), T631, T632) :- log2244(T630, s(T631), T632).
log2244(0, s(T649), T650) :- log2257(T649, T650).
log2244(s(0), s(T649), T650) :- log2257(T649, T650).
log2244(0, 0, s(s(s(s(s(0)))))).
log2244(s(0), 0, s(s(s(s(s(0)))))).
log2294(s(s(T755)), T756, T757) :- log2294(T755, s(T756), T757).
log2294(0, s(T774), T775) :- log2307(T774, T775).
log2294(s(0), s(T774), T775) :- log2307(T774, T775).
log2294(0, 0, s(s(s(s(s(s(0))))))).
log2294(s(0), 0, s(s(s(s(s(s(0))))))).
log2344(s(s(T880)), T881, T882) :- log2344(T880, s(T881), T882).
log2344(0, s(T899), T900) :- log2359(T899, s(s(s(s(s(s(s(0))))))), T900).
log2344(s(0), s(T899), T900) :- log2359(T899, s(s(s(s(s(s(s(0))))))), T900).
log2344(0, 0, s(s(s(s(s(s(s(0)))))))).
log2344(s(0), 0, s(s(s(s(s(s(s(0)))))))).
log2395(s(s(T1056)), T1057, T1058, T1059) :- log2395(T1056, s(T1057), T1058, T1059).
log2395(0, s(T1081), T1082, T1083) :- log2359(T1081, s(T1082), T1083).
log2395(s(0), s(T1081), T1082, T1083) :- log2359(T1081, s(T1082), T1083).
log2395(0, 0, T1101, s(T1101)).
log2395(s(0), 0, T1101, s(T1101)).
log2359(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) :- log2395(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031).
log2359(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) :- log2437(T1119, T1120).
log2359(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) :- log2437(T1119, T1120).
log2359(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) :- log2515(T1222, T1223).
log2359(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) :- log2515(T1222, T1223).
log2359(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) :- log2585(T1323, T1324).
log2359(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) :- log2585(T1323, T1324).
log2359(s(s(s(s(s(s(0)))))), T1394, T1395) :- log2650(T1394, T1395).
log2359(s(s(s(s(s(s(s(0))))))), T1394, T1395) :- log2650(T1394, T1395).
log2359(s(s(s(s(0)))), T1461, T1462) :- log2705(T1461, T1462).
log2359(s(s(s(s(s(0))))), T1461, T1462) :- log2705(T1461, T1462).
log2359(s(s(0)), T1490, T1491) :- log2742(T1490, T1491).
log2359(s(s(s(0))), T1490, T1491) :- log2742(T1490, T1491).
log2359(0, T1510, s(T1510)).
log2359(s(0), T1510, s(T1510)).
log2437(T1167, T1168) :- log2454(T1167, T1168).
log2454(T1174, s(s(s(T1174)))).
log2515(T1270, T1271) :- log2454(T1270, T1271).
log2585(T1355, T1356) :- log2598(T1355, T1356).
log2598(T1362, s(s(s(T1362)))).
log2650(T1426, T1427) :- log2598(T1426, T1427).
log2705(T1467, s(s(T1467))).
log2742(T1496, s(s(T1496))).
log2307(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) :- log2344(T860, s(s(s(s(s(s(s(0))))))), T861).
log2307(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) :- log2822(s(s(s(s(s(s(s(0))))))), T1530).
log2307(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) :- log2822(s(s(s(s(s(s(s(0))))))), T1530).
log2307(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) :- log2889(s(s(s(s(s(s(s(0))))))), T1620).
log2307(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) :- log2889(s(s(s(s(s(s(s(0))))))), T1620).
log2307(s(s(s(s(s(s(s(s(0)))))))), T1711) :- log2960(s(s(s(s(s(s(s(0))))))), T1711).
log2307(s(s(s(s(s(s(s(s(s(0))))))))), T1711) :- log2960(s(s(s(s(s(s(s(0))))))), T1711).
log2307(s(s(s(s(s(s(0)))))), T1769) :- log21012(s(s(s(s(s(s(s(0))))))), T1769).
log2307(s(s(s(s(s(s(s(0))))))), T1769) :- log21012(s(s(s(s(s(s(s(0))))))), T1769).
log2307(s(s(s(s(0)))), T1826) :- log21068(s(s(s(s(s(s(s(0))))))), T1826).
log2307(s(s(s(s(s(0))))), T1826) :- log21068(s(s(s(s(s(s(s(0))))))), T1826).
log2307(s(s(0)), T1844) :- log21106(s(s(s(s(s(s(s(0))))))), T1844).
log2307(s(s(s(0))), T1844) :- log21106(s(s(s(s(s(s(s(0))))))), T1844).
log2307(0, s(s(s(s(s(s(s(0)))))))).
log2307(s(0), s(s(s(s(s(s(s(0)))))))).
log21183(T1899) :- log21068(s(s(s(s(s(s(s(0))))))), T1899).
log21249(T1943) :- log21068(s(s(s(s(s(s(s(0))))))), T1943).
log21319(T1979) :- log21106(s(s(s(s(s(s(s(0))))))), T1979).
log21370(T2010) :- log21106(s(s(s(s(s(s(s(0))))))), T2010).
log21425(s(s(s(s(s(s(s(0)))))))).
log21462(s(s(s(s(s(s(s(0)))))))).
log2257(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) :- log2294(T735, s(s(s(s(s(s(s(0))))))), T736).
log2257(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) :- log21183(T1876).
log2257(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) :- log21183(T1876).
log2257(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) :- log21249(T1920).
log2257(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) :- log21249(T1920).
log2257(s(s(s(s(s(s(s(s(0)))))))), T1964) :- log21319(T1964).
log2257(s(s(s(s(s(s(s(s(s(0))))))))), T1964) :- log21319(T1964).
log2257(s(s(s(s(s(s(0)))))), T1995) :- log21370(T1995).
log2257(s(s(s(s(s(s(s(0))))))), T1995) :- log21370(T1995).
log2257(s(s(s(s(0)))), T2024) :- log21425(T2024).
log2257(s(s(s(s(s(0))))), T2024) :- log21425(T2024).
log2257(s(s(0)), T2037) :- log21462(T2037).
log2257(s(s(s(0))), T2037) :- log21462(T2037).
log2257(0, s(s(s(s(s(s(0))))))).
log2257(s(0), s(s(s(s(s(s(0))))))).
log21540(T2087) :- log21425(T2087).
log21606(T2131) :- log21425(T2131).
log21676(T2167) :- log21462(T2167).
log21727(T2198) :- log21462(T2198).
log21782(s(s(s(s(s(s(0))))))).
log21819(s(s(s(s(s(s(0))))))).
log2207(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) :- log2244(T610, s(s(s(s(s(s(s(0))))))), T611).
log2207(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) :- log21540(T2064).
log2207(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) :- log21540(T2064).
log2207(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) :- log21606(T2108).
log2207(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) :- log21606(T2108).
log2207(s(s(s(s(s(s(s(s(0)))))))), T2152) :- log21676(T2152).
log2207(s(s(s(s(s(s(s(s(s(0))))))))), T2152) :- log21676(T2152).
log2207(s(s(s(s(s(s(0)))))), T2183) :- log21727(T2183).
log2207(s(s(s(s(s(s(s(0))))))), T2183) :- log21727(T2183).
log2207(s(s(s(s(0)))), T2212) :- log21782(T2212).
log2207(s(s(s(s(s(0))))), T2212) :- log21782(T2212).
log2207(s(s(0)), T2225) :- log21819(T2225).
log2207(s(s(s(0))), T2225) :- log21819(T2225).
log2207(0, s(s(s(s(s(0)))))).
log2207(s(0), s(s(s(s(s(0)))))).
log21897(T2275) :- log21782(T2275).
log21963(T2319) :- log21782(T2319).
log22033(T2355) :- log21819(T2355).
log22084(T2386) :- log21819(T2386).
log22139(s(s(s(s(s(0)))))).
log22176(s(s(s(s(s(0)))))).
log2157(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) :- log2194(T485, s(s(s(s(s(s(s(0))))))), T486).
log2157(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) :- log21897(T2252).
log2157(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) :- log21897(T2252).
log2157(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) :- log21963(T2296).
log2157(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) :- log21963(T2296).
log2157(s(s(s(s(s(s(s(s(0)))))))), T2340) :- log22033(T2340).
log2157(s(s(s(s(s(s(s(s(s(0))))))))), T2340) :- log22033(T2340).
log2157(s(s(s(s(s(s(0)))))), T2371) :- log22084(T2371).
log2157(s(s(s(s(s(s(s(0))))))), T2371) :- log22084(T2371).
log2157(s(s(s(s(0)))), T2400) :- log22139(T2400).
log2157(s(s(s(s(s(0))))), T2400) :- log22139(T2400).
log2157(s(s(0)), T2413) :- log22176(T2413).
log2157(s(s(s(0))), T2413) :- log22176(T2413).
log2157(0, s(s(s(s(0))))).
log2157(s(0), s(s(s(s(0))))).
log22254(T2463) :- log22139(T2463).
log22320(T2507) :- log22139(T2507).
log22390(T2543) :- log22176(T2543).
log22441(T2574) :- log22176(T2574).
log22496(s(s(s(s(0))))).
log22533(s(s(s(s(0))))).
log2107(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) :- log2144(T360, s(s(s(s(s(s(s(0))))))), T361).
log2107(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) :- log22254(T2440).
log2107(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) :- log22254(T2440).
log2107(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) :- log22320(T2484).
log2107(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) :- log22320(T2484).
log2107(s(s(s(s(s(s(s(s(0)))))))), T2528) :- log22390(T2528).
log2107(s(s(s(s(s(s(s(s(s(0))))))))), T2528) :- log22390(T2528).
log2107(s(s(s(s(s(s(0)))))), T2559) :- log22441(T2559).
log2107(s(s(s(s(s(s(s(0))))))), T2559) :- log22441(T2559).
log2107(s(s(s(s(0)))), T2588) :- log22496(T2588).
log2107(s(s(s(s(s(0))))), T2588) :- log22496(T2588).
log2107(s(s(0)), T2601) :- log22533(T2601).
log2107(s(s(s(0))), T2601) :- log22533(T2601).
log2107(0, s(s(s(0)))).
log2107(s(0), s(s(s(0)))).
log22611(T2651) :- log22496(T2651).
log22677(T2695) :- log22496(T2695).
log22747(T2731) :- log22533(T2731).
log22798(T2762) :- log22533(T2762).
log22853(s(s(s(0)))).
log22890(s(s(s(0)))).
log257(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) :- log294(T235, s(s(s(s(s(s(s(0))))))), T236).
log257(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) :- log22611(T2628).
log257(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) :- log22611(T2628).
log257(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) :- log22677(T2672).
log257(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) :- log22677(T2672).
log257(s(s(s(s(s(s(s(s(0)))))))), T2716) :- log22747(T2716).
log257(s(s(s(s(s(s(s(s(s(0))))))))), T2716) :- log22747(T2716).
log257(s(s(s(s(s(s(0)))))), T2747) :- log22798(T2747).
log257(s(s(s(s(s(s(s(0))))))), T2747) :- log22798(T2747).
log257(s(s(s(s(0)))), T2776) :- log22853(T2776).
log257(s(s(s(s(s(0))))), T2776) :- log22853(T2776).
log257(s(s(0)), T2789) :- log22890(T2789).
log257(s(s(s(0))), T2789) :- log22890(T2789).
log257(0, s(s(0))).
log257(s(0), s(s(0))).
log22968(T2843) :- log22853(T2843).
log23034(T2891) :- log22853(T2891).
log23104(T2931) :- log22890(T2931).
log23155(T2966) :- log22890(T2966).
log23210(s(s(0))).
log23247(s(s(0))).
log2822(T1578, T1579) :- log2705(T1578, T1579).
log2889(T1668, T1669) :- log2705(T1668, T1669).
log2960(T1743, T1744) :- log2742(T1743, T1744).
log21012(T1801, T1802) :- log2742(T1801, T1802).
log21068(T1831, s(T1831)).
log21106(T1849, s(T1849)).
log21(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) :- log244(T109, s(s(s(s(s(s(s(0))))))), T108).
log21(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) :- log22968(T2819).
log21(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) :- log22968(T2819).
log21(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) :- log23034(T2867).
log21(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) :- log23034(T2867).
log21(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) :- log23104(T2915).
log21(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) :- log23104(T2915).
log21(s(s(s(s(s(s(s(s(0)))))))), T2950) :- log23155(T2950).
log21(s(s(s(s(s(s(s(s(s(0))))))))), T2950) :- log23155(T2950).
log21(s(s(s(s(s(s(0)))))), T2983) :- log23210(T2983).
log21(s(s(s(s(s(s(s(0))))))), T2983) :- log23210(T2983).
log21(s(s(s(s(0)))), T3000) :- log23247(T3000).
log21(s(s(s(s(s(0))))), T3000) :- log23247(T3000).
log21(s(s(0)), s(0)).
log21(s(s(s(0))), s(0)).
log21(0, s(0)).
log21(s(0), s(0)).

Queries:

log21(a,g).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
log21_in: (f,b)
log244_in: (f,b,b)
log257_in: (b,b)
log294_in: (b,b,b)
log2107_in: (b,b)
log2144_in: (b,b,b)
log2157_in: (b,b)
log2194_in: (b,b,b)
log2207_in: (b,b)
log2244_in: (b,b,b)
log2257_in: (b,b)
log2294_in: (b,b,b)
log2307_in: (b,b)
log2344_in: (b,b,b)
log2359_in: (b,b,b)
log2395_in: (b,b,b,b)
log2437_in: (b,b)
log2515_in: (b,b)
log2585_in: (b,b)
log2650_in: (b,b)
log2822_in: (b,b)
log2889_in: (b,b)
log2960_in: (b,b)
log21012_in: (b,b)
log21183_in: (b)
log21249_in: (b)
log21319_in: (b)
log21370_in: (b)
log21540_in: (b)
log21606_in: (b)
log21676_in: (b)
log21727_in: (b)
log21897_in: (b)
log21963_in: (b)
log22033_in: (b)
log22084_in: (b)
log22254_in: (b)
log22320_in: (b)
log22390_in: (b)
log22441_in: (b)
log22611_in: (b)
log22677_in: (b)
log22747_in: (b)
log22798_in: (b)
log22968_in: (b)
log23034_in: (b)
log23104_in: (b)
log23155_in: (b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)

(5) 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:

LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_AG(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → LOG244_IN_AGG(T109, s(s(s(s(s(s(s(0))))))), T108)
LOG244_IN_AGG(s(s(T131)), T129, T130) → U1_AGG(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
LOG244_IN_AGG(s(s(T131)), T129, T130) → LOG244_IN_AGG(T131, s(T129), T130)
LOG244_IN_AGG(0, s(T148), T149) → U2_AGG(T148, T149, log257_in_gg(T148, T149))
LOG244_IN_AGG(0, s(T148), T149) → LOG257_IN_GG(T148, T149)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_GG(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → LOG294_IN_GGG(T235, s(s(s(s(s(s(s(0))))))), T236)
LOG294_IN_GGG(s(s(T255)), T256, T257) → U4_GGG(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)
LOG294_IN_GGG(0, s(T274), T275) → U5_GGG(T274, T275, log2107_in_gg(T274, T275))
LOG294_IN_GGG(0, s(T274), T275) → LOG2107_IN_GG(T274, T275)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_GG(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → LOG2144_IN_GGG(T360, s(s(s(s(s(s(s(0))))))), T361)
LOG2144_IN_GGG(s(s(T380)), T381, T382) → U7_GGG(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)
LOG2144_IN_GGG(0, s(T399), T400) → U8_GGG(T399, T400, log2157_in_gg(T399, T400))
LOG2144_IN_GGG(0, s(T399), T400) → LOG2157_IN_GG(T399, T400)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_GG(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → LOG2194_IN_GGG(T485, s(s(s(s(s(s(s(0))))))), T486)
LOG2194_IN_GGG(s(s(T505)), T506, T507) → U10_GGG(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)
LOG2194_IN_GGG(0, s(T524), T525) → U11_GGG(T524, T525, log2207_in_gg(T524, T525))
LOG2194_IN_GGG(0, s(T524), T525) → LOG2207_IN_GG(T524, T525)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_GG(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → LOG2244_IN_GGG(T610, s(s(s(s(s(s(s(0))))))), T611)
LOG2244_IN_GGG(s(s(T630)), T631, T632) → U13_GGG(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)
LOG2244_IN_GGG(0, s(T649), T650) → U14_GGG(T649, T650, log2257_in_gg(T649, T650))
LOG2244_IN_GGG(0, s(T649), T650) → LOG2257_IN_GG(T649, T650)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_GG(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → LOG2294_IN_GGG(T735, s(s(s(s(s(s(s(0))))))), T736)
LOG2294_IN_GGG(s(s(T755)), T756, T757) → U16_GGG(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)
LOG2294_IN_GGG(0, s(T774), T775) → U17_GGG(T774, T775, log2307_in_gg(T774, T775))
LOG2294_IN_GGG(0, s(T774), T775) → LOG2307_IN_GG(T774, T775)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_GG(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → LOG2344_IN_GGG(T860, s(s(s(s(s(s(s(0))))))), T861)
LOG2344_IN_GGG(s(s(T880)), T881, T882) → U19_GGG(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)
LOG2344_IN_GGG(0, s(T899), T900) → U20_GGG(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
LOG2344_IN_GGG(0, s(T899), T900) → LOG2359_IN_GGG(T899, s(s(s(s(s(s(s(0))))))), T900)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_GGG(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → U22_GGGG(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → U23_GGGG(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_GGG(T1119, T1120, log2437_in_gg(T1119, T1120))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → LOG2437_IN_GG(T1119, T1120)
LOG2437_IN_GG(T1167, T1168) → U38_GG(T1167, T1168, log2454_in_gg(T1167, T1168))
LOG2437_IN_GG(T1167, T1168) → LOG2454_IN_GG(T1167, T1168)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_GGG(T1119, T1120, log2437_in_gg(T1119, T1120))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → LOG2437_IN_GG(T1119, T1120)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_GGG(T1222, T1223, log2515_in_gg(T1222, T1223))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → LOG2515_IN_GG(T1222, T1223)
LOG2515_IN_GG(T1270, T1271) → U39_GG(T1270, T1271, log2454_in_gg(T1270, T1271))
LOG2515_IN_GG(T1270, T1271) → LOG2454_IN_GG(T1270, T1271)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_GGG(T1222, T1223, log2515_in_gg(T1222, T1223))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → LOG2515_IN_GG(T1222, T1223)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_GGG(T1323, T1324, log2585_in_gg(T1323, T1324))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → LOG2585_IN_GG(T1323, T1324)
LOG2585_IN_GG(T1355, T1356) → U40_GG(T1355, T1356, log2598_in_gg(T1355, T1356))
LOG2585_IN_GG(T1355, T1356) → LOG2598_IN_GG(T1355, T1356)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_GGG(T1323, T1324, log2585_in_gg(T1323, T1324))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → LOG2585_IN_GG(T1323, T1324)
LOG2359_IN_GGG(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_GGG(T1394, T1395, log2650_in_gg(T1394, T1395))
LOG2359_IN_GGG(s(s(s(s(s(s(0)))))), T1394, T1395) → LOG2650_IN_GG(T1394, T1395)
LOG2650_IN_GG(T1426, T1427) → U41_GG(T1426, T1427, log2598_in_gg(T1426, T1427))
LOG2650_IN_GG(T1426, T1427) → LOG2598_IN_GG(T1426, T1427)
LOG2359_IN_GGG(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_GGG(T1394, T1395, log2650_in_gg(T1394, T1395))
LOG2359_IN_GGG(s(s(s(s(s(s(s(0))))))), T1394, T1395) → LOG2650_IN_GG(T1394, T1395)
LOG2359_IN_GGG(s(s(s(s(0)))), T1461, T1462) → U34_GGG(T1461, T1462, log2705_in_gg(T1461, T1462))
LOG2359_IN_GGG(s(s(s(s(0)))), T1461, T1462) → LOG2705_IN_GG(T1461, T1462)
LOG2359_IN_GGG(s(s(s(s(s(0))))), T1461, T1462) → U35_GGG(T1461, T1462, log2705_in_gg(T1461, T1462))
LOG2359_IN_GGG(s(s(s(s(s(0))))), T1461, T1462) → LOG2705_IN_GG(T1461, T1462)
LOG2359_IN_GGG(s(s(0)), T1490, T1491) → U36_GGG(T1490, T1491, log2742_in_gg(T1490, T1491))
LOG2359_IN_GGG(s(s(0)), T1490, T1491) → LOG2742_IN_GG(T1490, T1491)
LOG2359_IN_GGG(s(s(s(0))), T1490, T1491) → U37_GGG(T1490, T1491, log2742_in_gg(T1490, T1491))
LOG2359_IN_GGG(s(s(s(0))), T1490, T1491) → LOG2742_IN_GG(T1490, T1491)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → U24_GGGG(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2344_IN_GGG(s(0), s(T899), T900) → U21_GGG(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
LOG2344_IN_GGG(s(0), s(T899), T900) → LOG2359_IN_GGG(T899, s(s(s(s(s(s(s(0))))))), T900)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_GG(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → LOG2822_IN_GG(s(s(s(s(s(s(s(0))))))), T1530)
LOG2822_IN_GG(T1578, T1579) → U144_GG(T1578, T1579, log2705_in_gg(T1578, T1579))
LOG2822_IN_GG(T1578, T1579) → LOG2705_IN_GG(T1578, T1579)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_GG(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → LOG2822_IN_GG(s(s(s(s(s(s(s(0))))))), T1530)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_GG(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → LOG2889_IN_GG(s(s(s(s(s(s(s(0))))))), T1620)
LOG2889_IN_GG(T1668, T1669) → U145_GG(T1668, T1669, log2705_in_gg(T1668, T1669))
LOG2889_IN_GG(T1668, T1669) → LOG2705_IN_GG(T1668, T1669)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_GG(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → LOG2889_IN_GG(s(s(s(s(s(s(s(0))))))), T1620)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_GG(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1711) → LOG2960_IN_GG(s(s(s(s(s(s(s(0))))))), T1711)
LOG2960_IN_GG(T1743, T1744) → U146_GG(T1743, T1744, log2742_in_gg(T1743, T1744))
LOG2960_IN_GG(T1743, T1744) → LOG2742_IN_GG(T1743, T1744)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_GG(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → LOG2960_IN_GG(s(s(s(s(s(s(s(0))))))), T1711)
LOG2307_IN_GG(s(s(s(s(s(s(0)))))), T1769) → U49_GG(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
LOG2307_IN_GG(s(s(s(s(s(s(0)))))), T1769) → LOG21012_IN_GG(s(s(s(s(s(s(s(0))))))), T1769)
LOG21012_IN_GG(T1801, T1802) → U147_GG(T1801, T1802, log2742_in_gg(T1801, T1802))
LOG21012_IN_GG(T1801, T1802) → LOG2742_IN_GG(T1801, T1802)
LOG2307_IN_GG(s(s(s(s(s(s(s(0))))))), T1769) → U50_GG(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
LOG2307_IN_GG(s(s(s(s(s(s(s(0))))))), T1769) → LOG21012_IN_GG(s(s(s(s(s(s(s(0))))))), T1769)
LOG2307_IN_GG(s(s(s(s(0)))), T1826) → U51_GG(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
LOG2307_IN_GG(s(s(s(s(0)))), T1826) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1826)
LOG2307_IN_GG(s(s(s(s(s(0))))), T1826) → U52_GG(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
LOG2307_IN_GG(s(s(s(s(s(0))))), T1826) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1826)
LOG2307_IN_GG(s(s(0)), T1844) → U53_GG(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
LOG2307_IN_GG(s(s(0)), T1844) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1844)
LOG2307_IN_GG(s(s(s(0))), T1844) → U54_GG(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
LOG2307_IN_GG(s(s(s(0))), T1844) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1844)
LOG2294_IN_GGG(s(0), s(T774), T775) → U18_GGG(T774, T775, log2307_in_gg(T774, T775))
LOG2294_IN_GGG(s(0), s(T774), T775) → LOG2307_IN_GG(T774, T775)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_GG(T1876, log21183_in_g(T1876))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → LOG21183_IN_G(T1876)
LOG21183_IN_G(T1899) → U55_G(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
LOG21183_IN_G(T1899) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1899)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_GG(T1876, log21183_in_g(T1876))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → LOG21183_IN_G(T1876)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_GG(T1920, log21249_in_g(T1920))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → LOG21249_IN_G(T1920)
LOG21249_IN_G(T1943) → U56_G(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
LOG21249_IN_G(T1943) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1943)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_GG(T1920, log21249_in_g(T1920))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → LOG21249_IN_G(T1920)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_GG(T1964, log21319_in_g(T1964))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1964) → LOG21319_IN_G(T1964)
LOG21319_IN_G(T1979) → U57_G(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
LOG21319_IN_G(T1979) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1979)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_GG(T1964, log21319_in_g(T1964))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → LOG21319_IN_G(T1964)
LOG2257_IN_GG(s(s(s(s(s(s(0)))))), T1995) → U66_GG(T1995, log21370_in_g(T1995))
LOG2257_IN_GG(s(s(s(s(s(s(0)))))), T1995) → LOG21370_IN_G(T1995)
LOG21370_IN_G(T2010) → U58_G(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
LOG21370_IN_G(T2010) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T2010)
LOG2257_IN_GG(s(s(s(s(s(s(s(0))))))), T1995) → U67_GG(T1995, log21370_in_g(T1995))
LOG2257_IN_GG(s(s(s(s(s(s(s(0))))))), T1995) → LOG21370_IN_G(T1995)
LOG2257_IN_GG(s(s(s(s(0)))), T2024) → U68_GG(T2024, log21425_in_g(T2024))
LOG2257_IN_GG(s(s(s(s(0)))), T2024) → LOG21425_IN_G(T2024)
LOG2257_IN_GG(s(s(s(s(s(0))))), T2024) → U69_GG(T2024, log21425_in_g(T2024))
LOG2257_IN_GG(s(s(s(s(s(0))))), T2024) → LOG21425_IN_G(T2024)
LOG2257_IN_GG(s(s(0)), T2037) → U70_GG(T2037, log21462_in_g(T2037))
LOG2257_IN_GG(s(s(0)), T2037) → LOG21462_IN_G(T2037)
LOG2257_IN_GG(s(s(s(0))), T2037) → U71_GG(T2037, log21462_in_g(T2037))
LOG2257_IN_GG(s(s(s(0))), T2037) → LOG21462_IN_G(T2037)
LOG2244_IN_GGG(s(0), s(T649), T650) → U15_GGG(T649, T650, log2257_in_gg(T649, T650))
LOG2244_IN_GGG(s(0), s(T649), T650) → LOG2257_IN_GG(T649, T650)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_GG(T2064, log21540_in_g(T2064))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → LOG21540_IN_G(T2064)
LOG21540_IN_G(T2087) → U72_G(T2087, log21425_in_g(T2087))
LOG21540_IN_G(T2087) → LOG21425_IN_G(T2087)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_GG(T2064, log21540_in_g(T2064))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → LOG21540_IN_G(T2064)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_GG(T2108, log21606_in_g(T2108))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → LOG21606_IN_G(T2108)
LOG21606_IN_G(T2131) → U73_G(T2131, log21425_in_g(T2131))
LOG21606_IN_G(T2131) → LOG21425_IN_G(T2131)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_GG(T2108, log21606_in_g(T2108))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → LOG21606_IN_G(T2108)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_GG(T2152, log21676_in_g(T2152))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2152) → LOG21676_IN_G(T2152)
LOG21676_IN_G(T2167) → U74_G(T2167, log21462_in_g(T2167))
LOG21676_IN_G(T2167) → LOG21462_IN_G(T2167)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_GG(T2152, log21676_in_g(T2152))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → LOG21676_IN_G(T2152)
LOG2207_IN_GG(s(s(s(s(s(s(0)))))), T2183) → U83_GG(T2183, log21727_in_g(T2183))
LOG2207_IN_GG(s(s(s(s(s(s(0)))))), T2183) → LOG21727_IN_G(T2183)
LOG21727_IN_G(T2198) → U75_G(T2198, log21462_in_g(T2198))
LOG21727_IN_G(T2198) → LOG21462_IN_G(T2198)
LOG2207_IN_GG(s(s(s(s(s(s(s(0))))))), T2183) → U84_GG(T2183, log21727_in_g(T2183))
LOG2207_IN_GG(s(s(s(s(s(s(s(0))))))), T2183) → LOG21727_IN_G(T2183)
LOG2207_IN_GG(s(s(s(s(0)))), T2212) → U85_GG(T2212, log21782_in_g(T2212))
LOG2207_IN_GG(s(s(s(s(0)))), T2212) → LOG21782_IN_G(T2212)
LOG2207_IN_GG(s(s(s(s(s(0))))), T2212) → U86_GG(T2212, log21782_in_g(T2212))
LOG2207_IN_GG(s(s(s(s(s(0))))), T2212) → LOG21782_IN_G(T2212)
LOG2207_IN_GG(s(s(0)), T2225) → U87_GG(T2225, log21819_in_g(T2225))
LOG2207_IN_GG(s(s(0)), T2225) → LOG21819_IN_G(T2225)
LOG2207_IN_GG(s(s(s(0))), T2225) → U88_GG(T2225, log21819_in_g(T2225))
LOG2207_IN_GG(s(s(s(0))), T2225) → LOG21819_IN_G(T2225)
LOG2194_IN_GGG(s(0), s(T524), T525) → U12_GGG(T524, T525, log2207_in_gg(T524, T525))
LOG2194_IN_GGG(s(0), s(T524), T525) → LOG2207_IN_GG(T524, T525)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_GG(T2252, log21897_in_g(T2252))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → LOG21897_IN_G(T2252)
LOG21897_IN_G(T2275) → U89_G(T2275, log21782_in_g(T2275))
LOG21897_IN_G(T2275) → LOG21782_IN_G(T2275)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_GG(T2252, log21897_in_g(T2252))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → LOG21897_IN_G(T2252)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_GG(T2296, log21963_in_g(T2296))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → LOG21963_IN_G(T2296)
LOG21963_IN_G(T2319) → U90_G(T2319, log21782_in_g(T2319))
LOG21963_IN_G(T2319) → LOG21782_IN_G(T2319)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_GG(T2296, log21963_in_g(T2296))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → LOG21963_IN_G(T2296)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_GG(T2340, log22033_in_g(T2340))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2340) → LOG22033_IN_G(T2340)
LOG22033_IN_G(T2355) → U91_G(T2355, log21819_in_g(T2355))
LOG22033_IN_G(T2355) → LOG21819_IN_G(T2355)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_GG(T2340, log22033_in_g(T2340))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → LOG22033_IN_G(T2340)
LOG2157_IN_GG(s(s(s(s(s(s(0)))))), T2371) → U100_GG(T2371, log22084_in_g(T2371))
LOG2157_IN_GG(s(s(s(s(s(s(0)))))), T2371) → LOG22084_IN_G(T2371)
LOG22084_IN_G(T2386) → U92_G(T2386, log21819_in_g(T2386))
LOG22084_IN_G(T2386) → LOG21819_IN_G(T2386)
LOG2157_IN_GG(s(s(s(s(s(s(s(0))))))), T2371) → U101_GG(T2371, log22084_in_g(T2371))
LOG2157_IN_GG(s(s(s(s(s(s(s(0))))))), T2371) → LOG22084_IN_G(T2371)
LOG2157_IN_GG(s(s(s(s(0)))), T2400) → U102_GG(T2400, log22139_in_g(T2400))
LOG2157_IN_GG(s(s(s(s(0)))), T2400) → LOG22139_IN_G(T2400)
LOG2157_IN_GG(s(s(s(s(s(0))))), T2400) → U103_GG(T2400, log22139_in_g(T2400))
LOG2157_IN_GG(s(s(s(s(s(0))))), T2400) → LOG22139_IN_G(T2400)
LOG2157_IN_GG(s(s(0)), T2413) → U104_GG(T2413, log22176_in_g(T2413))
LOG2157_IN_GG(s(s(0)), T2413) → LOG22176_IN_G(T2413)
LOG2157_IN_GG(s(s(s(0))), T2413) → U105_GG(T2413, log22176_in_g(T2413))
LOG2157_IN_GG(s(s(s(0))), T2413) → LOG22176_IN_G(T2413)
LOG2144_IN_GGG(s(0), s(T399), T400) → U9_GGG(T399, T400, log2157_in_gg(T399, T400))
LOG2144_IN_GGG(s(0), s(T399), T400) → LOG2157_IN_GG(T399, T400)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_GG(T2440, log22254_in_g(T2440))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → LOG22254_IN_G(T2440)
LOG22254_IN_G(T2463) → U106_G(T2463, log22139_in_g(T2463))
LOG22254_IN_G(T2463) → LOG22139_IN_G(T2463)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_GG(T2440, log22254_in_g(T2440))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → LOG22254_IN_G(T2440)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_GG(T2484, log22320_in_g(T2484))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → LOG22320_IN_G(T2484)
LOG22320_IN_G(T2507) → U107_G(T2507, log22139_in_g(T2507))
LOG22320_IN_G(T2507) → LOG22139_IN_G(T2507)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_GG(T2484, log22320_in_g(T2484))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → LOG22320_IN_G(T2484)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_GG(T2528, log22390_in_g(T2528))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2528) → LOG22390_IN_G(T2528)
LOG22390_IN_G(T2543) → U108_G(T2543, log22176_in_g(T2543))
LOG22390_IN_G(T2543) → LOG22176_IN_G(T2543)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_GG(T2528, log22390_in_g(T2528))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → LOG22390_IN_G(T2528)
LOG2107_IN_GG(s(s(s(s(s(s(0)))))), T2559) → U117_GG(T2559, log22441_in_g(T2559))
LOG2107_IN_GG(s(s(s(s(s(s(0)))))), T2559) → LOG22441_IN_G(T2559)
LOG22441_IN_G(T2574) → U109_G(T2574, log22176_in_g(T2574))
LOG22441_IN_G(T2574) → LOG22176_IN_G(T2574)
LOG2107_IN_GG(s(s(s(s(s(s(s(0))))))), T2559) → U118_GG(T2559, log22441_in_g(T2559))
LOG2107_IN_GG(s(s(s(s(s(s(s(0))))))), T2559) → LOG22441_IN_G(T2559)
LOG2107_IN_GG(s(s(s(s(0)))), T2588) → U119_GG(T2588, log22496_in_g(T2588))
LOG2107_IN_GG(s(s(s(s(0)))), T2588) → LOG22496_IN_G(T2588)
LOG2107_IN_GG(s(s(s(s(s(0))))), T2588) → U120_GG(T2588, log22496_in_g(T2588))
LOG2107_IN_GG(s(s(s(s(s(0))))), T2588) → LOG22496_IN_G(T2588)
LOG2107_IN_GG(s(s(0)), T2601) → U121_GG(T2601, log22533_in_g(T2601))
LOG2107_IN_GG(s(s(0)), T2601) → LOG22533_IN_G(T2601)
LOG2107_IN_GG(s(s(s(0))), T2601) → U122_GG(T2601, log22533_in_g(T2601))
LOG2107_IN_GG(s(s(s(0))), T2601) → LOG22533_IN_G(T2601)
LOG294_IN_GGG(s(0), s(T274), T275) → U6_GGG(T274, T275, log2107_in_gg(T274, T275))
LOG294_IN_GGG(s(0), s(T274), T275) → LOG2107_IN_GG(T274, T275)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_GG(T2628, log22611_in_g(T2628))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → LOG22611_IN_G(T2628)
LOG22611_IN_G(T2651) → U123_G(T2651, log22496_in_g(T2651))
LOG22611_IN_G(T2651) → LOG22496_IN_G(T2651)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_GG(T2628, log22611_in_g(T2628))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → LOG22611_IN_G(T2628)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_GG(T2672, log22677_in_g(T2672))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → LOG22677_IN_G(T2672)
LOG22677_IN_G(T2695) → U124_G(T2695, log22496_in_g(T2695))
LOG22677_IN_G(T2695) → LOG22496_IN_G(T2695)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_GG(T2672, log22677_in_g(T2672))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → LOG22677_IN_G(T2672)
LOG257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_GG(T2716, log22747_in_g(T2716))
LOG257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2716) → LOG22747_IN_G(T2716)
LOG22747_IN_G(T2731) → U125_G(T2731, log22533_in_g(T2731))
LOG22747_IN_G(T2731) → LOG22533_IN_G(T2731)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_GG(T2716, log22747_in_g(T2716))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → LOG22747_IN_G(T2716)
LOG257_IN_GG(s(s(s(s(s(s(0)))))), T2747) → U134_GG(T2747, log22798_in_g(T2747))
LOG257_IN_GG(s(s(s(s(s(s(0)))))), T2747) → LOG22798_IN_G(T2747)
LOG22798_IN_G(T2762) → U126_G(T2762, log22533_in_g(T2762))
LOG22798_IN_G(T2762) → LOG22533_IN_G(T2762)
LOG257_IN_GG(s(s(s(s(s(s(s(0))))))), T2747) → U135_GG(T2747, log22798_in_g(T2747))
LOG257_IN_GG(s(s(s(s(s(s(s(0))))))), T2747) → LOG22798_IN_G(T2747)
LOG257_IN_GG(s(s(s(s(0)))), T2776) → U136_GG(T2776, log22853_in_g(T2776))
LOG257_IN_GG(s(s(s(s(0)))), T2776) → LOG22853_IN_G(T2776)
LOG257_IN_GG(s(s(s(s(s(0))))), T2776) → U137_GG(T2776, log22853_in_g(T2776))
LOG257_IN_GG(s(s(s(s(s(0))))), T2776) → LOG22853_IN_G(T2776)
LOG257_IN_GG(s(s(0)), T2789) → U138_GG(T2789, log22890_in_g(T2789))
LOG257_IN_GG(s(s(0)), T2789) → LOG22890_IN_G(T2789)
LOG257_IN_GG(s(s(s(0))), T2789) → U139_GG(T2789, log22890_in_g(T2789))
LOG257_IN_GG(s(s(s(0))), T2789) → LOG22890_IN_G(T2789)
LOG244_IN_AGG(s(0), s(T148), T149) → U3_AGG(T148, T149, log257_in_gg(T148, T149))
LOG244_IN_AGG(s(0), s(T148), T149) → LOG257_IN_GG(T148, T149)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_AG(T2819, log22968_in_g(T2819))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → LOG22968_IN_G(T2819)
LOG22968_IN_G(T2843) → U140_G(T2843, log22853_in_g(T2843))
LOG22968_IN_G(T2843) → LOG22853_IN_G(T2843)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_AG(T2819, log22968_in_g(T2819))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → LOG22968_IN_G(T2819)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_AG(T2867, log23034_in_g(T2867))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → LOG23034_IN_G(T2867)
LOG23034_IN_G(T2891) → U141_G(T2891, log22853_in_g(T2891))
LOG23034_IN_G(T2891) → LOG22853_IN_G(T2891)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_AG(T2867, log23034_in_g(T2867))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → LOG23034_IN_G(T2867)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_AG(T2915, log23104_in_g(T2915))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → LOG23104_IN_G(T2915)
LOG23104_IN_G(T2931) → U142_G(T2931, log22890_in_g(T2931))
LOG23104_IN_G(T2931) → LOG22890_IN_G(T2931)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_AG(T2915, log23104_in_g(T2915))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → LOG23104_IN_G(T2915)
LOG21_IN_AG(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_AG(T2950, log23155_in_g(T2950))
LOG21_IN_AG(s(s(s(s(s(s(s(s(0)))))))), T2950) → LOG23155_IN_G(T2950)
LOG23155_IN_G(T2966) → U143_G(T2966, log22890_in_g(T2966))
LOG23155_IN_G(T2966) → LOG22890_IN_G(T2966)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_AG(T2950, log23155_in_g(T2950))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → LOG23155_IN_G(T2950)
LOG21_IN_AG(s(s(s(s(s(s(0)))))), T2983) → U157_AG(T2983, log23210_in_g(T2983))
LOG21_IN_AG(s(s(s(s(s(s(0)))))), T2983) → LOG23210_IN_G(T2983)
LOG21_IN_AG(s(s(s(s(s(s(s(0))))))), T2983) → U158_AG(T2983, log23210_in_g(T2983))
LOG21_IN_AG(s(s(s(s(s(s(s(0))))))), T2983) → LOG23210_IN_G(T2983)
LOG21_IN_AG(s(s(s(s(0)))), T3000) → U159_AG(T3000, log23247_in_g(T3000))
LOG21_IN_AG(s(s(s(s(0)))), T3000) → LOG23247_IN_G(T3000)
LOG21_IN_AG(s(s(s(s(s(0))))), T3000) → U160_AG(T3000, log23247_in_g(T3000))
LOG21_IN_AG(s(s(s(s(s(0))))), T3000) → LOG23247_IN_G(T3000)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG21_IN_AG(x1, x2)  =  LOG21_IN_AG(x2)
U148_AG(x1, x2, x3)  =  U148_AG(x3)
LOG244_IN_AGG(x1, x2, x3)  =  LOG244_IN_AGG(x2, x3)
U1_AGG(x1, x2, x3, x4)  =  U1_AGG(x4)
U2_AGG(x1, x2, x3)  =  U2_AGG(x3)
LOG257_IN_GG(x1, x2)  =  LOG257_IN_GG(x1, x2)
U127_GG(x1, x2, x3)  =  U127_GG(x3)
LOG294_IN_GGG(x1, x2, x3)  =  LOG294_IN_GGG(x1, x2, x3)
U4_GGG(x1, x2, x3, x4)  =  U4_GGG(x4)
U5_GGG(x1, x2, x3)  =  U5_GGG(x3)
LOG2107_IN_GG(x1, x2)  =  LOG2107_IN_GG(x1, x2)
U110_GG(x1, x2, x3)  =  U110_GG(x3)
LOG2144_IN_GGG(x1, x2, x3)  =  LOG2144_IN_GGG(x1, x2, x3)
U7_GGG(x1, x2, x3, x4)  =  U7_GGG(x4)
U8_GGG(x1, x2, x3)  =  U8_GGG(x3)
LOG2157_IN_GG(x1, x2)  =  LOG2157_IN_GG(x1, x2)
U93_GG(x1, x2, x3)  =  U93_GG(x3)
LOG2194_IN_GGG(x1, x2, x3)  =  LOG2194_IN_GGG(x1, x2, x3)
U10_GGG(x1, x2, x3, x4)  =  U10_GGG(x4)
U11_GGG(x1, x2, x3)  =  U11_GGG(x3)
LOG2207_IN_GG(x1, x2)  =  LOG2207_IN_GG(x1, x2)
U76_GG(x1, x2, x3)  =  U76_GG(x3)
LOG2244_IN_GGG(x1, x2, x3)  =  LOG2244_IN_GGG(x1, x2, x3)
U13_GGG(x1, x2, x3, x4)  =  U13_GGG(x4)
U14_GGG(x1, x2, x3)  =  U14_GGG(x3)
LOG2257_IN_GG(x1, x2)  =  LOG2257_IN_GG(x1, x2)
U59_GG(x1, x2, x3)  =  U59_GG(x3)
LOG2294_IN_GGG(x1, x2, x3)  =  LOG2294_IN_GGG(x1, x2, x3)
U16_GGG(x1, x2, x3, x4)  =  U16_GGG(x4)
U17_GGG(x1, x2, x3)  =  U17_GGG(x3)
LOG2307_IN_GG(x1, x2)  =  LOG2307_IN_GG(x1, x2)
U42_GG(x1, x2, x3)  =  U42_GG(x3)
LOG2344_IN_GGG(x1, x2, x3)  =  LOG2344_IN_GGG(x1, x2, x3)
U19_GGG(x1, x2, x3, x4)  =  U19_GGG(x4)
U20_GGG(x1, x2, x3)  =  U20_GGG(x3)
LOG2359_IN_GGG(x1, x2, x3)  =  LOG2359_IN_GGG(x1, x2, x3)
U25_GGG(x1, x2, x3, x4)  =  U25_GGG(x4)
LOG2395_IN_GGGG(x1, x2, x3, x4)  =  LOG2395_IN_GGGG(x1, x2, x3, x4)
U22_GGGG(x1, x2, x3, x4, x5)  =  U22_GGGG(x5)
U23_GGGG(x1, x2, x3, x4)  =  U23_GGGG(x4)
U26_GGG(x1, x2, x3)  =  U26_GGG(x3)
LOG2437_IN_GG(x1, x2)  =  LOG2437_IN_GG(x1, x2)
U38_GG(x1, x2, x3)  =  U38_GG(x3)
LOG2454_IN_GG(x1, x2)  =  LOG2454_IN_GG(x1, x2)
U27_GGG(x1, x2, x3)  =  U27_GGG(x3)
U28_GGG(x1, x2, x3)  =  U28_GGG(x3)
LOG2515_IN_GG(x1, x2)  =  LOG2515_IN_GG(x1, x2)
U39_GG(x1, x2, x3)  =  U39_GG(x3)
U29_GGG(x1, x2, x3)  =  U29_GGG(x3)
U30_GGG(x1, x2, x3)  =  U30_GGG(x3)
LOG2585_IN_GG(x1, x2)  =  LOG2585_IN_GG(x1, x2)
U40_GG(x1, x2, x3)  =  U40_GG(x3)
LOG2598_IN_GG(x1, x2)  =  LOG2598_IN_GG(x1, x2)
U31_GGG(x1, x2, x3)  =  U31_GGG(x3)
U32_GGG(x1, x2, x3)  =  U32_GGG(x3)
LOG2650_IN_GG(x1, x2)  =  LOG2650_IN_GG(x1, x2)
U41_GG(x1, x2, x3)  =  U41_GG(x3)
U33_GGG(x1, x2, x3)  =  U33_GGG(x3)
U34_GGG(x1, x2, x3)  =  U34_GGG(x3)
LOG2705_IN_GG(x1, x2)  =  LOG2705_IN_GG(x1, x2)
U35_GGG(x1, x2, x3)  =  U35_GGG(x3)
U36_GGG(x1, x2, x3)  =  U36_GGG(x3)
LOG2742_IN_GG(x1, x2)  =  LOG2742_IN_GG(x1, x2)
U37_GGG(x1, x2, x3)  =  U37_GGG(x3)
U24_GGGG(x1, x2, x3, x4)  =  U24_GGGG(x4)
U21_GGG(x1, x2, x3)  =  U21_GGG(x3)
U43_GG(x1, x2)  =  U43_GG(x2)
LOG2822_IN_GG(x1, x2)  =  LOG2822_IN_GG(x1, x2)
U144_GG(x1, x2, x3)  =  U144_GG(x3)
U44_GG(x1, x2)  =  U44_GG(x2)
U45_GG(x1, x2)  =  U45_GG(x2)
LOG2889_IN_GG(x1, x2)  =  LOG2889_IN_GG(x1, x2)
U145_GG(x1, x2, x3)  =  U145_GG(x3)
U46_GG(x1, x2)  =  U46_GG(x2)
U47_GG(x1, x2)  =  U47_GG(x2)
LOG2960_IN_GG(x1, x2)  =  LOG2960_IN_GG(x1, x2)
U146_GG(x1, x2, x3)  =  U146_GG(x3)
U48_GG(x1, x2)  =  U48_GG(x2)
U49_GG(x1, x2)  =  U49_GG(x2)
LOG21012_IN_GG(x1, x2)  =  LOG21012_IN_GG(x1, x2)
U147_GG(x1, x2, x3)  =  U147_GG(x3)
U50_GG(x1, x2)  =  U50_GG(x2)
U51_GG(x1, x2)  =  U51_GG(x2)
LOG21068_IN_GG(x1, x2)  =  LOG21068_IN_GG(x1, x2)
U52_GG(x1, x2)  =  U52_GG(x2)
U53_GG(x1, x2)  =  U53_GG(x2)
LOG21106_IN_GG(x1, x2)  =  LOG21106_IN_GG(x1, x2)
U54_GG(x1, x2)  =  U54_GG(x2)
U18_GGG(x1, x2, x3)  =  U18_GGG(x3)
U60_GG(x1, x2)  =  U60_GG(x2)
LOG21183_IN_G(x1)  =  LOG21183_IN_G(x1)
U55_G(x1, x2)  =  U55_G(x2)
U61_GG(x1, x2)  =  U61_GG(x2)
U62_GG(x1, x2)  =  U62_GG(x2)
LOG21249_IN_G(x1)  =  LOG21249_IN_G(x1)
U56_G(x1, x2)  =  U56_G(x2)
U63_GG(x1, x2)  =  U63_GG(x2)
U64_GG(x1, x2)  =  U64_GG(x2)
LOG21319_IN_G(x1)  =  LOG21319_IN_G(x1)
U57_G(x1, x2)  =  U57_G(x2)
U65_GG(x1, x2)  =  U65_GG(x2)
U66_GG(x1, x2)  =  U66_GG(x2)
LOG21370_IN_G(x1)  =  LOG21370_IN_G(x1)
U58_G(x1, x2)  =  U58_G(x2)
U67_GG(x1, x2)  =  U67_GG(x2)
U68_GG(x1, x2)  =  U68_GG(x2)
LOG21425_IN_G(x1)  =  LOG21425_IN_G(x1)
U69_GG(x1, x2)  =  U69_GG(x2)
U70_GG(x1, x2)  =  U70_GG(x2)
LOG21462_IN_G(x1)  =  LOG21462_IN_G(x1)
U71_GG(x1, x2)  =  U71_GG(x2)
U15_GGG(x1, x2, x3)  =  U15_GGG(x3)
U77_GG(x1, x2)  =  U77_GG(x2)
LOG21540_IN_G(x1)  =  LOG21540_IN_G(x1)
U72_G(x1, x2)  =  U72_G(x2)
U78_GG(x1, x2)  =  U78_GG(x2)
U79_GG(x1, x2)  =  U79_GG(x2)
LOG21606_IN_G(x1)  =  LOG21606_IN_G(x1)
U73_G(x1, x2)  =  U73_G(x2)
U80_GG(x1, x2)  =  U80_GG(x2)
U81_GG(x1, x2)  =  U81_GG(x2)
LOG21676_IN_G(x1)  =  LOG21676_IN_G(x1)
U74_G(x1, x2)  =  U74_G(x2)
U82_GG(x1, x2)  =  U82_GG(x2)
U83_GG(x1, x2)  =  U83_GG(x2)
LOG21727_IN_G(x1)  =  LOG21727_IN_G(x1)
U75_G(x1, x2)  =  U75_G(x2)
U84_GG(x1, x2)  =  U84_GG(x2)
U85_GG(x1, x2)  =  U85_GG(x2)
LOG21782_IN_G(x1)  =  LOG21782_IN_G(x1)
U86_GG(x1, x2)  =  U86_GG(x2)
U87_GG(x1, x2)  =  U87_GG(x2)
LOG21819_IN_G(x1)  =  LOG21819_IN_G(x1)
U88_GG(x1, x2)  =  U88_GG(x2)
U12_GGG(x1, x2, x3)  =  U12_GGG(x3)
U94_GG(x1, x2)  =  U94_GG(x2)
LOG21897_IN_G(x1)  =  LOG21897_IN_G(x1)
U89_G(x1, x2)  =  U89_G(x2)
U95_GG(x1, x2)  =  U95_GG(x2)
U96_GG(x1, x2)  =  U96_GG(x2)
LOG21963_IN_G(x1)  =  LOG21963_IN_G(x1)
U90_G(x1, x2)  =  U90_G(x2)
U97_GG(x1, x2)  =  U97_GG(x2)
U98_GG(x1, x2)  =  U98_GG(x2)
LOG22033_IN_G(x1)  =  LOG22033_IN_G(x1)
U91_G(x1, x2)  =  U91_G(x2)
U99_GG(x1, x2)  =  U99_GG(x2)
U100_GG(x1, x2)  =  U100_GG(x2)
LOG22084_IN_G(x1)  =  LOG22084_IN_G(x1)
U92_G(x1, x2)  =  U92_G(x2)
U101_GG(x1, x2)  =  U101_GG(x2)
U102_GG(x1, x2)  =  U102_GG(x2)
LOG22139_IN_G(x1)  =  LOG22139_IN_G(x1)
U103_GG(x1, x2)  =  U103_GG(x2)
U104_GG(x1, x2)  =  U104_GG(x2)
LOG22176_IN_G(x1)  =  LOG22176_IN_G(x1)
U105_GG(x1, x2)  =  U105_GG(x2)
U9_GGG(x1, x2, x3)  =  U9_GGG(x3)
U111_GG(x1, x2)  =  U111_GG(x2)
LOG22254_IN_G(x1)  =  LOG22254_IN_G(x1)
U106_G(x1, x2)  =  U106_G(x2)
U112_GG(x1, x2)  =  U112_GG(x2)
U113_GG(x1, x2)  =  U113_GG(x2)
LOG22320_IN_G(x1)  =  LOG22320_IN_G(x1)
U107_G(x1, x2)  =  U107_G(x2)
U114_GG(x1, x2)  =  U114_GG(x2)
U115_GG(x1, x2)  =  U115_GG(x2)
LOG22390_IN_G(x1)  =  LOG22390_IN_G(x1)
U108_G(x1, x2)  =  U108_G(x2)
U116_GG(x1, x2)  =  U116_GG(x2)
U117_GG(x1, x2)  =  U117_GG(x2)
LOG22441_IN_G(x1)  =  LOG22441_IN_G(x1)
U109_G(x1, x2)  =  U109_G(x2)
U118_GG(x1, x2)  =  U118_GG(x2)
U119_GG(x1, x2)  =  U119_GG(x2)
LOG22496_IN_G(x1)  =  LOG22496_IN_G(x1)
U120_GG(x1, x2)  =  U120_GG(x2)
U121_GG(x1, x2)  =  U121_GG(x2)
LOG22533_IN_G(x1)  =  LOG22533_IN_G(x1)
U122_GG(x1, x2)  =  U122_GG(x2)
U6_GGG(x1, x2, x3)  =  U6_GGG(x3)
U128_GG(x1, x2)  =  U128_GG(x2)
LOG22611_IN_G(x1)  =  LOG22611_IN_G(x1)
U123_G(x1, x2)  =  U123_G(x2)
U129_GG(x1, x2)  =  U129_GG(x2)
U130_GG(x1, x2)  =  U130_GG(x2)
LOG22677_IN_G(x1)  =  LOG22677_IN_G(x1)
U124_G(x1, x2)  =  U124_G(x2)
U131_GG(x1, x2)  =  U131_GG(x2)
U132_GG(x1, x2)  =  U132_GG(x2)
LOG22747_IN_G(x1)  =  LOG22747_IN_G(x1)
U125_G(x1, x2)  =  U125_G(x2)
U133_GG(x1, x2)  =  U133_GG(x2)
U134_GG(x1, x2)  =  U134_GG(x2)
LOG22798_IN_G(x1)  =  LOG22798_IN_G(x1)
U126_G(x1, x2)  =  U126_G(x2)
U135_GG(x1, x2)  =  U135_GG(x2)
U136_GG(x1, x2)  =  U136_GG(x2)
LOG22853_IN_G(x1)  =  LOG22853_IN_G(x1)
U137_GG(x1, x2)  =  U137_GG(x2)
U138_GG(x1, x2)  =  U138_GG(x2)
LOG22890_IN_G(x1)  =  LOG22890_IN_G(x1)
U139_GG(x1, x2)  =  U139_GG(x2)
U3_AGG(x1, x2, x3)  =  U3_AGG(x3)
U149_AG(x1, x2)  =  U149_AG(x2)
LOG22968_IN_G(x1)  =  LOG22968_IN_G(x1)
U140_G(x1, x2)  =  U140_G(x2)
U150_AG(x1, x2)  =  U150_AG(x2)
U151_AG(x1, x2)  =  U151_AG(x2)
LOG23034_IN_G(x1)  =  LOG23034_IN_G(x1)
U141_G(x1, x2)  =  U141_G(x2)
U152_AG(x1, x2)  =  U152_AG(x2)
U153_AG(x1, x2)  =  U153_AG(x2)
LOG23104_IN_G(x1)  =  LOG23104_IN_G(x1)
U142_G(x1, x2)  =  U142_G(x2)
U154_AG(x1, x2)  =  U154_AG(x2)
U155_AG(x1, x2)  =  U155_AG(x2)
LOG23155_IN_G(x1)  =  LOG23155_IN_G(x1)
U143_G(x1, x2)  =  U143_G(x2)
U156_AG(x1, x2)  =  U156_AG(x2)
U157_AG(x1, x2)  =  U157_AG(x2)
LOG23210_IN_G(x1)  =  LOG23210_IN_G(x1)
U158_AG(x1, x2)  =  U158_AG(x2)
U159_AG(x1, x2)  =  U159_AG(x2)
LOG23247_IN_G(x1)  =  LOG23247_IN_G(x1)
U160_AG(x1, x2)  =  U160_AG(x2)

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

(6) Obligation:

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

LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_AG(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → LOG244_IN_AGG(T109, s(s(s(s(s(s(s(0))))))), T108)
LOG244_IN_AGG(s(s(T131)), T129, T130) → U1_AGG(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
LOG244_IN_AGG(s(s(T131)), T129, T130) → LOG244_IN_AGG(T131, s(T129), T130)
LOG244_IN_AGG(0, s(T148), T149) → U2_AGG(T148, T149, log257_in_gg(T148, T149))
LOG244_IN_AGG(0, s(T148), T149) → LOG257_IN_GG(T148, T149)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_GG(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → LOG294_IN_GGG(T235, s(s(s(s(s(s(s(0))))))), T236)
LOG294_IN_GGG(s(s(T255)), T256, T257) → U4_GGG(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)
LOG294_IN_GGG(0, s(T274), T275) → U5_GGG(T274, T275, log2107_in_gg(T274, T275))
LOG294_IN_GGG(0, s(T274), T275) → LOG2107_IN_GG(T274, T275)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_GG(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → LOG2144_IN_GGG(T360, s(s(s(s(s(s(s(0))))))), T361)
LOG2144_IN_GGG(s(s(T380)), T381, T382) → U7_GGG(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)
LOG2144_IN_GGG(0, s(T399), T400) → U8_GGG(T399, T400, log2157_in_gg(T399, T400))
LOG2144_IN_GGG(0, s(T399), T400) → LOG2157_IN_GG(T399, T400)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_GG(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → LOG2194_IN_GGG(T485, s(s(s(s(s(s(s(0))))))), T486)
LOG2194_IN_GGG(s(s(T505)), T506, T507) → U10_GGG(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)
LOG2194_IN_GGG(0, s(T524), T525) → U11_GGG(T524, T525, log2207_in_gg(T524, T525))
LOG2194_IN_GGG(0, s(T524), T525) → LOG2207_IN_GG(T524, T525)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_GG(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → LOG2244_IN_GGG(T610, s(s(s(s(s(s(s(0))))))), T611)
LOG2244_IN_GGG(s(s(T630)), T631, T632) → U13_GGG(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)
LOG2244_IN_GGG(0, s(T649), T650) → U14_GGG(T649, T650, log2257_in_gg(T649, T650))
LOG2244_IN_GGG(0, s(T649), T650) → LOG2257_IN_GG(T649, T650)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_GG(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → LOG2294_IN_GGG(T735, s(s(s(s(s(s(s(0))))))), T736)
LOG2294_IN_GGG(s(s(T755)), T756, T757) → U16_GGG(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)
LOG2294_IN_GGG(0, s(T774), T775) → U17_GGG(T774, T775, log2307_in_gg(T774, T775))
LOG2294_IN_GGG(0, s(T774), T775) → LOG2307_IN_GG(T774, T775)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_GG(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → LOG2344_IN_GGG(T860, s(s(s(s(s(s(s(0))))))), T861)
LOG2344_IN_GGG(s(s(T880)), T881, T882) → U19_GGG(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)
LOG2344_IN_GGG(0, s(T899), T900) → U20_GGG(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
LOG2344_IN_GGG(0, s(T899), T900) → LOG2359_IN_GGG(T899, s(s(s(s(s(s(s(0))))))), T900)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_GGG(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → U22_GGGG(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → U23_GGGG(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_GGG(T1119, T1120, log2437_in_gg(T1119, T1120))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → LOG2437_IN_GG(T1119, T1120)
LOG2437_IN_GG(T1167, T1168) → U38_GG(T1167, T1168, log2454_in_gg(T1167, T1168))
LOG2437_IN_GG(T1167, T1168) → LOG2454_IN_GG(T1167, T1168)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_GGG(T1119, T1120, log2437_in_gg(T1119, T1120))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → LOG2437_IN_GG(T1119, T1120)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_GGG(T1222, T1223, log2515_in_gg(T1222, T1223))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → LOG2515_IN_GG(T1222, T1223)
LOG2515_IN_GG(T1270, T1271) → U39_GG(T1270, T1271, log2454_in_gg(T1270, T1271))
LOG2515_IN_GG(T1270, T1271) → LOG2454_IN_GG(T1270, T1271)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_GGG(T1222, T1223, log2515_in_gg(T1222, T1223))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → LOG2515_IN_GG(T1222, T1223)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_GGG(T1323, T1324, log2585_in_gg(T1323, T1324))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → LOG2585_IN_GG(T1323, T1324)
LOG2585_IN_GG(T1355, T1356) → U40_GG(T1355, T1356, log2598_in_gg(T1355, T1356))
LOG2585_IN_GG(T1355, T1356) → LOG2598_IN_GG(T1355, T1356)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_GGG(T1323, T1324, log2585_in_gg(T1323, T1324))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → LOG2585_IN_GG(T1323, T1324)
LOG2359_IN_GGG(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_GGG(T1394, T1395, log2650_in_gg(T1394, T1395))
LOG2359_IN_GGG(s(s(s(s(s(s(0)))))), T1394, T1395) → LOG2650_IN_GG(T1394, T1395)
LOG2650_IN_GG(T1426, T1427) → U41_GG(T1426, T1427, log2598_in_gg(T1426, T1427))
LOG2650_IN_GG(T1426, T1427) → LOG2598_IN_GG(T1426, T1427)
LOG2359_IN_GGG(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_GGG(T1394, T1395, log2650_in_gg(T1394, T1395))
LOG2359_IN_GGG(s(s(s(s(s(s(s(0))))))), T1394, T1395) → LOG2650_IN_GG(T1394, T1395)
LOG2359_IN_GGG(s(s(s(s(0)))), T1461, T1462) → U34_GGG(T1461, T1462, log2705_in_gg(T1461, T1462))
LOG2359_IN_GGG(s(s(s(s(0)))), T1461, T1462) → LOG2705_IN_GG(T1461, T1462)
LOG2359_IN_GGG(s(s(s(s(s(0))))), T1461, T1462) → U35_GGG(T1461, T1462, log2705_in_gg(T1461, T1462))
LOG2359_IN_GGG(s(s(s(s(s(0))))), T1461, T1462) → LOG2705_IN_GG(T1461, T1462)
LOG2359_IN_GGG(s(s(0)), T1490, T1491) → U36_GGG(T1490, T1491, log2742_in_gg(T1490, T1491))
LOG2359_IN_GGG(s(s(0)), T1490, T1491) → LOG2742_IN_GG(T1490, T1491)
LOG2359_IN_GGG(s(s(s(0))), T1490, T1491) → U37_GGG(T1490, T1491, log2742_in_gg(T1490, T1491))
LOG2359_IN_GGG(s(s(s(0))), T1490, T1491) → LOG2742_IN_GG(T1490, T1491)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → U24_GGGG(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2344_IN_GGG(s(0), s(T899), T900) → U21_GGG(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
LOG2344_IN_GGG(s(0), s(T899), T900) → LOG2359_IN_GGG(T899, s(s(s(s(s(s(s(0))))))), T900)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_GG(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → LOG2822_IN_GG(s(s(s(s(s(s(s(0))))))), T1530)
LOG2822_IN_GG(T1578, T1579) → U144_GG(T1578, T1579, log2705_in_gg(T1578, T1579))
LOG2822_IN_GG(T1578, T1579) → LOG2705_IN_GG(T1578, T1579)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_GG(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → LOG2822_IN_GG(s(s(s(s(s(s(s(0))))))), T1530)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_GG(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → LOG2889_IN_GG(s(s(s(s(s(s(s(0))))))), T1620)
LOG2889_IN_GG(T1668, T1669) → U145_GG(T1668, T1669, log2705_in_gg(T1668, T1669))
LOG2889_IN_GG(T1668, T1669) → LOG2705_IN_GG(T1668, T1669)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_GG(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → LOG2889_IN_GG(s(s(s(s(s(s(s(0))))))), T1620)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_GG(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1711) → LOG2960_IN_GG(s(s(s(s(s(s(s(0))))))), T1711)
LOG2960_IN_GG(T1743, T1744) → U146_GG(T1743, T1744, log2742_in_gg(T1743, T1744))
LOG2960_IN_GG(T1743, T1744) → LOG2742_IN_GG(T1743, T1744)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_GG(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → LOG2960_IN_GG(s(s(s(s(s(s(s(0))))))), T1711)
LOG2307_IN_GG(s(s(s(s(s(s(0)))))), T1769) → U49_GG(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
LOG2307_IN_GG(s(s(s(s(s(s(0)))))), T1769) → LOG21012_IN_GG(s(s(s(s(s(s(s(0))))))), T1769)
LOG21012_IN_GG(T1801, T1802) → U147_GG(T1801, T1802, log2742_in_gg(T1801, T1802))
LOG21012_IN_GG(T1801, T1802) → LOG2742_IN_GG(T1801, T1802)
LOG2307_IN_GG(s(s(s(s(s(s(s(0))))))), T1769) → U50_GG(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
LOG2307_IN_GG(s(s(s(s(s(s(s(0))))))), T1769) → LOG21012_IN_GG(s(s(s(s(s(s(s(0))))))), T1769)
LOG2307_IN_GG(s(s(s(s(0)))), T1826) → U51_GG(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
LOG2307_IN_GG(s(s(s(s(0)))), T1826) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1826)
LOG2307_IN_GG(s(s(s(s(s(0))))), T1826) → U52_GG(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
LOG2307_IN_GG(s(s(s(s(s(0))))), T1826) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1826)
LOG2307_IN_GG(s(s(0)), T1844) → U53_GG(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
LOG2307_IN_GG(s(s(0)), T1844) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1844)
LOG2307_IN_GG(s(s(s(0))), T1844) → U54_GG(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
LOG2307_IN_GG(s(s(s(0))), T1844) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1844)
LOG2294_IN_GGG(s(0), s(T774), T775) → U18_GGG(T774, T775, log2307_in_gg(T774, T775))
LOG2294_IN_GGG(s(0), s(T774), T775) → LOG2307_IN_GG(T774, T775)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_GG(T1876, log21183_in_g(T1876))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → LOG21183_IN_G(T1876)
LOG21183_IN_G(T1899) → U55_G(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
LOG21183_IN_G(T1899) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1899)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_GG(T1876, log21183_in_g(T1876))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → LOG21183_IN_G(T1876)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_GG(T1920, log21249_in_g(T1920))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → LOG21249_IN_G(T1920)
LOG21249_IN_G(T1943) → U56_G(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
LOG21249_IN_G(T1943) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1943)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_GG(T1920, log21249_in_g(T1920))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → LOG21249_IN_G(T1920)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_GG(T1964, log21319_in_g(T1964))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1964) → LOG21319_IN_G(T1964)
LOG21319_IN_G(T1979) → U57_G(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
LOG21319_IN_G(T1979) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1979)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_GG(T1964, log21319_in_g(T1964))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → LOG21319_IN_G(T1964)
LOG2257_IN_GG(s(s(s(s(s(s(0)))))), T1995) → U66_GG(T1995, log21370_in_g(T1995))
LOG2257_IN_GG(s(s(s(s(s(s(0)))))), T1995) → LOG21370_IN_G(T1995)
LOG21370_IN_G(T2010) → U58_G(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
LOG21370_IN_G(T2010) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T2010)
LOG2257_IN_GG(s(s(s(s(s(s(s(0))))))), T1995) → U67_GG(T1995, log21370_in_g(T1995))
LOG2257_IN_GG(s(s(s(s(s(s(s(0))))))), T1995) → LOG21370_IN_G(T1995)
LOG2257_IN_GG(s(s(s(s(0)))), T2024) → U68_GG(T2024, log21425_in_g(T2024))
LOG2257_IN_GG(s(s(s(s(0)))), T2024) → LOG21425_IN_G(T2024)
LOG2257_IN_GG(s(s(s(s(s(0))))), T2024) → U69_GG(T2024, log21425_in_g(T2024))
LOG2257_IN_GG(s(s(s(s(s(0))))), T2024) → LOG21425_IN_G(T2024)
LOG2257_IN_GG(s(s(0)), T2037) → U70_GG(T2037, log21462_in_g(T2037))
LOG2257_IN_GG(s(s(0)), T2037) → LOG21462_IN_G(T2037)
LOG2257_IN_GG(s(s(s(0))), T2037) → U71_GG(T2037, log21462_in_g(T2037))
LOG2257_IN_GG(s(s(s(0))), T2037) → LOG21462_IN_G(T2037)
LOG2244_IN_GGG(s(0), s(T649), T650) → U15_GGG(T649, T650, log2257_in_gg(T649, T650))
LOG2244_IN_GGG(s(0), s(T649), T650) → LOG2257_IN_GG(T649, T650)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_GG(T2064, log21540_in_g(T2064))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → LOG21540_IN_G(T2064)
LOG21540_IN_G(T2087) → U72_G(T2087, log21425_in_g(T2087))
LOG21540_IN_G(T2087) → LOG21425_IN_G(T2087)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_GG(T2064, log21540_in_g(T2064))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → LOG21540_IN_G(T2064)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_GG(T2108, log21606_in_g(T2108))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → LOG21606_IN_G(T2108)
LOG21606_IN_G(T2131) → U73_G(T2131, log21425_in_g(T2131))
LOG21606_IN_G(T2131) → LOG21425_IN_G(T2131)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_GG(T2108, log21606_in_g(T2108))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → LOG21606_IN_G(T2108)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_GG(T2152, log21676_in_g(T2152))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2152) → LOG21676_IN_G(T2152)
LOG21676_IN_G(T2167) → U74_G(T2167, log21462_in_g(T2167))
LOG21676_IN_G(T2167) → LOG21462_IN_G(T2167)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_GG(T2152, log21676_in_g(T2152))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → LOG21676_IN_G(T2152)
LOG2207_IN_GG(s(s(s(s(s(s(0)))))), T2183) → U83_GG(T2183, log21727_in_g(T2183))
LOG2207_IN_GG(s(s(s(s(s(s(0)))))), T2183) → LOG21727_IN_G(T2183)
LOG21727_IN_G(T2198) → U75_G(T2198, log21462_in_g(T2198))
LOG21727_IN_G(T2198) → LOG21462_IN_G(T2198)
LOG2207_IN_GG(s(s(s(s(s(s(s(0))))))), T2183) → U84_GG(T2183, log21727_in_g(T2183))
LOG2207_IN_GG(s(s(s(s(s(s(s(0))))))), T2183) → LOG21727_IN_G(T2183)
LOG2207_IN_GG(s(s(s(s(0)))), T2212) → U85_GG(T2212, log21782_in_g(T2212))
LOG2207_IN_GG(s(s(s(s(0)))), T2212) → LOG21782_IN_G(T2212)
LOG2207_IN_GG(s(s(s(s(s(0))))), T2212) → U86_GG(T2212, log21782_in_g(T2212))
LOG2207_IN_GG(s(s(s(s(s(0))))), T2212) → LOG21782_IN_G(T2212)
LOG2207_IN_GG(s(s(0)), T2225) → U87_GG(T2225, log21819_in_g(T2225))
LOG2207_IN_GG(s(s(0)), T2225) → LOG21819_IN_G(T2225)
LOG2207_IN_GG(s(s(s(0))), T2225) → U88_GG(T2225, log21819_in_g(T2225))
LOG2207_IN_GG(s(s(s(0))), T2225) → LOG21819_IN_G(T2225)
LOG2194_IN_GGG(s(0), s(T524), T525) → U12_GGG(T524, T525, log2207_in_gg(T524, T525))
LOG2194_IN_GGG(s(0), s(T524), T525) → LOG2207_IN_GG(T524, T525)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_GG(T2252, log21897_in_g(T2252))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → LOG21897_IN_G(T2252)
LOG21897_IN_G(T2275) → U89_G(T2275, log21782_in_g(T2275))
LOG21897_IN_G(T2275) → LOG21782_IN_G(T2275)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_GG(T2252, log21897_in_g(T2252))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → LOG21897_IN_G(T2252)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_GG(T2296, log21963_in_g(T2296))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → LOG21963_IN_G(T2296)
LOG21963_IN_G(T2319) → U90_G(T2319, log21782_in_g(T2319))
LOG21963_IN_G(T2319) → LOG21782_IN_G(T2319)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_GG(T2296, log21963_in_g(T2296))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → LOG21963_IN_G(T2296)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_GG(T2340, log22033_in_g(T2340))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2340) → LOG22033_IN_G(T2340)
LOG22033_IN_G(T2355) → U91_G(T2355, log21819_in_g(T2355))
LOG22033_IN_G(T2355) → LOG21819_IN_G(T2355)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_GG(T2340, log22033_in_g(T2340))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → LOG22033_IN_G(T2340)
LOG2157_IN_GG(s(s(s(s(s(s(0)))))), T2371) → U100_GG(T2371, log22084_in_g(T2371))
LOG2157_IN_GG(s(s(s(s(s(s(0)))))), T2371) → LOG22084_IN_G(T2371)
LOG22084_IN_G(T2386) → U92_G(T2386, log21819_in_g(T2386))
LOG22084_IN_G(T2386) → LOG21819_IN_G(T2386)
LOG2157_IN_GG(s(s(s(s(s(s(s(0))))))), T2371) → U101_GG(T2371, log22084_in_g(T2371))
LOG2157_IN_GG(s(s(s(s(s(s(s(0))))))), T2371) → LOG22084_IN_G(T2371)
LOG2157_IN_GG(s(s(s(s(0)))), T2400) → U102_GG(T2400, log22139_in_g(T2400))
LOG2157_IN_GG(s(s(s(s(0)))), T2400) → LOG22139_IN_G(T2400)
LOG2157_IN_GG(s(s(s(s(s(0))))), T2400) → U103_GG(T2400, log22139_in_g(T2400))
LOG2157_IN_GG(s(s(s(s(s(0))))), T2400) → LOG22139_IN_G(T2400)
LOG2157_IN_GG(s(s(0)), T2413) → U104_GG(T2413, log22176_in_g(T2413))
LOG2157_IN_GG(s(s(0)), T2413) → LOG22176_IN_G(T2413)
LOG2157_IN_GG(s(s(s(0))), T2413) → U105_GG(T2413, log22176_in_g(T2413))
LOG2157_IN_GG(s(s(s(0))), T2413) → LOG22176_IN_G(T2413)
LOG2144_IN_GGG(s(0), s(T399), T400) → U9_GGG(T399, T400, log2157_in_gg(T399, T400))
LOG2144_IN_GGG(s(0), s(T399), T400) → LOG2157_IN_GG(T399, T400)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_GG(T2440, log22254_in_g(T2440))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → LOG22254_IN_G(T2440)
LOG22254_IN_G(T2463) → U106_G(T2463, log22139_in_g(T2463))
LOG22254_IN_G(T2463) → LOG22139_IN_G(T2463)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_GG(T2440, log22254_in_g(T2440))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → LOG22254_IN_G(T2440)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_GG(T2484, log22320_in_g(T2484))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → LOG22320_IN_G(T2484)
LOG22320_IN_G(T2507) → U107_G(T2507, log22139_in_g(T2507))
LOG22320_IN_G(T2507) → LOG22139_IN_G(T2507)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_GG(T2484, log22320_in_g(T2484))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → LOG22320_IN_G(T2484)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_GG(T2528, log22390_in_g(T2528))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2528) → LOG22390_IN_G(T2528)
LOG22390_IN_G(T2543) → U108_G(T2543, log22176_in_g(T2543))
LOG22390_IN_G(T2543) → LOG22176_IN_G(T2543)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_GG(T2528, log22390_in_g(T2528))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → LOG22390_IN_G(T2528)
LOG2107_IN_GG(s(s(s(s(s(s(0)))))), T2559) → U117_GG(T2559, log22441_in_g(T2559))
LOG2107_IN_GG(s(s(s(s(s(s(0)))))), T2559) → LOG22441_IN_G(T2559)
LOG22441_IN_G(T2574) → U109_G(T2574, log22176_in_g(T2574))
LOG22441_IN_G(T2574) → LOG22176_IN_G(T2574)
LOG2107_IN_GG(s(s(s(s(s(s(s(0))))))), T2559) → U118_GG(T2559, log22441_in_g(T2559))
LOG2107_IN_GG(s(s(s(s(s(s(s(0))))))), T2559) → LOG22441_IN_G(T2559)
LOG2107_IN_GG(s(s(s(s(0)))), T2588) → U119_GG(T2588, log22496_in_g(T2588))
LOG2107_IN_GG(s(s(s(s(0)))), T2588) → LOG22496_IN_G(T2588)
LOG2107_IN_GG(s(s(s(s(s(0))))), T2588) → U120_GG(T2588, log22496_in_g(T2588))
LOG2107_IN_GG(s(s(s(s(s(0))))), T2588) → LOG22496_IN_G(T2588)
LOG2107_IN_GG(s(s(0)), T2601) → U121_GG(T2601, log22533_in_g(T2601))
LOG2107_IN_GG(s(s(0)), T2601) → LOG22533_IN_G(T2601)
LOG2107_IN_GG(s(s(s(0))), T2601) → U122_GG(T2601, log22533_in_g(T2601))
LOG2107_IN_GG(s(s(s(0))), T2601) → LOG22533_IN_G(T2601)
LOG294_IN_GGG(s(0), s(T274), T275) → U6_GGG(T274, T275, log2107_in_gg(T274, T275))
LOG294_IN_GGG(s(0), s(T274), T275) → LOG2107_IN_GG(T274, T275)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_GG(T2628, log22611_in_g(T2628))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → LOG22611_IN_G(T2628)
LOG22611_IN_G(T2651) → U123_G(T2651, log22496_in_g(T2651))
LOG22611_IN_G(T2651) → LOG22496_IN_G(T2651)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_GG(T2628, log22611_in_g(T2628))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → LOG22611_IN_G(T2628)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_GG(T2672, log22677_in_g(T2672))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → LOG22677_IN_G(T2672)
LOG22677_IN_G(T2695) → U124_G(T2695, log22496_in_g(T2695))
LOG22677_IN_G(T2695) → LOG22496_IN_G(T2695)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_GG(T2672, log22677_in_g(T2672))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → LOG22677_IN_G(T2672)
LOG257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_GG(T2716, log22747_in_g(T2716))
LOG257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2716) → LOG22747_IN_G(T2716)
LOG22747_IN_G(T2731) → U125_G(T2731, log22533_in_g(T2731))
LOG22747_IN_G(T2731) → LOG22533_IN_G(T2731)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_GG(T2716, log22747_in_g(T2716))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → LOG22747_IN_G(T2716)
LOG257_IN_GG(s(s(s(s(s(s(0)))))), T2747) → U134_GG(T2747, log22798_in_g(T2747))
LOG257_IN_GG(s(s(s(s(s(s(0)))))), T2747) → LOG22798_IN_G(T2747)
LOG22798_IN_G(T2762) → U126_G(T2762, log22533_in_g(T2762))
LOG22798_IN_G(T2762) → LOG22533_IN_G(T2762)
LOG257_IN_GG(s(s(s(s(s(s(s(0))))))), T2747) → U135_GG(T2747, log22798_in_g(T2747))
LOG257_IN_GG(s(s(s(s(s(s(s(0))))))), T2747) → LOG22798_IN_G(T2747)
LOG257_IN_GG(s(s(s(s(0)))), T2776) → U136_GG(T2776, log22853_in_g(T2776))
LOG257_IN_GG(s(s(s(s(0)))), T2776) → LOG22853_IN_G(T2776)
LOG257_IN_GG(s(s(s(s(s(0))))), T2776) → U137_GG(T2776, log22853_in_g(T2776))
LOG257_IN_GG(s(s(s(s(s(0))))), T2776) → LOG22853_IN_G(T2776)
LOG257_IN_GG(s(s(0)), T2789) → U138_GG(T2789, log22890_in_g(T2789))
LOG257_IN_GG(s(s(0)), T2789) → LOG22890_IN_G(T2789)
LOG257_IN_GG(s(s(s(0))), T2789) → U139_GG(T2789, log22890_in_g(T2789))
LOG257_IN_GG(s(s(s(0))), T2789) → LOG22890_IN_G(T2789)
LOG244_IN_AGG(s(0), s(T148), T149) → U3_AGG(T148, T149, log257_in_gg(T148, T149))
LOG244_IN_AGG(s(0), s(T148), T149) → LOG257_IN_GG(T148, T149)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_AG(T2819, log22968_in_g(T2819))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → LOG22968_IN_G(T2819)
LOG22968_IN_G(T2843) → U140_G(T2843, log22853_in_g(T2843))
LOG22968_IN_G(T2843) → LOG22853_IN_G(T2843)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_AG(T2819, log22968_in_g(T2819))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → LOG22968_IN_G(T2819)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_AG(T2867, log23034_in_g(T2867))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → LOG23034_IN_G(T2867)
LOG23034_IN_G(T2891) → U141_G(T2891, log22853_in_g(T2891))
LOG23034_IN_G(T2891) → LOG22853_IN_G(T2891)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_AG(T2867, log23034_in_g(T2867))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → LOG23034_IN_G(T2867)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_AG(T2915, log23104_in_g(T2915))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → LOG23104_IN_G(T2915)
LOG23104_IN_G(T2931) → U142_G(T2931, log22890_in_g(T2931))
LOG23104_IN_G(T2931) → LOG22890_IN_G(T2931)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_AG(T2915, log23104_in_g(T2915))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → LOG23104_IN_G(T2915)
LOG21_IN_AG(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_AG(T2950, log23155_in_g(T2950))
LOG21_IN_AG(s(s(s(s(s(s(s(s(0)))))))), T2950) → LOG23155_IN_G(T2950)
LOG23155_IN_G(T2966) → U143_G(T2966, log22890_in_g(T2966))
LOG23155_IN_G(T2966) → LOG22890_IN_G(T2966)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_AG(T2950, log23155_in_g(T2950))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → LOG23155_IN_G(T2950)
LOG21_IN_AG(s(s(s(s(s(s(0)))))), T2983) → U157_AG(T2983, log23210_in_g(T2983))
LOG21_IN_AG(s(s(s(s(s(s(0)))))), T2983) → LOG23210_IN_G(T2983)
LOG21_IN_AG(s(s(s(s(s(s(s(0))))))), T2983) → U158_AG(T2983, log23210_in_g(T2983))
LOG21_IN_AG(s(s(s(s(s(s(s(0))))))), T2983) → LOG23210_IN_G(T2983)
LOG21_IN_AG(s(s(s(s(0)))), T3000) → U159_AG(T3000, log23247_in_g(T3000))
LOG21_IN_AG(s(s(s(s(0)))), T3000) → LOG23247_IN_G(T3000)
LOG21_IN_AG(s(s(s(s(s(0))))), T3000) → U160_AG(T3000, log23247_in_g(T3000))
LOG21_IN_AG(s(s(s(s(s(0))))), T3000) → LOG23247_IN_G(T3000)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG21_IN_AG(x1, x2)  =  LOG21_IN_AG(x2)
U148_AG(x1, x2, x3)  =  U148_AG(x3)
LOG244_IN_AGG(x1, x2, x3)  =  LOG244_IN_AGG(x2, x3)
U1_AGG(x1, x2, x3, x4)  =  U1_AGG(x4)
U2_AGG(x1, x2, x3)  =  U2_AGG(x3)
LOG257_IN_GG(x1, x2)  =  LOG257_IN_GG(x1, x2)
U127_GG(x1, x2, x3)  =  U127_GG(x3)
LOG294_IN_GGG(x1, x2, x3)  =  LOG294_IN_GGG(x1, x2, x3)
U4_GGG(x1, x2, x3, x4)  =  U4_GGG(x4)
U5_GGG(x1, x2, x3)  =  U5_GGG(x3)
LOG2107_IN_GG(x1, x2)  =  LOG2107_IN_GG(x1, x2)
U110_GG(x1, x2, x3)  =  U110_GG(x3)
LOG2144_IN_GGG(x1, x2, x3)  =  LOG2144_IN_GGG(x1, x2, x3)
U7_GGG(x1, x2, x3, x4)  =  U7_GGG(x4)
U8_GGG(x1, x2, x3)  =  U8_GGG(x3)
LOG2157_IN_GG(x1, x2)  =  LOG2157_IN_GG(x1, x2)
U93_GG(x1, x2, x3)  =  U93_GG(x3)
LOG2194_IN_GGG(x1, x2, x3)  =  LOG2194_IN_GGG(x1, x2, x3)
U10_GGG(x1, x2, x3, x4)  =  U10_GGG(x4)
U11_GGG(x1, x2, x3)  =  U11_GGG(x3)
LOG2207_IN_GG(x1, x2)  =  LOG2207_IN_GG(x1, x2)
U76_GG(x1, x2, x3)  =  U76_GG(x3)
LOG2244_IN_GGG(x1, x2, x3)  =  LOG2244_IN_GGG(x1, x2, x3)
U13_GGG(x1, x2, x3, x4)  =  U13_GGG(x4)
U14_GGG(x1, x2, x3)  =  U14_GGG(x3)
LOG2257_IN_GG(x1, x2)  =  LOG2257_IN_GG(x1, x2)
U59_GG(x1, x2, x3)  =  U59_GG(x3)
LOG2294_IN_GGG(x1, x2, x3)  =  LOG2294_IN_GGG(x1, x2, x3)
U16_GGG(x1, x2, x3, x4)  =  U16_GGG(x4)
U17_GGG(x1, x2, x3)  =  U17_GGG(x3)
LOG2307_IN_GG(x1, x2)  =  LOG2307_IN_GG(x1, x2)
U42_GG(x1, x2, x3)  =  U42_GG(x3)
LOG2344_IN_GGG(x1, x2, x3)  =  LOG2344_IN_GGG(x1, x2, x3)
U19_GGG(x1, x2, x3, x4)  =  U19_GGG(x4)
U20_GGG(x1, x2, x3)  =  U20_GGG(x3)
LOG2359_IN_GGG(x1, x2, x3)  =  LOG2359_IN_GGG(x1, x2, x3)
U25_GGG(x1, x2, x3, x4)  =  U25_GGG(x4)
LOG2395_IN_GGGG(x1, x2, x3, x4)  =  LOG2395_IN_GGGG(x1, x2, x3, x4)
U22_GGGG(x1, x2, x3, x4, x5)  =  U22_GGGG(x5)
U23_GGGG(x1, x2, x3, x4)  =  U23_GGGG(x4)
U26_GGG(x1, x2, x3)  =  U26_GGG(x3)
LOG2437_IN_GG(x1, x2)  =  LOG2437_IN_GG(x1, x2)
U38_GG(x1, x2, x3)  =  U38_GG(x3)
LOG2454_IN_GG(x1, x2)  =  LOG2454_IN_GG(x1, x2)
U27_GGG(x1, x2, x3)  =  U27_GGG(x3)
U28_GGG(x1, x2, x3)  =  U28_GGG(x3)
LOG2515_IN_GG(x1, x2)  =  LOG2515_IN_GG(x1, x2)
U39_GG(x1, x2, x3)  =  U39_GG(x3)
U29_GGG(x1, x2, x3)  =  U29_GGG(x3)
U30_GGG(x1, x2, x3)  =  U30_GGG(x3)
LOG2585_IN_GG(x1, x2)  =  LOG2585_IN_GG(x1, x2)
U40_GG(x1, x2, x3)  =  U40_GG(x3)
LOG2598_IN_GG(x1, x2)  =  LOG2598_IN_GG(x1, x2)
U31_GGG(x1, x2, x3)  =  U31_GGG(x3)
U32_GGG(x1, x2, x3)  =  U32_GGG(x3)
LOG2650_IN_GG(x1, x2)  =  LOG2650_IN_GG(x1, x2)
U41_GG(x1, x2, x3)  =  U41_GG(x3)
U33_GGG(x1, x2, x3)  =  U33_GGG(x3)
U34_GGG(x1, x2, x3)  =  U34_GGG(x3)
LOG2705_IN_GG(x1, x2)  =  LOG2705_IN_GG(x1, x2)
U35_GGG(x1, x2, x3)  =  U35_GGG(x3)
U36_GGG(x1, x2, x3)  =  U36_GGG(x3)
LOG2742_IN_GG(x1, x2)  =  LOG2742_IN_GG(x1, x2)
U37_GGG(x1, x2, x3)  =  U37_GGG(x3)
U24_GGGG(x1, x2, x3, x4)  =  U24_GGGG(x4)
U21_GGG(x1, x2, x3)  =  U21_GGG(x3)
U43_GG(x1, x2)  =  U43_GG(x2)
LOG2822_IN_GG(x1, x2)  =  LOG2822_IN_GG(x1, x2)
U144_GG(x1, x2, x3)  =  U144_GG(x3)
U44_GG(x1, x2)  =  U44_GG(x2)
U45_GG(x1, x2)  =  U45_GG(x2)
LOG2889_IN_GG(x1, x2)  =  LOG2889_IN_GG(x1, x2)
U145_GG(x1, x2, x3)  =  U145_GG(x3)
U46_GG(x1, x2)  =  U46_GG(x2)
U47_GG(x1, x2)  =  U47_GG(x2)
LOG2960_IN_GG(x1, x2)  =  LOG2960_IN_GG(x1, x2)
U146_GG(x1, x2, x3)  =  U146_GG(x3)
U48_GG(x1, x2)  =  U48_GG(x2)
U49_GG(x1, x2)  =  U49_GG(x2)
LOG21012_IN_GG(x1, x2)  =  LOG21012_IN_GG(x1, x2)
U147_GG(x1, x2, x3)  =  U147_GG(x3)
U50_GG(x1, x2)  =  U50_GG(x2)
U51_GG(x1, x2)  =  U51_GG(x2)
LOG21068_IN_GG(x1, x2)  =  LOG21068_IN_GG(x1, x2)
U52_GG(x1, x2)  =  U52_GG(x2)
U53_GG(x1, x2)  =  U53_GG(x2)
LOG21106_IN_GG(x1, x2)  =  LOG21106_IN_GG(x1, x2)
U54_GG(x1, x2)  =  U54_GG(x2)
U18_GGG(x1, x2, x3)  =  U18_GGG(x3)
U60_GG(x1, x2)  =  U60_GG(x2)
LOG21183_IN_G(x1)  =  LOG21183_IN_G(x1)
U55_G(x1, x2)  =  U55_G(x2)
U61_GG(x1, x2)  =  U61_GG(x2)
U62_GG(x1, x2)  =  U62_GG(x2)
LOG21249_IN_G(x1)  =  LOG21249_IN_G(x1)
U56_G(x1, x2)  =  U56_G(x2)
U63_GG(x1, x2)  =  U63_GG(x2)
U64_GG(x1, x2)  =  U64_GG(x2)
LOG21319_IN_G(x1)  =  LOG21319_IN_G(x1)
U57_G(x1, x2)  =  U57_G(x2)
U65_GG(x1, x2)  =  U65_GG(x2)
U66_GG(x1, x2)  =  U66_GG(x2)
LOG21370_IN_G(x1)  =  LOG21370_IN_G(x1)
U58_G(x1, x2)  =  U58_G(x2)
U67_GG(x1, x2)  =  U67_GG(x2)
U68_GG(x1, x2)  =  U68_GG(x2)
LOG21425_IN_G(x1)  =  LOG21425_IN_G(x1)
U69_GG(x1, x2)  =  U69_GG(x2)
U70_GG(x1, x2)  =  U70_GG(x2)
LOG21462_IN_G(x1)  =  LOG21462_IN_G(x1)
U71_GG(x1, x2)  =  U71_GG(x2)
U15_GGG(x1, x2, x3)  =  U15_GGG(x3)
U77_GG(x1, x2)  =  U77_GG(x2)
LOG21540_IN_G(x1)  =  LOG21540_IN_G(x1)
U72_G(x1, x2)  =  U72_G(x2)
U78_GG(x1, x2)  =  U78_GG(x2)
U79_GG(x1, x2)  =  U79_GG(x2)
LOG21606_IN_G(x1)  =  LOG21606_IN_G(x1)
U73_G(x1, x2)  =  U73_G(x2)
U80_GG(x1, x2)  =  U80_GG(x2)
U81_GG(x1, x2)  =  U81_GG(x2)
LOG21676_IN_G(x1)  =  LOG21676_IN_G(x1)
U74_G(x1, x2)  =  U74_G(x2)
U82_GG(x1, x2)  =  U82_GG(x2)
U83_GG(x1, x2)  =  U83_GG(x2)
LOG21727_IN_G(x1)  =  LOG21727_IN_G(x1)
U75_G(x1, x2)  =  U75_G(x2)
U84_GG(x1, x2)  =  U84_GG(x2)
U85_GG(x1, x2)  =  U85_GG(x2)
LOG21782_IN_G(x1)  =  LOG21782_IN_G(x1)
U86_GG(x1, x2)  =  U86_GG(x2)
U87_GG(x1, x2)  =  U87_GG(x2)
LOG21819_IN_G(x1)  =  LOG21819_IN_G(x1)
U88_GG(x1, x2)  =  U88_GG(x2)
U12_GGG(x1, x2, x3)  =  U12_GGG(x3)
U94_GG(x1, x2)  =  U94_GG(x2)
LOG21897_IN_G(x1)  =  LOG21897_IN_G(x1)
U89_G(x1, x2)  =  U89_G(x2)
U95_GG(x1, x2)  =  U95_GG(x2)
U96_GG(x1, x2)  =  U96_GG(x2)
LOG21963_IN_G(x1)  =  LOG21963_IN_G(x1)
U90_G(x1, x2)  =  U90_G(x2)
U97_GG(x1, x2)  =  U97_GG(x2)
U98_GG(x1, x2)  =  U98_GG(x2)
LOG22033_IN_G(x1)  =  LOG22033_IN_G(x1)
U91_G(x1, x2)  =  U91_G(x2)
U99_GG(x1, x2)  =  U99_GG(x2)
U100_GG(x1, x2)  =  U100_GG(x2)
LOG22084_IN_G(x1)  =  LOG22084_IN_G(x1)
U92_G(x1, x2)  =  U92_G(x2)
U101_GG(x1, x2)  =  U101_GG(x2)
U102_GG(x1, x2)  =  U102_GG(x2)
LOG22139_IN_G(x1)  =  LOG22139_IN_G(x1)
U103_GG(x1, x2)  =  U103_GG(x2)
U104_GG(x1, x2)  =  U104_GG(x2)
LOG22176_IN_G(x1)  =  LOG22176_IN_G(x1)
U105_GG(x1, x2)  =  U105_GG(x2)
U9_GGG(x1, x2, x3)  =  U9_GGG(x3)
U111_GG(x1, x2)  =  U111_GG(x2)
LOG22254_IN_G(x1)  =  LOG22254_IN_G(x1)
U106_G(x1, x2)  =  U106_G(x2)
U112_GG(x1, x2)  =  U112_GG(x2)
U113_GG(x1, x2)  =  U113_GG(x2)
LOG22320_IN_G(x1)  =  LOG22320_IN_G(x1)
U107_G(x1, x2)  =  U107_G(x2)
U114_GG(x1, x2)  =  U114_GG(x2)
U115_GG(x1, x2)  =  U115_GG(x2)
LOG22390_IN_G(x1)  =  LOG22390_IN_G(x1)
U108_G(x1, x2)  =  U108_G(x2)
U116_GG(x1, x2)  =  U116_GG(x2)
U117_GG(x1, x2)  =  U117_GG(x2)
LOG22441_IN_G(x1)  =  LOG22441_IN_G(x1)
U109_G(x1, x2)  =  U109_G(x2)
U118_GG(x1, x2)  =  U118_GG(x2)
U119_GG(x1, x2)  =  U119_GG(x2)
LOG22496_IN_G(x1)  =  LOG22496_IN_G(x1)
U120_GG(x1, x2)  =  U120_GG(x2)
U121_GG(x1, x2)  =  U121_GG(x2)
LOG22533_IN_G(x1)  =  LOG22533_IN_G(x1)
U122_GG(x1, x2)  =  U122_GG(x2)
U6_GGG(x1, x2, x3)  =  U6_GGG(x3)
U128_GG(x1, x2)  =  U128_GG(x2)
LOG22611_IN_G(x1)  =  LOG22611_IN_G(x1)
U123_G(x1, x2)  =  U123_G(x2)
U129_GG(x1, x2)  =  U129_GG(x2)
U130_GG(x1, x2)  =  U130_GG(x2)
LOG22677_IN_G(x1)  =  LOG22677_IN_G(x1)
U124_G(x1, x2)  =  U124_G(x2)
U131_GG(x1, x2)  =  U131_GG(x2)
U132_GG(x1, x2)  =  U132_GG(x2)
LOG22747_IN_G(x1)  =  LOG22747_IN_G(x1)
U125_G(x1, x2)  =  U125_G(x2)
U133_GG(x1, x2)  =  U133_GG(x2)
U134_GG(x1, x2)  =  U134_GG(x2)
LOG22798_IN_G(x1)  =  LOG22798_IN_G(x1)
U126_G(x1, x2)  =  U126_G(x2)
U135_GG(x1, x2)  =  U135_GG(x2)
U136_GG(x1, x2)  =  U136_GG(x2)
LOG22853_IN_G(x1)  =  LOG22853_IN_G(x1)
U137_GG(x1, x2)  =  U137_GG(x2)
U138_GG(x1, x2)  =  U138_GG(x2)
LOG22890_IN_G(x1)  =  LOG22890_IN_G(x1)
U139_GG(x1, x2)  =  U139_GG(x2)
U3_AGG(x1, x2, x3)  =  U3_AGG(x3)
U149_AG(x1, x2)  =  U149_AG(x2)
LOG22968_IN_G(x1)  =  LOG22968_IN_G(x1)
U140_G(x1, x2)  =  U140_G(x2)
U150_AG(x1, x2)  =  U150_AG(x2)
U151_AG(x1, x2)  =  U151_AG(x2)
LOG23034_IN_G(x1)  =  LOG23034_IN_G(x1)
U141_G(x1, x2)  =  U141_G(x2)
U152_AG(x1, x2)  =  U152_AG(x2)
U153_AG(x1, x2)  =  U153_AG(x2)
LOG23104_IN_G(x1)  =  LOG23104_IN_G(x1)
U142_G(x1, x2)  =  U142_G(x2)
U154_AG(x1, x2)  =  U154_AG(x2)
U155_AG(x1, x2)  =  U155_AG(x2)
LOG23155_IN_G(x1)  =  LOG23155_IN_G(x1)
U143_G(x1, x2)  =  U143_G(x2)
U156_AG(x1, x2)  =  U156_AG(x2)
U157_AG(x1, x2)  =  U157_AG(x2)
LOG23210_IN_G(x1)  =  LOG23210_IN_G(x1)
U158_AG(x1, x2)  =  U158_AG(x2)
U159_AG(x1, x2)  =  U159_AG(x2)
LOG23247_IN_G(x1)  =  LOG23247_IN_G(x1)
U160_AG(x1, x2)  =  U160_AG(x2)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

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

(8) Complex Obligation (AND)

(9) Obligation:

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

LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG2359_IN_GGG(x1, x2, x3)  =  LOG2359_IN_GGG(x1, x2, x3)
LOG2395_IN_GGGG(x1, x2, x3, x4)  =  LOG2395_IN_GGGG(x1, x2, x3, x4)

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

(10) UsableRulesProof (EQUIVALENT transformation)

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

(11) Obligation:

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

LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)

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

(12) PiDPToQDPProof (EQUIVALENT transformation)

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

(13) Obligation:

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

LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)

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

(14) 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:

LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)


Used ordering: Polynomial interpretation [POLO]:

POL(0) = 0   
POL(LOG2359_IN_GGG(x1, x2, x3)) = x1 + x2 + x3   
POL(LOG2395_IN_GGGG(x1, x2, x3, x4)) = 1 + x1 + x2 + x3 + x4   
POL(s(x1)) = 1 + x1   

(15) Obligation:

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

(16) PisEmptyProof (EQUIVALENT transformation)

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

(17) YES

(18) Obligation:

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

LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG2344_IN_GGG(x1, x2, x3)  =  LOG2344_IN_GGG(x1, x2, x3)

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

(19) UsableRulesProof (EQUIVALENT transformation)

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

(20) Obligation:

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

LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)

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

(21) PiDPToQDPProof (EQUIVALENT transformation)

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

(22) Obligation:

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

LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)

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

(23) 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:

  • LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)
    The graph contains the following edges 1 > 1, 3 >= 3

(24) YES

(25) Obligation:

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

LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG2294_IN_GGG(x1, x2, x3)  =  LOG2294_IN_GGG(x1, x2, x3)

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

(26) UsableRulesProof (EQUIVALENT transformation)

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

(27) Obligation:

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

LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)

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

(28) PiDPToQDPProof (EQUIVALENT transformation)

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

(29) Obligation:

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

LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)

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

(30) 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:

  • LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)
    The graph contains the following edges 1 > 1, 3 >= 3

(31) YES

(32) Obligation:

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

LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG2244_IN_GGG(x1, x2, x3)  =  LOG2244_IN_GGG(x1, x2, x3)

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

(33) UsableRulesProof (EQUIVALENT transformation)

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

(34) Obligation:

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

LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)

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

(35) PiDPToQDPProof (EQUIVALENT transformation)

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

(36) Obligation:

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

LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)

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

(37) 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:

  • LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)
    The graph contains the following edges 1 > 1, 3 >= 3

(38) YES

(39) Obligation:

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

LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG2194_IN_GGG(x1, x2, x3)  =  LOG2194_IN_GGG(x1, x2, x3)

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

(40) UsableRulesProof (EQUIVALENT transformation)

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

(41) Obligation:

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

LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)

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

(42) PiDPToQDPProof (EQUIVALENT transformation)

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

(43) Obligation:

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

LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)

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

(44) 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:

  • LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)
    The graph contains the following edges 1 > 1, 3 >= 3

(45) YES

(46) Obligation:

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

LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG2144_IN_GGG(x1, x2, x3)  =  LOG2144_IN_GGG(x1, x2, x3)

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

(47) UsableRulesProof (EQUIVALENT transformation)

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

(48) Obligation:

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

LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)

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

(49) PiDPToQDPProof (EQUIVALENT transformation)

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

(50) Obligation:

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

LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)

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

(51) 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:

  • LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)
    The graph contains the following edges 1 > 1, 3 >= 3

(52) YES

(53) Obligation:

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

LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG294_IN_GGG(x1, x2, x3)  =  LOG294_IN_GGG(x1, x2, x3)

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

(54) UsableRulesProof (EQUIVALENT transformation)

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

(55) Obligation:

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

LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)

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

(56) PiDPToQDPProof (EQUIVALENT transformation)

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

(57) Obligation:

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

LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)

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

(58) 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:

  • LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)
    The graph contains the following edges 1 > 1, 3 >= 3

(59) YES

(60) Obligation:

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

LOG244_IN_AGG(s(s(T131)), T129, T130) → LOG244_IN_AGG(T131, s(T129), T130)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg
log2437_out_gg(x1, x2)  =  log2437_out_gg
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg
U27_ggg(x1, x2, x3)  =  U27_ggg(x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg
U29_ggg(x1, x2, x3)  =  U29_ggg(x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg
log2585_out_gg(x1, x2)  =  log2585_out_gg
U31_ggg(x1, x2, x3)  =  U31_ggg(x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg
U33_ggg(x1, x2, x3)  =  U33_ggg(x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg
U35_ggg(x1, x2, x3)  =  U35_ggg(x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg
U37_ggg(x1, x2, x3)  =  U37_ggg(x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg
U21_ggg(x1, x2, x3)  =  U21_ggg(x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg
U43_gg(x1, x2)  =  U43_gg(x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg
U44_gg(x1, x2)  =  U44_gg(x2)
U45_gg(x1, x2)  =  U45_gg(x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg
U46_gg(x1, x2)  =  U46_gg(x2)
U47_gg(x1, x2)  =  U47_gg(x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg
U48_gg(x1, x2)  =  U48_gg(x2)
U49_gg(x1, x2)  =  U49_gg(x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg
U50_gg(x1, x2)  =  U50_gg(x2)
U51_gg(x1, x2)  =  U51_gg(x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg
U52_gg(x1, x2)  =  U52_gg(x2)
U53_gg(x1, x2)  =  U53_gg(x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg
U18_ggg(x1, x2, x3)  =  U18_ggg(x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg
U60_gg(x1, x2)  =  U60_gg(x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x2)
log21183_out_g(x1)  =  log21183_out_g
U61_gg(x1, x2)  =  U61_gg(x2)
U62_gg(x1, x2)  =  U62_gg(x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x2)
log21249_out_g(x1)  =  log21249_out_g
U63_gg(x1, x2)  =  U63_gg(x2)
U64_gg(x1, x2)  =  U64_gg(x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x2)
log21319_out_g(x1)  =  log21319_out_g
U65_gg(x1, x2)  =  U65_gg(x2)
U66_gg(x1, x2)  =  U66_gg(x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x2)
log21370_out_g(x1)  =  log21370_out_g
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2)  =  U68_gg(x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g
U69_gg(x1, x2)  =  U69_gg(x2)
U70_gg(x1, x2)  =  U70_gg(x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g
U71_gg(x1, x2)  =  U71_gg(x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg
U15_ggg(x1, x2, x3)  =  U15_ggg(x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg
U77_gg(x1, x2)  =  U77_gg(x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x2)
log21540_out_g(x1)  =  log21540_out_g
U78_gg(x1, x2)  =  U78_gg(x2)
U79_gg(x1, x2)  =  U79_gg(x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x2)
log21606_out_g(x1)  =  log21606_out_g
U80_gg(x1, x2)  =  U80_gg(x2)
U81_gg(x1, x2)  =  U81_gg(x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x2)
log21676_out_g(x1)  =  log21676_out_g
U82_gg(x1, x2)  =  U82_gg(x2)
U83_gg(x1, x2)  =  U83_gg(x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x2)
log21727_out_g(x1)  =  log21727_out_g
U84_gg(x1, x2)  =  U84_gg(x2)
U85_gg(x1, x2)  =  U85_gg(x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g
U86_gg(x1, x2)  =  U86_gg(x2)
U87_gg(x1, x2)  =  U87_gg(x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g
U88_gg(x1, x2)  =  U88_gg(x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg
U12_ggg(x1, x2, x3)  =  U12_ggg(x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg
U94_gg(x1, x2)  =  U94_gg(x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x2)
log21897_out_g(x1)  =  log21897_out_g
U95_gg(x1, x2)  =  U95_gg(x2)
U96_gg(x1, x2)  =  U96_gg(x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x2)
log21963_out_g(x1)  =  log21963_out_g
U97_gg(x1, x2)  =  U97_gg(x2)
U98_gg(x1, x2)  =  U98_gg(x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x2)
log22033_out_g(x1)  =  log22033_out_g
U99_gg(x1, x2)  =  U99_gg(x2)
U100_gg(x1, x2)  =  U100_gg(x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x2)
log22084_out_g(x1)  =  log22084_out_g
U101_gg(x1, x2)  =  U101_gg(x2)
U102_gg(x1, x2)  =  U102_gg(x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g
U103_gg(x1, x2)  =  U103_gg(x2)
U104_gg(x1, x2)  =  U104_gg(x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g
U105_gg(x1, x2)  =  U105_gg(x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg
U9_ggg(x1, x2, x3)  =  U9_ggg(x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg
U111_gg(x1, x2)  =  U111_gg(x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x2)
log22254_out_g(x1)  =  log22254_out_g
U112_gg(x1, x2)  =  U112_gg(x2)
U113_gg(x1, x2)  =  U113_gg(x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x2)
log22320_out_g(x1)  =  log22320_out_g
U114_gg(x1, x2)  =  U114_gg(x2)
U115_gg(x1, x2)  =  U115_gg(x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x2)
log22390_out_g(x1)  =  log22390_out_g
U116_gg(x1, x2)  =  U116_gg(x2)
U117_gg(x1, x2)  =  U117_gg(x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x2)
log22441_out_g(x1)  =  log22441_out_g
U118_gg(x1, x2)  =  U118_gg(x2)
U119_gg(x1, x2)  =  U119_gg(x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g
U120_gg(x1, x2)  =  U120_gg(x2)
U121_gg(x1, x2)  =  U121_gg(x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g
U122_gg(x1, x2)  =  U122_gg(x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg
U6_ggg(x1, x2, x3)  =  U6_ggg(x3)
log257_out_gg(x1, x2)  =  log257_out_gg
U128_gg(x1, x2)  =  U128_gg(x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x2)
log22611_out_g(x1)  =  log22611_out_g
U129_gg(x1, x2)  =  U129_gg(x2)
U130_gg(x1, x2)  =  U130_gg(x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x2)
log22677_out_g(x1)  =  log22677_out_g
U131_gg(x1, x2)  =  U131_gg(x2)
U132_gg(x1, x2)  =  U132_gg(x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x2)
log22747_out_g(x1)  =  log22747_out_g
U133_gg(x1, x2)  =  U133_gg(x2)
U134_gg(x1, x2)  =  U134_gg(x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x2)
log22798_out_g(x1)  =  log22798_out_g
U135_gg(x1, x2)  =  U135_gg(x2)
U136_gg(x1, x2)  =  U136_gg(x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g
U137_gg(x1, x2)  =  U137_gg(x2)
U138_gg(x1, x2)  =  U138_gg(x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g
U139_gg(x1, x2)  =  U139_gg(x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1)
U3_agg(x1, x2, x3)  =  U3_agg(x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1)
U149_ag(x1, x2)  =  U149_ag(x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x2)
log22968_out_g(x1)  =  log22968_out_g
U150_ag(x1, x2)  =  U150_ag(x2)
U151_ag(x1, x2)  =  U151_ag(x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x2)
log23034_out_g(x1)  =  log23034_out_g
U152_ag(x1, x2)  =  U152_ag(x2)
U153_ag(x1, x2)  =  U153_ag(x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x2)
log23104_out_g(x1)  =  log23104_out_g
U154_ag(x1, x2)  =  U154_ag(x2)
U155_ag(x1, x2)  =  U155_ag(x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x2)
log23155_out_g(x1)  =  log23155_out_g
U156_ag(x1, x2)  =  U156_ag(x2)
U157_ag(x1, x2)  =  U157_ag(x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g
U158_ag(x1, x2)  =  U158_ag(x2)
U159_ag(x1, x2)  =  U159_ag(x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g
U160_ag(x1, x2)  =  U160_ag(x2)
LOG244_IN_AGG(x1, x2, x3)  =  LOG244_IN_AGG(x2, x3)

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

(61) UsableRulesProof (EQUIVALENT transformation)

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

(62) Obligation:

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

LOG244_IN_AGG(s(s(T131)), T129, T130) → LOG244_IN_AGG(T131, s(T129), T130)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LOG244_IN_AGG(x1, x2, x3)  =  LOG244_IN_AGG(x2, x3)

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

(63) PiDPToQDPProof (SOUND transformation)

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

(64) Obligation:

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

LOG244_IN_AGG(T129, T130) → LOG244_IN_AGG(s(T129), T130)

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

(65) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule LOG244_IN_AGG(T129, T130) → LOG244_IN_AGG(s(T129), T130) we obtained the following new rules [LPAR04]:

LOG244_IN_AGG(s(z0), z1) → LOG244_IN_AGG(s(s(z0)), z1)

(66) Obligation:

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

LOG244_IN_AGG(s(z0), z1) → LOG244_IN_AGG(s(s(z0)), z1)

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

(67) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule LOG244_IN_AGG(s(z0), z1) → LOG244_IN_AGG(s(s(z0)), z1) we obtained the following new rules [LPAR04]:

LOG244_IN_AGG(s(s(z0)), z1) → LOG244_IN_AGG(s(s(s(z0))), z1)

(68) Obligation:

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

LOG244_IN_AGG(s(s(z0)), z1) → LOG244_IN_AGG(s(s(s(z0))), z1)

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

(69) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = LOG244_IN_AGG(s(s(z0)), z1) evaluates to t =LOG244_IN_AGG(s(s(s(z0))), z1)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Semiunifier: [ ]
  • Matcher: [z0 / s(z0)]




Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from LOG244_IN_AGG(s(s(z0)), z1) to LOG244_IN_AGG(s(s(s(z0))), z1).



(70) NO

(71) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
log21_in: (f,b)
log244_in: (f,b,b)
log257_in: (b,b)
log294_in: (b,b,b)
log2107_in: (b,b)
log2144_in: (b,b,b)
log2157_in: (b,b)
log2194_in: (b,b,b)
log2207_in: (b,b)
log2244_in: (b,b,b)
log2257_in: (b,b)
log2294_in: (b,b,b)
log2307_in: (b,b)
log2344_in: (b,b,b)
log2359_in: (b,b,b)
log2395_in: (b,b,b,b)
log2437_in: (b,b)
log2515_in: (b,b)
log2585_in: (b,b)
log2650_in: (b,b)
log2822_in: (b,b)
log2889_in: (b,b)
log2960_in: (b,b)
log21012_in: (b,b)
log21183_in: (b)
log21249_in: (b)
log21319_in: (b)
log21370_in: (b)
log21540_in: (b)
log21606_in: (b)
log21676_in: (b)
log21727_in: (b)
log21897_in: (b)
log21963_in: (b)
log22033_in: (b)
log22084_in: (b)
log22254_in: (b)
log22320_in: (b)
log22390_in: (b)
log22441_in: (b)
log22611_in: (b)
log22677_in: (b)
log22747_in: (b)
log22798_in: (b)
log22968_in: (b)
log23034_in: (b)
log23104_in: (b)
log23155_in: (b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(72) Obligation:

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

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)

(73) 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:

LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_AG(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → LOG244_IN_AGG(T109, s(s(s(s(s(s(s(0))))))), T108)
LOG244_IN_AGG(s(s(T131)), T129, T130) → U1_AGG(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
LOG244_IN_AGG(s(s(T131)), T129, T130) → LOG244_IN_AGG(T131, s(T129), T130)
LOG244_IN_AGG(0, s(T148), T149) → U2_AGG(T148, T149, log257_in_gg(T148, T149))
LOG244_IN_AGG(0, s(T148), T149) → LOG257_IN_GG(T148, T149)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_GG(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → LOG294_IN_GGG(T235, s(s(s(s(s(s(s(0))))))), T236)
LOG294_IN_GGG(s(s(T255)), T256, T257) → U4_GGG(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)
LOG294_IN_GGG(0, s(T274), T275) → U5_GGG(T274, T275, log2107_in_gg(T274, T275))
LOG294_IN_GGG(0, s(T274), T275) → LOG2107_IN_GG(T274, T275)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_GG(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → LOG2144_IN_GGG(T360, s(s(s(s(s(s(s(0))))))), T361)
LOG2144_IN_GGG(s(s(T380)), T381, T382) → U7_GGG(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)
LOG2144_IN_GGG(0, s(T399), T400) → U8_GGG(T399, T400, log2157_in_gg(T399, T400))
LOG2144_IN_GGG(0, s(T399), T400) → LOG2157_IN_GG(T399, T400)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_GG(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → LOG2194_IN_GGG(T485, s(s(s(s(s(s(s(0))))))), T486)
LOG2194_IN_GGG(s(s(T505)), T506, T507) → U10_GGG(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)
LOG2194_IN_GGG(0, s(T524), T525) → U11_GGG(T524, T525, log2207_in_gg(T524, T525))
LOG2194_IN_GGG(0, s(T524), T525) → LOG2207_IN_GG(T524, T525)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_GG(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → LOG2244_IN_GGG(T610, s(s(s(s(s(s(s(0))))))), T611)
LOG2244_IN_GGG(s(s(T630)), T631, T632) → U13_GGG(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)
LOG2244_IN_GGG(0, s(T649), T650) → U14_GGG(T649, T650, log2257_in_gg(T649, T650))
LOG2244_IN_GGG(0, s(T649), T650) → LOG2257_IN_GG(T649, T650)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_GG(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → LOG2294_IN_GGG(T735, s(s(s(s(s(s(s(0))))))), T736)
LOG2294_IN_GGG(s(s(T755)), T756, T757) → U16_GGG(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)
LOG2294_IN_GGG(0, s(T774), T775) → U17_GGG(T774, T775, log2307_in_gg(T774, T775))
LOG2294_IN_GGG(0, s(T774), T775) → LOG2307_IN_GG(T774, T775)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_GG(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → LOG2344_IN_GGG(T860, s(s(s(s(s(s(s(0))))))), T861)
LOG2344_IN_GGG(s(s(T880)), T881, T882) → U19_GGG(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)
LOG2344_IN_GGG(0, s(T899), T900) → U20_GGG(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
LOG2344_IN_GGG(0, s(T899), T900) → LOG2359_IN_GGG(T899, s(s(s(s(s(s(s(0))))))), T900)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_GGG(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → U22_GGGG(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → U23_GGGG(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_GGG(T1119, T1120, log2437_in_gg(T1119, T1120))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → LOG2437_IN_GG(T1119, T1120)
LOG2437_IN_GG(T1167, T1168) → U38_GG(T1167, T1168, log2454_in_gg(T1167, T1168))
LOG2437_IN_GG(T1167, T1168) → LOG2454_IN_GG(T1167, T1168)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_GGG(T1119, T1120, log2437_in_gg(T1119, T1120))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → LOG2437_IN_GG(T1119, T1120)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_GGG(T1222, T1223, log2515_in_gg(T1222, T1223))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → LOG2515_IN_GG(T1222, T1223)
LOG2515_IN_GG(T1270, T1271) → U39_GG(T1270, T1271, log2454_in_gg(T1270, T1271))
LOG2515_IN_GG(T1270, T1271) → LOG2454_IN_GG(T1270, T1271)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_GGG(T1222, T1223, log2515_in_gg(T1222, T1223))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → LOG2515_IN_GG(T1222, T1223)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_GGG(T1323, T1324, log2585_in_gg(T1323, T1324))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → LOG2585_IN_GG(T1323, T1324)
LOG2585_IN_GG(T1355, T1356) → U40_GG(T1355, T1356, log2598_in_gg(T1355, T1356))
LOG2585_IN_GG(T1355, T1356) → LOG2598_IN_GG(T1355, T1356)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_GGG(T1323, T1324, log2585_in_gg(T1323, T1324))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → LOG2585_IN_GG(T1323, T1324)
LOG2359_IN_GGG(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_GGG(T1394, T1395, log2650_in_gg(T1394, T1395))
LOG2359_IN_GGG(s(s(s(s(s(s(0)))))), T1394, T1395) → LOG2650_IN_GG(T1394, T1395)
LOG2650_IN_GG(T1426, T1427) → U41_GG(T1426, T1427, log2598_in_gg(T1426, T1427))
LOG2650_IN_GG(T1426, T1427) → LOG2598_IN_GG(T1426, T1427)
LOG2359_IN_GGG(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_GGG(T1394, T1395, log2650_in_gg(T1394, T1395))
LOG2359_IN_GGG(s(s(s(s(s(s(s(0))))))), T1394, T1395) → LOG2650_IN_GG(T1394, T1395)
LOG2359_IN_GGG(s(s(s(s(0)))), T1461, T1462) → U34_GGG(T1461, T1462, log2705_in_gg(T1461, T1462))
LOG2359_IN_GGG(s(s(s(s(0)))), T1461, T1462) → LOG2705_IN_GG(T1461, T1462)
LOG2359_IN_GGG(s(s(s(s(s(0))))), T1461, T1462) → U35_GGG(T1461, T1462, log2705_in_gg(T1461, T1462))
LOG2359_IN_GGG(s(s(s(s(s(0))))), T1461, T1462) → LOG2705_IN_GG(T1461, T1462)
LOG2359_IN_GGG(s(s(0)), T1490, T1491) → U36_GGG(T1490, T1491, log2742_in_gg(T1490, T1491))
LOG2359_IN_GGG(s(s(0)), T1490, T1491) → LOG2742_IN_GG(T1490, T1491)
LOG2359_IN_GGG(s(s(s(0))), T1490, T1491) → U37_GGG(T1490, T1491, log2742_in_gg(T1490, T1491))
LOG2359_IN_GGG(s(s(s(0))), T1490, T1491) → LOG2742_IN_GG(T1490, T1491)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → U24_GGGG(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2344_IN_GGG(s(0), s(T899), T900) → U21_GGG(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
LOG2344_IN_GGG(s(0), s(T899), T900) → LOG2359_IN_GGG(T899, s(s(s(s(s(s(s(0))))))), T900)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_GG(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → LOG2822_IN_GG(s(s(s(s(s(s(s(0))))))), T1530)
LOG2822_IN_GG(T1578, T1579) → U144_GG(T1578, T1579, log2705_in_gg(T1578, T1579))
LOG2822_IN_GG(T1578, T1579) → LOG2705_IN_GG(T1578, T1579)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_GG(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → LOG2822_IN_GG(s(s(s(s(s(s(s(0))))))), T1530)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_GG(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → LOG2889_IN_GG(s(s(s(s(s(s(s(0))))))), T1620)
LOG2889_IN_GG(T1668, T1669) → U145_GG(T1668, T1669, log2705_in_gg(T1668, T1669))
LOG2889_IN_GG(T1668, T1669) → LOG2705_IN_GG(T1668, T1669)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_GG(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → LOG2889_IN_GG(s(s(s(s(s(s(s(0))))))), T1620)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_GG(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1711) → LOG2960_IN_GG(s(s(s(s(s(s(s(0))))))), T1711)
LOG2960_IN_GG(T1743, T1744) → U146_GG(T1743, T1744, log2742_in_gg(T1743, T1744))
LOG2960_IN_GG(T1743, T1744) → LOG2742_IN_GG(T1743, T1744)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_GG(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → LOG2960_IN_GG(s(s(s(s(s(s(s(0))))))), T1711)
LOG2307_IN_GG(s(s(s(s(s(s(0)))))), T1769) → U49_GG(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
LOG2307_IN_GG(s(s(s(s(s(s(0)))))), T1769) → LOG21012_IN_GG(s(s(s(s(s(s(s(0))))))), T1769)
LOG21012_IN_GG(T1801, T1802) → U147_GG(T1801, T1802, log2742_in_gg(T1801, T1802))
LOG21012_IN_GG(T1801, T1802) → LOG2742_IN_GG(T1801, T1802)
LOG2307_IN_GG(s(s(s(s(s(s(s(0))))))), T1769) → U50_GG(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
LOG2307_IN_GG(s(s(s(s(s(s(s(0))))))), T1769) → LOG21012_IN_GG(s(s(s(s(s(s(s(0))))))), T1769)
LOG2307_IN_GG(s(s(s(s(0)))), T1826) → U51_GG(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
LOG2307_IN_GG(s(s(s(s(0)))), T1826) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1826)
LOG2307_IN_GG(s(s(s(s(s(0))))), T1826) → U52_GG(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
LOG2307_IN_GG(s(s(s(s(s(0))))), T1826) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1826)
LOG2307_IN_GG(s(s(0)), T1844) → U53_GG(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
LOG2307_IN_GG(s(s(0)), T1844) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1844)
LOG2307_IN_GG(s(s(s(0))), T1844) → U54_GG(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
LOG2307_IN_GG(s(s(s(0))), T1844) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1844)
LOG2294_IN_GGG(s(0), s(T774), T775) → U18_GGG(T774, T775, log2307_in_gg(T774, T775))
LOG2294_IN_GGG(s(0), s(T774), T775) → LOG2307_IN_GG(T774, T775)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_GG(T1876, log21183_in_g(T1876))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → LOG21183_IN_G(T1876)
LOG21183_IN_G(T1899) → U55_G(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
LOG21183_IN_G(T1899) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1899)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_GG(T1876, log21183_in_g(T1876))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → LOG21183_IN_G(T1876)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_GG(T1920, log21249_in_g(T1920))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → LOG21249_IN_G(T1920)
LOG21249_IN_G(T1943) → U56_G(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
LOG21249_IN_G(T1943) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1943)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_GG(T1920, log21249_in_g(T1920))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → LOG21249_IN_G(T1920)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_GG(T1964, log21319_in_g(T1964))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1964) → LOG21319_IN_G(T1964)
LOG21319_IN_G(T1979) → U57_G(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
LOG21319_IN_G(T1979) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1979)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_GG(T1964, log21319_in_g(T1964))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → LOG21319_IN_G(T1964)
LOG2257_IN_GG(s(s(s(s(s(s(0)))))), T1995) → U66_GG(T1995, log21370_in_g(T1995))
LOG2257_IN_GG(s(s(s(s(s(s(0)))))), T1995) → LOG21370_IN_G(T1995)
LOG21370_IN_G(T2010) → U58_G(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
LOG21370_IN_G(T2010) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T2010)
LOG2257_IN_GG(s(s(s(s(s(s(s(0))))))), T1995) → U67_GG(T1995, log21370_in_g(T1995))
LOG2257_IN_GG(s(s(s(s(s(s(s(0))))))), T1995) → LOG21370_IN_G(T1995)
LOG2257_IN_GG(s(s(s(s(0)))), T2024) → U68_GG(T2024, log21425_in_g(T2024))
LOG2257_IN_GG(s(s(s(s(0)))), T2024) → LOG21425_IN_G(T2024)
LOG2257_IN_GG(s(s(s(s(s(0))))), T2024) → U69_GG(T2024, log21425_in_g(T2024))
LOG2257_IN_GG(s(s(s(s(s(0))))), T2024) → LOG21425_IN_G(T2024)
LOG2257_IN_GG(s(s(0)), T2037) → U70_GG(T2037, log21462_in_g(T2037))
LOG2257_IN_GG(s(s(0)), T2037) → LOG21462_IN_G(T2037)
LOG2257_IN_GG(s(s(s(0))), T2037) → U71_GG(T2037, log21462_in_g(T2037))
LOG2257_IN_GG(s(s(s(0))), T2037) → LOG21462_IN_G(T2037)
LOG2244_IN_GGG(s(0), s(T649), T650) → U15_GGG(T649, T650, log2257_in_gg(T649, T650))
LOG2244_IN_GGG(s(0), s(T649), T650) → LOG2257_IN_GG(T649, T650)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_GG(T2064, log21540_in_g(T2064))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → LOG21540_IN_G(T2064)
LOG21540_IN_G(T2087) → U72_G(T2087, log21425_in_g(T2087))
LOG21540_IN_G(T2087) → LOG21425_IN_G(T2087)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_GG(T2064, log21540_in_g(T2064))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → LOG21540_IN_G(T2064)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_GG(T2108, log21606_in_g(T2108))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → LOG21606_IN_G(T2108)
LOG21606_IN_G(T2131) → U73_G(T2131, log21425_in_g(T2131))
LOG21606_IN_G(T2131) → LOG21425_IN_G(T2131)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_GG(T2108, log21606_in_g(T2108))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → LOG21606_IN_G(T2108)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_GG(T2152, log21676_in_g(T2152))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2152) → LOG21676_IN_G(T2152)
LOG21676_IN_G(T2167) → U74_G(T2167, log21462_in_g(T2167))
LOG21676_IN_G(T2167) → LOG21462_IN_G(T2167)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_GG(T2152, log21676_in_g(T2152))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → LOG21676_IN_G(T2152)
LOG2207_IN_GG(s(s(s(s(s(s(0)))))), T2183) → U83_GG(T2183, log21727_in_g(T2183))
LOG2207_IN_GG(s(s(s(s(s(s(0)))))), T2183) → LOG21727_IN_G(T2183)
LOG21727_IN_G(T2198) → U75_G(T2198, log21462_in_g(T2198))
LOG21727_IN_G(T2198) → LOG21462_IN_G(T2198)
LOG2207_IN_GG(s(s(s(s(s(s(s(0))))))), T2183) → U84_GG(T2183, log21727_in_g(T2183))
LOG2207_IN_GG(s(s(s(s(s(s(s(0))))))), T2183) → LOG21727_IN_G(T2183)
LOG2207_IN_GG(s(s(s(s(0)))), T2212) → U85_GG(T2212, log21782_in_g(T2212))
LOG2207_IN_GG(s(s(s(s(0)))), T2212) → LOG21782_IN_G(T2212)
LOG2207_IN_GG(s(s(s(s(s(0))))), T2212) → U86_GG(T2212, log21782_in_g(T2212))
LOG2207_IN_GG(s(s(s(s(s(0))))), T2212) → LOG21782_IN_G(T2212)
LOG2207_IN_GG(s(s(0)), T2225) → U87_GG(T2225, log21819_in_g(T2225))
LOG2207_IN_GG(s(s(0)), T2225) → LOG21819_IN_G(T2225)
LOG2207_IN_GG(s(s(s(0))), T2225) → U88_GG(T2225, log21819_in_g(T2225))
LOG2207_IN_GG(s(s(s(0))), T2225) → LOG21819_IN_G(T2225)
LOG2194_IN_GGG(s(0), s(T524), T525) → U12_GGG(T524, T525, log2207_in_gg(T524, T525))
LOG2194_IN_GGG(s(0), s(T524), T525) → LOG2207_IN_GG(T524, T525)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_GG(T2252, log21897_in_g(T2252))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → LOG21897_IN_G(T2252)
LOG21897_IN_G(T2275) → U89_G(T2275, log21782_in_g(T2275))
LOG21897_IN_G(T2275) → LOG21782_IN_G(T2275)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_GG(T2252, log21897_in_g(T2252))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → LOG21897_IN_G(T2252)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_GG(T2296, log21963_in_g(T2296))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → LOG21963_IN_G(T2296)
LOG21963_IN_G(T2319) → U90_G(T2319, log21782_in_g(T2319))
LOG21963_IN_G(T2319) → LOG21782_IN_G(T2319)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_GG(T2296, log21963_in_g(T2296))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → LOG21963_IN_G(T2296)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_GG(T2340, log22033_in_g(T2340))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2340) → LOG22033_IN_G(T2340)
LOG22033_IN_G(T2355) → U91_G(T2355, log21819_in_g(T2355))
LOG22033_IN_G(T2355) → LOG21819_IN_G(T2355)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_GG(T2340, log22033_in_g(T2340))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → LOG22033_IN_G(T2340)
LOG2157_IN_GG(s(s(s(s(s(s(0)))))), T2371) → U100_GG(T2371, log22084_in_g(T2371))
LOG2157_IN_GG(s(s(s(s(s(s(0)))))), T2371) → LOG22084_IN_G(T2371)
LOG22084_IN_G(T2386) → U92_G(T2386, log21819_in_g(T2386))
LOG22084_IN_G(T2386) → LOG21819_IN_G(T2386)
LOG2157_IN_GG(s(s(s(s(s(s(s(0))))))), T2371) → U101_GG(T2371, log22084_in_g(T2371))
LOG2157_IN_GG(s(s(s(s(s(s(s(0))))))), T2371) → LOG22084_IN_G(T2371)
LOG2157_IN_GG(s(s(s(s(0)))), T2400) → U102_GG(T2400, log22139_in_g(T2400))
LOG2157_IN_GG(s(s(s(s(0)))), T2400) → LOG22139_IN_G(T2400)
LOG2157_IN_GG(s(s(s(s(s(0))))), T2400) → U103_GG(T2400, log22139_in_g(T2400))
LOG2157_IN_GG(s(s(s(s(s(0))))), T2400) → LOG22139_IN_G(T2400)
LOG2157_IN_GG(s(s(0)), T2413) → U104_GG(T2413, log22176_in_g(T2413))
LOG2157_IN_GG(s(s(0)), T2413) → LOG22176_IN_G(T2413)
LOG2157_IN_GG(s(s(s(0))), T2413) → U105_GG(T2413, log22176_in_g(T2413))
LOG2157_IN_GG(s(s(s(0))), T2413) → LOG22176_IN_G(T2413)
LOG2144_IN_GGG(s(0), s(T399), T400) → U9_GGG(T399, T400, log2157_in_gg(T399, T400))
LOG2144_IN_GGG(s(0), s(T399), T400) → LOG2157_IN_GG(T399, T400)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_GG(T2440, log22254_in_g(T2440))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → LOG22254_IN_G(T2440)
LOG22254_IN_G(T2463) → U106_G(T2463, log22139_in_g(T2463))
LOG22254_IN_G(T2463) → LOG22139_IN_G(T2463)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_GG(T2440, log22254_in_g(T2440))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → LOG22254_IN_G(T2440)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_GG(T2484, log22320_in_g(T2484))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → LOG22320_IN_G(T2484)
LOG22320_IN_G(T2507) → U107_G(T2507, log22139_in_g(T2507))
LOG22320_IN_G(T2507) → LOG22139_IN_G(T2507)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_GG(T2484, log22320_in_g(T2484))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → LOG22320_IN_G(T2484)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_GG(T2528, log22390_in_g(T2528))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2528) → LOG22390_IN_G(T2528)
LOG22390_IN_G(T2543) → U108_G(T2543, log22176_in_g(T2543))
LOG22390_IN_G(T2543) → LOG22176_IN_G(T2543)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_GG(T2528, log22390_in_g(T2528))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → LOG22390_IN_G(T2528)
LOG2107_IN_GG(s(s(s(s(s(s(0)))))), T2559) → U117_GG(T2559, log22441_in_g(T2559))
LOG2107_IN_GG(s(s(s(s(s(s(0)))))), T2559) → LOG22441_IN_G(T2559)
LOG22441_IN_G(T2574) → U109_G(T2574, log22176_in_g(T2574))
LOG22441_IN_G(T2574) → LOG22176_IN_G(T2574)
LOG2107_IN_GG(s(s(s(s(s(s(s(0))))))), T2559) → U118_GG(T2559, log22441_in_g(T2559))
LOG2107_IN_GG(s(s(s(s(s(s(s(0))))))), T2559) → LOG22441_IN_G(T2559)
LOG2107_IN_GG(s(s(s(s(0)))), T2588) → U119_GG(T2588, log22496_in_g(T2588))
LOG2107_IN_GG(s(s(s(s(0)))), T2588) → LOG22496_IN_G(T2588)
LOG2107_IN_GG(s(s(s(s(s(0))))), T2588) → U120_GG(T2588, log22496_in_g(T2588))
LOG2107_IN_GG(s(s(s(s(s(0))))), T2588) → LOG22496_IN_G(T2588)
LOG2107_IN_GG(s(s(0)), T2601) → U121_GG(T2601, log22533_in_g(T2601))
LOG2107_IN_GG(s(s(0)), T2601) → LOG22533_IN_G(T2601)
LOG2107_IN_GG(s(s(s(0))), T2601) → U122_GG(T2601, log22533_in_g(T2601))
LOG2107_IN_GG(s(s(s(0))), T2601) → LOG22533_IN_G(T2601)
LOG294_IN_GGG(s(0), s(T274), T275) → U6_GGG(T274, T275, log2107_in_gg(T274, T275))
LOG294_IN_GGG(s(0), s(T274), T275) → LOG2107_IN_GG(T274, T275)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_GG(T2628, log22611_in_g(T2628))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → LOG22611_IN_G(T2628)
LOG22611_IN_G(T2651) → U123_G(T2651, log22496_in_g(T2651))
LOG22611_IN_G(T2651) → LOG22496_IN_G(T2651)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_GG(T2628, log22611_in_g(T2628))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → LOG22611_IN_G(T2628)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_GG(T2672, log22677_in_g(T2672))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → LOG22677_IN_G(T2672)
LOG22677_IN_G(T2695) → U124_G(T2695, log22496_in_g(T2695))
LOG22677_IN_G(T2695) → LOG22496_IN_G(T2695)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_GG(T2672, log22677_in_g(T2672))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → LOG22677_IN_G(T2672)
LOG257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_GG(T2716, log22747_in_g(T2716))
LOG257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2716) → LOG22747_IN_G(T2716)
LOG22747_IN_G(T2731) → U125_G(T2731, log22533_in_g(T2731))
LOG22747_IN_G(T2731) → LOG22533_IN_G(T2731)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_GG(T2716, log22747_in_g(T2716))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → LOG22747_IN_G(T2716)
LOG257_IN_GG(s(s(s(s(s(s(0)))))), T2747) → U134_GG(T2747, log22798_in_g(T2747))
LOG257_IN_GG(s(s(s(s(s(s(0)))))), T2747) → LOG22798_IN_G(T2747)
LOG22798_IN_G(T2762) → U126_G(T2762, log22533_in_g(T2762))
LOG22798_IN_G(T2762) → LOG22533_IN_G(T2762)
LOG257_IN_GG(s(s(s(s(s(s(s(0))))))), T2747) → U135_GG(T2747, log22798_in_g(T2747))
LOG257_IN_GG(s(s(s(s(s(s(s(0))))))), T2747) → LOG22798_IN_G(T2747)
LOG257_IN_GG(s(s(s(s(0)))), T2776) → U136_GG(T2776, log22853_in_g(T2776))
LOG257_IN_GG(s(s(s(s(0)))), T2776) → LOG22853_IN_G(T2776)
LOG257_IN_GG(s(s(s(s(s(0))))), T2776) → U137_GG(T2776, log22853_in_g(T2776))
LOG257_IN_GG(s(s(s(s(s(0))))), T2776) → LOG22853_IN_G(T2776)
LOG257_IN_GG(s(s(0)), T2789) → U138_GG(T2789, log22890_in_g(T2789))
LOG257_IN_GG(s(s(0)), T2789) → LOG22890_IN_G(T2789)
LOG257_IN_GG(s(s(s(0))), T2789) → U139_GG(T2789, log22890_in_g(T2789))
LOG257_IN_GG(s(s(s(0))), T2789) → LOG22890_IN_G(T2789)
LOG244_IN_AGG(s(0), s(T148), T149) → U3_AGG(T148, T149, log257_in_gg(T148, T149))
LOG244_IN_AGG(s(0), s(T148), T149) → LOG257_IN_GG(T148, T149)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_AG(T2819, log22968_in_g(T2819))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → LOG22968_IN_G(T2819)
LOG22968_IN_G(T2843) → U140_G(T2843, log22853_in_g(T2843))
LOG22968_IN_G(T2843) → LOG22853_IN_G(T2843)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_AG(T2819, log22968_in_g(T2819))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → LOG22968_IN_G(T2819)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_AG(T2867, log23034_in_g(T2867))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → LOG23034_IN_G(T2867)
LOG23034_IN_G(T2891) → U141_G(T2891, log22853_in_g(T2891))
LOG23034_IN_G(T2891) → LOG22853_IN_G(T2891)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_AG(T2867, log23034_in_g(T2867))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → LOG23034_IN_G(T2867)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_AG(T2915, log23104_in_g(T2915))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → LOG23104_IN_G(T2915)
LOG23104_IN_G(T2931) → U142_G(T2931, log22890_in_g(T2931))
LOG23104_IN_G(T2931) → LOG22890_IN_G(T2931)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_AG(T2915, log23104_in_g(T2915))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → LOG23104_IN_G(T2915)
LOG21_IN_AG(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_AG(T2950, log23155_in_g(T2950))
LOG21_IN_AG(s(s(s(s(s(s(s(s(0)))))))), T2950) → LOG23155_IN_G(T2950)
LOG23155_IN_G(T2966) → U143_G(T2966, log22890_in_g(T2966))
LOG23155_IN_G(T2966) → LOG22890_IN_G(T2966)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_AG(T2950, log23155_in_g(T2950))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → LOG23155_IN_G(T2950)
LOG21_IN_AG(s(s(s(s(s(s(0)))))), T2983) → U157_AG(T2983, log23210_in_g(T2983))
LOG21_IN_AG(s(s(s(s(s(s(0)))))), T2983) → LOG23210_IN_G(T2983)
LOG21_IN_AG(s(s(s(s(s(s(s(0))))))), T2983) → U158_AG(T2983, log23210_in_g(T2983))
LOG21_IN_AG(s(s(s(s(s(s(s(0))))))), T2983) → LOG23210_IN_G(T2983)
LOG21_IN_AG(s(s(s(s(0)))), T3000) → U159_AG(T3000, log23247_in_g(T3000))
LOG21_IN_AG(s(s(s(s(0)))), T3000) → LOG23247_IN_G(T3000)
LOG21_IN_AG(s(s(s(s(s(0))))), T3000) → U160_AG(T3000, log23247_in_g(T3000))
LOG21_IN_AG(s(s(s(s(s(0))))), T3000) → LOG23247_IN_G(T3000)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG21_IN_AG(x1, x2)  =  LOG21_IN_AG(x2)
U148_AG(x1, x2, x3)  =  U148_AG(x2, x3)
LOG244_IN_AGG(x1, x2, x3)  =  LOG244_IN_AGG(x2, x3)
U1_AGG(x1, x2, x3, x4)  =  U1_AGG(x2, x3, x4)
U2_AGG(x1, x2, x3)  =  U2_AGG(x1, x2, x3)
LOG257_IN_GG(x1, x2)  =  LOG257_IN_GG(x1, x2)
U127_GG(x1, x2, x3)  =  U127_GG(x1, x2, x3)
LOG294_IN_GGG(x1, x2, x3)  =  LOG294_IN_GGG(x1, x2, x3)
U4_GGG(x1, x2, x3, x4)  =  U4_GGG(x1, x2, x3, x4)
U5_GGG(x1, x2, x3)  =  U5_GGG(x1, x2, x3)
LOG2107_IN_GG(x1, x2)  =  LOG2107_IN_GG(x1, x2)
U110_GG(x1, x2, x3)  =  U110_GG(x1, x2, x3)
LOG2144_IN_GGG(x1, x2, x3)  =  LOG2144_IN_GGG(x1, x2, x3)
U7_GGG(x1, x2, x3, x4)  =  U7_GGG(x1, x2, x3, x4)
U8_GGG(x1, x2, x3)  =  U8_GGG(x1, x2, x3)
LOG2157_IN_GG(x1, x2)  =  LOG2157_IN_GG(x1, x2)
U93_GG(x1, x2, x3)  =  U93_GG(x1, x2, x3)
LOG2194_IN_GGG(x1, x2, x3)  =  LOG2194_IN_GGG(x1, x2, x3)
U10_GGG(x1, x2, x3, x4)  =  U10_GGG(x1, x2, x3, x4)
U11_GGG(x1, x2, x3)  =  U11_GGG(x1, x2, x3)
LOG2207_IN_GG(x1, x2)  =  LOG2207_IN_GG(x1, x2)
U76_GG(x1, x2, x3)  =  U76_GG(x1, x2, x3)
LOG2244_IN_GGG(x1, x2, x3)  =  LOG2244_IN_GGG(x1, x2, x3)
U13_GGG(x1, x2, x3, x4)  =  U13_GGG(x1, x2, x3, x4)
U14_GGG(x1, x2, x3)  =  U14_GGG(x1, x2, x3)
LOG2257_IN_GG(x1, x2)  =  LOG2257_IN_GG(x1, x2)
U59_GG(x1, x2, x3)  =  U59_GG(x1, x2, x3)
LOG2294_IN_GGG(x1, x2, x3)  =  LOG2294_IN_GGG(x1, x2, x3)
U16_GGG(x1, x2, x3, x4)  =  U16_GGG(x1, x2, x3, x4)
U17_GGG(x1, x2, x3)  =  U17_GGG(x1, x2, x3)
LOG2307_IN_GG(x1, x2)  =  LOG2307_IN_GG(x1, x2)
U42_GG(x1, x2, x3)  =  U42_GG(x1, x2, x3)
LOG2344_IN_GGG(x1, x2, x3)  =  LOG2344_IN_GGG(x1, x2, x3)
U19_GGG(x1, x2, x3, x4)  =  U19_GGG(x1, x2, x3, x4)
U20_GGG(x1, x2, x3)  =  U20_GGG(x1, x2, x3)
LOG2359_IN_GGG(x1, x2, x3)  =  LOG2359_IN_GGG(x1, x2, x3)
U25_GGG(x1, x2, x3, x4)  =  U25_GGG(x1, x2, x3, x4)
LOG2395_IN_GGGG(x1, x2, x3, x4)  =  LOG2395_IN_GGGG(x1, x2, x3, x4)
U22_GGGG(x1, x2, x3, x4, x5)  =  U22_GGGG(x1, x2, x3, x4, x5)
U23_GGGG(x1, x2, x3, x4)  =  U23_GGGG(x1, x2, x3, x4)
U26_GGG(x1, x2, x3)  =  U26_GGG(x1, x2, x3)
LOG2437_IN_GG(x1, x2)  =  LOG2437_IN_GG(x1, x2)
U38_GG(x1, x2, x3)  =  U38_GG(x1, x2, x3)
LOG2454_IN_GG(x1, x2)  =  LOG2454_IN_GG(x1, x2)
U27_GGG(x1, x2, x3)  =  U27_GGG(x1, x2, x3)
U28_GGG(x1, x2, x3)  =  U28_GGG(x1, x2, x3)
LOG2515_IN_GG(x1, x2)  =  LOG2515_IN_GG(x1, x2)
U39_GG(x1, x2, x3)  =  U39_GG(x1, x2, x3)
U29_GGG(x1, x2, x3)  =  U29_GGG(x1, x2, x3)
U30_GGG(x1, x2, x3)  =  U30_GGG(x1, x2, x3)
LOG2585_IN_GG(x1, x2)  =  LOG2585_IN_GG(x1, x2)
U40_GG(x1, x2, x3)  =  U40_GG(x1, x2, x3)
LOG2598_IN_GG(x1, x2)  =  LOG2598_IN_GG(x1, x2)
U31_GGG(x1, x2, x3)  =  U31_GGG(x1, x2, x3)
U32_GGG(x1, x2, x3)  =  U32_GGG(x1, x2, x3)
LOG2650_IN_GG(x1, x2)  =  LOG2650_IN_GG(x1, x2)
U41_GG(x1, x2, x3)  =  U41_GG(x1, x2, x3)
U33_GGG(x1, x2, x3)  =  U33_GGG(x1, x2, x3)
U34_GGG(x1, x2, x3)  =  U34_GGG(x1, x2, x3)
LOG2705_IN_GG(x1, x2)  =  LOG2705_IN_GG(x1, x2)
U35_GGG(x1, x2, x3)  =  U35_GGG(x1, x2, x3)
U36_GGG(x1, x2, x3)  =  U36_GGG(x1, x2, x3)
LOG2742_IN_GG(x1, x2)  =  LOG2742_IN_GG(x1, x2)
U37_GGG(x1, x2, x3)  =  U37_GGG(x1, x2, x3)
U24_GGGG(x1, x2, x3, x4)  =  U24_GGGG(x1, x2, x3, x4)
U21_GGG(x1, x2, x3)  =  U21_GGG(x1, x2, x3)
U43_GG(x1, x2)  =  U43_GG(x1, x2)
LOG2822_IN_GG(x1, x2)  =  LOG2822_IN_GG(x1, x2)
U144_GG(x1, x2, x3)  =  U144_GG(x1, x2, x3)
U44_GG(x1, x2)  =  U44_GG(x1, x2)
U45_GG(x1, x2)  =  U45_GG(x1, x2)
LOG2889_IN_GG(x1, x2)  =  LOG2889_IN_GG(x1, x2)
U145_GG(x1, x2, x3)  =  U145_GG(x1, x2, x3)
U46_GG(x1, x2)  =  U46_GG(x1, x2)
U47_GG(x1, x2)  =  U47_GG(x1, x2)
LOG2960_IN_GG(x1, x2)  =  LOG2960_IN_GG(x1, x2)
U146_GG(x1, x2, x3)  =  U146_GG(x1, x2, x3)
U48_GG(x1, x2)  =  U48_GG(x1, x2)
U49_GG(x1, x2)  =  U49_GG(x1, x2)
LOG21012_IN_GG(x1, x2)  =  LOG21012_IN_GG(x1, x2)
U147_GG(x1, x2, x3)  =  U147_GG(x1, x2, x3)
U50_GG(x1, x2)  =  U50_GG(x1, x2)
U51_GG(x1, x2)  =  U51_GG(x1, x2)
LOG21068_IN_GG(x1, x2)  =  LOG21068_IN_GG(x1, x2)
U52_GG(x1, x2)  =  U52_GG(x1, x2)
U53_GG(x1, x2)  =  U53_GG(x1, x2)
LOG21106_IN_GG(x1, x2)  =  LOG21106_IN_GG(x1, x2)
U54_GG(x1, x2)  =  U54_GG(x1, x2)
U18_GGG(x1, x2, x3)  =  U18_GGG(x1, x2, x3)
U60_GG(x1, x2)  =  U60_GG(x1, x2)
LOG21183_IN_G(x1)  =  LOG21183_IN_G(x1)
U55_G(x1, x2)  =  U55_G(x1, x2)
U61_GG(x1, x2)  =  U61_GG(x1, x2)
U62_GG(x1, x2)  =  U62_GG(x1, x2)
LOG21249_IN_G(x1)  =  LOG21249_IN_G(x1)
U56_G(x1, x2)  =  U56_G(x1, x2)
U63_GG(x1, x2)  =  U63_GG(x1, x2)
U64_GG(x1, x2)  =  U64_GG(x1, x2)
LOG21319_IN_G(x1)  =  LOG21319_IN_G(x1)
U57_G(x1, x2)  =  U57_G(x1, x2)
U65_GG(x1, x2)  =  U65_GG(x1, x2)
U66_GG(x1, x2)  =  U66_GG(x1, x2)
LOG21370_IN_G(x1)  =  LOG21370_IN_G(x1)
U58_G(x1, x2)  =  U58_G(x1, x2)
U67_GG(x1, x2)  =  U67_GG(x1, x2)
U68_GG(x1, x2)  =  U68_GG(x1, x2)
LOG21425_IN_G(x1)  =  LOG21425_IN_G(x1)
U69_GG(x1, x2)  =  U69_GG(x1, x2)
U70_GG(x1, x2)  =  U70_GG(x1, x2)
LOG21462_IN_G(x1)  =  LOG21462_IN_G(x1)
U71_GG(x1, x2)  =  U71_GG(x1, x2)
U15_GGG(x1, x2, x3)  =  U15_GGG(x1, x2, x3)
U77_GG(x1, x2)  =  U77_GG(x1, x2)
LOG21540_IN_G(x1)  =  LOG21540_IN_G(x1)
U72_G(x1, x2)  =  U72_G(x1, x2)
U78_GG(x1, x2)  =  U78_GG(x1, x2)
U79_GG(x1, x2)  =  U79_GG(x1, x2)
LOG21606_IN_G(x1)  =  LOG21606_IN_G(x1)
U73_G(x1, x2)  =  U73_G(x1, x2)
U80_GG(x1, x2)  =  U80_GG(x1, x2)
U81_GG(x1, x2)  =  U81_GG(x1, x2)
LOG21676_IN_G(x1)  =  LOG21676_IN_G(x1)
U74_G(x1, x2)  =  U74_G(x1, x2)
U82_GG(x1, x2)  =  U82_GG(x1, x2)
U83_GG(x1, x2)  =  U83_GG(x1, x2)
LOG21727_IN_G(x1)  =  LOG21727_IN_G(x1)
U75_G(x1, x2)  =  U75_G(x1, x2)
U84_GG(x1, x2)  =  U84_GG(x1, x2)
U85_GG(x1, x2)  =  U85_GG(x1, x2)
LOG21782_IN_G(x1)  =  LOG21782_IN_G(x1)
U86_GG(x1, x2)  =  U86_GG(x1, x2)
U87_GG(x1, x2)  =  U87_GG(x1, x2)
LOG21819_IN_G(x1)  =  LOG21819_IN_G(x1)
U88_GG(x1, x2)  =  U88_GG(x1, x2)
U12_GGG(x1, x2, x3)  =  U12_GGG(x1, x2, x3)
U94_GG(x1, x2)  =  U94_GG(x1, x2)
LOG21897_IN_G(x1)  =  LOG21897_IN_G(x1)
U89_G(x1, x2)  =  U89_G(x1, x2)
U95_GG(x1, x2)  =  U95_GG(x1, x2)
U96_GG(x1, x2)  =  U96_GG(x1, x2)
LOG21963_IN_G(x1)  =  LOG21963_IN_G(x1)
U90_G(x1, x2)  =  U90_G(x1, x2)
U97_GG(x1, x2)  =  U97_GG(x1, x2)
U98_GG(x1, x2)  =  U98_GG(x1, x2)
LOG22033_IN_G(x1)  =  LOG22033_IN_G(x1)
U91_G(x1, x2)  =  U91_G(x1, x2)
U99_GG(x1, x2)  =  U99_GG(x1, x2)
U100_GG(x1, x2)  =  U100_GG(x1, x2)
LOG22084_IN_G(x1)  =  LOG22084_IN_G(x1)
U92_G(x1, x2)  =  U92_G(x1, x2)
U101_GG(x1, x2)  =  U101_GG(x1, x2)
U102_GG(x1, x2)  =  U102_GG(x1, x2)
LOG22139_IN_G(x1)  =  LOG22139_IN_G(x1)
U103_GG(x1, x2)  =  U103_GG(x1, x2)
U104_GG(x1, x2)  =  U104_GG(x1, x2)
LOG22176_IN_G(x1)  =  LOG22176_IN_G(x1)
U105_GG(x1, x2)  =  U105_GG(x1, x2)
U9_GGG(x1, x2, x3)  =  U9_GGG(x1, x2, x3)
U111_GG(x1, x2)  =  U111_GG(x1, x2)
LOG22254_IN_G(x1)  =  LOG22254_IN_G(x1)
U106_G(x1, x2)  =  U106_G(x1, x2)
U112_GG(x1, x2)  =  U112_GG(x1, x2)
U113_GG(x1, x2)  =  U113_GG(x1, x2)
LOG22320_IN_G(x1)  =  LOG22320_IN_G(x1)
U107_G(x1, x2)  =  U107_G(x1, x2)
U114_GG(x1, x2)  =  U114_GG(x1, x2)
U115_GG(x1, x2)  =  U115_GG(x1, x2)
LOG22390_IN_G(x1)  =  LOG22390_IN_G(x1)
U108_G(x1, x2)  =  U108_G(x1, x2)
U116_GG(x1, x2)  =  U116_GG(x1, x2)
U117_GG(x1, x2)  =  U117_GG(x1, x2)
LOG22441_IN_G(x1)  =  LOG22441_IN_G(x1)
U109_G(x1, x2)  =  U109_G(x1, x2)
U118_GG(x1, x2)  =  U118_GG(x1, x2)
U119_GG(x1, x2)  =  U119_GG(x1, x2)
LOG22496_IN_G(x1)  =  LOG22496_IN_G(x1)
U120_GG(x1, x2)  =  U120_GG(x1, x2)
U121_GG(x1, x2)  =  U121_GG(x1, x2)
LOG22533_IN_G(x1)  =  LOG22533_IN_G(x1)
U122_GG(x1, x2)  =  U122_GG(x1, x2)
U6_GGG(x1, x2, x3)  =  U6_GGG(x1, x2, x3)
U128_GG(x1, x2)  =  U128_GG(x1, x2)
LOG22611_IN_G(x1)  =  LOG22611_IN_G(x1)
U123_G(x1, x2)  =  U123_G(x1, x2)
U129_GG(x1, x2)  =  U129_GG(x1, x2)
U130_GG(x1, x2)  =  U130_GG(x1, x2)
LOG22677_IN_G(x1)  =  LOG22677_IN_G(x1)
U124_G(x1, x2)  =  U124_G(x1, x2)
U131_GG(x1, x2)  =  U131_GG(x1, x2)
U132_GG(x1, x2)  =  U132_GG(x1, x2)
LOG22747_IN_G(x1)  =  LOG22747_IN_G(x1)
U125_G(x1, x2)  =  U125_G(x1, x2)
U133_GG(x1, x2)  =  U133_GG(x1, x2)
U134_GG(x1, x2)  =  U134_GG(x1, x2)
LOG22798_IN_G(x1)  =  LOG22798_IN_G(x1)
U126_G(x1, x2)  =  U126_G(x1, x2)
U135_GG(x1, x2)  =  U135_GG(x1, x2)
U136_GG(x1, x2)  =  U136_GG(x1, x2)
LOG22853_IN_G(x1)  =  LOG22853_IN_G(x1)
U137_GG(x1, x2)  =  U137_GG(x1, x2)
U138_GG(x1, x2)  =  U138_GG(x1, x2)
LOG22890_IN_G(x1)  =  LOG22890_IN_G(x1)
U139_GG(x1, x2)  =  U139_GG(x1, x2)
U3_AGG(x1, x2, x3)  =  U3_AGG(x1, x2, x3)
U149_AG(x1, x2)  =  U149_AG(x1, x2)
LOG22968_IN_G(x1)  =  LOG22968_IN_G(x1)
U140_G(x1, x2)  =  U140_G(x1, x2)
U150_AG(x1, x2)  =  U150_AG(x1, x2)
U151_AG(x1, x2)  =  U151_AG(x1, x2)
LOG23034_IN_G(x1)  =  LOG23034_IN_G(x1)
U141_G(x1, x2)  =  U141_G(x1, x2)
U152_AG(x1, x2)  =  U152_AG(x1, x2)
U153_AG(x1, x2)  =  U153_AG(x1, x2)
LOG23104_IN_G(x1)  =  LOG23104_IN_G(x1)
U142_G(x1, x2)  =  U142_G(x1, x2)
U154_AG(x1, x2)  =  U154_AG(x1, x2)
U155_AG(x1, x2)  =  U155_AG(x1, x2)
LOG23155_IN_G(x1)  =  LOG23155_IN_G(x1)
U143_G(x1, x2)  =  U143_G(x1, x2)
U156_AG(x1, x2)  =  U156_AG(x1, x2)
U157_AG(x1, x2)  =  U157_AG(x1, x2)
LOG23210_IN_G(x1)  =  LOG23210_IN_G(x1)
U158_AG(x1, x2)  =  U158_AG(x1, x2)
U159_AG(x1, x2)  =  U159_AG(x1, x2)
LOG23247_IN_G(x1)  =  LOG23247_IN_G(x1)
U160_AG(x1, x2)  =  U160_AG(x1, x2)

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

(74) Obligation:

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

LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_AG(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → LOG244_IN_AGG(T109, s(s(s(s(s(s(s(0))))))), T108)
LOG244_IN_AGG(s(s(T131)), T129, T130) → U1_AGG(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
LOG244_IN_AGG(s(s(T131)), T129, T130) → LOG244_IN_AGG(T131, s(T129), T130)
LOG244_IN_AGG(0, s(T148), T149) → U2_AGG(T148, T149, log257_in_gg(T148, T149))
LOG244_IN_AGG(0, s(T148), T149) → LOG257_IN_GG(T148, T149)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_GG(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → LOG294_IN_GGG(T235, s(s(s(s(s(s(s(0))))))), T236)
LOG294_IN_GGG(s(s(T255)), T256, T257) → U4_GGG(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)
LOG294_IN_GGG(0, s(T274), T275) → U5_GGG(T274, T275, log2107_in_gg(T274, T275))
LOG294_IN_GGG(0, s(T274), T275) → LOG2107_IN_GG(T274, T275)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_GG(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → LOG2144_IN_GGG(T360, s(s(s(s(s(s(s(0))))))), T361)
LOG2144_IN_GGG(s(s(T380)), T381, T382) → U7_GGG(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)
LOG2144_IN_GGG(0, s(T399), T400) → U8_GGG(T399, T400, log2157_in_gg(T399, T400))
LOG2144_IN_GGG(0, s(T399), T400) → LOG2157_IN_GG(T399, T400)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_GG(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → LOG2194_IN_GGG(T485, s(s(s(s(s(s(s(0))))))), T486)
LOG2194_IN_GGG(s(s(T505)), T506, T507) → U10_GGG(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)
LOG2194_IN_GGG(0, s(T524), T525) → U11_GGG(T524, T525, log2207_in_gg(T524, T525))
LOG2194_IN_GGG(0, s(T524), T525) → LOG2207_IN_GG(T524, T525)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_GG(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → LOG2244_IN_GGG(T610, s(s(s(s(s(s(s(0))))))), T611)
LOG2244_IN_GGG(s(s(T630)), T631, T632) → U13_GGG(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)
LOG2244_IN_GGG(0, s(T649), T650) → U14_GGG(T649, T650, log2257_in_gg(T649, T650))
LOG2244_IN_GGG(0, s(T649), T650) → LOG2257_IN_GG(T649, T650)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_GG(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → LOG2294_IN_GGG(T735, s(s(s(s(s(s(s(0))))))), T736)
LOG2294_IN_GGG(s(s(T755)), T756, T757) → U16_GGG(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)
LOG2294_IN_GGG(0, s(T774), T775) → U17_GGG(T774, T775, log2307_in_gg(T774, T775))
LOG2294_IN_GGG(0, s(T774), T775) → LOG2307_IN_GG(T774, T775)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_GG(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → LOG2344_IN_GGG(T860, s(s(s(s(s(s(s(0))))))), T861)
LOG2344_IN_GGG(s(s(T880)), T881, T882) → U19_GGG(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)
LOG2344_IN_GGG(0, s(T899), T900) → U20_GGG(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
LOG2344_IN_GGG(0, s(T899), T900) → LOG2359_IN_GGG(T899, s(s(s(s(s(s(s(0))))))), T900)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_GGG(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → U22_GGGG(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → U23_GGGG(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_GGG(T1119, T1120, log2437_in_gg(T1119, T1120))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → LOG2437_IN_GG(T1119, T1120)
LOG2437_IN_GG(T1167, T1168) → U38_GG(T1167, T1168, log2454_in_gg(T1167, T1168))
LOG2437_IN_GG(T1167, T1168) → LOG2454_IN_GG(T1167, T1168)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_GGG(T1119, T1120, log2437_in_gg(T1119, T1120))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → LOG2437_IN_GG(T1119, T1120)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_GGG(T1222, T1223, log2515_in_gg(T1222, T1223))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → LOG2515_IN_GG(T1222, T1223)
LOG2515_IN_GG(T1270, T1271) → U39_GG(T1270, T1271, log2454_in_gg(T1270, T1271))
LOG2515_IN_GG(T1270, T1271) → LOG2454_IN_GG(T1270, T1271)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_GGG(T1222, T1223, log2515_in_gg(T1222, T1223))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → LOG2515_IN_GG(T1222, T1223)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_GGG(T1323, T1324, log2585_in_gg(T1323, T1324))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → LOG2585_IN_GG(T1323, T1324)
LOG2585_IN_GG(T1355, T1356) → U40_GG(T1355, T1356, log2598_in_gg(T1355, T1356))
LOG2585_IN_GG(T1355, T1356) → LOG2598_IN_GG(T1355, T1356)
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_GGG(T1323, T1324, log2585_in_gg(T1323, T1324))
LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → LOG2585_IN_GG(T1323, T1324)
LOG2359_IN_GGG(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_GGG(T1394, T1395, log2650_in_gg(T1394, T1395))
LOG2359_IN_GGG(s(s(s(s(s(s(0)))))), T1394, T1395) → LOG2650_IN_GG(T1394, T1395)
LOG2650_IN_GG(T1426, T1427) → U41_GG(T1426, T1427, log2598_in_gg(T1426, T1427))
LOG2650_IN_GG(T1426, T1427) → LOG2598_IN_GG(T1426, T1427)
LOG2359_IN_GGG(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_GGG(T1394, T1395, log2650_in_gg(T1394, T1395))
LOG2359_IN_GGG(s(s(s(s(s(s(s(0))))))), T1394, T1395) → LOG2650_IN_GG(T1394, T1395)
LOG2359_IN_GGG(s(s(s(s(0)))), T1461, T1462) → U34_GGG(T1461, T1462, log2705_in_gg(T1461, T1462))
LOG2359_IN_GGG(s(s(s(s(0)))), T1461, T1462) → LOG2705_IN_GG(T1461, T1462)
LOG2359_IN_GGG(s(s(s(s(s(0))))), T1461, T1462) → U35_GGG(T1461, T1462, log2705_in_gg(T1461, T1462))
LOG2359_IN_GGG(s(s(s(s(s(0))))), T1461, T1462) → LOG2705_IN_GG(T1461, T1462)
LOG2359_IN_GGG(s(s(0)), T1490, T1491) → U36_GGG(T1490, T1491, log2742_in_gg(T1490, T1491))
LOG2359_IN_GGG(s(s(0)), T1490, T1491) → LOG2742_IN_GG(T1490, T1491)
LOG2359_IN_GGG(s(s(s(0))), T1490, T1491) → U37_GGG(T1490, T1491, log2742_in_gg(T1490, T1491))
LOG2359_IN_GGG(s(s(s(0))), T1490, T1491) → LOG2742_IN_GG(T1490, T1491)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → U24_GGGG(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2344_IN_GGG(s(0), s(T899), T900) → U21_GGG(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
LOG2344_IN_GGG(s(0), s(T899), T900) → LOG2359_IN_GGG(T899, s(s(s(s(s(s(s(0))))))), T900)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_GG(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → LOG2822_IN_GG(s(s(s(s(s(s(s(0))))))), T1530)
LOG2822_IN_GG(T1578, T1579) → U144_GG(T1578, T1579, log2705_in_gg(T1578, T1579))
LOG2822_IN_GG(T1578, T1579) → LOG2705_IN_GG(T1578, T1579)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_GG(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → LOG2822_IN_GG(s(s(s(s(s(s(s(0))))))), T1530)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_GG(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → LOG2889_IN_GG(s(s(s(s(s(s(s(0))))))), T1620)
LOG2889_IN_GG(T1668, T1669) → U145_GG(T1668, T1669, log2705_in_gg(T1668, T1669))
LOG2889_IN_GG(T1668, T1669) → LOG2705_IN_GG(T1668, T1669)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_GG(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → LOG2889_IN_GG(s(s(s(s(s(s(s(0))))))), T1620)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_GG(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1711) → LOG2960_IN_GG(s(s(s(s(s(s(s(0))))))), T1711)
LOG2960_IN_GG(T1743, T1744) → U146_GG(T1743, T1744, log2742_in_gg(T1743, T1744))
LOG2960_IN_GG(T1743, T1744) → LOG2742_IN_GG(T1743, T1744)
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_GG(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
LOG2307_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → LOG2960_IN_GG(s(s(s(s(s(s(s(0))))))), T1711)
LOG2307_IN_GG(s(s(s(s(s(s(0)))))), T1769) → U49_GG(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
LOG2307_IN_GG(s(s(s(s(s(s(0)))))), T1769) → LOG21012_IN_GG(s(s(s(s(s(s(s(0))))))), T1769)
LOG21012_IN_GG(T1801, T1802) → U147_GG(T1801, T1802, log2742_in_gg(T1801, T1802))
LOG21012_IN_GG(T1801, T1802) → LOG2742_IN_GG(T1801, T1802)
LOG2307_IN_GG(s(s(s(s(s(s(s(0))))))), T1769) → U50_GG(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
LOG2307_IN_GG(s(s(s(s(s(s(s(0))))))), T1769) → LOG21012_IN_GG(s(s(s(s(s(s(s(0))))))), T1769)
LOG2307_IN_GG(s(s(s(s(0)))), T1826) → U51_GG(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
LOG2307_IN_GG(s(s(s(s(0)))), T1826) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1826)
LOG2307_IN_GG(s(s(s(s(s(0))))), T1826) → U52_GG(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
LOG2307_IN_GG(s(s(s(s(s(0))))), T1826) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1826)
LOG2307_IN_GG(s(s(0)), T1844) → U53_GG(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
LOG2307_IN_GG(s(s(0)), T1844) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1844)
LOG2307_IN_GG(s(s(s(0))), T1844) → U54_GG(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
LOG2307_IN_GG(s(s(s(0))), T1844) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1844)
LOG2294_IN_GGG(s(0), s(T774), T775) → U18_GGG(T774, T775, log2307_in_gg(T774, T775))
LOG2294_IN_GGG(s(0), s(T774), T775) → LOG2307_IN_GG(T774, T775)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_GG(T1876, log21183_in_g(T1876))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → LOG21183_IN_G(T1876)
LOG21183_IN_G(T1899) → U55_G(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
LOG21183_IN_G(T1899) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1899)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_GG(T1876, log21183_in_g(T1876))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → LOG21183_IN_G(T1876)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_GG(T1920, log21249_in_g(T1920))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → LOG21249_IN_G(T1920)
LOG21249_IN_G(T1943) → U56_G(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
LOG21249_IN_G(T1943) → LOG21068_IN_GG(s(s(s(s(s(s(s(0))))))), T1943)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_GG(T1920, log21249_in_g(T1920))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → LOG21249_IN_G(T1920)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_GG(T1964, log21319_in_g(T1964))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T1964) → LOG21319_IN_G(T1964)
LOG21319_IN_G(T1979) → U57_G(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
LOG21319_IN_G(T1979) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T1979)
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_GG(T1964, log21319_in_g(T1964))
LOG2257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → LOG21319_IN_G(T1964)
LOG2257_IN_GG(s(s(s(s(s(s(0)))))), T1995) → U66_GG(T1995, log21370_in_g(T1995))
LOG2257_IN_GG(s(s(s(s(s(s(0)))))), T1995) → LOG21370_IN_G(T1995)
LOG21370_IN_G(T2010) → U58_G(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
LOG21370_IN_G(T2010) → LOG21106_IN_GG(s(s(s(s(s(s(s(0))))))), T2010)
LOG2257_IN_GG(s(s(s(s(s(s(s(0))))))), T1995) → U67_GG(T1995, log21370_in_g(T1995))
LOG2257_IN_GG(s(s(s(s(s(s(s(0))))))), T1995) → LOG21370_IN_G(T1995)
LOG2257_IN_GG(s(s(s(s(0)))), T2024) → U68_GG(T2024, log21425_in_g(T2024))
LOG2257_IN_GG(s(s(s(s(0)))), T2024) → LOG21425_IN_G(T2024)
LOG2257_IN_GG(s(s(s(s(s(0))))), T2024) → U69_GG(T2024, log21425_in_g(T2024))
LOG2257_IN_GG(s(s(s(s(s(0))))), T2024) → LOG21425_IN_G(T2024)
LOG2257_IN_GG(s(s(0)), T2037) → U70_GG(T2037, log21462_in_g(T2037))
LOG2257_IN_GG(s(s(0)), T2037) → LOG21462_IN_G(T2037)
LOG2257_IN_GG(s(s(s(0))), T2037) → U71_GG(T2037, log21462_in_g(T2037))
LOG2257_IN_GG(s(s(s(0))), T2037) → LOG21462_IN_G(T2037)
LOG2244_IN_GGG(s(0), s(T649), T650) → U15_GGG(T649, T650, log2257_in_gg(T649, T650))
LOG2244_IN_GGG(s(0), s(T649), T650) → LOG2257_IN_GG(T649, T650)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_GG(T2064, log21540_in_g(T2064))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → LOG21540_IN_G(T2064)
LOG21540_IN_G(T2087) → U72_G(T2087, log21425_in_g(T2087))
LOG21540_IN_G(T2087) → LOG21425_IN_G(T2087)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_GG(T2064, log21540_in_g(T2064))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → LOG21540_IN_G(T2064)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_GG(T2108, log21606_in_g(T2108))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → LOG21606_IN_G(T2108)
LOG21606_IN_G(T2131) → U73_G(T2131, log21425_in_g(T2131))
LOG21606_IN_G(T2131) → LOG21425_IN_G(T2131)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_GG(T2108, log21606_in_g(T2108))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → LOG21606_IN_G(T2108)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_GG(T2152, log21676_in_g(T2152))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2152) → LOG21676_IN_G(T2152)
LOG21676_IN_G(T2167) → U74_G(T2167, log21462_in_g(T2167))
LOG21676_IN_G(T2167) → LOG21462_IN_G(T2167)
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_GG(T2152, log21676_in_g(T2152))
LOG2207_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → LOG21676_IN_G(T2152)
LOG2207_IN_GG(s(s(s(s(s(s(0)))))), T2183) → U83_GG(T2183, log21727_in_g(T2183))
LOG2207_IN_GG(s(s(s(s(s(s(0)))))), T2183) → LOG21727_IN_G(T2183)
LOG21727_IN_G(T2198) → U75_G(T2198, log21462_in_g(T2198))
LOG21727_IN_G(T2198) → LOG21462_IN_G(T2198)
LOG2207_IN_GG(s(s(s(s(s(s(s(0))))))), T2183) → U84_GG(T2183, log21727_in_g(T2183))
LOG2207_IN_GG(s(s(s(s(s(s(s(0))))))), T2183) → LOG21727_IN_G(T2183)
LOG2207_IN_GG(s(s(s(s(0)))), T2212) → U85_GG(T2212, log21782_in_g(T2212))
LOG2207_IN_GG(s(s(s(s(0)))), T2212) → LOG21782_IN_G(T2212)
LOG2207_IN_GG(s(s(s(s(s(0))))), T2212) → U86_GG(T2212, log21782_in_g(T2212))
LOG2207_IN_GG(s(s(s(s(s(0))))), T2212) → LOG21782_IN_G(T2212)
LOG2207_IN_GG(s(s(0)), T2225) → U87_GG(T2225, log21819_in_g(T2225))
LOG2207_IN_GG(s(s(0)), T2225) → LOG21819_IN_G(T2225)
LOG2207_IN_GG(s(s(s(0))), T2225) → U88_GG(T2225, log21819_in_g(T2225))
LOG2207_IN_GG(s(s(s(0))), T2225) → LOG21819_IN_G(T2225)
LOG2194_IN_GGG(s(0), s(T524), T525) → U12_GGG(T524, T525, log2207_in_gg(T524, T525))
LOG2194_IN_GGG(s(0), s(T524), T525) → LOG2207_IN_GG(T524, T525)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_GG(T2252, log21897_in_g(T2252))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → LOG21897_IN_G(T2252)
LOG21897_IN_G(T2275) → U89_G(T2275, log21782_in_g(T2275))
LOG21897_IN_G(T2275) → LOG21782_IN_G(T2275)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_GG(T2252, log21897_in_g(T2252))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → LOG21897_IN_G(T2252)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_GG(T2296, log21963_in_g(T2296))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → LOG21963_IN_G(T2296)
LOG21963_IN_G(T2319) → U90_G(T2319, log21782_in_g(T2319))
LOG21963_IN_G(T2319) → LOG21782_IN_G(T2319)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_GG(T2296, log21963_in_g(T2296))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → LOG21963_IN_G(T2296)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_GG(T2340, log22033_in_g(T2340))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2340) → LOG22033_IN_G(T2340)
LOG22033_IN_G(T2355) → U91_G(T2355, log21819_in_g(T2355))
LOG22033_IN_G(T2355) → LOG21819_IN_G(T2355)
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_GG(T2340, log22033_in_g(T2340))
LOG2157_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → LOG22033_IN_G(T2340)
LOG2157_IN_GG(s(s(s(s(s(s(0)))))), T2371) → U100_GG(T2371, log22084_in_g(T2371))
LOG2157_IN_GG(s(s(s(s(s(s(0)))))), T2371) → LOG22084_IN_G(T2371)
LOG22084_IN_G(T2386) → U92_G(T2386, log21819_in_g(T2386))
LOG22084_IN_G(T2386) → LOG21819_IN_G(T2386)
LOG2157_IN_GG(s(s(s(s(s(s(s(0))))))), T2371) → U101_GG(T2371, log22084_in_g(T2371))
LOG2157_IN_GG(s(s(s(s(s(s(s(0))))))), T2371) → LOG22084_IN_G(T2371)
LOG2157_IN_GG(s(s(s(s(0)))), T2400) → U102_GG(T2400, log22139_in_g(T2400))
LOG2157_IN_GG(s(s(s(s(0)))), T2400) → LOG22139_IN_G(T2400)
LOG2157_IN_GG(s(s(s(s(s(0))))), T2400) → U103_GG(T2400, log22139_in_g(T2400))
LOG2157_IN_GG(s(s(s(s(s(0))))), T2400) → LOG22139_IN_G(T2400)
LOG2157_IN_GG(s(s(0)), T2413) → U104_GG(T2413, log22176_in_g(T2413))
LOG2157_IN_GG(s(s(0)), T2413) → LOG22176_IN_G(T2413)
LOG2157_IN_GG(s(s(s(0))), T2413) → U105_GG(T2413, log22176_in_g(T2413))
LOG2157_IN_GG(s(s(s(0))), T2413) → LOG22176_IN_G(T2413)
LOG2144_IN_GGG(s(0), s(T399), T400) → U9_GGG(T399, T400, log2157_in_gg(T399, T400))
LOG2144_IN_GGG(s(0), s(T399), T400) → LOG2157_IN_GG(T399, T400)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_GG(T2440, log22254_in_g(T2440))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → LOG22254_IN_G(T2440)
LOG22254_IN_G(T2463) → U106_G(T2463, log22139_in_g(T2463))
LOG22254_IN_G(T2463) → LOG22139_IN_G(T2463)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_GG(T2440, log22254_in_g(T2440))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → LOG22254_IN_G(T2440)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_GG(T2484, log22320_in_g(T2484))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → LOG22320_IN_G(T2484)
LOG22320_IN_G(T2507) → U107_G(T2507, log22139_in_g(T2507))
LOG22320_IN_G(T2507) → LOG22139_IN_G(T2507)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_GG(T2484, log22320_in_g(T2484))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → LOG22320_IN_G(T2484)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_GG(T2528, log22390_in_g(T2528))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2528) → LOG22390_IN_G(T2528)
LOG22390_IN_G(T2543) → U108_G(T2543, log22176_in_g(T2543))
LOG22390_IN_G(T2543) → LOG22176_IN_G(T2543)
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_GG(T2528, log22390_in_g(T2528))
LOG2107_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → LOG22390_IN_G(T2528)
LOG2107_IN_GG(s(s(s(s(s(s(0)))))), T2559) → U117_GG(T2559, log22441_in_g(T2559))
LOG2107_IN_GG(s(s(s(s(s(s(0)))))), T2559) → LOG22441_IN_G(T2559)
LOG22441_IN_G(T2574) → U109_G(T2574, log22176_in_g(T2574))
LOG22441_IN_G(T2574) → LOG22176_IN_G(T2574)
LOG2107_IN_GG(s(s(s(s(s(s(s(0))))))), T2559) → U118_GG(T2559, log22441_in_g(T2559))
LOG2107_IN_GG(s(s(s(s(s(s(s(0))))))), T2559) → LOG22441_IN_G(T2559)
LOG2107_IN_GG(s(s(s(s(0)))), T2588) → U119_GG(T2588, log22496_in_g(T2588))
LOG2107_IN_GG(s(s(s(s(0)))), T2588) → LOG22496_IN_G(T2588)
LOG2107_IN_GG(s(s(s(s(s(0))))), T2588) → U120_GG(T2588, log22496_in_g(T2588))
LOG2107_IN_GG(s(s(s(s(s(0))))), T2588) → LOG22496_IN_G(T2588)
LOG2107_IN_GG(s(s(0)), T2601) → U121_GG(T2601, log22533_in_g(T2601))
LOG2107_IN_GG(s(s(0)), T2601) → LOG22533_IN_G(T2601)
LOG2107_IN_GG(s(s(s(0))), T2601) → U122_GG(T2601, log22533_in_g(T2601))
LOG2107_IN_GG(s(s(s(0))), T2601) → LOG22533_IN_G(T2601)
LOG294_IN_GGG(s(0), s(T274), T275) → U6_GGG(T274, T275, log2107_in_gg(T274, T275))
LOG294_IN_GGG(s(0), s(T274), T275) → LOG2107_IN_GG(T274, T275)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_GG(T2628, log22611_in_g(T2628))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → LOG22611_IN_G(T2628)
LOG22611_IN_G(T2651) → U123_G(T2651, log22496_in_g(T2651))
LOG22611_IN_G(T2651) → LOG22496_IN_G(T2651)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_GG(T2628, log22611_in_g(T2628))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → LOG22611_IN_G(T2628)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_GG(T2672, log22677_in_g(T2672))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → LOG22677_IN_G(T2672)
LOG22677_IN_G(T2695) → U124_G(T2695, log22496_in_g(T2695))
LOG22677_IN_G(T2695) → LOG22496_IN_G(T2695)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_GG(T2672, log22677_in_g(T2672))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → LOG22677_IN_G(T2672)
LOG257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_GG(T2716, log22747_in_g(T2716))
LOG257_IN_GG(s(s(s(s(s(s(s(s(0)))))))), T2716) → LOG22747_IN_G(T2716)
LOG22747_IN_G(T2731) → U125_G(T2731, log22533_in_g(T2731))
LOG22747_IN_G(T2731) → LOG22533_IN_G(T2731)
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_GG(T2716, log22747_in_g(T2716))
LOG257_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → LOG22747_IN_G(T2716)
LOG257_IN_GG(s(s(s(s(s(s(0)))))), T2747) → U134_GG(T2747, log22798_in_g(T2747))
LOG257_IN_GG(s(s(s(s(s(s(0)))))), T2747) → LOG22798_IN_G(T2747)
LOG22798_IN_G(T2762) → U126_G(T2762, log22533_in_g(T2762))
LOG22798_IN_G(T2762) → LOG22533_IN_G(T2762)
LOG257_IN_GG(s(s(s(s(s(s(s(0))))))), T2747) → U135_GG(T2747, log22798_in_g(T2747))
LOG257_IN_GG(s(s(s(s(s(s(s(0))))))), T2747) → LOG22798_IN_G(T2747)
LOG257_IN_GG(s(s(s(s(0)))), T2776) → U136_GG(T2776, log22853_in_g(T2776))
LOG257_IN_GG(s(s(s(s(0)))), T2776) → LOG22853_IN_G(T2776)
LOG257_IN_GG(s(s(s(s(s(0))))), T2776) → U137_GG(T2776, log22853_in_g(T2776))
LOG257_IN_GG(s(s(s(s(s(0))))), T2776) → LOG22853_IN_G(T2776)
LOG257_IN_GG(s(s(0)), T2789) → U138_GG(T2789, log22890_in_g(T2789))
LOG257_IN_GG(s(s(0)), T2789) → LOG22890_IN_G(T2789)
LOG257_IN_GG(s(s(s(0))), T2789) → U139_GG(T2789, log22890_in_g(T2789))
LOG257_IN_GG(s(s(s(0))), T2789) → LOG22890_IN_G(T2789)
LOG244_IN_AGG(s(0), s(T148), T149) → U3_AGG(T148, T149, log257_in_gg(T148, T149))
LOG244_IN_AGG(s(0), s(T148), T149) → LOG257_IN_GG(T148, T149)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_AG(T2819, log22968_in_g(T2819))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → LOG22968_IN_G(T2819)
LOG22968_IN_G(T2843) → U140_G(T2843, log22853_in_g(T2843))
LOG22968_IN_G(T2843) → LOG22853_IN_G(T2843)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_AG(T2819, log22968_in_g(T2819))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → LOG22968_IN_G(T2819)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_AG(T2867, log23034_in_g(T2867))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → LOG23034_IN_G(T2867)
LOG23034_IN_G(T2891) → U141_G(T2891, log22853_in_g(T2891))
LOG23034_IN_G(T2891) → LOG22853_IN_G(T2891)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_AG(T2867, log23034_in_g(T2867))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → LOG23034_IN_G(T2867)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_AG(T2915, log23104_in_g(T2915))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → LOG23104_IN_G(T2915)
LOG23104_IN_G(T2931) → U142_G(T2931, log22890_in_g(T2931))
LOG23104_IN_G(T2931) → LOG22890_IN_G(T2931)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_AG(T2915, log23104_in_g(T2915))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → LOG23104_IN_G(T2915)
LOG21_IN_AG(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_AG(T2950, log23155_in_g(T2950))
LOG21_IN_AG(s(s(s(s(s(s(s(s(0)))))))), T2950) → LOG23155_IN_G(T2950)
LOG23155_IN_G(T2966) → U143_G(T2966, log22890_in_g(T2966))
LOG23155_IN_G(T2966) → LOG22890_IN_G(T2966)
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_AG(T2950, log23155_in_g(T2950))
LOG21_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → LOG23155_IN_G(T2950)
LOG21_IN_AG(s(s(s(s(s(s(0)))))), T2983) → U157_AG(T2983, log23210_in_g(T2983))
LOG21_IN_AG(s(s(s(s(s(s(0)))))), T2983) → LOG23210_IN_G(T2983)
LOG21_IN_AG(s(s(s(s(s(s(s(0))))))), T2983) → U158_AG(T2983, log23210_in_g(T2983))
LOG21_IN_AG(s(s(s(s(s(s(s(0))))))), T2983) → LOG23210_IN_G(T2983)
LOG21_IN_AG(s(s(s(s(0)))), T3000) → U159_AG(T3000, log23247_in_g(T3000))
LOG21_IN_AG(s(s(s(s(0)))), T3000) → LOG23247_IN_G(T3000)
LOG21_IN_AG(s(s(s(s(s(0))))), T3000) → U160_AG(T3000, log23247_in_g(T3000))
LOG21_IN_AG(s(s(s(s(s(0))))), T3000) → LOG23247_IN_G(T3000)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG21_IN_AG(x1, x2)  =  LOG21_IN_AG(x2)
U148_AG(x1, x2, x3)  =  U148_AG(x2, x3)
LOG244_IN_AGG(x1, x2, x3)  =  LOG244_IN_AGG(x2, x3)
U1_AGG(x1, x2, x3, x4)  =  U1_AGG(x2, x3, x4)
U2_AGG(x1, x2, x3)  =  U2_AGG(x1, x2, x3)
LOG257_IN_GG(x1, x2)  =  LOG257_IN_GG(x1, x2)
U127_GG(x1, x2, x3)  =  U127_GG(x1, x2, x3)
LOG294_IN_GGG(x1, x2, x3)  =  LOG294_IN_GGG(x1, x2, x3)
U4_GGG(x1, x2, x3, x4)  =  U4_GGG(x1, x2, x3, x4)
U5_GGG(x1, x2, x3)  =  U5_GGG(x1, x2, x3)
LOG2107_IN_GG(x1, x2)  =  LOG2107_IN_GG(x1, x2)
U110_GG(x1, x2, x3)  =  U110_GG(x1, x2, x3)
LOG2144_IN_GGG(x1, x2, x3)  =  LOG2144_IN_GGG(x1, x2, x3)
U7_GGG(x1, x2, x3, x4)  =  U7_GGG(x1, x2, x3, x4)
U8_GGG(x1, x2, x3)  =  U8_GGG(x1, x2, x3)
LOG2157_IN_GG(x1, x2)  =  LOG2157_IN_GG(x1, x2)
U93_GG(x1, x2, x3)  =  U93_GG(x1, x2, x3)
LOG2194_IN_GGG(x1, x2, x3)  =  LOG2194_IN_GGG(x1, x2, x3)
U10_GGG(x1, x2, x3, x4)  =  U10_GGG(x1, x2, x3, x4)
U11_GGG(x1, x2, x3)  =  U11_GGG(x1, x2, x3)
LOG2207_IN_GG(x1, x2)  =  LOG2207_IN_GG(x1, x2)
U76_GG(x1, x2, x3)  =  U76_GG(x1, x2, x3)
LOG2244_IN_GGG(x1, x2, x3)  =  LOG2244_IN_GGG(x1, x2, x3)
U13_GGG(x1, x2, x3, x4)  =  U13_GGG(x1, x2, x3, x4)
U14_GGG(x1, x2, x3)  =  U14_GGG(x1, x2, x3)
LOG2257_IN_GG(x1, x2)  =  LOG2257_IN_GG(x1, x2)
U59_GG(x1, x2, x3)  =  U59_GG(x1, x2, x3)
LOG2294_IN_GGG(x1, x2, x3)  =  LOG2294_IN_GGG(x1, x2, x3)
U16_GGG(x1, x2, x3, x4)  =  U16_GGG(x1, x2, x3, x4)
U17_GGG(x1, x2, x3)  =  U17_GGG(x1, x2, x3)
LOG2307_IN_GG(x1, x2)  =  LOG2307_IN_GG(x1, x2)
U42_GG(x1, x2, x3)  =  U42_GG(x1, x2, x3)
LOG2344_IN_GGG(x1, x2, x3)  =  LOG2344_IN_GGG(x1, x2, x3)
U19_GGG(x1, x2, x3, x4)  =  U19_GGG(x1, x2, x3, x4)
U20_GGG(x1, x2, x3)  =  U20_GGG(x1, x2, x3)
LOG2359_IN_GGG(x1, x2, x3)  =  LOG2359_IN_GGG(x1, x2, x3)
U25_GGG(x1, x2, x3, x4)  =  U25_GGG(x1, x2, x3, x4)
LOG2395_IN_GGGG(x1, x2, x3, x4)  =  LOG2395_IN_GGGG(x1, x2, x3, x4)
U22_GGGG(x1, x2, x3, x4, x5)  =  U22_GGGG(x1, x2, x3, x4, x5)
U23_GGGG(x1, x2, x3, x4)  =  U23_GGGG(x1, x2, x3, x4)
U26_GGG(x1, x2, x3)  =  U26_GGG(x1, x2, x3)
LOG2437_IN_GG(x1, x2)  =  LOG2437_IN_GG(x1, x2)
U38_GG(x1, x2, x3)  =  U38_GG(x1, x2, x3)
LOG2454_IN_GG(x1, x2)  =  LOG2454_IN_GG(x1, x2)
U27_GGG(x1, x2, x3)  =  U27_GGG(x1, x2, x3)
U28_GGG(x1, x2, x3)  =  U28_GGG(x1, x2, x3)
LOG2515_IN_GG(x1, x2)  =  LOG2515_IN_GG(x1, x2)
U39_GG(x1, x2, x3)  =  U39_GG(x1, x2, x3)
U29_GGG(x1, x2, x3)  =  U29_GGG(x1, x2, x3)
U30_GGG(x1, x2, x3)  =  U30_GGG(x1, x2, x3)
LOG2585_IN_GG(x1, x2)  =  LOG2585_IN_GG(x1, x2)
U40_GG(x1, x2, x3)  =  U40_GG(x1, x2, x3)
LOG2598_IN_GG(x1, x2)  =  LOG2598_IN_GG(x1, x2)
U31_GGG(x1, x2, x3)  =  U31_GGG(x1, x2, x3)
U32_GGG(x1, x2, x3)  =  U32_GGG(x1, x2, x3)
LOG2650_IN_GG(x1, x2)  =  LOG2650_IN_GG(x1, x2)
U41_GG(x1, x2, x3)  =  U41_GG(x1, x2, x3)
U33_GGG(x1, x2, x3)  =  U33_GGG(x1, x2, x3)
U34_GGG(x1, x2, x3)  =  U34_GGG(x1, x2, x3)
LOG2705_IN_GG(x1, x2)  =  LOG2705_IN_GG(x1, x2)
U35_GGG(x1, x2, x3)  =  U35_GGG(x1, x2, x3)
U36_GGG(x1, x2, x3)  =  U36_GGG(x1, x2, x3)
LOG2742_IN_GG(x1, x2)  =  LOG2742_IN_GG(x1, x2)
U37_GGG(x1, x2, x3)  =  U37_GGG(x1, x2, x3)
U24_GGGG(x1, x2, x3, x4)  =  U24_GGGG(x1, x2, x3, x4)
U21_GGG(x1, x2, x3)  =  U21_GGG(x1, x2, x3)
U43_GG(x1, x2)  =  U43_GG(x1, x2)
LOG2822_IN_GG(x1, x2)  =  LOG2822_IN_GG(x1, x2)
U144_GG(x1, x2, x3)  =  U144_GG(x1, x2, x3)
U44_GG(x1, x2)  =  U44_GG(x1, x2)
U45_GG(x1, x2)  =  U45_GG(x1, x2)
LOG2889_IN_GG(x1, x2)  =  LOG2889_IN_GG(x1, x2)
U145_GG(x1, x2, x3)  =  U145_GG(x1, x2, x3)
U46_GG(x1, x2)  =  U46_GG(x1, x2)
U47_GG(x1, x2)  =  U47_GG(x1, x2)
LOG2960_IN_GG(x1, x2)  =  LOG2960_IN_GG(x1, x2)
U146_GG(x1, x2, x3)  =  U146_GG(x1, x2, x3)
U48_GG(x1, x2)  =  U48_GG(x1, x2)
U49_GG(x1, x2)  =  U49_GG(x1, x2)
LOG21012_IN_GG(x1, x2)  =  LOG21012_IN_GG(x1, x2)
U147_GG(x1, x2, x3)  =  U147_GG(x1, x2, x3)
U50_GG(x1, x2)  =  U50_GG(x1, x2)
U51_GG(x1, x2)  =  U51_GG(x1, x2)
LOG21068_IN_GG(x1, x2)  =  LOG21068_IN_GG(x1, x2)
U52_GG(x1, x2)  =  U52_GG(x1, x2)
U53_GG(x1, x2)  =  U53_GG(x1, x2)
LOG21106_IN_GG(x1, x2)  =  LOG21106_IN_GG(x1, x2)
U54_GG(x1, x2)  =  U54_GG(x1, x2)
U18_GGG(x1, x2, x3)  =  U18_GGG(x1, x2, x3)
U60_GG(x1, x2)  =  U60_GG(x1, x2)
LOG21183_IN_G(x1)  =  LOG21183_IN_G(x1)
U55_G(x1, x2)  =  U55_G(x1, x2)
U61_GG(x1, x2)  =  U61_GG(x1, x2)
U62_GG(x1, x2)  =  U62_GG(x1, x2)
LOG21249_IN_G(x1)  =  LOG21249_IN_G(x1)
U56_G(x1, x2)  =  U56_G(x1, x2)
U63_GG(x1, x2)  =  U63_GG(x1, x2)
U64_GG(x1, x2)  =  U64_GG(x1, x2)
LOG21319_IN_G(x1)  =  LOG21319_IN_G(x1)
U57_G(x1, x2)  =  U57_G(x1, x2)
U65_GG(x1, x2)  =  U65_GG(x1, x2)
U66_GG(x1, x2)  =  U66_GG(x1, x2)
LOG21370_IN_G(x1)  =  LOG21370_IN_G(x1)
U58_G(x1, x2)  =  U58_G(x1, x2)
U67_GG(x1, x2)  =  U67_GG(x1, x2)
U68_GG(x1, x2)  =  U68_GG(x1, x2)
LOG21425_IN_G(x1)  =  LOG21425_IN_G(x1)
U69_GG(x1, x2)  =  U69_GG(x1, x2)
U70_GG(x1, x2)  =  U70_GG(x1, x2)
LOG21462_IN_G(x1)  =  LOG21462_IN_G(x1)
U71_GG(x1, x2)  =  U71_GG(x1, x2)
U15_GGG(x1, x2, x3)  =  U15_GGG(x1, x2, x3)
U77_GG(x1, x2)  =  U77_GG(x1, x2)
LOG21540_IN_G(x1)  =  LOG21540_IN_G(x1)
U72_G(x1, x2)  =  U72_G(x1, x2)
U78_GG(x1, x2)  =  U78_GG(x1, x2)
U79_GG(x1, x2)  =  U79_GG(x1, x2)
LOG21606_IN_G(x1)  =  LOG21606_IN_G(x1)
U73_G(x1, x2)  =  U73_G(x1, x2)
U80_GG(x1, x2)  =  U80_GG(x1, x2)
U81_GG(x1, x2)  =  U81_GG(x1, x2)
LOG21676_IN_G(x1)  =  LOG21676_IN_G(x1)
U74_G(x1, x2)  =  U74_G(x1, x2)
U82_GG(x1, x2)  =  U82_GG(x1, x2)
U83_GG(x1, x2)  =  U83_GG(x1, x2)
LOG21727_IN_G(x1)  =  LOG21727_IN_G(x1)
U75_G(x1, x2)  =  U75_G(x1, x2)
U84_GG(x1, x2)  =  U84_GG(x1, x2)
U85_GG(x1, x2)  =  U85_GG(x1, x2)
LOG21782_IN_G(x1)  =  LOG21782_IN_G(x1)
U86_GG(x1, x2)  =  U86_GG(x1, x2)
U87_GG(x1, x2)  =  U87_GG(x1, x2)
LOG21819_IN_G(x1)  =  LOG21819_IN_G(x1)
U88_GG(x1, x2)  =  U88_GG(x1, x2)
U12_GGG(x1, x2, x3)  =  U12_GGG(x1, x2, x3)
U94_GG(x1, x2)  =  U94_GG(x1, x2)
LOG21897_IN_G(x1)  =  LOG21897_IN_G(x1)
U89_G(x1, x2)  =  U89_G(x1, x2)
U95_GG(x1, x2)  =  U95_GG(x1, x2)
U96_GG(x1, x2)  =  U96_GG(x1, x2)
LOG21963_IN_G(x1)  =  LOG21963_IN_G(x1)
U90_G(x1, x2)  =  U90_G(x1, x2)
U97_GG(x1, x2)  =  U97_GG(x1, x2)
U98_GG(x1, x2)  =  U98_GG(x1, x2)
LOG22033_IN_G(x1)  =  LOG22033_IN_G(x1)
U91_G(x1, x2)  =  U91_G(x1, x2)
U99_GG(x1, x2)  =  U99_GG(x1, x2)
U100_GG(x1, x2)  =  U100_GG(x1, x2)
LOG22084_IN_G(x1)  =  LOG22084_IN_G(x1)
U92_G(x1, x2)  =  U92_G(x1, x2)
U101_GG(x1, x2)  =  U101_GG(x1, x2)
U102_GG(x1, x2)  =  U102_GG(x1, x2)
LOG22139_IN_G(x1)  =  LOG22139_IN_G(x1)
U103_GG(x1, x2)  =  U103_GG(x1, x2)
U104_GG(x1, x2)  =  U104_GG(x1, x2)
LOG22176_IN_G(x1)  =  LOG22176_IN_G(x1)
U105_GG(x1, x2)  =  U105_GG(x1, x2)
U9_GGG(x1, x2, x3)  =  U9_GGG(x1, x2, x3)
U111_GG(x1, x2)  =  U111_GG(x1, x2)
LOG22254_IN_G(x1)  =  LOG22254_IN_G(x1)
U106_G(x1, x2)  =  U106_G(x1, x2)
U112_GG(x1, x2)  =  U112_GG(x1, x2)
U113_GG(x1, x2)  =  U113_GG(x1, x2)
LOG22320_IN_G(x1)  =  LOG22320_IN_G(x1)
U107_G(x1, x2)  =  U107_G(x1, x2)
U114_GG(x1, x2)  =  U114_GG(x1, x2)
U115_GG(x1, x2)  =  U115_GG(x1, x2)
LOG22390_IN_G(x1)  =  LOG22390_IN_G(x1)
U108_G(x1, x2)  =  U108_G(x1, x2)
U116_GG(x1, x2)  =  U116_GG(x1, x2)
U117_GG(x1, x2)  =  U117_GG(x1, x2)
LOG22441_IN_G(x1)  =  LOG22441_IN_G(x1)
U109_G(x1, x2)  =  U109_G(x1, x2)
U118_GG(x1, x2)  =  U118_GG(x1, x2)
U119_GG(x1, x2)  =  U119_GG(x1, x2)
LOG22496_IN_G(x1)  =  LOG22496_IN_G(x1)
U120_GG(x1, x2)  =  U120_GG(x1, x2)
U121_GG(x1, x2)  =  U121_GG(x1, x2)
LOG22533_IN_G(x1)  =  LOG22533_IN_G(x1)
U122_GG(x1, x2)  =  U122_GG(x1, x2)
U6_GGG(x1, x2, x3)  =  U6_GGG(x1, x2, x3)
U128_GG(x1, x2)  =  U128_GG(x1, x2)
LOG22611_IN_G(x1)  =  LOG22611_IN_G(x1)
U123_G(x1, x2)  =  U123_G(x1, x2)
U129_GG(x1, x2)  =  U129_GG(x1, x2)
U130_GG(x1, x2)  =  U130_GG(x1, x2)
LOG22677_IN_G(x1)  =  LOG22677_IN_G(x1)
U124_G(x1, x2)  =  U124_G(x1, x2)
U131_GG(x1, x2)  =  U131_GG(x1, x2)
U132_GG(x1, x2)  =  U132_GG(x1, x2)
LOG22747_IN_G(x1)  =  LOG22747_IN_G(x1)
U125_G(x1, x2)  =  U125_G(x1, x2)
U133_GG(x1, x2)  =  U133_GG(x1, x2)
U134_GG(x1, x2)  =  U134_GG(x1, x2)
LOG22798_IN_G(x1)  =  LOG22798_IN_G(x1)
U126_G(x1, x2)  =  U126_G(x1, x2)
U135_GG(x1, x2)  =  U135_GG(x1, x2)
U136_GG(x1, x2)  =  U136_GG(x1, x2)
LOG22853_IN_G(x1)  =  LOG22853_IN_G(x1)
U137_GG(x1, x2)  =  U137_GG(x1, x2)
U138_GG(x1, x2)  =  U138_GG(x1, x2)
LOG22890_IN_G(x1)  =  LOG22890_IN_G(x1)
U139_GG(x1, x2)  =  U139_GG(x1, x2)
U3_AGG(x1, x2, x3)  =  U3_AGG(x1, x2, x3)
U149_AG(x1, x2)  =  U149_AG(x1, x2)
LOG22968_IN_G(x1)  =  LOG22968_IN_G(x1)
U140_G(x1, x2)  =  U140_G(x1, x2)
U150_AG(x1, x2)  =  U150_AG(x1, x2)
U151_AG(x1, x2)  =  U151_AG(x1, x2)
LOG23034_IN_G(x1)  =  LOG23034_IN_G(x1)
U141_G(x1, x2)  =  U141_G(x1, x2)
U152_AG(x1, x2)  =  U152_AG(x1, x2)
U153_AG(x1, x2)  =  U153_AG(x1, x2)
LOG23104_IN_G(x1)  =  LOG23104_IN_G(x1)
U142_G(x1, x2)  =  U142_G(x1, x2)
U154_AG(x1, x2)  =  U154_AG(x1, x2)
U155_AG(x1, x2)  =  U155_AG(x1, x2)
LOG23155_IN_G(x1)  =  LOG23155_IN_G(x1)
U143_G(x1, x2)  =  U143_G(x1, x2)
U156_AG(x1, x2)  =  U156_AG(x1, x2)
U157_AG(x1, x2)  =  U157_AG(x1, x2)
LOG23210_IN_G(x1)  =  LOG23210_IN_G(x1)
U158_AG(x1, x2)  =  U158_AG(x1, x2)
U159_AG(x1, x2)  =  U159_AG(x1, x2)
LOG23247_IN_G(x1)  =  LOG23247_IN_G(x1)
U160_AG(x1, x2)  =  U160_AG(x1, x2)

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

(75) DependencyGraphProof (EQUIVALENT transformation)

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

(76) Complex Obligation (AND)

(77) Obligation:

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

LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG2359_IN_GGG(x1, x2, x3)  =  LOG2359_IN_GGG(x1, x2, x3)
LOG2395_IN_GGGG(x1, x2, x3, x4)  =  LOG2395_IN_GGGG(x1, x2, x3, x4)

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

(78) UsableRulesProof (EQUIVALENT transformation)

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

(79) Obligation:

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

LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)

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

(80) PiDPToQDPProof (EQUIVALENT transformation)

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

(81) Obligation:

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

LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)

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

(82) 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:

LOG2359_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → LOG2395_IN_GGGG(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)
LOG2395_IN_GGGG(s(s(T1056)), T1057, T1058, T1059) → LOG2395_IN_GGGG(T1056, s(T1057), T1058, T1059)
LOG2395_IN_GGGG(0, s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)
LOG2395_IN_GGGG(s(0), s(T1081), T1082, T1083) → LOG2359_IN_GGG(T1081, s(T1082), T1083)


Used ordering: Polynomial interpretation [POLO]:

POL(0) = 0   
POL(LOG2359_IN_GGG(x1, x2, x3)) = x1 + x2 + x3   
POL(LOG2395_IN_GGGG(x1, x2, x3, x4)) = 1 + x1 + x2 + x3 + x4   
POL(s(x1)) = 1 + x1   

(83) Obligation:

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

(84) PisEmptyProof (EQUIVALENT transformation)

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

(85) YES

(86) Obligation:

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

LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG2344_IN_GGG(x1, x2, x3)  =  LOG2344_IN_GGG(x1, x2, x3)

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

(87) UsableRulesProof (EQUIVALENT transformation)

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

(88) Obligation:

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

LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)

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

(89) PiDPToQDPProof (EQUIVALENT transformation)

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

(90) Obligation:

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

LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)

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

(91) 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:

  • LOG2344_IN_GGG(s(s(T880)), T881, T882) → LOG2344_IN_GGG(T880, s(T881), T882)
    The graph contains the following edges 1 > 1, 3 >= 3

(92) YES

(93) Obligation:

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

LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG2294_IN_GGG(x1, x2, x3)  =  LOG2294_IN_GGG(x1, x2, x3)

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

(94) UsableRulesProof (EQUIVALENT transformation)

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

(95) Obligation:

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

LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)

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

(96) PiDPToQDPProof (EQUIVALENT transformation)

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

(97) Obligation:

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

LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)

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

(98) 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:

  • LOG2294_IN_GGG(s(s(T755)), T756, T757) → LOG2294_IN_GGG(T755, s(T756), T757)
    The graph contains the following edges 1 > 1, 3 >= 3

(99) YES

(100) Obligation:

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

LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG2244_IN_GGG(x1, x2, x3)  =  LOG2244_IN_GGG(x1, x2, x3)

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

(101) UsableRulesProof (EQUIVALENT transformation)

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

(102) Obligation:

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

LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)

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

(103) PiDPToQDPProof (EQUIVALENT transformation)

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

(104) Obligation:

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

LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)

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

(105) 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:

  • LOG2244_IN_GGG(s(s(T630)), T631, T632) → LOG2244_IN_GGG(T630, s(T631), T632)
    The graph contains the following edges 1 > 1, 3 >= 3

(106) YES

(107) Obligation:

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

LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG2194_IN_GGG(x1, x2, x3)  =  LOG2194_IN_GGG(x1, x2, x3)

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

(108) UsableRulesProof (EQUIVALENT transformation)

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

(109) Obligation:

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

LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)

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

(110) PiDPToQDPProof (EQUIVALENT transformation)

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

(111) Obligation:

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

LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)

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

(112) 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:

  • LOG2194_IN_GGG(s(s(T505)), T506, T507) → LOG2194_IN_GGG(T505, s(T506), T507)
    The graph contains the following edges 1 > 1, 3 >= 3

(113) YES

(114) Obligation:

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

LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG2144_IN_GGG(x1, x2, x3)  =  LOG2144_IN_GGG(x1, x2, x3)

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

(115) UsableRulesProof (EQUIVALENT transformation)

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

(116) Obligation:

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

LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)

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

(117) PiDPToQDPProof (EQUIVALENT transformation)

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

(118) Obligation:

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

LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)

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

(119) 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:

  • LOG2144_IN_GGG(s(s(T380)), T381, T382) → LOG2144_IN_GGG(T380, s(T381), T382)
    The graph contains the following edges 1 > 1, 3 >= 3

(120) YES

(121) Obligation:

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

LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG294_IN_GGG(x1, x2, x3)  =  LOG294_IN_GGG(x1, x2, x3)

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

(122) UsableRulesProof (EQUIVALENT transformation)

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

(123) Obligation:

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

LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)

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

(124) PiDPToQDPProof (EQUIVALENT transformation)

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

(125) Obligation:

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

LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)

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

(126) 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:

  • LOG294_IN_GGG(s(s(T255)), T256, T257) → LOG294_IN_GGG(T255, s(T256), T257)
    The graph contains the following edges 1 > 1, 3 >= 3

(127) YES

(128) Obligation:

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

LOG244_IN_AGG(s(s(T131)), T129, T130) → LOG244_IN_AGG(T131, s(T129), T130)

The TRS R consists of the following rules:

log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108) → U148_ag(T109, T108, log244_in_agg(T109, s(s(s(s(s(s(s(0))))))), T108))
log244_in_agg(s(s(T131)), T129, T130) → U1_agg(T131, T129, T130, log244_in_agg(T131, s(T129), T130))
log244_in_agg(0, s(T148), T149) → U2_agg(T148, T149, log257_in_gg(T148, T149))
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236) → U127_gg(T235, T236, log294_in_ggg(T235, s(s(s(s(s(s(s(0))))))), T236))
log294_in_ggg(s(s(T255)), T256, T257) → U4_ggg(T255, T256, T257, log294_in_ggg(T255, s(T256), T257))
log294_in_ggg(0, s(T274), T275) → U5_ggg(T274, T275, log2107_in_gg(T274, T275))
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361) → U110_gg(T360, T361, log2144_in_ggg(T360, s(s(s(s(s(s(s(0))))))), T361))
log2144_in_ggg(s(s(T380)), T381, T382) → U7_ggg(T380, T381, T382, log2144_in_ggg(T380, s(T381), T382))
log2144_in_ggg(0, s(T399), T400) → U8_ggg(T399, T400, log2157_in_gg(T399, T400))
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486) → U93_gg(T485, T486, log2194_in_ggg(T485, s(s(s(s(s(s(s(0))))))), T486))
log2194_in_ggg(s(s(T505)), T506, T507) → U10_ggg(T505, T506, T507, log2194_in_ggg(T505, s(T506), T507))
log2194_in_ggg(0, s(T524), T525) → U11_ggg(T524, T525, log2207_in_gg(T524, T525))
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611) → U76_gg(T610, T611, log2244_in_ggg(T610, s(s(s(s(s(s(s(0))))))), T611))
log2244_in_ggg(s(s(T630)), T631, T632) → U13_ggg(T630, T631, T632, log2244_in_ggg(T630, s(T631), T632))
log2244_in_ggg(0, s(T649), T650) → U14_ggg(T649, T650, log2257_in_gg(T649, T650))
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736) → U59_gg(T735, T736, log2294_in_ggg(T735, s(s(s(s(s(s(s(0))))))), T736))
log2294_in_ggg(s(s(T755)), T756, T757) → U16_ggg(T755, T756, T757, log2294_in_ggg(T755, s(T756), T757))
log2294_in_ggg(0, s(T774), T775) → U17_ggg(T774, T775, log2307_in_gg(T774, T775))
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861) → U42_gg(T860, T861, log2344_in_ggg(T860, s(s(s(s(s(s(s(0))))))), T861))
log2344_in_ggg(s(s(T880)), T881, T882) → U19_ggg(T880, T881, T882, log2344_in_ggg(T880, s(T881), T882))
log2344_in_ggg(0, s(T899), T900) → U20_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031) → U25_ggg(T1029, T1030, T1031, log2395_in_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031))
log2395_in_gggg(s(s(T1056)), T1057, T1058, T1059) → U22_gggg(T1056, T1057, T1058, T1059, log2395_in_gggg(T1056, s(T1057), T1058, T1059))
log2395_in_gggg(0, s(T1081), T1082, T1083) → U23_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120) → U26_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
log2437_in_gg(T1167, T1168) → U38_gg(T1167, T1168, log2454_in_gg(T1167, T1168))
log2454_in_gg(T1174, s(s(s(T1174)))) → log2454_out_gg(T1174, s(s(s(T1174))))
U38_gg(T1167, T1168, log2454_out_gg(T1167, T1168)) → log2437_out_gg(T1167, T1168)
U26_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120) → U27_ggg(T1119, T1120, log2437_in_gg(T1119, T1120))
U27_ggg(T1119, T1120, log2437_out_gg(T1119, T1120)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1119, T1120)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223) → U28_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
log2515_in_gg(T1270, T1271) → U39_gg(T1270, T1271, log2454_in_gg(T1270, T1271))
U39_gg(T1270, T1271, log2454_out_gg(T1270, T1271)) → log2515_out_gg(T1270, T1271)
U28_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223) → U29_ggg(T1222, T1223, log2515_in_gg(T1222, T1223))
U29_ggg(T1222, T1223, log2515_out_gg(T1222, T1223)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1222, T1223)
log2359_in_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324) → U30_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
log2585_in_gg(T1355, T1356) → U40_gg(T1355, T1356, log2598_in_gg(T1355, T1356))
log2598_in_gg(T1362, s(s(s(T1362)))) → log2598_out_gg(T1362, s(s(s(T1362))))
U40_gg(T1355, T1356, log2598_out_gg(T1355, T1356)) → log2585_out_gg(T1355, T1356)
U30_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(0)))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324) → U31_ggg(T1323, T1324, log2585_in_gg(T1323, T1324))
U31_ggg(T1323, T1324, log2585_out_gg(T1323, T1324)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(0))))))))), T1323, T1324)
log2359_in_ggg(s(s(s(s(s(s(0)))))), T1394, T1395) → U32_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
log2650_in_gg(T1426, T1427) → U41_gg(T1426, T1427, log2598_in_gg(T1426, T1427))
U41_gg(T1426, T1427, log2598_out_gg(T1426, T1427)) → log2650_out_gg(T1426, T1427)
U32_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(0)))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395) → U33_ggg(T1394, T1395, log2650_in_gg(T1394, T1395))
U33_ggg(T1394, T1395, log2650_out_gg(T1394, T1395)) → log2359_out_ggg(s(s(s(s(s(s(s(0))))))), T1394, T1395)
log2359_in_ggg(s(s(s(s(0)))), T1461, T1462) → U34_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
log2705_in_gg(T1467, s(s(T1467))) → log2705_out_gg(T1467, s(s(T1467)))
U34_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(0)))), T1461, T1462)
log2359_in_ggg(s(s(s(s(s(0))))), T1461, T1462) → U35_ggg(T1461, T1462, log2705_in_gg(T1461, T1462))
U35_ggg(T1461, T1462, log2705_out_gg(T1461, T1462)) → log2359_out_ggg(s(s(s(s(s(0))))), T1461, T1462)
log2359_in_ggg(s(s(0)), T1490, T1491) → U36_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
log2742_in_gg(T1496, s(s(T1496))) → log2742_out_gg(T1496, s(s(T1496)))
U36_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(0)), T1490, T1491)
log2359_in_ggg(s(s(s(0))), T1490, T1491) → U37_ggg(T1490, T1491, log2742_in_gg(T1490, T1491))
U37_ggg(T1490, T1491, log2742_out_gg(T1490, T1491)) → log2359_out_ggg(s(s(s(0))), T1490, T1491)
log2359_in_ggg(0, T1510, s(T1510)) → log2359_out_ggg(0, T1510, s(T1510))
log2359_in_ggg(s(0), T1510, s(T1510)) → log2359_out_ggg(s(0), T1510, s(T1510))
U23_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(0, s(T1081), T1082, T1083)
log2395_in_gggg(s(0), s(T1081), T1082, T1083) → U24_gggg(T1081, T1082, T1083, log2359_in_ggg(T1081, s(T1082), T1083))
U24_gggg(T1081, T1082, T1083, log2359_out_ggg(T1081, s(T1082), T1083)) → log2395_out_gggg(s(0), s(T1081), T1082, T1083)
log2395_in_gggg(0, 0, T1101, s(T1101)) → log2395_out_gggg(0, 0, T1101, s(T1101))
log2395_in_gggg(s(0), 0, T1101, s(T1101)) → log2395_out_gggg(s(0), 0, T1101, s(T1101))
U22_gggg(T1056, T1057, T1058, T1059, log2395_out_gggg(T1056, s(T1057), T1058, T1059)) → log2395_out_gggg(s(s(T1056)), T1057, T1058, T1059)
U25_ggg(T1029, T1030, T1031, log2395_out_gggg(T1029, s(s(s(s(s(s(s(0))))))), T1030, T1031)) → log2359_out_ggg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1029)))))))))))))), T1030, T1031)
U20_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(0, s(T899), T900)
log2344_in_ggg(s(0), s(T899), T900) → U21_ggg(T899, T900, log2359_in_ggg(T899, s(s(s(s(s(s(s(0))))))), T900))
U21_ggg(T899, T900, log2359_out_ggg(T899, s(s(s(s(s(s(s(0))))))), T900)) → log2344_out_ggg(s(0), s(T899), T900)
log2344_in_ggg(0, 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(0, 0, s(s(s(s(s(s(s(0))))))))
log2344_in_ggg(s(0), 0, s(s(s(s(s(s(s(0)))))))) → log2344_out_ggg(s(0), 0, s(s(s(s(s(s(s(0))))))))
U19_ggg(T880, T881, T882, log2344_out_ggg(T880, s(T881), T882)) → log2344_out_ggg(s(s(T880)), T881, T882)
U42_gg(T860, T861, log2344_out_ggg(T860, s(s(s(s(s(s(s(0))))))), T861)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T860)))))))))))))), T861)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530) → U43_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
log2822_in_gg(T1578, T1579) → U144_gg(T1578, T1579, log2705_in_gg(T1578, T1579))
U144_gg(T1578, T1579, log2705_out_gg(T1578, T1579)) → log2822_out_gg(T1578, T1579)
U43_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530) → U44_gg(T1530, log2822_in_gg(s(s(s(s(s(s(s(0))))))), T1530))
U44_gg(T1530, log2822_out_gg(s(s(s(s(s(s(s(0))))))), T1530)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1530)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620) → U45_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
log2889_in_gg(T1668, T1669) → U145_gg(T1668, T1669, log2705_in_gg(T1668, T1669))
U145_gg(T1668, T1669, log2705_out_gg(T1668, T1669)) → log2889_out_gg(T1668, T1669)
U45_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620) → U46_gg(T1620, log2889_in_gg(s(s(s(s(s(s(s(0))))))), T1620))
U46_gg(T1620, log2889_out_gg(s(s(s(s(s(s(s(0))))))), T1620)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1620)
log2307_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1711) → U47_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
log2960_in_gg(T1743, T1744) → U146_gg(T1743, T1744, log2742_in_gg(T1743, T1744))
U146_gg(T1743, T1744, log2742_out_gg(T1743, T1744)) → log2960_out_gg(T1743, T1744)
U47_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711) → U48_gg(T1711, log2960_in_gg(s(s(s(s(s(s(s(0))))))), T1711))
U48_gg(T1711, log2960_out_gg(s(s(s(s(s(s(s(0))))))), T1711)) → log2307_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1711)
log2307_in_gg(s(s(s(s(s(s(0)))))), T1769) → U49_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
log21012_in_gg(T1801, T1802) → U147_gg(T1801, T1802, log2742_in_gg(T1801, T1802))
U147_gg(T1801, T1802, log2742_out_gg(T1801, T1802)) → log21012_out_gg(T1801, T1802)
U49_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(0)))))), T1769)
log2307_in_gg(s(s(s(s(s(s(s(0))))))), T1769) → U50_gg(T1769, log21012_in_gg(s(s(s(s(s(s(s(0))))))), T1769))
U50_gg(T1769, log21012_out_gg(s(s(s(s(s(s(s(0))))))), T1769)) → log2307_out_gg(s(s(s(s(s(s(s(0))))))), T1769)
log2307_in_gg(s(s(s(s(0)))), T1826) → U51_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
log21068_in_gg(T1831, s(T1831)) → log21068_out_gg(T1831, s(T1831))
U51_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(0)))), T1826)
log2307_in_gg(s(s(s(s(s(0))))), T1826) → U52_gg(T1826, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1826))
U52_gg(T1826, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1826)) → log2307_out_gg(s(s(s(s(s(0))))), T1826)
log2307_in_gg(s(s(0)), T1844) → U53_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
log21106_in_gg(T1849, s(T1849)) → log21106_out_gg(T1849, s(T1849))
U53_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(0)), T1844)
log2307_in_gg(s(s(s(0))), T1844) → U54_gg(T1844, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1844))
U54_gg(T1844, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1844)) → log2307_out_gg(s(s(s(0))), T1844)
log2307_in_gg(0, s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(0, s(s(s(s(s(s(s(0))))))))
log2307_in_gg(s(0), s(s(s(s(s(s(s(0)))))))) → log2307_out_gg(s(0), s(s(s(s(s(s(s(0))))))))
U17_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(0, s(T774), T775)
log2294_in_ggg(s(0), s(T774), T775) → U18_ggg(T774, T775, log2307_in_gg(T774, T775))
U18_ggg(T774, T775, log2307_out_gg(T774, T775)) → log2294_out_ggg(s(0), s(T774), T775)
log2294_in_ggg(0, 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(0, 0, s(s(s(s(s(s(0)))))))
log2294_in_ggg(s(0), 0, s(s(s(s(s(s(0))))))) → log2294_out_ggg(s(0), 0, s(s(s(s(s(s(0)))))))
U16_ggg(T755, T756, T757, log2294_out_ggg(T755, s(T756), T757)) → log2294_out_ggg(s(s(T755)), T756, T757)
U59_gg(T735, T736, log2294_out_ggg(T735, s(s(s(s(s(s(s(0))))))), T736)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T735)))))))))))))), T736)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876) → U60_gg(T1876, log21183_in_g(T1876))
log21183_in_g(T1899) → U55_g(T1899, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1899))
U55_g(T1899, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1899)) → log21183_out_g(T1899)
U60_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876) → U61_gg(T1876, log21183_in_g(T1876))
U61_gg(T1876, log21183_out_g(T1876)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1876)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920) → U62_gg(T1920, log21249_in_g(T1920))
log21249_in_g(T1943) → U56_g(T1943, log21068_in_gg(s(s(s(s(s(s(s(0))))))), T1943))
U56_g(T1943, log21068_out_gg(s(s(s(s(s(s(s(0))))))), T1943)) → log21249_out_g(T1943)
U62_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920) → U63_gg(T1920, log21249_in_g(T1920))
U63_gg(T1920, log21249_out_g(T1920)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1920)
log2257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T1964) → U64_gg(T1964, log21319_in_g(T1964))
log21319_in_g(T1979) → U57_g(T1979, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T1979))
U57_g(T1979, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T1979)) → log21319_out_g(T1979)
U64_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964) → U65_gg(T1964, log21319_in_g(T1964))
U65_gg(T1964, log21319_out_g(T1964)) → log2257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T1964)
log2257_in_gg(s(s(s(s(s(s(0)))))), T1995) → U66_gg(T1995, log21370_in_g(T1995))
log21370_in_g(T2010) → U58_g(T2010, log21106_in_gg(s(s(s(s(s(s(s(0))))))), T2010))
U58_g(T2010, log21106_out_gg(s(s(s(s(s(s(s(0))))))), T2010)) → log21370_out_g(T2010)
U66_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(0)))))), T1995)
log2257_in_gg(s(s(s(s(s(s(s(0))))))), T1995) → U67_gg(T1995, log21370_in_g(T1995))
U67_gg(T1995, log21370_out_g(T1995)) → log2257_out_gg(s(s(s(s(s(s(s(0))))))), T1995)
log2257_in_gg(s(s(s(s(0)))), T2024) → U68_gg(T2024, log21425_in_g(T2024))
log21425_in_g(s(s(s(s(s(s(s(0)))))))) → log21425_out_g(s(s(s(s(s(s(s(0))))))))
U68_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(0)))), T2024)
log2257_in_gg(s(s(s(s(s(0))))), T2024) → U69_gg(T2024, log21425_in_g(T2024))
U69_gg(T2024, log21425_out_g(T2024)) → log2257_out_gg(s(s(s(s(s(0))))), T2024)
log2257_in_gg(s(s(0)), T2037) → U70_gg(T2037, log21462_in_g(T2037))
log21462_in_g(s(s(s(s(s(s(s(0)))))))) → log21462_out_g(s(s(s(s(s(s(s(0))))))))
U70_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(0)), T2037)
log2257_in_gg(s(s(s(0))), T2037) → U71_gg(T2037, log21462_in_g(T2037))
U71_gg(T2037, log21462_out_g(T2037)) → log2257_out_gg(s(s(s(0))), T2037)
log2257_in_gg(0, s(s(s(s(s(s(0))))))) → log2257_out_gg(0, s(s(s(s(s(s(0)))))))
log2257_in_gg(s(0), s(s(s(s(s(s(0))))))) → log2257_out_gg(s(0), s(s(s(s(s(s(0)))))))
U14_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(0, s(T649), T650)
log2244_in_ggg(s(0), s(T649), T650) → U15_ggg(T649, T650, log2257_in_gg(T649, T650))
U15_ggg(T649, T650, log2257_out_gg(T649, T650)) → log2244_out_ggg(s(0), s(T649), T650)
log2244_in_ggg(0, 0, s(s(s(s(s(0)))))) → log2244_out_ggg(0, 0, s(s(s(s(s(0))))))
log2244_in_ggg(s(0), 0, s(s(s(s(s(0)))))) → log2244_out_ggg(s(0), 0, s(s(s(s(s(0))))))
U13_ggg(T630, T631, T632, log2244_out_ggg(T630, s(T631), T632)) → log2244_out_ggg(s(s(T630)), T631, T632)
U76_gg(T610, T611, log2244_out_ggg(T610, s(s(s(s(s(s(s(0))))))), T611)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T610)))))))))))))), T611)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064) → U77_gg(T2064, log21540_in_g(T2064))
log21540_in_g(T2087) → U72_g(T2087, log21425_in_g(T2087))
U72_g(T2087, log21425_out_g(T2087)) → log21540_out_g(T2087)
U77_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064) → U78_gg(T2064, log21540_in_g(T2064))
U78_gg(T2064, log21540_out_g(T2064)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2064)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108) → U79_gg(T2108, log21606_in_g(T2108))
log21606_in_g(T2131) → U73_g(T2131, log21425_in_g(T2131))
U73_g(T2131, log21425_out_g(T2131)) → log21606_out_g(T2131)
U79_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108) → U80_gg(T2108, log21606_in_g(T2108))
U80_gg(T2108, log21606_out_g(T2108)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2108)
log2207_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2152) → U81_gg(T2152, log21676_in_g(T2152))
log21676_in_g(T2167) → U74_g(T2167, log21462_in_g(T2167))
U74_g(T2167, log21462_out_g(T2167)) → log21676_out_g(T2167)
U81_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152) → U82_gg(T2152, log21676_in_g(T2152))
U82_gg(T2152, log21676_out_g(T2152)) → log2207_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2152)
log2207_in_gg(s(s(s(s(s(s(0)))))), T2183) → U83_gg(T2183, log21727_in_g(T2183))
log21727_in_g(T2198) → U75_g(T2198, log21462_in_g(T2198))
U75_g(T2198, log21462_out_g(T2198)) → log21727_out_g(T2198)
U83_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(0)))))), T2183)
log2207_in_gg(s(s(s(s(s(s(s(0))))))), T2183) → U84_gg(T2183, log21727_in_g(T2183))
U84_gg(T2183, log21727_out_g(T2183)) → log2207_out_gg(s(s(s(s(s(s(s(0))))))), T2183)
log2207_in_gg(s(s(s(s(0)))), T2212) → U85_gg(T2212, log21782_in_g(T2212))
log21782_in_g(s(s(s(s(s(s(0))))))) → log21782_out_g(s(s(s(s(s(s(0)))))))
U85_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(0)))), T2212)
log2207_in_gg(s(s(s(s(s(0))))), T2212) → U86_gg(T2212, log21782_in_g(T2212))
U86_gg(T2212, log21782_out_g(T2212)) → log2207_out_gg(s(s(s(s(s(0))))), T2212)
log2207_in_gg(s(s(0)), T2225) → U87_gg(T2225, log21819_in_g(T2225))
log21819_in_g(s(s(s(s(s(s(0))))))) → log21819_out_g(s(s(s(s(s(s(0)))))))
U87_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(0)), T2225)
log2207_in_gg(s(s(s(0))), T2225) → U88_gg(T2225, log21819_in_g(T2225))
U88_gg(T2225, log21819_out_g(T2225)) → log2207_out_gg(s(s(s(0))), T2225)
log2207_in_gg(0, s(s(s(s(s(0)))))) → log2207_out_gg(0, s(s(s(s(s(0))))))
log2207_in_gg(s(0), s(s(s(s(s(0)))))) → log2207_out_gg(s(0), s(s(s(s(s(0))))))
U11_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(0, s(T524), T525)
log2194_in_ggg(s(0), s(T524), T525) → U12_ggg(T524, T525, log2207_in_gg(T524, T525))
U12_ggg(T524, T525, log2207_out_gg(T524, T525)) → log2194_out_ggg(s(0), s(T524), T525)
log2194_in_ggg(0, 0, s(s(s(s(0))))) → log2194_out_ggg(0, 0, s(s(s(s(0)))))
log2194_in_ggg(s(0), 0, s(s(s(s(0))))) → log2194_out_ggg(s(0), 0, s(s(s(s(0)))))
U10_ggg(T505, T506, T507, log2194_out_ggg(T505, s(T506), T507)) → log2194_out_ggg(s(s(T505)), T506, T507)
U93_gg(T485, T486, log2194_out_ggg(T485, s(s(s(s(s(s(s(0))))))), T486)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T485)))))))))))))), T486)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252) → U94_gg(T2252, log21897_in_g(T2252))
log21897_in_g(T2275) → U89_g(T2275, log21782_in_g(T2275))
U89_g(T2275, log21782_out_g(T2275)) → log21897_out_g(T2275)
U94_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252) → U95_gg(T2252, log21897_in_g(T2252))
U95_gg(T2252, log21897_out_g(T2252)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2252)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296) → U96_gg(T2296, log21963_in_g(T2296))
log21963_in_g(T2319) → U90_g(T2319, log21782_in_g(T2319))
U90_g(T2319, log21782_out_g(T2319)) → log21963_out_g(T2319)
U96_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296) → U97_gg(T2296, log21963_in_g(T2296))
U97_gg(T2296, log21963_out_g(T2296)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2296)
log2157_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2340) → U98_gg(T2340, log22033_in_g(T2340))
log22033_in_g(T2355) → U91_g(T2355, log21819_in_g(T2355))
U91_g(T2355, log21819_out_g(T2355)) → log22033_out_g(T2355)
U98_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340) → U99_gg(T2340, log22033_in_g(T2340))
U99_gg(T2340, log22033_out_g(T2340)) → log2157_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2340)
log2157_in_gg(s(s(s(s(s(s(0)))))), T2371) → U100_gg(T2371, log22084_in_g(T2371))
log22084_in_g(T2386) → U92_g(T2386, log21819_in_g(T2386))
U92_g(T2386, log21819_out_g(T2386)) → log22084_out_g(T2386)
U100_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(0)))))), T2371)
log2157_in_gg(s(s(s(s(s(s(s(0))))))), T2371) → U101_gg(T2371, log22084_in_g(T2371))
U101_gg(T2371, log22084_out_g(T2371)) → log2157_out_gg(s(s(s(s(s(s(s(0))))))), T2371)
log2157_in_gg(s(s(s(s(0)))), T2400) → U102_gg(T2400, log22139_in_g(T2400))
log22139_in_g(s(s(s(s(s(0)))))) → log22139_out_g(s(s(s(s(s(0))))))
U102_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(0)))), T2400)
log2157_in_gg(s(s(s(s(s(0))))), T2400) → U103_gg(T2400, log22139_in_g(T2400))
U103_gg(T2400, log22139_out_g(T2400)) → log2157_out_gg(s(s(s(s(s(0))))), T2400)
log2157_in_gg(s(s(0)), T2413) → U104_gg(T2413, log22176_in_g(T2413))
log22176_in_g(s(s(s(s(s(0)))))) → log22176_out_g(s(s(s(s(s(0))))))
U104_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(0)), T2413)
log2157_in_gg(s(s(s(0))), T2413) → U105_gg(T2413, log22176_in_g(T2413))
U105_gg(T2413, log22176_out_g(T2413)) → log2157_out_gg(s(s(s(0))), T2413)
log2157_in_gg(0, s(s(s(s(0))))) → log2157_out_gg(0, s(s(s(s(0)))))
log2157_in_gg(s(0), s(s(s(s(0))))) → log2157_out_gg(s(0), s(s(s(s(0)))))
U8_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(0, s(T399), T400)
log2144_in_ggg(s(0), s(T399), T400) → U9_ggg(T399, T400, log2157_in_gg(T399, T400))
U9_ggg(T399, T400, log2157_out_gg(T399, T400)) → log2144_out_ggg(s(0), s(T399), T400)
log2144_in_ggg(0, 0, s(s(s(0)))) → log2144_out_ggg(0, 0, s(s(s(0))))
log2144_in_ggg(s(0), 0, s(s(s(0)))) → log2144_out_ggg(s(0), 0, s(s(s(0))))
U7_ggg(T380, T381, T382, log2144_out_ggg(T380, s(T381), T382)) → log2144_out_ggg(s(s(T380)), T381, T382)
U110_gg(T360, T361, log2144_out_ggg(T360, s(s(s(s(s(s(s(0))))))), T361)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T360)))))))))))))), T361)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440) → U111_gg(T2440, log22254_in_g(T2440))
log22254_in_g(T2463) → U106_g(T2463, log22139_in_g(T2463))
U106_g(T2463, log22139_out_g(T2463)) → log22254_out_g(T2463)
U111_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440) → U112_gg(T2440, log22254_in_g(T2440))
U112_gg(T2440, log22254_out_g(T2440)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2440)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484) → U113_gg(T2484, log22320_in_g(T2484))
log22320_in_g(T2507) → U107_g(T2507, log22139_in_g(T2507))
U107_g(T2507, log22139_out_g(T2507)) → log22320_out_g(T2507)
U113_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484) → U114_gg(T2484, log22320_in_g(T2484))
U114_gg(T2484, log22320_out_g(T2484)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2484)
log2107_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2528) → U115_gg(T2528, log22390_in_g(T2528))
log22390_in_g(T2543) → U108_g(T2543, log22176_in_g(T2543))
U108_g(T2543, log22176_out_g(T2543)) → log22390_out_g(T2543)
U115_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528) → U116_gg(T2528, log22390_in_g(T2528))
U116_gg(T2528, log22390_out_g(T2528)) → log2107_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2528)
log2107_in_gg(s(s(s(s(s(s(0)))))), T2559) → U117_gg(T2559, log22441_in_g(T2559))
log22441_in_g(T2574) → U109_g(T2574, log22176_in_g(T2574))
U109_g(T2574, log22176_out_g(T2574)) → log22441_out_g(T2574)
U117_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(0)))))), T2559)
log2107_in_gg(s(s(s(s(s(s(s(0))))))), T2559) → U118_gg(T2559, log22441_in_g(T2559))
U118_gg(T2559, log22441_out_g(T2559)) → log2107_out_gg(s(s(s(s(s(s(s(0))))))), T2559)
log2107_in_gg(s(s(s(s(0)))), T2588) → U119_gg(T2588, log22496_in_g(T2588))
log22496_in_g(s(s(s(s(0))))) → log22496_out_g(s(s(s(s(0)))))
U119_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(0)))), T2588)
log2107_in_gg(s(s(s(s(s(0))))), T2588) → U120_gg(T2588, log22496_in_g(T2588))
U120_gg(T2588, log22496_out_g(T2588)) → log2107_out_gg(s(s(s(s(s(0))))), T2588)
log2107_in_gg(s(s(0)), T2601) → U121_gg(T2601, log22533_in_g(T2601))
log22533_in_g(s(s(s(s(0))))) → log22533_out_g(s(s(s(s(0)))))
U121_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(0)), T2601)
log2107_in_gg(s(s(s(0))), T2601) → U122_gg(T2601, log22533_in_g(T2601))
U122_gg(T2601, log22533_out_g(T2601)) → log2107_out_gg(s(s(s(0))), T2601)
log2107_in_gg(0, s(s(s(0)))) → log2107_out_gg(0, s(s(s(0))))
log2107_in_gg(s(0), s(s(s(0)))) → log2107_out_gg(s(0), s(s(s(0))))
U5_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(0, s(T274), T275)
log294_in_ggg(s(0), s(T274), T275) → U6_ggg(T274, T275, log2107_in_gg(T274, T275))
U6_ggg(T274, T275, log2107_out_gg(T274, T275)) → log294_out_ggg(s(0), s(T274), T275)
log294_in_ggg(0, 0, s(s(0))) → log294_out_ggg(0, 0, s(s(0)))
log294_in_ggg(s(0), 0, s(s(0))) → log294_out_ggg(s(0), 0, s(s(0)))
U4_ggg(T255, T256, T257, log294_out_ggg(T255, s(T256), T257)) → log294_out_ggg(s(s(T255)), T256, T257)
U127_gg(T235, T236, log294_out_ggg(T235, s(s(s(s(s(s(s(0))))))), T236)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T235)))))))))))))), T236)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628) → U128_gg(T2628, log22611_in_g(T2628))
log22611_in_g(T2651) → U123_g(T2651, log22496_in_g(T2651))
U123_g(T2651, log22496_out_g(T2651)) → log22611_out_g(T2651)
U128_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628) → U129_gg(T2628, log22611_in_g(T2628))
U129_gg(T2628, log22611_out_g(T2628)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2628)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672) → U130_gg(T2672, log22677_in_g(T2672))
log22677_in_g(T2695) → U124_g(T2695, log22496_in_g(T2695))
U124_g(T2695, log22496_out_g(T2695)) → log22677_out_g(T2695)
U130_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672) → U131_gg(T2672, log22677_in_g(T2672))
U131_gg(T2672, log22677_out_g(T2672)) → log257_out_gg(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2672)
log257_in_gg(s(s(s(s(s(s(s(s(0)))))))), T2716) → U132_gg(T2716, log22747_in_g(T2716))
log22747_in_g(T2731) → U125_g(T2731, log22533_in_g(T2731))
U125_g(T2731, log22533_out_g(T2731)) → log22747_out_g(T2731)
U132_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(0)))))))), T2716)
log257_in_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716) → U133_gg(T2716, log22747_in_g(T2716))
U133_gg(T2716, log22747_out_g(T2716)) → log257_out_gg(s(s(s(s(s(s(s(s(s(0))))))))), T2716)
log257_in_gg(s(s(s(s(s(s(0)))))), T2747) → U134_gg(T2747, log22798_in_g(T2747))
log22798_in_g(T2762) → U126_g(T2762, log22533_in_g(T2762))
U126_g(T2762, log22533_out_g(T2762)) → log22798_out_g(T2762)
U134_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(0)))))), T2747)
log257_in_gg(s(s(s(s(s(s(s(0))))))), T2747) → U135_gg(T2747, log22798_in_g(T2747))
U135_gg(T2747, log22798_out_g(T2747)) → log257_out_gg(s(s(s(s(s(s(s(0))))))), T2747)
log257_in_gg(s(s(s(s(0)))), T2776) → U136_gg(T2776, log22853_in_g(T2776))
log22853_in_g(s(s(s(0)))) → log22853_out_g(s(s(s(0))))
U136_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(0)))), T2776)
log257_in_gg(s(s(s(s(s(0))))), T2776) → U137_gg(T2776, log22853_in_g(T2776))
U137_gg(T2776, log22853_out_g(T2776)) → log257_out_gg(s(s(s(s(s(0))))), T2776)
log257_in_gg(s(s(0)), T2789) → U138_gg(T2789, log22890_in_g(T2789))
log22890_in_g(s(s(s(0)))) → log22890_out_g(s(s(s(0))))
U138_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(0)), T2789)
log257_in_gg(s(s(s(0))), T2789) → U139_gg(T2789, log22890_in_g(T2789))
U139_gg(T2789, log22890_out_g(T2789)) → log257_out_gg(s(s(s(0))), T2789)
log257_in_gg(0, s(s(0))) → log257_out_gg(0, s(s(0)))
log257_in_gg(s(0), s(s(0))) → log257_out_gg(s(0), s(s(0)))
U2_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(0, s(T148), T149)
log244_in_agg(s(0), s(T148), T149) → U3_agg(T148, T149, log257_in_gg(T148, T149))
U3_agg(T148, T149, log257_out_gg(T148, T149)) → log244_out_agg(s(0), s(T148), T149)
log244_in_agg(0, 0, s(0)) → log244_out_agg(0, 0, s(0))
log244_in_agg(s(0), 0, s(0)) → log244_out_agg(s(0), 0, s(0))
U1_agg(T131, T129, T130, log244_out_agg(T131, s(T129), T130)) → log244_out_agg(s(s(T131)), T129, T130)
U148_ag(T109, T108, log244_out_agg(T109, s(s(s(s(s(s(s(0))))))), T108)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T109)))))))))))))))), T108)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819) → U149_ag(T2819, log22968_in_g(T2819))
log22968_in_g(T2843) → U140_g(T2843, log22853_in_g(T2843))
U140_g(T2843, log22853_out_g(T2843)) → log22968_out_g(T2843)
U149_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819) → U150_ag(T2819, log22968_in_g(T2819))
U150_ag(T2819, log22968_out_g(T2819)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), T2819)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867) → U151_ag(T2867, log23034_in_g(T2867))
log23034_in_g(T2891) → U141_g(T2891, log22853_in_g(T2891))
U141_g(T2891, log22853_out_g(T2891)) → log23034_out_g(T2891)
U151_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867) → U152_ag(T2867, log23034_in_g(T2867))
U152_ag(T2867, log23034_out_g(T2867)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T2867)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915) → U153_ag(T2915, log23104_in_g(T2915))
log23104_in_g(T2931) → U142_g(T2931, log22890_in_g(T2931))
U142_g(T2931, log22890_out_g(T2931)) → log23104_out_g(T2931)
U153_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(0)))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915) → U154_ag(T2915, log23104_in_g(T2915))
U154_ag(T2915, log23104_out_g(T2915)) → log21_out_ag(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T2915)
log21_in_ag(s(s(s(s(s(s(s(s(0)))))))), T2950) → U155_ag(T2950, log23155_in_g(T2950))
log23155_in_g(T2966) → U143_g(T2966, log22890_in_g(T2966))
U143_g(T2966, log22890_out_g(T2966)) → log23155_out_g(T2966)
U155_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(0)))))))), T2950)
log21_in_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950) → U156_ag(T2950, log23155_in_g(T2950))
U156_ag(T2950, log23155_out_g(T2950)) → log21_out_ag(s(s(s(s(s(s(s(s(s(0))))))))), T2950)
log21_in_ag(s(s(s(s(s(s(0)))))), T2983) → U157_ag(T2983, log23210_in_g(T2983))
log23210_in_g(s(s(0))) → log23210_out_g(s(s(0)))
U157_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(0)))))), T2983)
log21_in_ag(s(s(s(s(s(s(s(0))))))), T2983) → U158_ag(T2983, log23210_in_g(T2983))
U158_ag(T2983, log23210_out_g(T2983)) → log21_out_ag(s(s(s(s(s(s(s(0))))))), T2983)
log21_in_ag(s(s(s(s(0)))), T3000) → U159_ag(T3000, log23247_in_g(T3000))
log23247_in_g(s(s(0))) → log23247_out_g(s(s(0)))
U159_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(0)))), T3000)
log21_in_ag(s(s(s(s(s(0))))), T3000) → U160_ag(T3000, log23247_in_g(T3000))
U160_ag(T3000, log23247_out_g(T3000)) → log21_out_ag(s(s(s(s(s(0))))), T3000)
log21_in_ag(s(s(0)), s(0)) → log21_out_ag(s(s(0)), s(0))
log21_in_ag(s(s(s(0))), s(0)) → log21_out_ag(s(s(s(0))), s(0))
log21_in_ag(0, s(0)) → log21_out_ag(0, s(0))
log21_in_ag(s(0), s(0)) → log21_out_ag(s(0), s(0))

The argument filtering Pi contains the following mapping:
log21_in_ag(x1, x2)  =  log21_in_ag(x2)
U148_ag(x1, x2, x3)  =  U148_ag(x2, x3)
log244_in_agg(x1, x2, x3)  =  log244_in_agg(x2, x3)
U1_agg(x1, x2, x3, x4)  =  U1_agg(x2, x3, x4)
s(x1)  =  s(x1)
U2_agg(x1, x2, x3)  =  U2_agg(x1, x2, x3)
log257_in_gg(x1, x2)  =  log257_in_gg(x1, x2)
U127_gg(x1, x2, x3)  =  U127_gg(x1, x2, x3)
log294_in_ggg(x1, x2, x3)  =  log294_in_ggg(x1, x2, x3)
U4_ggg(x1, x2, x3, x4)  =  U4_ggg(x1, x2, x3, x4)
0  =  0
U5_ggg(x1, x2, x3)  =  U5_ggg(x1, x2, x3)
log2107_in_gg(x1, x2)  =  log2107_in_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
log2144_in_ggg(x1, x2, x3)  =  log2144_in_ggg(x1, x2, x3)
U7_ggg(x1, x2, x3, x4)  =  U7_ggg(x1, x2, x3, x4)
U8_ggg(x1, x2, x3)  =  U8_ggg(x1, x2, x3)
log2157_in_gg(x1, x2)  =  log2157_in_gg(x1, x2)
U93_gg(x1, x2, x3)  =  U93_gg(x1, x2, x3)
log2194_in_ggg(x1, x2, x3)  =  log2194_in_ggg(x1, x2, x3)
U10_ggg(x1, x2, x3, x4)  =  U10_ggg(x1, x2, x3, x4)
U11_ggg(x1, x2, x3)  =  U11_ggg(x1, x2, x3)
log2207_in_gg(x1, x2)  =  log2207_in_gg(x1, x2)
U76_gg(x1, x2, x3)  =  U76_gg(x1, x2, x3)
log2244_in_ggg(x1, x2, x3)  =  log2244_in_ggg(x1, x2, x3)
U13_ggg(x1, x2, x3, x4)  =  U13_ggg(x1, x2, x3, x4)
U14_ggg(x1, x2, x3)  =  U14_ggg(x1, x2, x3)
log2257_in_gg(x1, x2)  =  log2257_in_gg(x1, x2)
U59_gg(x1, x2, x3)  =  U59_gg(x1, x2, x3)
log2294_in_ggg(x1, x2, x3)  =  log2294_in_ggg(x1, x2, x3)
U16_ggg(x1, x2, x3, x4)  =  U16_ggg(x1, x2, x3, x4)
U17_ggg(x1, x2, x3)  =  U17_ggg(x1, x2, x3)
log2307_in_gg(x1, x2)  =  log2307_in_gg(x1, x2)
U42_gg(x1, x2, x3)  =  U42_gg(x1, x2, x3)
log2344_in_ggg(x1, x2, x3)  =  log2344_in_ggg(x1, x2, x3)
U19_ggg(x1, x2, x3, x4)  =  U19_ggg(x1, x2, x3, x4)
U20_ggg(x1, x2, x3)  =  U20_ggg(x1, x2, x3)
log2359_in_ggg(x1, x2, x3)  =  log2359_in_ggg(x1, x2, x3)
U25_ggg(x1, x2, x3, x4)  =  U25_ggg(x1, x2, x3, x4)
log2395_in_gggg(x1, x2, x3, x4)  =  log2395_in_gggg(x1, x2, x3, x4)
U22_gggg(x1, x2, x3, x4, x5)  =  U22_gggg(x1, x2, x3, x4, x5)
U23_gggg(x1, x2, x3, x4)  =  U23_gggg(x1, x2, x3, x4)
U26_ggg(x1, x2, x3)  =  U26_ggg(x1, x2, x3)
log2437_in_gg(x1, x2)  =  log2437_in_gg(x1, x2)
U38_gg(x1, x2, x3)  =  U38_gg(x1, x2, x3)
log2454_in_gg(x1, x2)  =  log2454_in_gg(x1, x2)
log2454_out_gg(x1, x2)  =  log2454_out_gg(x1, x2)
log2437_out_gg(x1, x2)  =  log2437_out_gg(x1, x2)
log2359_out_ggg(x1, x2, x3)  =  log2359_out_ggg(x1, x2, x3)
U27_ggg(x1, x2, x3)  =  U27_ggg(x1, x2, x3)
U28_ggg(x1, x2, x3)  =  U28_ggg(x1, x2, x3)
log2515_in_gg(x1, x2)  =  log2515_in_gg(x1, x2)
U39_gg(x1, x2, x3)  =  U39_gg(x1, x2, x3)
log2515_out_gg(x1, x2)  =  log2515_out_gg(x1, x2)
U29_ggg(x1, x2, x3)  =  U29_ggg(x1, x2, x3)
U30_ggg(x1, x2, x3)  =  U30_ggg(x1, x2, x3)
log2585_in_gg(x1, x2)  =  log2585_in_gg(x1, x2)
U40_gg(x1, x2, x3)  =  U40_gg(x1, x2, x3)
log2598_in_gg(x1, x2)  =  log2598_in_gg(x1, x2)
log2598_out_gg(x1, x2)  =  log2598_out_gg(x1, x2)
log2585_out_gg(x1, x2)  =  log2585_out_gg(x1, x2)
U31_ggg(x1, x2, x3)  =  U31_ggg(x1, x2, x3)
U32_ggg(x1, x2, x3)  =  U32_ggg(x1, x2, x3)
log2650_in_gg(x1, x2)  =  log2650_in_gg(x1, x2)
U41_gg(x1, x2, x3)  =  U41_gg(x1, x2, x3)
log2650_out_gg(x1, x2)  =  log2650_out_gg(x1, x2)
U33_ggg(x1, x2, x3)  =  U33_ggg(x1, x2, x3)
U34_ggg(x1, x2, x3)  =  U34_ggg(x1, x2, x3)
log2705_in_gg(x1, x2)  =  log2705_in_gg(x1, x2)
log2705_out_gg(x1, x2)  =  log2705_out_gg(x1, x2)
U35_ggg(x1, x2, x3)  =  U35_ggg(x1, x2, x3)
U36_ggg(x1, x2, x3)  =  U36_ggg(x1, x2, x3)
log2742_in_gg(x1, x2)  =  log2742_in_gg(x1, x2)
log2742_out_gg(x1, x2)  =  log2742_out_gg(x1, x2)
U37_ggg(x1, x2, x3)  =  U37_ggg(x1, x2, x3)
log2395_out_gggg(x1, x2, x3, x4)  =  log2395_out_gggg(x1, x2, x3, x4)
U24_gggg(x1, x2, x3, x4)  =  U24_gggg(x1, x2, x3, x4)
log2344_out_ggg(x1, x2, x3)  =  log2344_out_ggg(x1, x2, x3)
U21_ggg(x1, x2, x3)  =  U21_ggg(x1, x2, x3)
log2307_out_gg(x1, x2)  =  log2307_out_gg(x1, x2)
U43_gg(x1, x2)  =  U43_gg(x1, x2)
log2822_in_gg(x1, x2)  =  log2822_in_gg(x1, x2)
U144_gg(x1, x2, x3)  =  U144_gg(x1, x2, x3)
log2822_out_gg(x1, x2)  =  log2822_out_gg(x1, x2)
U44_gg(x1, x2)  =  U44_gg(x1, x2)
U45_gg(x1, x2)  =  U45_gg(x1, x2)
log2889_in_gg(x1, x2)  =  log2889_in_gg(x1, x2)
U145_gg(x1, x2, x3)  =  U145_gg(x1, x2, x3)
log2889_out_gg(x1, x2)  =  log2889_out_gg(x1, x2)
U46_gg(x1, x2)  =  U46_gg(x1, x2)
U47_gg(x1, x2)  =  U47_gg(x1, x2)
log2960_in_gg(x1, x2)  =  log2960_in_gg(x1, x2)
U146_gg(x1, x2, x3)  =  U146_gg(x1, x2, x3)
log2960_out_gg(x1, x2)  =  log2960_out_gg(x1, x2)
U48_gg(x1, x2)  =  U48_gg(x1, x2)
U49_gg(x1, x2)  =  U49_gg(x1, x2)
log21012_in_gg(x1, x2)  =  log21012_in_gg(x1, x2)
U147_gg(x1, x2, x3)  =  U147_gg(x1, x2, x3)
log21012_out_gg(x1, x2)  =  log21012_out_gg(x1, x2)
U50_gg(x1, x2)  =  U50_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
log21068_in_gg(x1, x2)  =  log21068_in_gg(x1, x2)
log21068_out_gg(x1, x2)  =  log21068_out_gg(x1, x2)
U52_gg(x1, x2)  =  U52_gg(x1, x2)
U53_gg(x1, x2)  =  U53_gg(x1, x2)
log21106_in_gg(x1, x2)  =  log21106_in_gg(x1, x2)
log21106_out_gg(x1, x2)  =  log21106_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
log2294_out_ggg(x1, x2, x3)  =  log2294_out_ggg(x1, x2, x3)
U18_ggg(x1, x2, x3)  =  U18_ggg(x1, x2, x3)
log2257_out_gg(x1, x2)  =  log2257_out_gg(x1, x2)
U60_gg(x1, x2)  =  U60_gg(x1, x2)
log21183_in_g(x1)  =  log21183_in_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
log21183_out_g(x1)  =  log21183_out_g(x1)
U61_gg(x1, x2)  =  U61_gg(x1, x2)
U62_gg(x1, x2)  =  U62_gg(x1, x2)
log21249_in_g(x1)  =  log21249_in_g(x1)
U56_g(x1, x2)  =  U56_g(x1, x2)
log21249_out_g(x1)  =  log21249_out_g(x1)
U63_gg(x1, x2)  =  U63_gg(x1, x2)
U64_gg(x1, x2)  =  U64_gg(x1, x2)
log21319_in_g(x1)  =  log21319_in_g(x1)
U57_g(x1, x2)  =  U57_g(x1, x2)
log21319_out_g(x1)  =  log21319_out_g(x1)
U65_gg(x1, x2)  =  U65_gg(x1, x2)
U66_gg(x1, x2)  =  U66_gg(x1, x2)
log21370_in_g(x1)  =  log21370_in_g(x1)
U58_g(x1, x2)  =  U58_g(x1, x2)
log21370_out_g(x1)  =  log21370_out_g(x1)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2)  =  U68_gg(x1, x2)
log21425_in_g(x1)  =  log21425_in_g(x1)
log21425_out_g(x1)  =  log21425_out_g(x1)
U69_gg(x1, x2)  =  U69_gg(x1, x2)
U70_gg(x1, x2)  =  U70_gg(x1, x2)
log21462_in_g(x1)  =  log21462_in_g(x1)
log21462_out_g(x1)  =  log21462_out_g(x1)
U71_gg(x1, x2)  =  U71_gg(x1, x2)
log2244_out_ggg(x1, x2, x3)  =  log2244_out_ggg(x1, x2, x3)
U15_ggg(x1, x2, x3)  =  U15_ggg(x1, x2, x3)
log2207_out_gg(x1, x2)  =  log2207_out_gg(x1, x2)
U77_gg(x1, x2)  =  U77_gg(x1, x2)
log21540_in_g(x1)  =  log21540_in_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
log21540_out_g(x1)  =  log21540_out_g(x1)
U78_gg(x1, x2)  =  U78_gg(x1, x2)
U79_gg(x1, x2)  =  U79_gg(x1, x2)
log21606_in_g(x1)  =  log21606_in_g(x1)
U73_g(x1, x2)  =  U73_g(x1, x2)
log21606_out_g(x1)  =  log21606_out_g(x1)
U80_gg(x1, x2)  =  U80_gg(x1, x2)
U81_gg(x1, x2)  =  U81_gg(x1, x2)
log21676_in_g(x1)  =  log21676_in_g(x1)
U74_g(x1, x2)  =  U74_g(x1, x2)
log21676_out_g(x1)  =  log21676_out_g(x1)
U82_gg(x1, x2)  =  U82_gg(x1, x2)
U83_gg(x1, x2)  =  U83_gg(x1, x2)
log21727_in_g(x1)  =  log21727_in_g(x1)
U75_g(x1, x2)  =  U75_g(x1, x2)
log21727_out_g(x1)  =  log21727_out_g(x1)
U84_gg(x1, x2)  =  U84_gg(x1, x2)
U85_gg(x1, x2)  =  U85_gg(x1, x2)
log21782_in_g(x1)  =  log21782_in_g(x1)
log21782_out_g(x1)  =  log21782_out_g(x1)
U86_gg(x1, x2)  =  U86_gg(x1, x2)
U87_gg(x1, x2)  =  U87_gg(x1, x2)
log21819_in_g(x1)  =  log21819_in_g(x1)
log21819_out_g(x1)  =  log21819_out_g(x1)
U88_gg(x1, x2)  =  U88_gg(x1, x2)
log2194_out_ggg(x1, x2, x3)  =  log2194_out_ggg(x1, x2, x3)
U12_ggg(x1, x2, x3)  =  U12_ggg(x1, x2, x3)
log2157_out_gg(x1, x2)  =  log2157_out_gg(x1, x2)
U94_gg(x1, x2)  =  U94_gg(x1, x2)
log21897_in_g(x1)  =  log21897_in_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
log21897_out_g(x1)  =  log21897_out_g(x1)
U95_gg(x1, x2)  =  U95_gg(x1, x2)
U96_gg(x1, x2)  =  U96_gg(x1, x2)
log21963_in_g(x1)  =  log21963_in_g(x1)
U90_g(x1, x2)  =  U90_g(x1, x2)
log21963_out_g(x1)  =  log21963_out_g(x1)
U97_gg(x1, x2)  =  U97_gg(x1, x2)
U98_gg(x1, x2)  =  U98_gg(x1, x2)
log22033_in_g(x1)  =  log22033_in_g(x1)
U91_g(x1, x2)  =  U91_g(x1, x2)
log22033_out_g(x1)  =  log22033_out_g(x1)
U99_gg(x1, x2)  =  U99_gg(x1, x2)
U100_gg(x1, x2)  =  U100_gg(x1, x2)
log22084_in_g(x1)  =  log22084_in_g(x1)
U92_g(x1, x2)  =  U92_g(x1, x2)
log22084_out_g(x1)  =  log22084_out_g(x1)
U101_gg(x1, x2)  =  U101_gg(x1, x2)
U102_gg(x1, x2)  =  U102_gg(x1, x2)
log22139_in_g(x1)  =  log22139_in_g(x1)
log22139_out_g(x1)  =  log22139_out_g(x1)
U103_gg(x1, x2)  =  U103_gg(x1, x2)
U104_gg(x1, x2)  =  U104_gg(x1, x2)
log22176_in_g(x1)  =  log22176_in_g(x1)
log22176_out_g(x1)  =  log22176_out_g(x1)
U105_gg(x1, x2)  =  U105_gg(x1, x2)
log2144_out_ggg(x1, x2, x3)  =  log2144_out_ggg(x1, x2, x3)
U9_ggg(x1, x2, x3)  =  U9_ggg(x1, x2, x3)
log2107_out_gg(x1, x2)  =  log2107_out_gg(x1, x2)
U111_gg(x1, x2)  =  U111_gg(x1, x2)
log22254_in_g(x1)  =  log22254_in_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
log22254_out_g(x1)  =  log22254_out_g(x1)
U112_gg(x1, x2)  =  U112_gg(x1, x2)
U113_gg(x1, x2)  =  U113_gg(x1, x2)
log22320_in_g(x1)  =  log22320_in_g(x1)
U107_g(x1, x2)  =  U107_g(x1, x2)
log22320_out_g(x1)  =  log22320_out_g(x1)
U114_gg(x1, x2)  =  U114_gg(x1, x2)
U115_gg(x1, x2)  =  U115_gg(x1, x2)
log22390_in_g(x1)  =  log22390_in_g(x1)
U108_g(x1, x2)  =  U108_g(x1, x2)
log22390_out_g(x1)  =  log22390_out_g(x1)
U116_gg(x1, x2)  =  U116_gg(x1, x2)
U117_gg(x1, x2)  =  U117_gg(x1, x2)
log22441_in_g(x1)  =  log22441_in_g(x1)
U109_g(x1, x2)  =  U109_g(x1, x2)
log22441_out_g(x1)  =  log22441_out_g(x1)
U118_gg(x1, x2)  =  U118_gg(x1, x2)
U119_gg(x1, x2)  =  U119_gg(x1, x2)
log22496_in_g(x1)  =  log22496_in_g(x1)
log22496_out_g(x1)  =  log22496_out_g(x1)
U120_gg(x1, x2)  =  U120_gg(x1, x2)
U121_gg(x1, x2)  =  U121_gg(x1, x2)
log22533_in_g(x1)  =  log22533_in_g(x1)
log22533_out_g(x1)  =  log22533_out_g(x1)
U122_gg(x1, x2)  =  U122_gg(x1, x2)
log294_out_ggg(x1, x2, x3)  =  log294_out_ggg(x1, x2, x3)
U6_ggg(x1, x2, x3)  =  U6_ggg(x1, x2, x3)
log257_out_gg(x1, x2)  =  log257_out_gg(x1, x2)
U128_gg(x1, x2)  =  U128_gg(x1, x2)
log22611_in_g(x1)  =  log22611_in_g(x1)
U123_g(x1, x2)  =  U123_g(x1, x2)
log22611_out_g(x1)  =  log22611_out_g(x1)
U129_gg(x1, x2)  =  U129_gg(x1, x2)
U130_gg(x1, x2)  =  U130_gg(x1, x2)
log22677_in_g(x1)  =  log22677_in_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
log22677_out_g(x1)  =  log22677_out_g(x1)
U131_gg(x1, x2)  =  U131_gg(x1, x2)
U132_gg(x1, x2)  =  U132_gg(x1, x2)
log22747_in_g(x1)  =  log22747_in_g(x1)
U125_g(x1, x2)  =  U125_g(x1, x2)
log22747_out_g(x1)  =  log22747_out_g(x1)
U133_gg(x1, x2)  =  U133_gg(x1, x2)
U134_gg(x1, x2)  =  U134_gg(x1, x2)
log22798_in_g(x1)  =  log22798_in_g(x1)
U126_g(x1, x2)  =  U126_g(x1, x2)
log22798_out_g(x1)  =  log22798_out_g(x1)
U135_gg(x1, x2)  =  U135_gg(x1, x2)
U136_gg(x1, x2)  =  U136_gg(x1, x2)
log22853_in_g(x1)  =  log22853_in_g(x1)
log22853_out_g(x1)  =  log22853_out_g(x1)
U137_gg(x1, x2)  =  U137_gg(x1, x2)
U138_gg(x1, x2)  =  U138_gg(x1, x2)
log22890_in_g(x1)  =  log22890_in_g(x1)
log22890_out_g(x1)  =  log22890_out_g(x1)
U139_gg(x1, x2)  =  U139_gg(x1, x2)
log244_out_agg(x1, x2, x3)  =  log244_out_agg(x1, x2, x3)
U3_agg(x1, x2, x3)  =  U3_agg(x1, x2, x3)
log21_out_ag(x1, x2)  =  log21_out_ag(x1, x2)
U149_ag(x1, x2)  =  U149_ag(x1, x2)
log22968_in_g(x1)  =  log22968_in_g(x1)
U140_g(x1, x2)  =  U140_g(x1, x2)
log22968_out_g(x1)  =  log22968_out_g(x1)
U150_ag(x1, x2)  =  U150_ag(x1, x2)
U151_ag(x1, x2)  =  U151_ag(x1, x2)
log23034_in_g(x1)  =  log23034_in_g(x1)
U141_g(x1, x2)  =  U141_g(x1, x2)
log23034_out_g(x1)  =  log23034_out_g(x1)
U152_ag(x1, x2)  =  U152_ag(x1, x2)
U153_ag(x1, x2)  =  U153_ag(x1, x2)
log23104_in_g(x1)  =  log23104_in_g(x1)
U142_g(x1, x2)  =  U142_g(x1, x2)
log23104_out_g(x1)  =  log23104_out_g(x1)
U154_ag(x1, x2)  =  U154_ag(x1, x2)
U155_ag(x1, x2)  =  U155_ag(x1, x2)
log23155_in_g(x1)  =  log23155_in_g(x1)
U143_g(x1, x2)  =  U143_g(x1, x2)
log23155_out_g(x1)  =  log23155_out_g(x1)
U156_ag(x1, x2)  =  U156_ag(x1, x2)
U157_ag(x1, x2)  =  U157_ag(x1, x2)
log23210_in_g(x1)  =  log23210_in_g(x1)
log23210_out_g(x1)  =  log23210_out_g(x1)
U158_ag(x1, x2)  =  U158_ag(x1, x2)
U159_ag(x1, x2)  =  U159_ag(x1, x2)
log23247_in_g(x1)  =  log23247_in_g(x1)
log23247_out_g(x1)  =  log23247_out_g(x1)
U160_ag(x1, x2)  =  U160_ag(x1, x2)
LOG244_IN_AGG(x1, x2, x3)  =  LOG244_IN_AGG(x2, x3)

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

(129) UsableRulesProof (EQUIVALENT transformation)

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

(130) Obligation:

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

LOG244_IN_AGG(s(s(T131)), T129, T130) → LOG244_IN_AGG(T131, s(T129), T130)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LOG244_IN_AGG(x1, x2, x3)  =  LOG244_IN_AGG(x2, x3)

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

(131) PiDPToQDPProof (SOUND transformation)

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

(132) Obligation:

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

LOG244_IN_AGG(T129, T130) → LOG244_IN_AGG(s(T129), T130)

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

(133) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule LOG244_IN_AGG(T129, T130) → LOG244_IN_AGG(s(T129), T130) we obtained the following new rules [LPAR04]:

LOG244_IN_AGG(s(z0), z1) → LOG244_IN_AGG(s(s(z0)), z1)

(134) Obligation:

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

LOG244_IN_AGG(s(z0), z1) → LOG244_IN_AGG(s(s(z0)), z1)

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

(135) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule LOG244_IN_AGG(s(z0), z1) → LOG244_IN_AGG(s(s(z0)), z1) we obtained the following new rules [LPAR04]:

LOG244_IN_AGG(s(s(z0)), z1) → LOG244_IN_AGG(s(s(s(z0))), z1)

(136) Obligation:

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

LOG244_IN_AGG(s(s(z0)), z1) → LOG244_IN_AGG(s(s(s(z0))), z1)

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

(137) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = LOG244_IN_AGG(s(s(z0)), z1) evaluates to t =LOG244_IN_AGG(s(s(s(z0))), z1)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Semiunifier: [ ]
  • Matcher: [z0 / s(z0)]




Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from LOG244_IN_AGG(s(s(z0)), z1) to LOG244_IN_AGG(s(s(s(z0))), z1).



(138) NO