0 Prolog
↳1 PrologToDTProblemTransformerProof (⇐)
↳2 TRIPLES
↳3 TriplesToPiDPProof (⇐)
↳4 PiDP
↳5 DependencyGraphProof (⇔)
↳6 AND
↳7 PiDP
↳8 UsableRulesProof (⇔)
↳9 PiDP
↳10 PiDPToQDPProof (⇐)
↳11 QDP
↳12 QDPSizeChangeProof (⇔)
↳13 YES
↳14 PiDP
↳15 UsableRulesProof (⇔)
↳16 PiDP
↳17 PiDPToQDPProof (⇐)
↳18 QDP
↳19 QDPSizeChangeProof (⇔)
↳20 YES
↳21 PiDP
↳22 UsableRulesProof (⇔)
↳23 PiDP
↳24 PiDPToQDPProof (⇐)
↳25 QDP
↳26 NonTerminationProof (⇔)
↳27 NO
↳28 PiDP
↳29 UsableRulesProof (⇔)
↳30 PiDP
↳31 PiDPToQDPProof (⇐)
↳32 QDP
↳33 QDPSizeChangeProof (⇔)
↳34 YES
ACKERMANN1_IN_GAG(s(s(T19)), 0, T20) → U16_GAG(T19, T20, ackermann21_in_ga(T19, X40))
ACKERMANN1_IN_GAG(s(s(T19)), 0, T20) → ACKERMANN21_IN_GA(T19, X40)
ACKERMANN21_IN_GA(T28, X73) → U1_GA(T28, X73, ackermann27_in_ga(T28, X73))
ACKERMANN21_IN_GA(T28, X73) → ACKERMANN27_IN_GA(T28, X73)
ACKERMANN27_IN_GA(s(T32), X97) → U2_GA(T32, X97, ackermann21_in_ga(T32, X96))
ACKERMANN27_IN_GA(s(T32), X97) → ACKERMANN21_IN_GA(T32, X96)
ACKERMANN27_IN_GA(s(T32), X97) → U3_GA(T32, X97, ackermannc21_in_ga(T32, T34))
U3_GA(T32, X97, ackermannc21_out_ga(T32, T34)) → U4_GA(T32, X97, ackermann38_in_gga(T32, T34, X97))
U3_GA(T32, X97, ackermannc21_out_ga(T32, T34)) → ACKERMANN38_IN_GGA(T32, T34, X97)
ACKERMANN38_IN_GGA(s(T47), 0, X133) → U5_GGA(T47, X133, ackermann27_in_ga(T47, X133))
ACKERMANN38_IN_GGA(s(T47), 0, X133) → ACKERMANN27_IN_GA(T47, X133)
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → U6_GGA(T52, T53, X151, ackermann38_in_gga(s(T52), T53, X150))
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → ACKERMANN38_IN_GGA(s(T52), T53, X150)
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → U7_GGA(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U7_GGA(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U8_GGA(T52, T53, X151, ackermann38_in_gga(T52, T55, X151))
U7_GGA(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → ACKERMANN38_IN_GGA(T52, T55, X151)
ACKERMANN1_IN_GAG(s(s(T19)), 0, T20) → U17_GAG(T19, T20, ackermannc21_in_ga(T19, T22))
U17_GAG(T19, T20, ackermannc21_out_ga(T19, T22)) → U18_GAG(T19, T20, ackermann1_in_ggg(T19, T22, T20))
U17_GAG(T19, T20, ackermannc21_out_ga(T19, T22)) → ACKERMANN1_IN_GGG(T19, T22, T20)
ACKERMANN1_IN_GGG(s(s(T19)), 0, T20) → U16_GGG(T19, T20, ackermann21_in_ga(T19, X40))
ACKERMANN1_IN_GGG(s(s(T19)), 0, T20) → ACKERMANN21_IN_GA(T19, X40)
ACKERMANN1_IN_GGG(s(s(T19)), 0, T20) → U17_GGG(T19, T20, ackermannc21_in_ga(T19, T22))
U17_GGG(T19, T20, ackermannc21_out_ga(T19, T22)) → U18_GGG(T19, T20, ackermann1_in_ggg(T19, T22, T20))
U17_GGG(T19, T20, ackermannc21_out_ga(T19, T22)) → ACKERMANN1_IN_GGG(T19, T22, T20)
ACKERMANN1_IN_GGG(s(T68), s(T71), T70) → U19_GGG(T68, T71, T70, ackermann57_in_gga(T68, T71, X182))
ACKERMANN1_IN_GGG(s(T68), s(T71), T70) → ACKERMANN57_IN_GGA(T68, T71, X182)
ACKERMANN57_IN_GGA(T79, 0, X211) → U9_GGA(T79, X211, ackermann27_in_ga(T79, X211))
ACKERMANN57_IN_GGA(T79, 0, X211) → ACKERMANN27_IN_GA(T79, X211)
ACKERMANN57_IN_GGA(T84, s(T86), X229) → U10_GGA(T84, T86, X229, p65_in_ggaa(T84, T86, X228, X229))
ACKERMANN57_IN_GGA(T84, s(T86), X229) → P65_IN_GGAA(T84, T86, X228, X229)
P65_IN_GGAA(T84, T86, X228, X229) → U11_GGAA(T84, T86, X228, X229, ackermann57_in_gga(T84, T86, X228))
P65_IN_GGAA(T84, T86, X228, X229) → ACKERMANN57_IN_GGA(T84, T86, X228)
P65_IN_GGAA(T84, T86, T88, X229) → U12_GGAA(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U12_GGAA(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U13_GGAA(T84, T86, T88, X229, ackermann68_in_gga(T84, T88, X229))
U12_GGAA(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → ACKERMANN68_IN_GGA(T84, T88, X229)
ACKERMANN68_IN_GGA(s(T101), 0, X265) → U14_GGA(T101, X265, ackermann27_in_ga(T101, X265))
ACKERMANN68_IN_GGA(s(T101), 0, X265) → ACKERMANN27_IN_GA(T101, X265)
ACKERMANN68_IN_GGA(s(T106), s(T108), X283) → U15_GGA(T106, T108, X283, p65_in_ggaa(T106, T108, X282, X283))
ACKERMANN68_IN_GGA(s(T106), s(T108), X283) → P65_IN_GGAA(T106, T108, X282, X283)
ACKERMANN1_IN_GGG(s(T68), s(T71), T70) → U20_GGG(T68, T71, T70, ackermannc57_in_gga(T68, T71, T73))
U20_GGG(T68, T71, T70, ackermannc57_out_gga(T68, T71, T73)) → U21_GGG(T68, T71, T70, ackermann1_in_ggg(T68, T73, T70))
U20_GGG(T68, T71, T70, ackermannc57_out_gga(T68, T71, T73)) → ACKERMANN1_IN_GGG(T68, T73, T70)
ACKERMANN1_IN_GGG(s(T123), s(0), T117) → U22_GGG(T123, T117, ackermann27_in_ga(T123, X319))
ACKERMANN1_IN_GGG(s(T123), s(0), T117) → ACKERMANN27_IN_GA(T123, X319)
ACKERMANN1_IN_GGG(s(T123), s(0), T117) → U23_GGG(T123, T117, ackermannc27_in_ga(T123, T124))
U23_GGG(T123, T117, ackermannc27_out_ga(T123, T124)) → U24_GGG(T123, T117, ackermann1_in_ggg(T123, T124, T117))
U23_GGG(T123, T117, ackermannc27_out_ga(T123, T124)) → ACKERMANN1_IN_GGG(T123, T124, T117)
ACKERMANN1_IN_GGG(s(T131), s(s(T133)), T117) → U25_GGG(T131, T133, T117, ackermann57_in_gga(T131, T133, X340))
ACKERMANN1_IN_GGG(s(T131), s(s(T133)), T117) → ACKERMANN57_IN_GGA(T131, T133, X340)
ACKERMANN1_IN_GGG(s(T131), s(s(T133)), T117) → U26_GGG(T131, T133, T117, ackermannc57_in_gga(T131, T133, T135))
U26_GGG(T131, T133, T117, ackermannc57_out_gga(T131, T133, T135)) → U27_GGG(T131, T133, T117, ackermann68_in_gga(T131, T135, X341))
U26_GGG(T131, T133, T117, ackermannc57_out_gga(T131, T133, T135)) → ACKERMANN68_IN_GGA(T131, T135, X341)
U26_GGG(T131, T133, T117, ackermannc57_out_gga(T131, T133, T135)) → U28_GGG(T131, T133, T117, ackermannc68_in_gga(T131, T135, T139))
U28_GGG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → U29_GGG(T131, T133, T117, ackermann1_in_ggg(T131, T139, T117))
U28_GGG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → ACKERMANN1_IN_GGG(T131, T139, T117)
ACKERMANN1_IN_GAG(s(T68), s(T71), T70) → U19_GAG(T68, T71, T70, ackermann57_in_gaa(T68, T71, X182))
ACKERMANN1_IN_GAG(s(T68), s(T71), T70) → ACKERMANN57_IN_GAA(T68, T71, X182)
ACKERMANN57_IN_GAA(T79, 0, X211) → U9_GAA(T79, X211, ackermann27_in_ga(T79, X211))
ACKERMANN57_IN_GAA(T79, 0, X211) → ACKERMANN27_IN_GA(T79, X211)
ACKERMANN57_IN_GAA(T84, s(T86), X229) → U10_GAA(T84, T86, X229, p65_in_gaaa(T84, T86, X228, X229))
ACKERMANN57_IN_GAA(T84, s(T86), X229) → P65_IN_GAAA(T84, T86, X228, X229)
P65_IN_GAAA(T84, T86, X228, X229) → U11_GAAA(T84, T86, X228, X229, ackermann57_in_gaa(T84, T86, X228))
P65_IN_GAAA(T84, T86, X228, X229) → ACKERMANN57_IN_GAA(T84, T86, X228)
P65_IN_GAAA(T84, T86, T88, X229) → U12_GAAA(T84, T86, T88, X229, ackermannc57_in_gaa(T84, T86, T88))
U12_GAAA(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → U13_GAAA(T84, T86, T88, X229, ackermann68_in_gga(T84, T88, X229))
U12_GAAA(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → ACKERMANN68_IN_GGA(T84, T88, X229)
ACKERMANN1_IN_GAG(s(T68), s(T71), T70) → U20_GAG(T68, T71, T70, ackermannc57_in_gaa(T68, T71, T73))
U20_GAG(T68, T71, T70, ackermannc57_out_gaa(T68, T71, T73)) → U21_GAG(T68, T71, T70, ackermann1_in_ggg(T68, T73, T70))
U20_GAG(T68, T71, T70, ackermannc57_out_gaa(T68, T71, T73)) → ACKERMANN1_IN_GGG(T68, T73, T70)
ACKERMANN1_IN_GAG(s(T123), s(0), T117) → U22_GAG(T123, T117, ackermann27_in_ga(T123, X319))
ACKERMANN1_IN_GAG(s(T123), s(0), T117) → ACKERMANN27_IN_GA(T123, X319)
ACKERMANN1_IN_GAG(s(T123), s(0), T117) → U23_GAG(T123, T117, ackermannc27_in_ga(T123, T124))
U23_GAG(T123, T117, ackermannc27_out_ga(T123, T124)) → U24_GAG(T123, T117, ackermann1_in_ggg(T123, T124, T117))
U23_GAG(T123, T117, ackermannc27_out_ga(T123, T124)) → ACKERMANN1_IN_GGG(T123, T124, T117)
ACKERMANN1_IN_GAG(s(T131), s(s(T133)), T117) → U25_GAG(T131, T133, T117, ackermann57_in_gaa(T131, T133, X340))
ACKERMANN1_IN_GAG(s(T131), s(s(T133)), T117) → ACKERMANN57_IN_GAA(T131, T133, X340)
ACKERMANN1_IN_GAG(s(T131), s(s(T133)), T117) → U26_GAG(T131, T133, T117, ackermannc57_in_gaa(T131, T133, T135))
U26_GAG(T131, T133, T117, ackermannc57_out_gaa(T131, T133, T135)) → U27_GAG(T131, T133, T117, ackermann68_in_gga(T131, T135, X341))
U26_GAG(T131, T133, T117, ackermannc57_out_gaa(T131, T133, T135)) → ACKERMANN68_IN_GGA(T131, T135, X341)
U26_GAG(T131, T133, T117, ackermannc57_out_gaa(T131, T133, T135)) → U28_GAG(T131, T133, T117, ackermannc68_in_gga(T131, T135, T139))
U28_GAG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → U29_GAG(T131, T133, T117, ackermann1_in_ggg(T131, T139, T117))
U28_GAG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → ACKERMANN1_IN_GGG(T131, T139, T117)
ackermannc21_in_ga(T28, X73) → U40_ga(T28, X73, ackermannc27_in_ga(T28, X73))
ackermannc27_in_ga(0, s(s(0))) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32), X97) → U41_ga(T32, X97, ackermannc21_in_ga(T32, T34))
U41_ga(T32, X97, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, X97, ackermannc38_in_gga(T32, T34, X97))
ackermannc38_in_gga(0, T42, s(T42)) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0, X133) → U43_gga(T47, X133, ackermannc27_in_ga(T47, X133))
U43_gga(T47, X133, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
ackermannc38_in_gga(s(T52), s(T53), X151) → U44_gga(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U44_gga(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, X151, ackermannc38_in_gga(T52, T55, X151))
U45_gga(T52, T53, X151, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
U42_ga(T32, X97, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U40_ga(T28, X73, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
ackermannc57_in_gga(T79, 0, X211) → U46_gga(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gga(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
ackermannc57_in_gga(T84, s(T86), X229) → U47_gga(T84, T86, X229, qc65_in_ggaa(T84, T86, X228, X229))
qc65_in_ggaa(T84, T86, T88, X229) → U48_ggaa(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U48_ggaa(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
ackermannc68_in_gga(0, T96, s(T96)) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0, X265) → U50_gga(T101, X265, ackermannc27_in_ga(T101, X265))
U50_gga(T101, X265, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
ackermannc68_in_gga(s(T106), s(T108), X283) → U51_gga(T106, T108, X283, qc65_in_ggaa(T106, T108, X282, X283))
U51_gga(T106, T108, X283, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
U49_ggaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U47_gga(T84, T86, X229, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
ackermannc57_in_gaa(T79, 0, X211) → U46_gaa(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gaa(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gaa(T79, 0, X211)
ackermannc57_in_gaa(T84, s(T86), X229) → U47_gaa(T84, T86, X229, qc65_in_gaaa(T84, T86, X228, X229))
qc65_in_gaaa(T84, T86, T88, X229) → U48_gaaa(T84, T86, T88, X229, ackermannc57_in_gaa(T84, T86, T88))
U48_gaaa(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → U49_gaaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
U49_gaaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_gaaa(T84, T86, T88, X229)
U47_gaa(T84, T86, X229, qc65_out_gaaa(T84, T86, X228, X229)) → ackermannc57_out_gaa(T84, s(T86), X229)
Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES
ACKERMANN1_IN_GAG(s(s(T19)), 0, T20) → U16_GAG(T19, T20, ackermann21_in_ga(T19, X40))
ACKERMANN1_IN_GAG(s(s(T19)), 0, T20) → ACKERMANN21_IN_GA(T19, X40)
ACKERMANN21_IN_GA(T28, X73) → U1_GA(T28, X73, ackermann27_in_ga(T28, X73))
ACKERMANN21_IN_GA(T28, X73) → ACKERMANN27_IN_GA(T28, X73)
ACKERMANN27_IN_GA(s(T32), X97) → U2_GA(T32, X97, ackermann21_in_ga(T32, X96))
ACKERMANN27_IN_GA(s(T32), X97) → ACKERMANN21_IN_GA(T32, X96)
ACKERMANN27_IN_GA(s(T32), X97) → U3_GA(T32, X97, ackermannc21_in_ga(T32, T34))
U3_GA(T32, X97, ackermannc21_out_ga(T32, T34)) → U4_GA(T32, X97, ackermann38_in_gga(T32, T34, X97))
U3_GA(T32, X97, ackermannc21_out_ga(T32, T34)) → ACKERMANN38_IN_GGA(T32, T34, X97)
ACKERMANN38_IN_GGA(s(T47), 0, X133) → U5_GGA(T47, X133, ackermann27_in_ga(T47, X133))
ACKERMANN38_IN_GGA(s(T47), 0, X133) → ACKERMANN27_IN_GA(T47, X133)
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → U6_GGA(T52, T53, X151, ackermann38_in_gga(s(T52), T53, X150))
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → ACKERMANN38_IN_GGA(s(T52), T53, X150)
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → U7_GGA(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U7_GGA(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U8_GGA(T52, T53, X151, ackermann38_in_gga(T52, T55, X151))
U7_GGA(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → ACKERMANN38_IN_GGA(T52, T55, X151)
ACKERMANN1_IN_GAG(s(s(T19)), 0, T20) → U17_GAG(T19, T20, ackermannc21_in_ga(T19, T22))
U17_GAG(T19, T20, ackermannc21_out_ga(T19, T22)) → U18_GAG(T19, T20, ackermann1_in_ggg(T19, T22, T20))
U17_GAG(T19, T20, ackermannc21_out_ga(T19, T22)) → ACKERMANN1_IN_GGG(T19, T22, T20)
ACKERMANN1_IN_GGG(s(s(T19)), 0, T20) → U16_GGG(T19, T20, ackermann21_in_ga(T19, X40))
ACKERMANN1_IN_GGG(s(s(T19)), 0, T20) → ACKERMANN21_IN_GA(T19, X40)
ACKERMANN1_IN_GGG(s(s(T19)), 0, T20) → U17_GGG(T19, T20, ackermannc21_in_ga(T19, T22))
U17_GGG(T19, T20, ackermannc21_out_ga(T19, T22)) → U18_GGG(T19, T20, ackermann1_in_ggg(T19, T22, T20))
U17_GGG(T19, T20, ackermannc21_out_ga(T19, T22)) → ACKERMANN1_IN_GGG(T19, T22, T20)
ACKERMANN1_IN_GGG(s(T68), s(T71), T70) → U19_GGG(T68, T71, T70, ackermann57_in_gga(T68, T71, X182))
ACKERMANN1_IN_GGG(s(T68), s(T71), T70) → ACKERMANN57_IN_GGA(T68, T71, X182)
ACKERMANN57_IN_GGA(T79, 0, X211) → U9_GGA(T79, X211, ackermann27_in_ga(T79, X211))
ACKERMANN57_IN_GGA(T79, 0, X211) → ACKERMANN27_IN_GA(T79, X211)
ACKERMANN57_IN_GGA(T84, s(T86), X229) → U10_GGA(T84, T86, X229, p65_in_ggaa(T84, T86, X228, X229))
ACKERMANN57_IN_GGA(T84, s(T86), X229) → P65_IN_GGAA(T84, T86, X228, X229)
P65_IN_GGAA(T84, T86, X228, X229) → U11_GGAA(T84, T86, X228, X229, ackermann57_in_gga(T84, T86, X228))
P65_IN_GGAA(T84, T86, X228, X229) → ACKERMANN57_IN_GGA(T84, T86, X228)
P65_IN_GGAA(T84, T86, T88, X229) → U12_GGAA(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U12_GGAA(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U13_GGAA(T84, T86, T88, X229, ackermann68_in_gga(T84, T88, X229))
U12_GGAA(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → ACKERMANN68_IN_GGA(T84, T88, X229)
ACKERMANN68_IN_GGA(s(T101), 0, X265) → U14_GGA(T101, X265, ackermann27_in_ga(T101, X265))
ACKERMANN68_IN_GGA(s(T101), 0, X265) → ACKERMANN27_IN_GA(T101, X265)
ACKERMANN68_IN_GGA(s(T106), s(T108), X283) → U15_GGA(T106, T108, X283, p65_in_ggaa(T106, T108, X282, X283))
ACKERMANN68_IN_GGA(s(T106), s(T108), X283) → P65_IN_GGAA(T106, T108, X282, X283)
ACKERMANN1_IN_GGG(s(T68), s(T71), T70) → U20_GGG(T68, T71, T70, ackermannc57_in_gga(T68, T71, T73))
U20_GGG(T68, T71, T70, ackermannc57_out_gga(T68, T71, T73)) → U21_GGG(T68, T71, T70, ackermann1_in_ggg(T68, T73, T70))
U20_GGG(T68, T71, T70, ackermannc57_out_gga(T68, T71, T73)) → ACKERMANN1_IN_GGG(T68, T73, T70)
ACKERMANN1_IN_GGG(s(T123), s(0), T117) → U22_GGG(T123, T117, ackermann27_in_ga(T123, X319))
ACKERMANN1_IN_GGG(s(T123), s(0), T117) → ACKERMANN27_IN_GA(T123, X319)
ACKERMANN1_IN_GGG(s(T123), s(0), T117) → U23_GGG(T123, T117, ackermannc27_in_ga(T123, T124))
U23_GGG(T123, T117, ackermannc27_out_ga(T123, T124)) → U24_GGG(T123, T117, ackermann1_in_ggg(T123, T124, T117))
U23_GGG(T123, T117, ackermannc27_out_ga(T123, T124)) → ACKERMANN1_IN_GGG(T123, T124, T117)
ACKERMANN1_IN_GGG(s(T131), s(s(T133)), T117) → U25_GGG(T131, T133, T117, ackermann57_in_gga(T131, T133, X340))
ACKERMANN1_IN_GGG(s(T131), s(s(T133)), T117) → ACKERMANN57_IN_GGA(T131, T133, X340)
ACKERMANN1_IN_GGG(s(T131), s(s(T133)), T117) → U26_GGG(T131, T133, T117, ackermannc57_in_gga(T131, T133, T135))
U26_GGG(T131, T133, T117, ackermannc57_out_gga(T131, T133, T135)) → U27_GGG(T131, T133, T117, ackermann68_in_gga(T131, T135, X341))
U26_GGG(T131, T133, T117, ackermannc57_out_gga(T131, T133, T135)) → ACKERMANN68_IN_GGA(T131, T135, X341)
U26_GGG(T131, T133, T117, ackermannc57_out_gga(T131, T133, T135)) → U28_GGG(T131, T133, T117, ackermannc68_in_gga(T131, T135, T139))
U28_GGG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → U29_GGG(T131, T133, T117, ackermann1_in_ggg(T131, T139, T117))
U28_GGG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → ACKERMANN1_IN_GGG(T131, T139, T117)
ACKERMANN1_IN_GAG(s(T68), s(T71), T70) → U19_GAG(T68, T71, T70, ackermann57_in_gaa(T68, T71, X182))
ACKERMANN1_IN_GAG(s(T68), s(T71), T70) → ACKERMANN57_IN_GAA(T68, T71, X182)
ACKERMANN57_IN_GAA(T79, 0, X211) → U9_GAA(T79, X211, ackermann27_in_ga(T79, X211))
ACKERMANN57_IN_GAA(T79, 0, X211) → ACKERMANN27_IN_GA(T79, X211)
ACKERMANN57_IN_GAA(T84, s(T86), X229) → U10_GAA(T84, T86, X229, p65_in_gaaa(T84, T86, X228, X229))
ACKERMANN57_IN_GAA(T84, s(T86), X229) → P65_IN_GAAA(T84, T86, X228, X229)
P65_IN_GAAA(T84, T86, X228, X229) → U11_GAAA(T84, T86, X228, X229, ackermann57_in_gaa(T84, T86, X228))
P65_IN_GAAA(T84, T86, X228, X229) → ACKERMANN57_IN_GAA(T84, T86, X228)
P65_IN_GAAA(T84, T86, T88, X229) → U12_GAAA(T84, T86, T88, X229, ackermannc57_in_gaa(T84, T86, T88))
U12_GAAA(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → U13_GAAA(T84, T86, T88, X229, ackermann68_in_gga(T84, T88, X229))
U12_GAAA(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → ACKERMANN68_IN_GGA(T84, T88, X229)
ACKERMANN1_IN_GAG(s(T68), s(T71), T70) → U20_GAG(T68, T71, T70, ackermannc57_in_gaa(T68, T71, T73))
U20_GAG(T68, T71, T70, ackermannc57_out_gaa(T68, T71, T73)) → U21_GAG(T68, T71, T70, ackermann1_in_ggg(T68, T73, T70))
U20_GAG(T68, T71, T70, ackermannc57_out_gaa(T68, T71, T73)) → ACKERMANN1_IN_GGG(T68, T73, T70)
ACKERMANN1_IN_GAG(s(T123), s(0), T117) → U22_GAG(T123, T117, ackermann27_in_ga(T123, X319))
ACKERMANN1_IN_GAG(s(T123), s(0), T117) → ACKERMANN27_IN_GA(T123, X319)
ACKERMANN1_IN_GAG(s(T123), s(0), T117) → U23_GAG(T123, T117, ackermannc27_in_ga(T123, T124))
U23_GAG(T123, T117, ackermannc27_out_ga(T123, T124)) → U24_GAG(T123, T117, ackermann1_in_ggg(T123, T124, T117))
U23_GAG(T123, T117, ackermannc27_out_ga(T123, T124)) → ACKERMANN1_IN_GGG(T123, T124, T117)
ACKERMANN1_IN_GAG(s(T131), s(s(T133)), T117) → U25_GAG(T131, T133, T117, ackermann57_in_gaa(T131, T133, X340))
ACKERMANN1_IN_GAG(s(T131), s(s(T133)), T117) → ACKERMANN57_IN_GAA(T131, T133, X340)
ACKERMANN1_IN_GAG(s(T131), s(s(T133)), T117) → U26_GAG(T131, T133, T117, ackermannc57_in_gaa(T131, T133, T135))
U26_GAG(T131, T133, T117, ackermannc57_out_gaa(T131, T133, T135)) → U27_GAG(T131, T133, T117, ackermann68_in_gga(T131, T135, X341))
U26_GAG(T131, T133, T117, ackermannc57_out_gaa(T131, T133, T135)) → ACKERMANN68_IN_GGA(T131, T135, X341)
U26_GAG(T131, T133, T117, ackermannc57_out_gaa(T131, T133, T135)) → U28_GAG(T131, T133, T117, ackermannc68_in_gga(T131, T135, T139))
U28_GAG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → U29_GAG(T131, T133, T117, ackermann1_in_ggg(T131, T139, T117))
U28_GAG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → ACKERMANN1_IN_GGG(T131, T139, T117)
ackermannc21_in_ga(T28, X73) → U40_ga(T28, X73, ackermannc27_in_ga(T28, X73))
ackermannc27_in_ga(0, s(s(0))) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32), X97) → U41_ga(T32, X97, ackermannc21_in_ga(T32, T34))
U41_ga(T32, X97, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, X97, ackermannc38_in_gga(T32, T34, X97))
ackermannc38_in_gga(0, T42, s(T42)) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0, X133) → U43_gga(T47, X133, ackermannc27_in_ga(T47, X133))
U43_gga(T47, X133, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
ackermannc38_in_gga(s(T52), s(T53), X151) → U44_gga(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U44_gga(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, X151, ackermannc38_in_gga(T52, T55, X151))
U45_gga(T52, T53, X151, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
U42_ga(T32, X97, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U40_ga(T28, X73, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
ackermannc57_in_gga(T79, 0, X211) → U46_gga(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gga(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
ackermannc57_in_gga(T84, s(T86), X229) → U47_gga(T84, T86, X229, qc65_in_ggaa(T84, T86, X228, X229))
qc65_in_ggaa(T84, T86, T88, X229) → U48_ggaa(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U48_ggaa(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
ackermannc68_in_gga(0, T96, s(T96)) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0, X265) → U50_gga(T101, X265, ackermannc27_in_ga(T101, X265))
U50_gga(T101, X265, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
ackermannc68_in_gga(s(T106), s(T108), X283) → U51_gga(T106, T108, X283, qc65_in_ggaa(T106, T108, X282, X283))
U51_gga(T106, T108, X283, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
U49_ggaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U47_gga(T84, T86, X229, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
ackermannc57_in_gaa(T79, 0, X211) → U46_gaa(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gaa(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gaa(T79, 0, X211)
ackermannc57_in_gaa(T84, s(T86), X229) → U47_gaa(T84, T86, X229, qc65_in_gaaa(T84, T86, X228, X229))
qc65_in_gaaa(T84, T86, T88, X229) → U48_gaaa(T84, T86, T88, X229, ackermannc57_in_gaa(T84, T86, T88))
U48_gaaa(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → U49_gaaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
U49_gaaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_gaaa(T84, T86, T88, X229)
U47_gaa(T84, T86, X229, qc65_out_gaaa(T84, T86, X228, X229)) → ackermannc57_out_gaa(T84, s(T86), X229)
ACKERMANN21_IN_GA(T28, X73) → ACKERMANN27_IN_GA(T28, X73)
ACKERMANN27_IN_GA(s(T32), X97) → ACKERMANN21_IN_GA(T32, X96)
ACKERMANN27_IN_GA(s(T32), X97) → U3_GA(T32, X97, ackermannc21_in_ga(T32, T34))
U3_GA(T32, X97, ackermannc21_out_ga(T32, T34)) → ACKERMANN38_IN_GGA(T32, T34, X97)
ACKERMANN38_IN_GGA(s(T47), 0, X133) → ACKERMANN27_IN_GA(T47, X133)
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → ACKERMANN38_IN_GGA(s(T52), T53, X150)
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → U7_GGA(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U7_GGA(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → ACKERMANN38_IN_GGA(T52, T55, X151)
ackermannc21_in_ga(T28, X73) → U40_ga(T28, X73, ackermannc27_in_ga(T28, X73))
ackermannc27_in_ga(0, s(s(0))) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32), X97) → U41_ga(T32, X97, ackermannc21_in_ga(T32, T34))
U41_ga(T32, X97, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, X97, ackermannc38_in_gga(T32, T34, X97))
ackermannc38_in_gga(0, T42, s(T42)) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0, X133) → U43_gga(T47, X133, ackermannc27_in_ga(T47, X133))
U43_gga(T47, X133, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
ackermannc38_in_gga(s(T52), s(T53), X151) → U44_gga(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U44_gga(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, X151, ackermannc38_in_gga(T52, T55, X151))
U45_gga(T52, T53, X151, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
U42_ga(T32, X97, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U40_ga(T28, X73, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
ackermannc57_in_gga(T79, 0, X211) → U46_gga(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gga(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
ackermannc57_in_gga(T84, s(T86), X229) → U47_gga(T84, T86, X229, qc65_in_ggaa(T84, T86, X228, X229))
qc65_in_ggaa(T84, T86, T88, X229) → U48_ggaa(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U48_ggaa(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
ackermannc68_in_gga(0, T96, s(T96)) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0, X265) → U50_gga(T101, X265, ackermannc27_in_ga(T101, X265))
U50_gga(T101, X265, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
ackermannc68_in_gga(s(T106), s(T108), X283) → U51_gga(T106, T108, X283, qc65_in_ggaa(T106, T108, X282, X283))
U51_gga(T106, T108, X283, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
U49_ggaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U47_gga(T84, T86, X229, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
ackermannc57_in_gaa(T79, 0, X211) → U46_gaa(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gaa(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gaa(T79, 0, X211)
ackermannc57_in_gaa(T84, s(T86), X229) → U47_gaa(T84, T86, X229, qc65_in_gaaa(T84, T86, X228, X229))
qc65_in_gaaa(T84, T86, T88, X229) → U48_gaaa(T84, T86, T88, X229, ackermannc57_in_gaa(T84, T86, T88))
U48_gaaa(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → U49_gaaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
U49_gaaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_gaaa(T84, T86, T88, X229)
U47_gaa(T84, T86, X229, qc65_out_gaaa(T84, T86, X228, X229)) → ackermannc57_out_gaa(T84, s(T86), X229)
ACKERMANN21_IN_GA(T28, X73) → ACKERMANN27_IN_GA(T28, X73)
ACKERMANN27_IN_GA(s(T32), X97) → ACKERMANN21_IN_GA(T32, X96)
ACKERMANN27_IN_GA(s(T32), X97) → U3_GA(T32, X97, ackermannc21_in_ga(T32, T34))
U3_GA(T32, X97, ackermannc21_out_ga(T32, T34)) → ACKERMANN38_IN_GGA(T32, T34, X97)
ACKERMANN38_IN_GGA(s(T47), 0, X133) → ACKERMANN27_IN_GA(T47, X133)
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → ACKERMANN38_IN_GGA(s(T52), T53, X150)
ACKERMANN38_IN_GGA(s(T52), s(T53), X151) → U7_GGA(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U7_GGA(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → ACKERMANN38_IN_GGA(T52, T55, X151)
ackermannc21_in_ga(T28, X73) → U40_ga(T28, X73, ackermannc27_in_ga(T28, X73))
ackermannc38_in_gga(s(T47), 0, X133) → U43_gga(T47, X133, ackermannc27_in_ga(T47, X133))
ackermannc38_in_gga(s(T52), s(T53), X151) → U44_gga(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U40_ga(T28, X73, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
U43_gga(T47, X133, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
U44_gga(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, X151, ackermannc38_in_gga(T52, T55, X151))
ackermannc27_in_ga(0, s(s(0))) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32), X97) → U41_ga(T32, X97, ackermannc21_in_ga(T32, T34))
U45_gga(T52, T53, X151, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
U41_ga(T32, X97, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, X97, ackermannc38_in_gga(T32, T34, X97))
ackermannc38_in_gga(0, T42, s(T42)) → ackermannc38_out_gga(0, T42, s(T42))
U42_ga(T32, X97, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
ACKERMANN21_IN_GA(T28) → ACKERMANN27_IN_GA(T28)
ACKERMANN27_IN_GA(s(T32)) → ACKERMANN21_IN_GA(T32)
ACKERMANN27_IN_GA(s(T32)) → U3_GA(T32, ackermannc21_in_ga(T32))
U3_GA(T32, ackermannc21_out_ga(T32, T34)) → ACKERMANN38_IN_GGA(T32, T34)
ACKERMANN38_IN_GGA(s(T47), 0) → ACKERMANN27_IN_GA(T47)
ACKERMANN38_IN_GGA(s(T52), s(T53)) → ACKERMANN38_IN_GGA(s(T52), T53)
ACKERMANN38_IN_GGA(s(T52), s(T53)) → U7_GGA(T52, T53, ackermannc38_in_gga(s(T52), T53))
U7_GGA(T52, T53, ackermannc38_out_gga(s(T52), T53, T55)) → ACKERMANN38_IN_GGA(T52, T55)
ackermannc21_in_ga(T28) → U40_ga(T28, ackermannc27_in_ga(T28))
ackermannc38_in_gga(s(T47), 0) → U43_gga(T47, ackermannc27_in_ga(T47))
ackermannc38_in_gga(s(T52), s(T53)) → U44_gga(T52, T53, ackermannc38_in_gga(s(T52), T53))
U40_ga(T28, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
U43_gga(T47, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
U44_gga(T52, T53, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, ackermannc38_in_gga(T52, T55))
ackermannc27_in_ga(0) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32)) → U41_ga(T32, ackermannc21_in_ga(T32))
U45_gga(T52, T53, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
U41_ga(T32, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, ackermannc38_in_gga(T32, T34))
ackermannc38_in_gga(0, T42) → ackermannc38_out_gga(0, T42, s(T42))
U42_ga(T32, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
ackermannc21_in_ga(x0)
ackermannc38_in_gga(x0, x1)
U40_ga(x0, x1)
U43_gga(x0, x1)
U44_gga(x0, x1, x2)
ackermannc27_in_ga(x0)
U45_gga(x0, x1, x2)
U41_ga(x0, x1)
U42_ga(x0, x1)
From the DPs we obtained the following set of size-change graphs:
ACKERMANN57_IN_GGA(T84, s(T86), X229) → P65_IN_GGAA(T84, T86, X228, X229)
P65_IN_GGAA(T84, T86, X228, X229) → ACKERMANN57_IN_GGA(T84, T86, X228)
P65_IN_GGAA(T84, T86, T88, X229) → U12_GGAA(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U12_GGAA(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → ACKERMANN68_IN_GGA(T84, T88, X229)
ACKERMANN68_IN_GGA(s(T106), s(T108), X283) → P65_IN_GGAA(T106, T108, X282, X283)
ackermannc21_in_ga(T28, X73) → U40_ga(T28, X73, ackermannc27_in_ga(T28, X73))
ackermannc27_in_ga(0, s(s(0))) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32), X97) → U41_ga(T32, X97, ackermannc21_in_ga(T32, T34))
U41_ga(T32, X97, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, X97, ackermannc38_in_gga(T32, T34, X97))
ackermannc38_in_gga(0, T42, s(T42)) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0, X133) → U43_gga(T47, X133, ackermannc27_in_ga(T47, X133))
U43_gga(T47, X133, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
ackermannc38_in_gga(s(T52), s(T53), X151) → U44_gga(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U44_gga(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, X151, ackermannc38_in_gga(T52, T55, X151))
U45_gga(T52, T53, X151, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
U42_ga(T32, X97, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U40_ga(T28, X73, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
ackermannc57_in_gga(T79, 0, X211) → U46_gga(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gga(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
ackermannc57_in_gga(T84, s(T86), X229) → U47_gga(T84, T86, X229, qc65_in_ggaa(T84, T86, X228, X229))
qc65_in_ggaa(T84, T86, T88, X229) → U48_ggaa(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U48_ggaa(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
ackermannc68_in_gga(0, T96, s(T96)) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0, X265) → U50_gga(T101, X265, ackermannc27_in_ga(T101, X265))
U50_gga(T101, X265, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
ackermannc68_in_gga(s(T106), s(T108), X283) → U51_gga(T106, T108, X283, qc65_in_ggaa(T106, T108, X282, X283))
U51_gga(T106, T108, X283, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
U49_ggaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U47_gga(T84, T86, X229, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
ackermannc57_in_gaa(T79, 0, X211) → U46_gaa(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gaa(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gaa(T79, 0, X211)
ackermannc57_in_gaa(T84, s(T86), X229) → U47_gaa(T84, T86, X229, qc65_in_gaaa(T84, T86, X228, X229))
qc65_in_gaaa(T84, T86, T88, X229) → U48_gaaa(T84, T86, T88, X229, ackermannc57_in_gaa(T84, T86, T88))
U48_gaaa(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → U49_gaaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
U49_gaaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_gaaa(T84, T86, T88, X229)
U47_gaa(T84, T86, X229, qc65_out_gaaa(T84, T86, X228, X229)) → ackermannc57_out_gaa(T84, s(T86), X229)
ACKERMANN57_IN_GGA(T84, s(T86), X229) → P65_IN_GGAA(T84, T86, X228, X229)
P65_IN_GGAA(T84, T86, X228, X229) → ACKERMANN57_IN_GGA(T84, T86, X228)
P65_IN_GGAA(T84, T86, T88, X229) → U12_GGAA(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U12_GGAA(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → ACKERMANN68_IN_GGA(T84, T88, X229)
ACKERMANN68_IN_GGA(s(T106), s(T108), X283) → P65_IN_GGAA(T106, T108, X282, X283)
ackermannc57_in_gga(T79, 0, X211) → U46_gga(T79, X211, ackermannc27_in_ga(T79, X211))
ackermannc57_in_gga(T84, s(T86), X229) → U47_gga(T84, T86, X229, qc65_in_ggaa(T84, T86, X228, X229))
U46_gga(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
U47_gga(T84, T86, X229, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
ackermannc27_in_ga(0, s(s(0))) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32), X97) → U41_ga(T32, X97, ackermannc21_in_ga(T32, T34))
qc65_in_ggaa(T84, T86, T88, X229) → U48_ggaa(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U41_ga(T32, X97, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, X97, ackermannc38_in_gga(T32, T34, X97))
U48_ggaa(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
ackermannc21_in_ga(T28, X73) → U40_ga(T28, X73, ackermannc27_in_ga(T28, X73))
U42_ga(T32, X97, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U49_ggaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U40_ga(T28, X73, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
ackermannc38_in_gga(0, T42, s(T42)) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0, X133) → U43_gga(T47, X133, ackermannc27_in_ga(T47, X133))
ackermannc38_in_gga(s(T52), s(T53), X151) → U44_gga(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
ackermannc68_in_gga(0, T96, s(T96)) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0, X265) → U50_gga(T101, X265, ackermannc27_in_ga(T101, X265))
ackermannc68_in_gga(s(T106), s(T108), X283) → U51_gga(T106, T108, X283, qc65_in_ggaa(T106, T108, X282, X283))
U43_gga(T47, X133, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
U44_gga(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, X151, ackermannc38_in_gga(T52, T55, X151))
U50_gga(T101, X265, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
U51_gga(T106, T108, X283, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
U45_gga(T52, T53, X151, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
ACKERMANN57_IN_GGA(T84, s(T86)) → P65_IN_GGAA(T84, T86)
P65_IN_GGAA(T84, T86) → ACKERMANN57_IN_GGA(T84, T86)
P65_IN_GGAA(T84, T86) → U12_GGAA(T84, T86, ackermannc57_in_gga(T84, T86))
U12_GGAA(T84, T86, ackermannc57_out_gga(T84, T86, T88)) → ACKERMANN68_IN_GGA(T84, T88)
ACKERMANN68_IN_GGA(s(T106), s(T108)) → P65_IN_GGAA(T106, T108)
ackermannc57_in_gga(T79, 0) → U46_gga(T79, ackermannc27_in_ga(T79))
ackermannc57_in_gga(T84, s(T86)) → U47_gga(T84, T86, qc65_in_ggaa(T84, T86))
U46_gga(T79, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
U47_gga(T84, T86, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
ackermannc27_in_ga(0) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32)) → U41_ga(T32, ackermannc21_in_ga(T32))
qc65_in_ggaa(T84, T86) → U48_ggaa(T84, T86, ackermannc57_in_gga(T84, T86))
U41_ga(T32, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, ackermannc38_in_gga(T32, T34))
U48_ggaa(T84, T86, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, ackermannc68_in_gga(T84, T88))
ackermannc21_in_ga(T28) → U40_ga(T28, ackermannc27_in_ga(T28))
U42_ga(T32, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U49_ggaa(T84, T86, T88, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U40_ga(T28, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
ackermannc38_in_gga(0, T42) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0) → U43_gga(T47, ackermannc27_in_ga(T47))
ackermannc38_in_gga(s(T52), s(T53)) → U44_gga(T52, T53, ackermannc38_in_gga(s(T52), T53))
ackermannc68_in_gga(0, T96) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0) → U50_gga(T101, ackermannc27_in_ga(T101))
ackermannc68_in_gga(s(T106), s(T108)) → U51_gga(T106, T108, qc65_in_ggaa(T106, T108))
U43_gga(T47, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
U44_gga(T52, T53, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, ackermannc38_in_gga(T52, T55))
U50_gga(T101, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
U51_gga(T106, T108, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
U45_gga(T52, T53, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
ackermannc57_in_gga(x0, x1)
U46_gga(x0, x1)
U47_gga(x0, x1, x2)
ackermannc27_in_ga(x0)
qc65_in_ggaa(x0, x1)
U41_ga(x0, x1)
U48_ggaa(x0, x1, x2)
ackermannc21_in_ga(x0)
U42_ga(x0, x1)
U49_ggaa(x0, x1, x2, x3)
U40_ga(x0, x1)
ackermannc38_in_gga(x0, x1)
ackermannc68_in_gga(x0, x1)
U43_gga(x0, x1)
U44_gga(x0, x1, x2)
U50_gga(x0, x1)
U51_gga(x0, x1, x2)
U45_gga(x0, x1, x2)
From the DPs we obtained the following set of size-change graphs:
P65_IN_GAAA(T84, T86, X228, X229) → ACKERMANN57_IN_GAA(T84, T86, X228)
ACKERMANN57_IN_GAA(T84, s(T86), X229) → P65_IN_GAAA(T84, T86, X228, X229)
ackermannc21_in_ga(T28, X73) → U40_ga(T28, X73, ackermannc27_in_ga(T28, X73))
ackermannc27_in_ga(0, s(s(0))) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32), X97) → U41_ga(T32, X97, ackermannc21_in_ga(T32, T34))
U41_ga(T32, X97, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, X97, ackermannc38_in_gga(T32, T34, X97))
ackermannc38_in_gga(0, T42, s(T42)) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0, X133) → U43_gga(T47, X133, ackermannc27_in_ga(T47, X133))
U43_gga(T47, X133, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
ackermannc38_in_gga(s(T52), s(T53), X151) → U44_gga(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U44_gga(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, X151, ackermannc38_in_gga(T52, T55, X151))
U45_gga(T52, T53, X151, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
U42_ga(T32, X97, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U40_ga(T28, X73, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
ackermannc57_in_gga(T79, 0, X211) → U46_gga(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gga(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
ackermannc57_in_gga(T84, s(T86), X229) → U47_gga(T84, T86, X229, qc65_in_ggaa(T84, T86, X228, X229))
qc65_in_ggaa(T84, T86, T88, X229) → U48_ggaa(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U48_ggaa(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
ackermannc68_in_gga(0, T96, s(T96)) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0, X265) → U50_gga(T101, X265, ackermannc27_in_ga(T101, X265))
U50_gga(T101, X265, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
ackermannc68_in_gga(s(T106), s(T108), X283) → U51_gga(T106, T108, X283, qc65_in_ggaa(T106, T108, X282, X283))
U51_gga(T106, T108, X283, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
U49_ggaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U47_gga(T84, T86, X229, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
ackermannc57_in_gaa(T79, 0, X211) → U46_gaa(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gaa(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gaa(T79, 0, X211)
ackermannc57_in_gaa(T84, s(T86), X229) → U47_gaa(T84, T86, X229, qc65_in_gaaa(T84, T86, X228, X229))
qc65_in_gaaa(T84, T86, T88, X229) → U48_gaaa(T84, T86, T88, X229, ackermannc57_in_gaa(T84, T86, T88))
U48_gaaa(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → U49_gaaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
U49_gaaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_gaaa(T84, T86, T88, X229)
U47_gaa(T84, T86, X229, qc65_out_gaaa(T84, T86, X228, X229)) → ackermannc57_out_gaa(T84, s(T86), X229)
P65_IN_GAAA(T84, T86, X228, X229) → ACKERMANN57_IN_GAA(T84, T86, X228)
ACKERMANN57_IN_GAA(T84, s(T86), X229) → P65_IN_GAAA(T84, T86, X228, X229)
P65_IN_GAAA(T84) → ACKERMANN57_IN_GAA(T84)
ACKERMANN57_IN_GAA(T84) → P65_IN_GAAA(T84)
ACKERMANN1_IN_GGG(s(s(T19)), 0, T20) → U17_GGG(T19, T20, ackermannc21_in_ga(T19, T22))
U17_GGG(T19, T20, ackermannc21_out_ga(T19, T22)) → ACKERMANN1_IN_GGG(T19, T22, T20)
ACKERMANN1_IN_GGG(s(T68), s(T71), T70) → U20_GGG(T68, T71, T70, ackermannc57_in_gga(T68, T71, T73))
U20_GGG(T68, T71, T70, ackermannc57_out_gga(T68, T71, T73)) → ACKERMANN1_IN_GGG(T68, T73, T70)
ACKERMANN1_IN_GGG(s(T123), s(0), T117) → U23_GGG(T123, T117, ackermannc27_in_ga(T123, T124))
U23_GGG(T123, T117, ackermannc27_out_ga(T123, T124)) → ACKERMANN1_IN_GGG(T123, T124, T117)
ACKERMANN1_IN_GGG(s(T131), s(s(T133)), T117) → U26_GGG(T131, T133, T117, ackermannc57_in_gga(T131, T133, T135))
U26_GGG(T131, T133, T117, ackermannc57_out_gga(T131, T133, T135)) → U28_GGG(T131, T133, T117, ackermannc68_in_gga(T131, T135, T139))
U28_GGG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → ACKERMANN1_IN_GGG(T131, T139, T117)
ackermannc21_in_ga(T28, X73) → U40_ga(T28, X73, ackermannc27_in_ga(T28, X73))
ackermannc27_in_ga(0, s(s(0))) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32), X97) → U41_ga(T32, X97, ackermannc21_in_ga(T32, T34))
U41_ga(T32, X97, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, X97, ackermannc38_in_gga(T32, T34, X97))
ackermannc38_in_gga(0, T42, s(T42)) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0, X133) → U43_gga(T47, X133, ackermannc27_in_ga(T47, X133))
U43_gga(T47, X133, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
ackermannc38_in_gga(s(T52), s(T53), X151) → U44_gga(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U44_gga(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, X151, ackermannc38_in_gga(T52, T55, X151))
U45_gga(T52, T53, X151, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
U42_ga(T32, X97, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U40_ga(T28, X73, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
ackermannc57_in_gga(T79, 0, X211) → U46_gga(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gga(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
ackermannc57_in_gga(T84, s(T86), X229) → U47_gga(T84, T86, X229, qc65_in_ggaa(T84, T86, X228, X229))
qc65_in_ggaa(T84, T86, T88, X229) → U48_ggaa(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U48_ggaa(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
ackermannc68_in_gga(0, T96, s(T96)) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0, X265) → U50_gga(T101, X265, ackermannc27_in_ga(T101, X265))
U50_gga(T101, X265, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
ackermannc68_in_gga(s(T106), s(T108), X283) → U51_gga(T106, T108, X283, qc65_in_ggaa(T106, T108, X282, X283))
U51_gga(T106, T108, X283, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
U49_ggaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U47_gga(T84, T86, X229, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
ackermannc57_in_gaa(T79, 0, X211) → U46_gaa(T79, X211, ackermannc27_in_ga(T79, X211))
U46_gaa(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gaa(T79, 0, X211)
ackermannc57_in_gaa(T84, s(T86), X229) → U47_gaa(T84, T86, X229, qc65_in_gaaa(T84, T86, X228, X229))
qc65_in_gaaa(T84, T86, T88, X229) → U48_gaaa(T84, T86, T88, X229, ackermannc57_in_gaa(T84, T86, T88))
U48_gaaa(T84, T86, T88, X229, ackermannc57_out_gaa(T84, T86, T88)) → U49_gaaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
U49_gaaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_gaaa(T84, T86, T88, X229)
U47_gaa(T84, T86, X229, qc65_out_gaaa(T84, T86, X228, X229)) → ackermannc57_out_gaa(T84, s(T86), X229)
ACKERMANN1_IN_GGG(s(s(T19)), 0, T20) → U17_GGG(T19, T20, ackermannc21_in_ga(T19, T22))
U17_GGG(T19, T20, ackermannc21_out_ga(T19, T22)) → ACKERMANN1_IN_GGG(T19, T22, T20)
ACKERMANN1_IN_GGG(s(T68), s(T71), T70) → U20_GGG(T68, T71, T70, ackermannc57_in_gga(T68, T71, T73))
U20_GGG(T68, T71, T70, ackermannc57_out_gga(T68, T71, T73)) → ACKERMANN1_IN_GGG(T68, T73, T70)
ACKERMANN1_IN_GGG(s(T123), s(0), T117) → U23_GGG(T123, T117, ackermannc27_in_ga(T123, T124))
U23_GGG(T123, T117, ackermannc27_out_ga(T123, T124)) → ACKERMANN1_IN_GGG(T123, T124, T117)
ACKERMANN1_IN_GGG(s(T131), s(s(T133)), T117) → U26_GGG(T131, T133, T117, ackermannc57_in_gga(T131, T133, T135))
U26_GGG(T131, T133, T117, ackermannc57_out_gga(T131, T133, T135)) → U28_GGG(T131, T133, T117, ackermannc68_in_gga(T131, T135, T139))
U28_GGG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → ACKERMANN1_IN_GGG(T131, T139, T117)
ackermannc21_in_ga(T28, X73) → U40_ga(T28, X73, ackermannc27_in_ga(T28, X73))
ackermannc57_in_gga(T79, 0, X211) → U46_gga(T79, X211, ackermannc27_in_ga(T79, X211))
ackermannc57_in_gga(T84, s(T86), X229) → U47_gga(T84, T86, X229, qc65_in_ggaa(T84, T86, X228, X229))
ackermannc27_in_ga(0, s(s(0))) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32), X97) → U41_ga(T32, X97, ackermannc21_in_ga(T32, T34))
ackermannc68_in_gga(0, T96, s(T96)) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0, X265) → U50_gga(T101, X265, ackermannc27_in_ga(T101, X265))
ackermannc68_in_gga(s(T106), s(T108), X283) → U51_gga(T106, T108, X283, qc65_in_ggaa(T106, T108, X282, X283))
U40_ga(T28, X73, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
U46_gga(T79, X211, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
U47_gga(T84, T86, X229, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
U41_ga(T32, X97, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, X97, ackermannc38_in_gga(T32, T34, X97))
U50_gga(T101, X265, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
U51_gga(T106, T108, X283, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
qc65_in_ggaa(T84, T86, T88, X229) → U48_ggaa(T84, T86, T88, X229, ackermannc57_in_gga(T84, T86, T88))
U42_ga(T32, X97, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U48_ggaa(T84, T86, T88, X229, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, X229, ackermannc68_in_gga(T84, T88, X229))
ackermannc38_in_gga(0, T42, s(T42)) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0, X133) → U43_gga(T47, X133, ackermannc27_in_ga(T47, X133))
ackermannc38_in_gga(s(T52), s(T53), X151) → U44_gga(T52, T53, X151, ackermannc38_in_gga(s(T52), T53, T55))
U49_ggaa(T84, T86, T88, X229, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U43_gga(T47, X133, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
U44_gga(T52, T53, X151, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, X151, ackermannc38_in_gga(T52, T55, X151))
U45_gga(T52, T53, X151, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
ACKERMANN1_IN_GGG(s(s(T19)), 0, T20) → U17_GGG(T19, T20, ackermannc21_in_ga(T19))
U17_GGG(T19, T20, ackermannc21_out_ga(T19, T22)) → ACKERMANN1_IN_GGG(T19, T22, T20)
ACKERMANN1_IN_GGG(s(T68), s(T71), T70) → U20_GGG(T68, T71, T70, ackermannc57_in_gga(T68, T71))
U20_GGG(T68, T71, T70, ackermannc57_out_gga(T68, T71, T73)) → ACKERMANN1_IN_GGG(T68, T73, T70)
ACKERMANN1_IN_GGG(s(T123), s(0), T117) → U23_GGG(T123, T117, ackermannc27_in_ga(T123))
U23_GGG(T123, T117, ackermannc27_out_ga(T123, T124)) → ACKERMANN1_IN_GGG(T123, T124, T117)
ACKERMANN1_IN_GGG(s(T131), s(s(T133)), T117) → U26_GGG(T131, T133, T117, ackermannc57_in_gga(T131, T133))
U26_GGG(T131, T133, T117, ackermannc57_out_gga(T131, T133, T135)) → U28_GGG(T131, T133, T117, ackermannc68_in_gga(T131, T135))
U28_GGG(T131, T133, T117, ackermannc68_out_gga(T131, T135, T139)) → ACKERMANN1_IN_GGG(T131, T139, T117)
ackermannc21_in_ga(T28) → U40_ga(T28, ackermannc27_in_ga(T28))
ackermannc57_in_gga(T79, 0) → U46_gga(T79, ackermannc27_in_ga(T79))
ackermannc57_in_gga(T84, s(T86)) → U47_gga(T84, T86, qc65_in_ggaa(T84, T86))
ackermannc27_in_ga(0) → ackermannc27_out_ga(0, s(s(0)))
ackermannc27_in_ga(s(T32)) → U41_ga(T32, ackermannc21_in_ga(T32))
ackermannc68_in_gga(0, T96) → ackermannc68_out_gga(0, T96, s(T96))
ackermannc68_in_gga(s(T101), 0) → U50_gga(T101, ackermannc27_in_ga(T101))
ackermannc68_in_gga(s(T106), s(T108)) → U51_gga(T106, T108, qc65_in_ggaa(T106, T108))
U40_ga(T28, ackermannc27_out_ga(T28, X73)) → ackermannc21_out_ga(T28, X73)
U46_gga(T79, ackermannc27_out_ga(T79, X211)) → ackermannc57_out_gga(T79, 0, X211)
U47_gga(T84, T86, qc65_out_ggaa(T84, T86, X228, X229)) → ackermannc57_out_gga(T84, s(T86), X229)
U41_ga(T32, ackermannc21_out_ga(T32, T34)) → U42_ga(T32, ackermannc38_in_gga(T32, T34))
U50_gga(T101, ackermannc27_out_ga(T101, X265)) → ackermannc68_out_gga(s(T101), 0, X265)
U51_gga(T106, T108, qc65_out_ggaa(T106, T108, X282, X283)) → ackermannc68_out_gga(s(T106), s(T108), X283)
qc65_in_ggaa(T84, T86) → U48_ggaa(T84, T86, ackermannc57_in_gga(T84, T86))
U42_ga(T32, ackermannc38_out_gga(T32, T34, X97)) → ackermannc27_out_ga(s(T32), X97)
U48_ggaa(T84, T86, ackermannc57_out_gga(T84, T86, T88)) → U49_ggaa(T84, T86, T88, ackermannc68_in_gga(T84, T88))
ackermannc38_in_gga(0, T42) → ackermannc38_out_gga(0, T42, s(T42))
ackermannc38_in_gga(s(T47), 0) → U43_gga(T47, ackermannc27_in_ga(T47))
ackermannc38_in_gga(s(T52), s(T53)) → U44_gga(T52, T53, ackermannc38_in_gga(s(T52), T53))
U49_ggaa(T84, T86, T88, ackermannc68_out_gga(T84, T88, X229)) → qc65_out_ggaa(T84, T86, T88, X229)
U43_gga(T47, ackermannc27_out_ga(T47, X133)) → ackermannc38_out_gga(s(T47), 0, X133)
U44_gga(T52, T53, ackermannc38_out_gga(s(T52), T53, T55)) → U45_gga(T52, T53, ackermannc38_in_gga(T52, T55))
U45_gga(T52, T53, ackermannc38_out_gga(T52, T55, X151)) → ackermannc38_out_gga(s(T52), s(T53), X151)
ackermannc21_in_ga(x0)
ackermannc57_in_gga(x0, x1)
ackermannc27_in_ga(x0)
ackermannc68_in_gga(x0, x1)
U40_ga(x0, x1)
U46_gga(x0, x1)
U47_gga(x0, x1, x2)
U41_ga(x0, x1)
U50_gga(x0, x1)
U51_gga(x0, x1, x2)
qc65_in_ggaa(x0, x1)
U42_ga(x0, x1)
U48_ggaa(x0, x1, x2)
ackermannc38_in_gga(x0, x1)
U49_ggaa(x0, x1, x2, x3)
U43_gga(x0, x1)
U44_gga(x0, x1, x2)
U45_gga(x0, x1, x2)
From the DPs we obtained the following set of size-change graphs: