0 Prolog
↳1 PrologToPrologProblemTransformerProof (⇒, 87 ms)
↳2 Prolog
↳3 PrologToPiTRSProof (⇒, 11 ms)
↳4 PiTRS
↳5 DependencyPairsProof (⇔, 60 ms)
↳6 PiDP
↳7 DependencyGraphProof (⇔, 0 ms)
↳8 PiDP
↳9 UsableRulesProof (⇔, 0 ms)
↳10 PiDP
↳11 PiDPToQDPProof (⇒, 10 ms)
↳12 QDP
↳13 MRRProof (⇔, 42 ms)
↳14 QDP
↳15 PisEmptyProof (⇔, 0 ms)
↳16 YES
avgA_in_gga(s(s(T23)), T24, T26) → U1_gga(T23, T24, T26, avgA_in_gga(T23, s(s(T24)), T26))
avgA_in_gga(s(T42), s(s(T43)), s(T45)) → U2_gga(T42, T43, T45, avgA_in_gga(s(T42), T43, T45))
avgA_in_gga(s(0), 0, 0) → avgA_out_gga(s(0), 0, 0)
avgA_in_gga(s(0), s(0), s(0)) → avgA_out_gga(s(0), s(0), s(0))
avgA_in_gga(s(T61), s(s(s(T62))), s(T64)) → U3_gga(T61, T62, T64, avgA_in_gga(s(s(T61)), T62, T64))
avgA_in_gga(T101, s(s(s(T102))), s(T104)) → U4_gga(T101, T102, T104, avgA_in_gga(T101, s(T102), T104))
avgA_in_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → U5_gga(T123, T124, T126, avgA_in_gga(s(s(T123)), T124, T126))
avgA_in_gga(0, 0, 0) → avgA_out_gga(0, 0, 0)
avgA_in_gga(0, s(0), 0) → avgA_out_gga(0, s(0), 0)
avgA_in_gga(0, s(s(0)), s(0)) → avgA_out_gga(0, s(s(0)), s(0))
U5_gga(T123, T124, T126, avgA_out_gga(s(s(T123)), T124, T126)) → avgA_out_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126)))
U4_gga(T101, T102, T104, avgA_out_gga(T101, s(T102), T104)) → avgA_out_gga(T101, s(s(s(T102))), s(T104))
U3_gga(T61, T62, T64, avgA_out_gga(s(s(T61)), T62, T64)) → avgA_out_gga(s(T61), s(s(s(T62))), s(T64))
U2_gga(T42, T43, T45, avgA_out_gga(s(T42), T43, T45)) → avgA_out_gga(s(T42), s(s(T43)), s(T45))
U1_gga(T23, T24, T26, avgA_out_gga(T23, s(s(T24)), T26)) → avgA_out_gga(s(s(T23)), T24, T26)
Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
avgA_in_gga(s(s(T23)), T24, T26) → U1_gga(T23, T24, T26, avgA_in_gga(T23, s(s(T24)), T26))
avgA_in_gga(s(T42), s(s(T43)), s(T45)) → U2_gga(T42, T43, T45, avgA_in_gga(s(T42), T43, T45))
avgA_in_gga(s(0), 0, 0) → avgA_out_gga(s(0), 0, 0)
avgA_in_gga(s(0), s(0), s(0)) → avgA_out_gga(s(0), s(0), s(0))
avgA_in_gga(s(T61), s(s(s(T62))), s(T64)) → U3_gga(T61, T62, T64, avgA_in_gga(s(s(T61)), T62, T64))
avgA_in_gga(T101, s(s(s(T102))), s(T104)) → U4_gga(T101, T102, T104, avgA_in_gga(T101, s(T102), T104))
avgA_in_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → U5_gga(T123, T124, T126, avgA_in_gga(s(s(T123)), T124, T126))
avgA_in_gga(0, 0, 0) → avgA_out_gga(0, 0, 0)
avgA_in_gga(0, s(0), 0) → avgA_out_gga(0, s(0), 0)
avgA_in_gga(0, s(s(0)), s(0)) → avgA_out_gga(0, s(s(0)), s(0))
U5_gga(T123, T124, T126, avgA_out_gga(s(s(T123)), T124, T126)) → avgA_out_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126)))
U4_gga(T101, T102, T104, avgA_out_gga(T101, s(T102), T104)) → avgA_out_gga(T101, s(s(s(T102))), s(T104))
U3_gga(T61, T62, T64, avgA_out_gga(s(s(T61)), T62, T64)) → avgA_out_gga(s(T61), s(s(s(T62))), s(T64))
U2_gga(T42, T43, T45, avgA_out_gga(s(T42), T43, T45)) → avgA_out_gga(s(T42), s(s(T43)), s(T45))
U1_gga(T23, T24, T26, avgA_out_gga(T23, s(s(T24)), T26)) → avgA_out_gga(s(s(T23)), T24, T26)
AVGA_IN_GGA(s(s(T23)), T24, T26) → U1_GGA(T23, T24, T26, avgA_in_gga(T23, s(s(T24)), T26))
AVGA_IN_GGA(s(s(T23)), T24, T26) → AVGA_IN_GGA(T23, s(s(T24)), T26)
AVGA_IN_GGA(s(T42), s(s(T43)), s(T45)) → U2_GGA(T42, T43, T45, avgA_in_gga(s(T42), T43, T45))
AVGA_IN_GGA(s(T42), s(s(T43)), s(T45)) → AVGA_IN_GGA(s(T42), T43, T45)
AVGA_IN_GGA(s(T61), s(s(s(T62))), s(T64)) → U3_GGA(T61, T62, T64, avgA_in_gga(s(s(T61)), T62, T64))
AVGA_IN_GGA(s(T61), s(s(s(T62))), s(T64)) → AVGA_IN_GGA(s(s(T61)), T62, T64)
AVGA_IN_GGA(T101, s(s(s(T102))), s(T104)) → U4_GGA(T101, T102, T104, avgA_in_gga(T101, s(T102), T104))
AVGA_IN_GGA(T101, s(s(s(T102))), s(T104)) → AVGA_IN_GGA(T101, s(T102), T104)
AVGA_IN_GGA(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → U5_GGA(T123, T124, T126, avgA_in_gga(s(s(T123)), T124, T126))
AVGA_IN_GGA(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → AVGA_IN_GGA(s(s(T123)), T124, T126)
avgA_in_gga(s(s(T23)), T24, T26) → U1_gga(T23, T24, T26, avgA_in_gga(T23, s(s(T24)), T26))
avgA_in_gga(s(T42), s(s(T43)), s(T45)) → U2_gga(T42, T43, T45, avgA_in_gga(s(T42), T43, T45))
avgA_in_gga(s(0), 0, 0) → avgA_out_gga(s(0), 0, 0)
avgA_in_gga(s(0), s(0), s(0)) → avgA_out_gga(s(0), s(0), s(0))
avgA_in_gga(s(T61), s(s(s(T62))), s(T64)) → U3_gga(T61, T62, T64, avgA_in_gga(s(s(T61)), T62, T64))
avgA_in_gga(T101, s(s(s(T102))), s(T104)) → U4_gga(T101, T102, T104, avgA_in_gga(T101, s(T102), T104))
avgA_in_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → U5_gga(T123, T124, T126, avgA_in_gga(s(s(T123)), T124, T126))
avgA_in_gga(0, 0, 0) → avgA_out_gga(0, 0, 0)
avgA_in_gga(0, s(0), 0) → avgA_out_gga(0, s(0), 0)
avgA_in_gga(0, s(s(0)), s(0)) → avgA_out_gga(0, s(s(0)), s(0))
U5_gga(T123, T124, T126, avgA_out_gga(s(s(T123)), T124, T126)) → avgA_out_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126)))
U4_gga(T101, T102, T104, avgA_out_gga(T101, s(T102), T104)) → avgA_out_gga(T101, s(s(s(T102))), s(T104))
U3_gga(T61, T62, T64, avgA_out_gga(s(s(T61)), T62, T64)) → avgA_out_gga(s(T61), s(s(s(T62))), s(T64))
U2_gga(T42, T43, T45, avgA_out_gga(s(T42), T43, T45)) → avgA_out_gga(s(T42), s(s(T43)), s(T45))
U1_gga(T23, T24, T26, avgA_out_gga(T23, s(s(T24)), T26)) → avgA_out_gga(s(s(T23)), T24, T26)
AVGA_IN_GGA(s(s(T23)), T24, T26) → U1_GGA(T23, T24, T26, avgA_in_gga(T23, s(s(T24)), T26))
AVGA_IN_GGA(s(s(T23)), T24, T26) → AVGA_IN_GGA(T23, s(s(T24)), T26)
AVGA_IN_GGA(s(T42), s(s(T43)), s(T45)) → U2_GGA(T42, T43, T45, avgA_in_gga(s(T42), T43, T45))
AVGA_IN_GGA(s(T42), s(s(T43)), s(T45)) → AVGA_IN_GGA(s(T42), T43, T45)
AVGA_IN_GGA(s(T61), s(s(s(T62))), s(T64)) → U3_GGA(T61, T62, T64, avgA_in_gga(s(s(T61)), T62, T64))
AVGA_IN_GGA(s(T61), s(s(s(T62))), s(T64)) → AVGA_IN_GGA(s(s(T61)), T62, T64)
AVGA_IN_GGA(T101, s(s(s(T102))), s(T104)) → U4_GGA(T101, T102, T104, avgA_in_gga(T101, s(T102), T104))
AVGA_IN_GGA(T101, s(s(s(T102))), s(T104)) → AVGA_IN_GGA(T101, s(T102), T104)
AVGA_IN_GGA(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → U5_GGA(T123, T124, T126, avgA_in_gga(s(s(T123)), T124, T126))
AVGA_IN_GGA(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → AVGA_IN_GGA(s(s(T123)), T124, T126)
avgA_in_gga(s(s(T23)), T24, T26) → U1_gga(T23, T24, T26, avgA_in_gga(T23, s(s(T24)), T26))
avgA_in_gga(s(T42), s(s(T43)), s(T45)) → U2_gga(T42, T43, T45, avgA_in_gga(s(T42), T43, T45))
avgA_in_gga(s(0), 0, 0) → avgA_out_gga(s(0), 0, 0)
avgA_in_gga(s(0), s(0), s(0)) → avgA_out_gga(s(0), s(0), s(0))
avgA_in_gga(s(T61), s(s(s(T62))), s(T64)) → U3_gga(T61, T62, T64, avgA_in_gga(s(s(T61)), T62, T64))
avgA_in_gga(T101, s(s(s(T102))), s(T104)) → U4_gga(T101, T102, T104, avgA_in_gga(T101, s(T102), T104))
avgA_in_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → U5_gga(T123, T124, T126, avgA_in_gga(s(s(T123)), T124, T126))
avgA_in_gga(0, 0, 0) → avgA_out_gga(0, 0, 0)
avgA_in_gga(0, s(0), 0) → avgA_out_gga(0, s(0), 0)
avgA_in_gga(0, s(s(0)), s(0)) → avgA_out_gga(0, s(s(0)), s(0))
U5_gga(T123, T124, T126, avgA_out_gga(s(s(T123)), T124, T126)) → avgA_out_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126)))
U4_gga(T101, T102, T104, avgA_out_gga(T101, s(T102), T104)) → avgA_out_gga(T101, s(s(s(T102))), s(T104))
U3_gga(T61, T62, T64, avgA_out_gga(s(s(T61)), T62, T64)) → avgA_out_gga(s(T61), s(s(s(T62))), s(T64))
U2_gga(T42, T43, T45, avgA_out_gga(s(T42), T43, T45)) → avgA_out_gga(s(T42), s(s(T43)), s(T45))
U1_gga(T23, T24, T26, avgA_out_gga(T23, s(s(T24)), T26)) → avgA_out_gga(s(s(T23)), T24, T26)
AVGA_IN_GGA(s(T42), s(s(T43)), s(T45)) → AVGA_IN_GGA(s(T42), T43, T45)
AVGA_IN_GGA(s(s(T23)), T24, T26) → AVGA_IN_GGA(T23, s(s(T24)), T26)
AVGA_IN_GGA(s(T61), s(s(s(T62))), s(T64)) → AVGA_IN_GGA(s(s(T61)), T62, T64)
AVGA_IN_GGA(T101, s(s(s(T102))), s(T104)) → AVGA_IN_GGA(T101, s(T102), T104)
AVGA_IN_GGA(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → AVGA_IN_GGA(s(s(T123)), T124, T126)
avgA_in_gga(s(s(T23)), T24, T26) → U1_gga(T23, T24, T26, avgA_in_gga(T23, s(s(T24)), T26))
avgA_in_gga(s(T42), s(s(T43)), s(T45)) → U2_gga(T42, T43, T45, avgA_in_gga(s(T42), T43, T45))
avgA_in_gga(s(0), 0, 0) → avgA_out_gga(s(0), 0, 0)
avgA_in_gga(s(0), s(0), s(0)) → avgA_out_gga(s(0), s(0), s(0))
avgA_in_gga(s(T61), s(s(s(T62))), s(T64)) → U3_gga(T61, T62, T64, avgA_in_gga(s(s(T61)), T62, T64))
avgA_in_gga(T101, s(s(s(T102))), s(T104)) → U4_gga(T101, T102, T104, avgA_in_gga(T101, s(T102), T104))
avgA_in_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → U5_gga(T123, T124, T126, avgA_in_gga(s(s(T123)), T124, T126))
avgA_in_gga(0, 0, 0) → avgA_out_gga(0, 0, 0)
avgA_in_gga(0, s(0), 0) → avgA_out_gga(0, s(0), 0)
avgA_in_gga(0, s(s(0)), s(0)) → avgA_out_gga(0, s(s(0)), s(0))
U5_gga(T123, T124, T126, avgA_out_gga(s(s(T123)), T124, T126)) → avgA_out_gga(T123, s(s(s(s(s(s(T124)))))), s(s(T126)))
U4_gga(T101, T102, T104, avgA_out_gga(T101, s(T102), T104)) → avgA_out_gga(T101, s(s(s(T102))), s(T104))
U3_gga(T61, T62, T64, avgA_out_gga(s(s(T61)), T62, T64)) → avgA_out_gga(s(T61), s(s(s(T62))), s(T64))
U2_gga(T42, T43, T45, avgA_out_gga(s(T42), T43, T45)) → avgA_out_gga(s(T42), s(s(T43)), s(T45))
U1_gga(T23, T24, T26, avgA_out_gga(T23, s(s(T24)), T26)) → avgA_out_gga(s(s(T23)), T24, T26)
AVGA_IN_GGA(s(T42), s(s(T43)), s(T45)) → AVGA_IN_GGA(s(T42), T43, T45)
AVGA_IN_GGA(s(s(T23)), T24, T26) → AVGA_IN_GGA(T23, s(s(T24)), T26)
AVGA_IN_GGA(s(T61), s(s(s(T62))), s(T64)) → AVGA_IN_GGA(s(s(T61)), T62, T64)
AVGA_IN_GGA(T101, s(s(s(T102))), s(T104)) → AVGA_IN_GGA(T101, s(T102), T104)
AVGA_IN_GGA(T123, s(s(s(s(s(s(T124)))))), s(s(T126))) → AVGA_IN_GGA(s(s(T123)), T124, T126)
AVGA_IN_GGA(s(T42), s(s(T43))) → AVGA_IN_GGA(s(T42), T43)
AVGA_IN_GGA(s(s(T23)), T24) → AVGA_IN_GGA(T23, s(s(T24)))
AVGA_IN_GGA(s(T61), s(s(s(T62)))) → AVGA_IN_GGA(s(s(T61)), T62)
AVGA_IN_GGA(T101, s(s(s(T102)))) → AVGA_IN_GGA(T101, s(T102))
AVGA_IN_GGA(T123, s(s(s(s(s(s(T124))))))) → AVGA_IN_GGA(s(s(T123)), T124)
AVGA_IN_GGA(s(T42), s(s(T43))) → AVGA_IN_GGA(s(T42), T43)
AVGA_IN_GGA(s(s(T23)), T24) → AVGA_IN_GGA(T23, s(s(T24)))
AVGA_IN_GGA(s(T61), s(s(s(T62)))) → AVGA_IN_GGA(s(s(T61)), T62)
AVGA_IN_GGA(T101, s(s(s(T102)))) → AVGA_IN_GGA(T101, s(T102))
AVGA_IN_GGA(T123, s(s(s(s(s(s(T124))))))) → AVGA_IN_GGA(s(s(T123)), T124)
s1 > AVGAINGGA2
s_1=1
AVGA_IN_GGA_2=0