0 Prolog
↳1 PrologToPiTRSViaGraphTransformerProof (⇒, 404 ms)
↳2 PiTRS
↳3 DependencyPairsProof (⇔, 39 ms)
↳4 PiDP
↳5 DependencyGraphProof (⇔, 0 ms)
↳6 AND
↳7 PiDP
↳8 UsableRulesProof (⇔, 0 ms)
↳9 PiDP
↳10 PiDPToQDPProof (⇒, 0 ms)
↳11 QDP
↳12 QDPSizeChangeProof (⇔, 0 ms)
↳13 YES
↳14 PiDP
↳15 UsableRulesProof (⇔, 0 ms)
↳16 PiDP
↳17 PiDPToQDPProof (⇒, 0 ms)
↳18 QDP
↳19 QDPOrderProof (⇔, 61 ms)
↳20 QDP
↳21 DependencyGraphProof (⇔, 0 ms)
↳22 TRUE
divA_in_ggaa(0, T72, 0, 0) → divA_out_ggaa(0, T72, 0, 0)
divA_in_ggaa(T121, T135, s(T104), T105) → U1_ggaa(T121, T135, T104, T105, pB_in_ggaaa(T121, T135, X177, T104, T105))
pB_in_ggaaa(T121, T135, T144, T104, T105) → U5_ggaaa(T121, T135, T144, T104, T105, minusD_in_gga(T121, T135, T144))
minusD_in_gga(s(T154), s(T155), X255) → U3_gga(T154, T155, X255, minusC_in_gga(T154, T155, X255))
minusC_in_gga(T162, 0, T162) → minusC_out_gga(T162, 0, T162)
minusC_in_gga(s(T167), s(T168), X274) → U2_gga(T167, T168, X274, minusC_in_gga(T167, T168, X274))
U2_gga(T167, T168, X274, minusC_out_gga(T167, T168, X274)) → minusC_out_gga(s(T167), s(T168), X274)
U3_gga(T154, T155, X255, minusC_out_gga(T154, T155, X255)) → minusD_out_gga(s(T154), s(T155), X255)
U5_ggaaa(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → U6_ggaaa(T121, T135, T144, T104, T105, pE_in_ggaa(T144, T135, T104, T105))
pE_in_ggaa(T144, T135, T104, T105) → U4_ggaa(T144, T135, T104, T105, divA_in_ggaa(T144, T135, T104, T105))
divA_in_ggaa(T189, T195, T183, T189) → divA_out_ggaa(T189, T195, T183, T189)
U4_ggaa(T144, T135, T104, T105, divA_out_ggaa(T144, T135, T104, T105)) → pE_out_ggaa(T144, T135, T104, T105)
U6_ggaaa(T121, T135, T144, T104, T105, pE_out_ggaa(T144, T135, T104, T105)) → pB_out_ggaaa(T121, T135, T144, T104, T105)
U1_ggaa(T121, T135, T104, T105, pB_out_ggaaa(T121, T135, X177, T104, T105)) → divA_out_ggaa(T121, T135, s(T104), T105)
DIVA_IN_GGAA(T121, T135, s(T104), T105) → U1_GGAA(T121, T135, T104, T105, pB_in_ggaaa(T121, T135, X177, T104, T105))
DIVA_IN_GGAA(T121, T135, s(T104), T105) → PB_IN_GGAAA(T121, T135, X177, T104, T105)
PB_IN_GGAAA(T121, T135, T144, T104, T105) → U5_GGAAA(T121, T135, T144, T104, T105, minusD_in_gga(T121, T135, T144))
PB_IN_GGAAA(T121, T135, T144, T104, T105) → MINUSD_IN_GGA(T121, T135, T144)
MINUSD_IN_GGA(s(T154), s(T155), X255) → U3_GGA(T154, T155, X255, minusC_in_gga(T154, T155, X255))
MINUSD_IN_GGA(s(T154), s(T155), X255) → MINUSC_IN_GGA(T154, T155, X255)
MINUSC_IN_GGA(s(T167), s(T168), X274) → U2_GGA(T167, T168, X274, minusC_in_gga(T167, T168, X274))
MINUSC_IN_GGA(s(T167), s(T168), X274) → MINUSC_IN_GGA(T167, T168, X274)
U5_GGAAA(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → U6_GGAAA(T121, T135, T144, T104, T105, pE_in_ggaa(T144, T135, T104, T105))
U5_GGAAA(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → PE_IN_GGAA(T144, T135, T104, T105)
PE_IN_GGAA(T144, T135, T104, T105) → U4_GGAA(T144, T135, T104, T105, divA_in_ggaa(T144, T135, T104, T105))
PE_IN_GGAA(T144, T135, T104, T105) → DIVA_IN_GGAA(T144, T135, T104, T105)
divA_in_ggaa(0, T72, 0, 0) → divA_out_ggaa(0, T72, 0, 0)
divA_in_ggaa(T121, T135, s(T104), T105) → U1_ggaa(T121, T135, T104, T105, pB_in_ggaaa(T121, T135, X177, T104, T105))
pB_in_ggaaa(T121, T135, T144, T104, T105) → U5_ggaaa(T121, T135, T144, T104, T105, minusD_in_gga(T121, T135, T144))
minusD_in_gga(s(T154), s(T155), X255) → U3_gga(T154, T155, X255, minusC_in_gga(T154, T155, X255))
minusC_in_gga(T162, 0, T162) → minusC_out_gga(T162, 0, T162)
minusC_in_gga(s(T167), s(T168), X274) → U2_gga(T167, T168, X274, minusC_in_gga(T167, T168, X274))
U2_gga(T167, T168, X274, minusC_out_gga(T167, T168, X274)) → minusC_out_gga(s(T167), s(T168), X274)
U3_gga(T154, T155, X255, minusC_out_gga(T154, T155, X255)) → minusD_out_gga(s(T154), s(T155), X255)
U5_ggaaa(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → U6_ggaaa(T121, T135, T144, T104, T105, pE_in_ggaa(T144, T135, T104, T105))
pE_in_ggaa(T144, T135, T104, T105) → U4_ggaa(T144, T135, T104, T105, divA_in_ggaa(T144, T135, T104, T105))
divA_in_ggaa(T189, T195, T183, T189) → divA_out_ggaa(T189, T195, T183, T189)
U4_ggaa(T144, T135, T104, T105, divA_out_ggaa(T144, T135, T104, T105)) → pE_out_ggaa(T144, T135, T104, T105)
U6_ggaaa(T121, T135, T144, T104, T105, pE_out_ggaa(T144, T135, T104, T105)) → pB_out_ggaaa(T121, T135, T144, T104, T105)
U1_ggaa(T121, T135, T104, T105, pB_out_ggaaa(T121, T135, X177, T104, T105)) → divA_out_ggaa(T121, T135, s(T104), T105)
DIVA_IN_GGAA(T121, T135, s(T104), T105) → U1_GGAA(T121, T135, T104, T105, pB_in_ggaaa(T121, T135, X177, T104, T105))
DIVA_IN_GGAA(T121, T135, s(T104), T105) → PB_IN_GGAAA(T121, T135, X177, T104, T105)
PB_IN_GGAAA(T121, T135, T144, T104, T105) → U5_GGAAA(T121, T135, T144, T104, T105, minusD_in_gga(T121, T135, T144))
PB_IN_GGAAA(T121, T135, T144, T104, T105) → MINUSD_IN_GGA(T121, T135, T144)
MINUSD_IN_GGA(s(T154), s(T155), X255) → U3_GGA(T154, T155, X255, minusC_in_gga(T154, T155, X255))
MINUSD_IN_GGA(s(T154), s(T155), X255) → MINUSC_IN_GGA(T154, T155, X255)
MINUSC_IN_GGA(s(T167), s(T168), X274) → U2_GGA(T167, T168, X274, minusC_in_gga(T167, T168, X274))
MINUSC_IN_GGA(s(T167), s(T168), X274) → MINUSC_IN_GGA(T167, T168, X274)
U5_GGAAA(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → U6_GGAAA(T121, T135, T144, T104, T105, pE_in_ggaa(T144, T135, T104, T105))
U5_GGAAA(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → PE_IN_GGAA(T144, T135, T104, T105)
PE_IN_GGAA(T144, T135, T104, T105) → U4_GGAA(T144, T135, T104, T105, divA_in_ggaa(T144, T135, T104, T105))
PE_IN_GGAA(T144, T135, T104, T105) → DIVA_IN_GGAA(T144, T135, T104, T105)
divA_in_ggaa(0, T72, 0, 0) → divA_out_ggaa(0, T72, 0, 0)
divA_in_ggaa(T121, T135, s(T104), T105) → U1_ggaa(T121, T135, T104, T105, pB_in_ggaaa(T121, T135, X177, T104, T105))
pB_in_ggaaa(T121, T135, T144, T104, T105) → U5_ggaaa(T121, T135, T144, T104, T105, minusD_in_gga(T121, T135, T144))
minusD_in_gga(s(T154), s(T155), X255) → U3_gga(T154, T155, X255, minusC_in_gga(T154, T155, X255))
minusC_in_gga(T162, 0, T162) → minusC_out_gga(T162, 0, T162)
minusC_in_gga(s(T167), s(T168), X274) → U2_gga(T167, T168, X274, minusC_in_gga(T167, T168, X274))
U2_gga(T167, T168, X274, minusC_out_gga(T167, T168, X274)) → minusC_out_gga(s(T167), s(T168), X274)
U3_gga(T154, T155, X255, minusC_out_gga(T154, T155, X255)) → minusD_out_gga(s(T154), s(T155), X255)
U5_ggaaa(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → U6_ggaaa(T121, T135, T144, T104, T105, pE_in_ggaa(T144, T135, T104, T105))
pE_in_ggaa(T144, T135, T104, T105) → U4_ggaa(T144, T135, T104, T105, divA_in_ggaa(T144, T135, T104, T105))
divA_in_ggaa(T189, T195, T183, T189) → divA_out_ggaa(T189, T195, T183, T189)
U4_ggaa(T144, T135, T104, T105, divA_out_ggaa(T144, T135, T104, T105)) → pE_out_ggaa(T144, T135, T104, T105)
U6_ggaaa(T121, T135, T144, T104, T105, pE_out_ggaa(T144, T135, T104, T105)) → pB_out_ggaaa(T121, T135, T144, T104, T105)
U1_ggaa(T121, T135, T104, T105, pB_out_ggaaa(T121, T135, X177, T104, T105)) → divA_out_ggaa(T121, T135, s(T104), T105)
MINUSC_IN_GGA(s(T167), s(T168), X274) → MINUSC_IN_GGA(T167, T168, X274)
divA_in_ggaa(0, T72, 0, 0) → divA_out_ggaa(0, T72, 0, 0)
divA_in_ggaa(T121, T135, s(T104), T105) → U1_ggaa(T121, T135, T104, T105, pB_in_ggaaa(T121, T135, X177, T104, T105))
pB_in_ggaaa(T121, T135, T144, T104, T105) → U5_ggaaa(T121, T135, T144, T104, T105, minusD_in_gga(T121, T135, T144))
minusD_in_gga(s(T154), s(T155), X255) → U3_gga(T154, T155, X255, minusC_in_gga(T154, T155, X255))
minusC_in_gga(T162, 0, T162) → minusC_out_gga(T162, 0, T162)
minusC_in_gga(s(T167), s(T168), X274) → U2_gga(T167, T168, X274, minusC_in_gga(T167, T168, X274))
U2_gga(T167, T168, X274, minusC_out_gga(T167, T168, X274)) → minusC_out_gga(s(T167), s(T168), X274)
U3_gga(T154, T155, X255, minusC_out_gga(T154, T155, X255)) → minusD_out_gga(s(T154), s(T155), X255)
U5_ggaaa(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → U6_ggaaa(T121, T135, T144, T104, T105, pE_in_ggaa(T144, T135, T104, T105))
pE_in_ggaa(T144, T135, T104, T105) → U4_ggaa(T144, T135, T104, T105, divA_in_ggaa(T144, T135, T104, T105))
divA_in_ggaa(T189, T195, T183, T189) → divA_out_ggaa(T189, T195, T183, T189)
U4_ggaa(T144, T135, T104, T105, divA_out_ggaa(T144, T135, T104, T105)) → pE_out_ggaa(T144, T135, T104, T105)
U6_ggaaa(T121, T135, T144, T104, T105, pE_out_ggaa(T144, T135, T104, T105)) → pB_out_ggaaa(T121, T135, T144, T104, T105)
U1_ggaa(T121, T135, T104, T105, pB_out_ggaaa(T121, T135, X177, T104, T105)) → divA_out_ggaa(T121, T135, s(T104), T105)
MINUSC_IN_GGA(s(T167), s(T168), X274) → MINUSC_IN_GGA(T167, T168, X274)
MINUSC_IN_GGA(s(T167), s(T168)) → MINUSC_IN_GGA(T167, T168)
From the DPs we obtained the following set of size-change graphs:
DIVA_IN_GGAA(T121, T135, s(T104), T105) → PB_IN_GGAAA(T121, T135, X177, T104, T105)
PB_IN_GGAAA(T121, T135, T144, T104, T105) → U5_GGAAA(T121, T135, T144, T104, T105, minusD_in_gga(T121, T135, T144))
U5_GGAAA(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → PE_IN_GGAA(T144, T135, T104, T105)
PE_IN_GGAA(T144, T135, T104, T105) → DIVA_IN_GGAA(T144, T135, T104, T105)
divA_in_ggaa(0, T72, 0, 0) → divA_out_ggaa(0, T72, 0, 0)
divA_in_ggaa(T121, T135, s(T104), T105) → U1_ggaa(T121, T135, T104, T105, pB_in_ggaaa(T121, T135, X177, T104, T105))
pB_in_ggaaa(T121, T135, T144, T104, T105) → U5_ggaaa(T121, T135, T144, T104, T105, minusD_in_gga(T121, T135, T144))
minusD_in_gga(s(T154), s(T155), X255) → U3_gga(T154, T155, X255, minusC_in_gga(T154, T155, X255))
minusC_in_gga(T162, 0, T162) → minusC_out_gga(T162, 0, T162)
minusC_in_gga(s(T167), s(T168), X274) → U2_gga(T167, T168, X274, minusC_in_gga(T167, T168, X274))
U2_gga(T167, T168, X274, minusC_out_gga(T167, T168, X274)) → minusC_out_gga(s(T167), s(T168), X274)
U3_gga(T154, T155, X255, minusC_out_gga(T154, T155, X255)) → minusD_out_gga(s(T154), s(T155), X255)
U5_ggaaa(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → U6_ggaaa(T121, T135, T144, T104, T105, pE_in_ggaa(T144, T135, T104, T105))
pE_in_ggaa(T144, T135, T104, T105) → U4_ggaa(T144, T135, T104, T105, divA_in_ggaa(T144, T135, T104, T105))
divA_in_ggaa(T189, T195, T183, T189) → divA_out_ggaa(T189, T195, T183, T189)
U4_ggaa(T144, T135, T104, T105, divA_out_ggaa(T144, T135, T104, T105)) → pE_out_ggaa(T144, T135, T104, T105)
U6_ggaaa(T121, T135, T144, T104, T105, pE_out_ggaa(T144, T135, T104, T105)) → pB_out_ggaaa(T121, T135, T144, T104, T105)
U1_ggaa(T121, T135, T104, T105, pB_out_ggaaa(T121, T135, X177, T104, T105)) → divA_out_ggaa(T121, T135, s(T104), T105)
DIVA_IN_GGAA(T121, T135, s(T104), T105) → PB_IN_GGAAA(T121, T135, X177, T104, T105)
PB_IN_GGAAA(T121, T135, T144, T104, T105) → U5_GGAAA(T121, T135, T144, T104, T105, minusD_in_gga(T121, T135, T144))
U5_GGAAA(T121, T135, T144, T104, T105, minusD_out_gga(T121, T135, T144)) → PE_IN_GGAA(T144, T135, T104, T105)
PE_IN_GGAA(T144, T135, T104, T105) → DIVA_IN_GGAA(T144, T135, T104, T105)
minusD_in_gga(s(T154), s(T155), X255) → U3_gga(T154, T155, X255, minusC_in_gga(T154, T155, X255))
U3_gga(T154, T155, X255, minusC_out_gga(T154, T155, X255)) → minusD_out_gga(s(T154), s(T155), X255)
minusC_in_gga(T162, 0, T162) → minusC_out_gga(T162, 0, T162)
minusC_in_gga(s(T167), s(T168), X274) → U2_gga(T167, T168, X274, minusC_in_gga(T167, T168, X274))
U2_gga(T167, T168, X274, minusC_out_gga(T167, T168, X274)) → minusC_out_gga(s(T167), s(T168), X274)
DIVA_IN_GGAA(T121, T135) → PB_IN_GGAAA(T121, T135)
PB_IN_GGAAA(T121, T135) → U5_GGAAA(T121, T135, minusD_in_gga(T121, T135))
U5_GGAAA(T121, T135, minusD_out_gga(T121, T135, T144)) → PE_IN_GGAA(T144, T135)
PE_IN_GGAA(T144, T135) → DIVA_IN_GGAA(T144, T135)
minusD_in_gga(s(T154), s(T155)) → U3_gga(T154, T155, minusC_in_gga(T154, T155))
U3_gga(T154, T155, minusC_out_gga(T154, T155, X255)) → minusD_out_gga(s(T154), s(T155), X255)
minusC_in_gga(T162, 0) → minusC_out_gga(T162, 0, T162)
minusC_in_gga(s(T167), s(T168)) → U2_gga(T167, T168, minusC_in_gga(T167, T168))
U2_gga(T167, T168, minusC_out_gga(T167, T168, X274)) → minusC_out_gga(s(T167), s(T168), X274)
minusD_in_gga(x0, x1)
U3_gga(x0, x1, x2)
minusC_in_gga(x0, x1)
U2_gga(x0, x1, x2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
PB_IN_GGAAA(T121, T135) → U5_GGAAA(T121, T135, minusD_in_gga(T121, T135))
POL(0) = 0
POL(DIVA_IN_GGAA(x1, x2)) = 1 + x1
POL(PB_IN_GGAAA(x1, x2)) = 1 + x1
POL(PE_IN_GGAA(x1, x2)) = 1 + x1
POL(U2_gga(x1, x2, x3)) = x3
POL(U3_gga(x1, x2, x3)) = 1 + x3
POL(U5_GGAAA(x1, x2, x3)) = x3
POL(minusC_in_gga(x1, x2)) = x1
POL(minusC_out_gga(x1, x2, x3)) = x3
POL(minusD_in_gga(x1, x2)) = x1
POL(minusD_out_gga(x1, x2, x3)) = 1 + x3
POL(s(x1)) = 1 + x1
minusD_in_gga(s(T154), s(T155)) → U3_gga(T154, T155, minusC_in_gga(T154, T155))
minusC_in_gga(T162, 0) → minusC_out_gga(T162, 0, T162)
minusC_in_gga(s(T167), s(T168)) → U2_gga(T167, T168, minusC_in_gga(T167, T168))
U3_gga(T154, T155, minusC_out_gga(T154, T155, X255)) → minusD_out_gga(s(T154), s(T155), X255)
U2_gga(T167, T168, minusC_out_gga(T167, T168, X274)) → minusC_out_gga(s(T167), s(T168), X274)
DIVA_IN_GGAA(T121, T135) → PB_IN_GGAAA(T121, T135)
U5_GGAAA(T121, T135, minusD_out_gga(T121, T135, T144)) → PE_IN_GGAA(T144, T135)
PE_IN_GGAA(T144, T135) → DIVA_IN_GGAA(T144, T135)
minusD_in_gga(s(T154), s(T155)) → U3_gga(T154, T155, minusC_in_gga(T154, T155))
U3_gga(T154, T155, minusC_out_gga(T154, T155, X255)) → minusD_out_gga(s(T154), s(T155), X255)
minusC_in_gga(T162, 0) → minusC_out_gga(T162, 0, T162)
minusC_in_gga(s(T167), s(T168)) → U2_gga(T167, T168, minusC_in_gga(T167, T168))
U2_gga(T167, T168, minusC_out_gga(T167, T168, X274)) → minusC_out_gga(s(T167), s(T168), X274)
minusD_in_gga(x0, x1)
U3_gga(x0, x1, x2)
minusC_in_gga(x0, x1)
U2_gga(x0, x1, x2)