0 Prolog
↳1 PrologToDTProblemTransformerProof (⇒, 0 ms)
↳2 TRIPLES
↳3 TriplesToPiDPProof (⇒, 5 ms)
↳4 PiDP
↳5 DependencyGraphProof (⇔, 0 ms)
↳6 PiDP
↳7 PiDPToQDPProof (⇔, 21 ms)
↳8 QDP
↳9 QDPSizeChangeProof (⇔, 0 ms)
↳10 YES
BIN_TREEA_IN_G(tree(X1, X2, X3)) → U5_G(X1, X2, X3, pB_in_gg(X2, X3))
BIN_TREEA_IN_G(tree(X1, X2, X3)) → PB_IN_GG(X2, X3)
PB_IN_GG(void, X1) → U1_GG(X1, bin_treeA_in_g(X1))
PB_IN_GG(void, X1) → BIN_TREEA_IN_G(X1)
PB_IN_GG(tree(X1, X2, X3), X4) → U2_GG(X1, X2, X3, X4, bin_treeA_in_g(X2))
PB_IN_GG(tree(X1, X2, X3), X4) → BIN_TREEA_IN_G(X2)
PB_IN_GG(tree(X1, X2, X3), X4) → U3_GG(X1, X2, X3, X4, bin_treecA_in_g(X2))
U3_GG(X1, X2, X3, X4, bin_treecA_out_g(X2)) → U4_GG(X1, X2, X3, X4, pB_in_gg(X3, X4))
U3_GG(X1, X2, X3, X4, bin_treecA_out_g(X2)) → PB_IN_GG(X3, X4)
bin_treecA_in_g(void) → bin_treecA_out_g(void)
bin_treecA_in_g(tree(X1, X2, X3)) → U7_g(X1, X2, X3, qcB_in_gg(X2, X3))
qcB_in_gg(void, X1) → U8_gg(X1, bin_treecA_in_g(X1))
U8_gg(X1, bin_treecA_out_g(X1)) → qcB_out_gg(void, X1)
qcB_in_gg(tree(X1, X2, X3), X4) → U9_gg(X1, X2, X3, X4, bin_treecA_in_g(X2))
U9_gg(X1, X2, X3, X4, bin_treecA_out_g(X2)) → U10_gg(X1, X2, X3, X4, qcB_in_gg(X3, X4))
U10_gg(X1, X2, X3, X4, qcB_out_gg(X3, X4)) → qcB_out_gg(tree(X1, X2, X3), X4)
U7_g(X1, X2, X3, qcB_out_gg(X2, X3)) → bin_treecA_out_g(tree(X1, X2, X3))
Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES
BIN_TREEA_IN_G(tree(X1, X2, X3)) → U5_G(X1, X2, X3, pB_in_gg(X2, X3))
BIN_TREEA_IN_G(tree(X1, X2, X3)) → PB_IN_GG(X2, X3)
PB_IN_GG(void, X1) → U1_GG(X1, bin_treeA_in_g(X1))
PB_IN_GG(void, X1) → BIN_TREEA_IN_G(X1)
PB_IN_GG(tree(X1, X2, X3), X4) → U2_GG(X1, X2, X3, X4, bin_treeA_in_g(X2))
PB_IN_GG(tree(X1, X2, X3), X4) → BIN_TREEA_IN_G(X2)
PB_IN_GG(tree(X1, X2, X3), X4) → U3_GG(X1, X2, X3, X4, bin_treecA_in_g(X2))
U3_GG(X1, X2, X3, X4, bin_treecA_out_g(X2)) → U4_GG(X1, X2, X3, X4, pB_in_gg(X3, X4))
U3_GG(X1, X2, X3, X4, bin_treecA_out_g(X2)) → PB_IN_GG(X3, X4)
bin_treecA_in_g(void) → bin_treecA_out_g(void)
bin_treecA_in_g(tree(X1, X2, X3)) → U7_g(X1, X2, X3, qcB_in_gg(X2, X3))
qcB_in_gg(void, X1) → U8_gg(X1, bin_treecA_in_g(X1))
U8_gg(X1, bin_treecA_out_g(X1)) → qcB_out_gg(void, X1)
qcB_in_gg(tree(X1, X2, X3), X4) → U9_gg(X1, X2, X3, X4, bin_treecA_in_g(X2))
U9_gg(X1, X2, X3, X4, bin_treecA_out_g(X2)) → U10_gg(X1, X2, X3, X4, qcB_in_gg(X3, X4))
U10_gg(X1, X2, X3, X4, qcB_out_gg(X3, X4)) → qcB_out_gg(tree(X1, X2, X3), X4)
U7_g(X1, X2, X3, qcB_out_gg(X2, X3)) → bin_treecA_out_g(tree(X1, X2, X3))
BIN_TREEA_IN_G(tree(X1, X2, X3)) → PB_IN_GG(X2, X3)
PB_IN_GG(void, X1) → BIN_TREEA_IN_G(X1)
PB_IN_GG(tree(X1, X2, X3), X4) → BIN_TREEA_IN_G(X2)
PB_IN_GG(tree(X1, X2, X3), X4) → U3_GG(X1, X2, X3, X4, bin_treecA_in_g(X2))
U3_GG(X1, X2, X3, X4, bin_treecA_out_g(X2)) → PB_IN_GG(X3, X4)
bin_treecA_in_g(void) → bin_treecA_out_g(void)
bin_treecA_in_g(tree(X1, X2, X3)) → U7_g(X1, X2, X3, qcB_in_gg(X2, X3))
qcB_in_gg(void, X1) → U8_gg(X1, bin_treecA_in_g(X1))
U8_gg(X1, bin_treecA_out_g(X1)) → qcB_out_gg(void, X1)
qcB_in_gg(tree(X1, X2, X3), X4) → U9_gg(X1, X2, X3, X4, bin_treecA_in_g(X2))
U9_gg(X1, X2, X3, X4, bin_treecA_out_g(X2)) → U10_gg(X1, X2, X3, X4, qcB_in_gg(X3, X4))
U10_gg(X1, X2, X3, X4, qcB_out_gg(X3, X4)) → qcB_out_gg(tree(X1, X2, X3), X4)
U7_g(X1, X2, X3, qcB_out_gg(X2, X3)) → bin_treecA_out_g(tree(X1, X2, X3))
BIN_TREEA_IN_G(tree(X1, X2, X3)) → PB_IN_GG(X2, X3)
PB_IN_GG(void, X1) → BIN_TREEA_IN_G(X1)
PB_IN_GG(tree(X1, X2, X3), X4) → BIN_TREEA_IN_G(X2)
PB_IN_GG(tree(X1, X2, X3), X4) → U3_GG(X1, X2, X3, X4, bin_treecA_in_g(X2))
U3_GG(X1, X2, X3, X4, bin_treecA_out_g(X2)) → PB_IN_GG(X3, X4)
bin_treecA_in_g(void) → bin_treecA_out_g(void)
bin_treecA_in_g(tree(X1, X2, X3)) → U7_g(X1, X2, X3, qcB_in_gg(X2, X3))
qcB_in_gg(void, X1) → U8_gg(X1, bin_treecA_in_g(X1))
U8_gg(X1, bin_treecA_out_g(X1)) → qcB_out_gg(void, X1)
qcB_in_gg(tree(X1, X2, X3), X4) → U9_gg(X1, X2, X3, X4, bin_treecA_in_g(X2))
U9_gg(X1, X2, X3, X4, bin_treecA_out_g(X2)) → U10_gg(X1, X2, X3, X4, qcB_in_gg(X3, X4))
U10_gg(X1, X2, X3, X4, qcB_out_gg(X3, X4)) → qcB_out_gg(tree(X1, X2, X3), X4)
U7_g(X1, X2, X3, qcB_out_gg(X2, X3)) → bin_treecA_out_g(tree(X1, X2, X3))
bin_treecA_in_g(x0)
qcB_in_gg(x0, x1)
U8_gg(x0, x1)
U9_gg(x0, x1, x2, x3, x4)
U10_gg(x0, x1, x2, x3, x4)
U7_g(x0, x1, x2, x3)
From the DPs we obtained the following set of size-change graphs: