0 Prolog
↳1 PrologToPrologProblemTransformerProof (⇐)
↳2 Prolog
↳3 PrologToPiTRSProof (⇐)
↳4 PiTRS
↳5 DependencyPairsProof (⇔)
↳6 PiDP
↳7 DependencyGraphProof (⇔)
↳8 PiDP
↳9 PiDPToQDPProof (⇔)
↳10 QDP
↳11 QDPSizeChangeProof (⇔)
↳12 YES
bin_tree1_in_g(void) → bin_tree1_out_g(void)
bin_tree1_in_g(tree(T5, T6, T7)) → U4_g(T5, T6, T7, p7_in_gg(T6, T7))
p7_in_gg(void, T7) → U1_gg(T7, bin_tree1_in_g(T7))
U1_gg(T7, bin_tree1_out_g(T7)) → p7_out_gg(void, T7)
p7_in_gg(tree(T14, T15, T16), T7) → U2_gg(T14, T15, T16, T7, bin_tree1_in_g(T15))
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → p7_out_gg(tree(T14, T15, T16), T7)
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → U3_gg(T14, T15, T16, T7, p7_in_gg(T16, T7))
U3_gg(T14, T15, T16, T7, p7_out_gg(T16, T7)) → p7_out_gg(tree(T14, T15, T16), T7)
U4_g(T5, T6, T7, p7_out_gg(T6, T7)) → bin_tree1_out_g(tree(T5, T6, T7))
Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
bin_tree1_in_g(void) → bin_tree1_out_g(void)
bin_tree1_in_g(tree(T5, T6, T7)) → U4_g(T5, T6, T7, p7_in_gg(T6, T7))
p7_in_gg(void, T7) → U1_gg(T7, bin_tree1_in_g(T7))
U1_gg(T7, bin_tree1_out_g(T7)) → p7_out_gg(void, T7)
p7_in_gg(tree(T14, T15, T16), T7) → U2_gg(T14, T15, T16, T7, bin_tree1_in_g(T15))
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → p7_out_gg(tree(T14, T15, T16), T7)
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → U3_gg(T14, T15, T16, T7, p7_in_gg(T16, T7))
U3_gg(T14, T15, T16, T7, p7_out_gg(T16, T7)) → p7_out_gg(tree(T14, T15, T16), T7)
U4_g(T5, T6, T7, p7_out_gg(T6, T7)) → bin_tree1_out_g(tree(T5, T6, T7))
BIN_TREE1_IN_G(tree(T5, T6, T7)) → U4_G(T5, T6, T7, p7_in_gg(T6, T7))
BIN_TREE1_IN_G(tree(T5, T6, T7)) → P7_IN_GG(T6, T7)
P7_IN_GG(void, T7) → U1_GG(T7, bin_tree1_in_g(T7))
P7_IN_GG(void, T7) → BIN_TREE1_IN_G(T7)
P7_IN_GG(tree(T14, T15, T16), T7) → U2_GG(T14, T15, T16, T7, bin_tree1_in_g(T15))
P7_IN_GG(tree(T14, T15, T16), T7) → BIN_TREE1_IN_G(T15)
U2_GG(T14, T15, T16, T7, bin_tree1_out_g(T15)) → U3_GG(T14, T15, T16, T7, p7_in_gg(T16, T7))
U2_GG(T14, T15, T16, T7, bin_tree1_out_g(T15)) → P7_IN_GG(T16, T7)
bin_tree1_in_g(void) → bin_tree1_out_g(void)
bin_tree1_in_g(tree(T5, T6, T7)) → U4_g(T5, T6, T7, p7_in_gg(T6, T7))
p7_in_gg(void, T7) → U1_gg(T7, bin_tree1_in_g(T7))
U1_gg(T7, bin_tree1_out_g(T7)) → p7_out_gg(void, T7)
p7_in_gg(tree(T14, T15, T16), T7) → U2_gg(T14, T15, T16, T7, bin_tree1_in_g(T15))
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → p7_out_gg(tree(T14, T15, T16), T7)
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → U3_gg(T14, T15, T16, T7, p7_in_gg(T16, T7))
U3_gg(T14, T15, T16, T7, p7_out_gg(T16, T7)) → p7_out_gg(tree(T14, T15, T16), T7)
U4_g(T5, T6, T7, p7_out_gg(T6, T7)) → bin_tree1_out_g(tree(T5, T6, T7))
BIN_TREE1_IN_G(tree(T5, T6, T7)) → U4_G(T5, T6, T7, p7_in_gg(T6, T7))
BIN_TREE1_IN_G(tree(T5, T6, T7)) → P7_IN_GG(T6, T7)
P7_IN_GG(void, T7) → U1_GG(T7, bin_tree1_in_g(T7))
P7_IN_GG(void, T7) → BIN_TREE1_IN_G(T7)
P7_IN_GG(tree(T14, T15, T16), T7) → U2_GG(T14, T15, T16, T7, bin_tree1_in_g(T15))
P7_IN_GG(tree(T14, T15, T16), T7) → BIN_TREE1_IN_G(T15)
U2_GG(T14, T15, T16, T7, bin_tree1_out_g(T15)) → U3_GG(T14, T15, T16, T7, p7_in_gg(T16, T7))
U2_GG(T14, T15, T16, T7, bin_tree1_out_g(T15)) → P7_IN_GG(T16, T7)
bin_tree1_in_g(void) → bin_tree1_out_g(void)
bin_tree1_in_g(tree(T5, T6, T7)) → U4_g(T5, T6, T7, p7_in_gg(T6, T7))
p7_in_gg(void, T7) → U1_gg(T7, bin_tree1_in_g(T7))
U1_gg(T7, bin_tree1_out_g(T7)) → p7_out_gg(void, T7)
p7_in_gg(tree(T14, T15, T16), T7) → U2_gg(T14, T15, T16, T7, bin_tree1_in_g(T15))
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → p7_out_gg(tree(T14, T15, T16), T7)
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → U3_gg(T14, T15, T16, T7, p7_in_gg(T16, T7))
U3_gg(T14, T15, T16, T7, p7_out_gg(T16, T7)) → p7_out_gg(tree(T14, T15, T16), T7)
U4_g(T5, T6, T7, p7_out_gg(T6, T7)) → bin_tree1_out_g(tree(T5, T6, T7))
BIN_TREE1_IN_G(tree(T5, T6, T7)) → P7_IN_GG(T6, T7)
P7_IN_GG(void, T7) → BIN_TREE1_IN_G(T7)
P7_IN_GG(tree(T14, T15, T16), T7) → U2_GG(T14, T15, T16, T7, bin_tree1_in_g(T15))
U2_GG(T14, T15, T16, T7, bin_tree1_out_g(T15)) → P7_IN_GG(T16, T7)
P7_IN_GG(tree(T14, T15, T16), T7) → BIN_TREE1_IN_G(T15)
bin_tree1_in_g(void) → bin_tree1_out_g(void)
bin_tree1_in_g(tree(T5, T6, T7)) → U4_g(T5, T6, T7, p7_in_gg(T6, T7))
p7_in_gg(void, T7) → U1_gg(T7, bin_tree1_in_g(T7))
U1_gg(T7, bin_tree1_out_g(T7)) → p7_out_gg(void, T7)
p7_in_gg(tree(T14, T15, T16), T7) → U2_gg(T14, T15, T16, T7, bin_tree1_in_g(T15))
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → p7_out_gg(tree(T14, T15, T16), T7)
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → U3_gg(T14, T15, T16, T7, p7_in_gg(T16, T7))
U3_gg(T14, T15, T16, T7, p7_out_gg(T16, T7)) → p7_out_gg(tree(T14, T15, T16), T7)
U4_g(T5, T6, T7, p7_out_gg(T6, T7)) → bin_tree1_out_g(tree(T5, T6, T7))
BIN_TREE1_IN_G(tree(T5, T6, T7)) → P7_IN_GG(T6, T7)
P7_IN_GG(void, T7) → BIN_TREE1_IN_G(T7)
P7_IN_GG(tree(T14, T15, T16), T7) → U2_GG(T14, T15, T16, T7, bin_tree1_in_g(T15))
U2_GG(T14, T15, T16, T7, bin_tree1_out_g(T15)) → P7_IN_GG(T16, T7)
P7_IN_GG(tree(T14, T15, T16), T7) → BIN_TREE1_IN_G(T15)
bin_tree1_in_g(void) → bin_tree1_out_g(void)
bin_tree1_in_g(tree(T5, T6, T7)) → U4_g(T5, T6, T7, p7_in_gg(T6, T7))
p7_in_gg(void, T7) → U1_gg(T7, bin_tree1_in_g(T7))
U1_gg(T7, bin_tree1_out_g(T7)) → p7_out_gg(void, T7)
p7_in_gg(tree(T14, T15, T16), T7) → U2_gg(T14, T15, T16, T7, bin_tree1_in_g(T15))
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → p7_out_gg(tree(T14, T15, T16), T7)
U2_gg(T14, T15, T16, T7, bin_tree1_out_g(T15)) → U3_gg(T14, T15, T16, T7, p7_in_gg(T16, T7))
U3_gg(T14, T15, T16, T7, p7_out_gg(T16, T7)) → p7_out_gg(tree(T14, T15, T16), T7)
U4_g(T5, T6, T7, p7_out_gg(T6, T7)) → bin_tree1_out_g(tree(T5, T6, T7))
bin_tree1_in_g(x0)
p7_in_gg(x0, x1)
U1_gg(x0, x1)
U2_gg(x0, x1, x2, x3, x4)
U3_gg(x0, x1, x2, x3, x4)
U4_g(x0, x1, x2, x3)
From the DPs we obtained the following set of size-change graphs: