Left Termination of the query pattern
sameleaves(g,g)
w.r.t. the given Prolog program could successfully be proven:

(0) Obligation:

Clauses:

sameleaves(leaf(L), leaf(L)).
sameleaves(tree(T1, T2), tree(S1, S2)) :- ','(getleave(T1, T2, L, T), ','(getleave(S1, S2, L, S), sameleaves(T, S))).
getleave(leaf(A), C, A, C).
getleave(tree(A, B), C, L, O) :- getleave(A, tree(B, C), L, O).

Query: sameleaves(g,g)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
3 [label="A: sameleaves(T3, T4)\n\nT3 is ground\nT4 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
6 [label="6: sameleaves(T3, T4), SCOPE: 1, CLAUSE: 0 | sameleaves(T3, T4), SCOPE: 1, CLAUSE: 1\n\nT3 is ground\nT4 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: true | sameleaves(leaf(T6), leaf(T6)), SCOPE: 1, CLAUSE: 1\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: sameleaves(T3, T4), SCOPE: 1, CLAUSE: 1\n\nT3 is ground\nT4 is ground\nX2 is free\nsameleaves(T3, T4) !=? sameleaves(leaf(X2), leaf(X2))", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: sameleaves(leaf(T6), leaf(T6)), SCOPE: 1, CLAUSE: 1\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="B: ','(getleave(T11, T12, X15, X16), ','(getleave(T13, T14, X15, X17), sameleaves(X16, X17)))\n\nT11 is ground\nT12 is ground\nT13 is ground\nT14 is ground\nX15 is free\nX16 is free\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(getleave(T11, T12, X15, X16), ','(getleave(T13, T14, X15, X17), sameleaves(X16, X17))), SCOPE: 2, CLAUSE: 2 | ','(getleave(T11, T12, X15, X16), ','(getleave(T13, T14, X15, X17), sameleaves(X16, X17))), SCOPE: 2, CLAUSE: 3\n\nT11 is ground\nT12 is ground\nT13 is ground\nT14 is ground\nX15 is free\nX16 is free\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(getleave(T11, T12, X15, X16), ','(getleave(T13, T14, X15, X17), sameleaves(X16, X17))), SCOPE: 2, CLAUSE: 2\n\nT11 is ground\nT12 is ground\nT13 is ground\nT14 is ground\nX15 is free\nX16 is free\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(getleave(T11, T12, X15, X16), ','(getleave(T13, T14, X15, X17), sameleaves(X16, X17))), SCOPE: 2, CLAUSE: 3\n\nT11 is ground\nT12 is ground\nT13 is ground\nT14 is ground\nX15 is free\nX16 is free\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="D: ','(getleave(T13, T14, T23, X17), sameleaves(T24, X17))\n\nT13 is ground\nT14 is ground\nT23 is ground\nT24 is ground\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="C: getleave(T13, T14, T23, X17)\n\nT13 is ground\nT14 is ground\nT23 is ground\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: sameleaves(T24, T29)\n\nT24 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: getleave(T13, T14, T23, X17), SCOPE: 3, CLAUSE: 2 | getleave(T13, T14, T23, X17), SCOPE: 3, CLAUSE: 3\n\nT13 is ground\nT14 is ground\nT23 is ground\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: getleave(T13, T14, T23, X17), SCOPE: 3, CLAUSE: 2\n\nT13 is ground\nT14 is ground\nT23 is ground\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: getleave(T13, T14, T23, X17), SCOPE: 3, CLAUSE: 3\n\nT13 is ground\nT14 is ground\nT23 is ground\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: getleave(T52, tree(T53, T54), T55, X63)\n\nT52 is ground\nT53 is ground\nT54 is ground\nT55 is ground\nX63 is free", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(getleave(T70, tree(T71, T72), X89, X90), ','(getleave(T13, T14, X89, X17), sameleaves(X90, X17)))\n\nT13 is ground\nT14 is ground\nT70 is ground\nT71 is ground\nT72 is ground\nX17 is free\nX89 is free\nX90 is free", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 80 [arrowhead = none ];
80 -> 6;

81 [label="EVAL with clause\nsameleaves(leaf(X2), leaf(X2)).\nand substitutionX2 -> T6,\nT3 -> leaf(T6),\nT4 -> leaf(T6)", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 81 [arrowhead = none ];
81 -> 10;

82 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 82 [arrowhead = none ];
82 -> 12;

83 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 83 [arrowhead = none ];
83 -> 17;

84 [label="EVAL with clause\nsameleaves(tree(X11, X12), tree(X13, X14)) :- ','(getleave(X11, X12, X15, X16), ','(getleave(X13, X14, X15, X17), sameleaves(X16, X17))).\nand substitutionX11 -> T11,\nX12 -> T12,\nT3 -> tree(T11, T12),\nX13 -> T13,\nX14 -> T14,\nT4 -> tree(T13, T14)", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 84 [arrowhead = none ];
84 -> 23;

85 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 85 [arrowhead = none ];
85 -> 26;

86 [label="BACKTRACK\nfor clause: sameleaves(tree(T1, T2), tree(S1, S2)) :- ','(getleave(T1, T2, L, T), ','(getleave(S1, S2, L, S), sameleaves(T, S)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 86 [arrowhead = none ];
86 -> 19;

87 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
23 -> 87 [arrowhead = none ];
87 -> 27;

88 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
27 -> 88 [arrowhead = none ];
88 -> 30;

89 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
27 -> 89 [arrowhead = none ];
89 -> 31;

90 [label="EVAL with clause\ngetleave(leaf(X26), X27, X26, X27).\nand substitutionX26 -> T23,\nT11 -> leaf(T23),\nT12 -> T24,\nX27 -> T24,\nX15 -> T23,\nX16 -> T24", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 90 [arrowhead = none ];
90 -> 34;

91 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 91 [arrowhead = none ];
91 -> 35;

92 [label="EVAL with clause\ngetleave(tree(X84, X85), X86, X87, X88) :- getleave(X84, tree(X85, X86), X87, X88).\nand substitutionX84 -> T70,\nX85 -> T71,\nT11 -> tree(T70, T71),\nT12 -> T72,\nX86 -> T72,\nX15 -> X89,\nX87 -> X89,\nX16 -> X90,\nX88 -> X90", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 92 [arrowhead = none ];
92 -> 78;

93 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 93 [arrowhead = none ];
93 -> 79;

94 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
34 -> 94 [arrowhead = none ];
94 -> 50;

95 [label="SPLIT 2\nnew knowledge:\nT13 is ground\nT14 is ground\nT23 is ground\nT29 is ground\nreplacements:X17 -> T29", fontsize=14, style = filled, fillcolor = violet];
34 -> 95 [arrowhead = none ];
95 -> 52;

96 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
50 -> 96 [arrowhead = none ];
96 -> 54;

97 [label="INSTANCE with matching:\nT3 -> T24\nT4 -> T29", fontsize=14, style = filled, fillcolor = lightgrey];
52 -> 97 [arrowhead = none , style=dashed];
97 -> 3[style=dashed];

98 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 98 [arrowhead = none ];
98 -> 59;

99 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 99 [arrowhead = none ];
99 -> 60;

100 [label="EVAL with clause\ngetleave(leaf(X44), X45, X44, X45).\nand substitutionX44 -> T42,\nT13 -> leaf(T42),\nT14 -> T43,\nX45 -> T43,\nT23 -> T42,\nX17 -> T43", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 100 [arrowhead = none ];
100 -> 61;

101 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 101 [arrowhead = none ];
101 -> 62;

102 [label="EVAL with clause\ngetleave(tree(X58, X59), X60, X61, X62) :- getleave(X58, tree(X59, X60), X61, X62).\nand substitutionX58 -> T52,\nX59 -> T53,\nT13 -> tree(T52, T53),\nT14 -> T54,\nX60 -> T54,\nT23 -> T55,\nX61 -> T55,\nX17 -> X63,\nX62 -> X63", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 102 [arrowhead = none ];
102 -> 74;

103 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 103 [arrowhead = none ];
103 -> 75;

104 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
61 -> 104 [arrowhead = none ];
104 -> 63;

105 [label="INSTANCE with matching:\nT13 -> T52\nT14 -> tree(T53, T54)\nT23 -> T55\nX17 -> X63", fontsize=14, style = filled, fillcolor = lightgrey];
74 -> 105 [arrowhead = none , style=dashed];
105 -> 50[style=dashed];

106 [label="INSTANCE with matching:\nT11 -> T70\nT12 -> tree(T71, T72)\nX15 -> X89\nX16 -> X90", fontsize=14, style = filled, fillcolor = lightgrey];
78 -> 106 [arrowhead = none , style=dashed];
106 -> 23[style=dashed];

}

(2) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

sameleavesA_in_gg(leaf(T6), leaf(T6)) → sameleavesA_out_gg(leaf(T6), leaf(T6))
sameleavesA_in_gg(tree(T11, T12), tree(T13, T14)) → U1_gg(T11, T12, T13, T14, pB_in_ggaagga(T11, T12, X15, X16, T13, T14, X17))
pB_in_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17) → U3_ggaagga(T23, T24, T13, T14, X17, pD_in_gggag(T13, T14, T23, X17, T24))
pD_in_gggag(T13, T14, T23, T29, T24) → U5_gggag(T13, T14, T23, T29, T24, getleaveC_in_ggga(T13, T14, T23, T29))
getleaveC_in_ggga(leaf(T42), T43, T42, T43) → getleaveC_out_ggga(leaf(T42), T43, T42, T43)
getleaveC_in_ggga(tree(T52, T53), T54, T55, X63) → U2_ggga(T52, T53, T54, T55, X63, getleaveC_in_ggga(T52, tree(T53, T54), T55, X63))
U2_ggga(T52, T53, T54, T55, X63, getleaveC_out_ggga(T52, tree(T53, T54), T55, X63)) → getleaveC_out_ggga(tree(T52, T53), T54, T55, X63)
U5_gggag(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → U6_gggag(T13, T14, T23, T29, T24, sameleavesA_in_gg(T24, T29))
U6_gggag(T13, T14, T23, T29, T24, sameleavesA_out_gg(T24, T29)) → pD_out_gggag(T13, T14, T23, T29, T24)
U3_ggaagga(T23, T24, T13, T14, X17, pD_out_gggag(T13, T14, T23, X17, T24)) → pB_out_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17)
pB_in_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17) → U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_in_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17))
U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_out_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17)) → pB_out_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17)
U1_gg(T11, T12, T13, T14, pB_out_ggaagga(T11, T12, X15, X16, T13, T14, X17)) → sameleavesA_out_gg(tree(T11, T12), tree(T13, T14))

The argument filtering Pi contains the following mapping:
sameleavesA_in_gg(x1, x2)  =  sameleavesA_in_gg(x1, x2)
leaf(x1)  =  leaf(x1)
sameleavesA_out_gg(x1, x2)  =  sameleavesA_out_gg(x1, x2)
tree(x1, x2)  =  tree(x1, x2)
U1_gg(x1, x2, x3, x4, x5)  =  U1_gg(x1, x2, x3, x4, x5)
pB_in_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_in_ggaagga(x1, x2, x5, x6)
U3_ggaagga(x1, x2, x3, x4, x5, x6)  =  U3_ggaagga(x1, x2, x3, x4, x6)
pD_in_gggag(x1, x2, x3, x4, x5)  =  pD_in_gggag(x1, x2, x3, x5)
U5_gggag(x1, x2, x3, x4, x5, x6)  =  U5_gggag(x1, x2, x3, x5, x6)
getleaveC_in_ggga(x1, x2, x3, x4)  =  getleaveC_in_ggga(x1, x2, x3)
getleaveC_out_ggga(x1, x2, x3, x4)  =  getleaveC_out_ggga(x1, x2, x3, x4)
U2_ggga(x1, x2, x3, x4, x5, x6)  =  U2_ggga(x1, x2, x3, x4, x6)
U6_gggag(x1, x2, x3, x4, x5, x6)  =  U6_gggag(x1, x2, x3, x4, x5, x6)
pD_out_gggag(x1, x2, x3, x4, x5)  =  pD_out_gggag(x1, x2, x3, x4, x5)
pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)
U4_ggaagga(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_ggaagga(x1, x2, x3, x6, x7, x9)

(3) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

SAMELEAVESA_IN_GG(tree(T11, T12), tree(T13, T14)) → U1_GG(T11, T12, T13, T14, pB_in_ggaagga(T11, T12, X15, X16, T13, T14, X17))
SAMELEAVESA_IN_GG(tree(T11, T12), tree(T13, T14)) → PB_IN_GGAAGGA(T11, T12, X15, X16, T13, T14, X17)
PB_IN_GGAAGGA(leaf(T23), T24, T23, T24, T13, T14, X17) → U3_GGAAGGA(T23, T24, T13, T14, X17, pD_in_gggag(T13, T14, T23, X17, T24))
PB_IN_GGAAGGA(leaf(T23), T24, T23, T24, T13, T14, X17) → PD_IN_GGGAG(T13, T14, T23, X17, T24)
PD_IN_GGGAG(T13, T14, T23, T29, T24) → U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_in_ggga(T13, T14, T23, T29))
PD_IN_GGGAG(T13, T14, T23, T29, T24) → GETLEAVEC_IN_GGGA(T13, T14, T23, T29)
GETLEAVEC_IN_GGGA(tree(T52, T53), T54, T55, X63) → U2_GGGA(T52, T53, T54, T55, X63, getleaveC_in_ggga(T52, tree(T53, T54), T55, X63))
GETLEAVEC_IN_GGGA(tree(T52, T53), T54, T55, X63) → GETLEAVEC_IN_GGGA(T52, tree(T53, T54), T55, X63)
U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → U6_GGGAG(T13, T14, T23, T29, T24, sameleavesA_in_gg(T24, T29))
U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → SAMELEAVESA_IN_GG(T24, T29)
PB_IN_GGAAGGA(tree(T70, T71), T72, X89, X90, T13, T14, X17) → U4_GGAAGGA(T70, T71, T72, X89, X90, T13, T14, X17, pB_in_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17))
PB_IN_GGAAGGA(tree(T70, T71), T72, X89, X90, T13, T14, X17) → PB_IN_GGAAGGA(T70, tree(T71, T72), X89, X90, T13, T14, X17)

The TRS R consists of the following rules:

sameleavesA_in_gg(leaf(T6), leaf(T6)) → sameleavesA_out_gg(leaf(T6), leaf(T6))
sameleavesA_in_gg(tree(T11, T12), tree(T13, T14)) → U1_gg(T11, T12, T13, T14, pB_in_ggaagga(T11, T12, X15, X16, T13, T14, X17))
pB_in_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17) → U3_ggaagga(T23, T24, T13, T14, X17, pD_in_gggag(T13, T14, T23, X17, T24))
pD_in_gggag(T13, T14, T23, T29, T24) → U5_gggag(T13, T14, T23, T29, T24, getleaveC_in_ggga(T13, T14, T23, T29))
getleaveC_in_ggga(leaf(T42), T43, T42, T43) → getleaveC_out_ggga(leaf(T42), T43, T42, T43)
getleaveC_in_ggga(tree(T52, T53), T54, T55, X63) → U2_ggga(T52, T53, T54, T55, X63, getleaveC_in_ggga(T52, tree(T53, T54), T55, X63))
U2_ggga(T52, T53, T54, T55, X63, getleaveC_out_ggga(T52, tree(T53, T54), T55, X63)) → getleaveC_out_ggga(tree(T52, T53), T54, T55, X63)
U5_gggag(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → U6_gggag(T13, T14, T23, T29, T24, sameleavesA_in_gg(T24, T29))
U6_gggag(T13, T14, T23, T29, T24, sameleavesA_out_gg(T24, T29)) → pD_out_gggag(T13, T14, T23, T29, T24)
U3_ggaagga(T23, T24, T13, T14, X17, pD_out_gggag(T13, T14, T23, X17, T24)) → pB_out_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17)
pB_in_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17) → U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_in_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17))
U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_out_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17)) → pB_out_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17)
U1_gg(T11, T12, T13, T14, pB_out_ggaagga(T11, T12, X15, X16, T13, T14, X17)) → sameleavesA_out_gg(tree(T11, T12), tree(T13, T14))

The argument filtering Pi contains the following mapping:
sameleavesA_in_gg(x1, x2)  =  sameleavesA_in_gg(x1, x2)
leaf(x1)  =  leaf(x1)
sameleavesA_out_gg(x1, x2)  =  sameleavesA_out_gg(x1, x2)
tree(x1, x2)  =  tree(x1, x2)
U1_gg(x1, x2, x3, x4, x5)  =  U1_gg(x1, x2, x3, x4, x5)
pB_in_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_in_ggaagga(x1, x2, x5, x6)
U3_ggaagga(x1, x2, x3, x4, x5, x6)  =  U3_ggaagga(x1, x2, x3, x4, x6)
pD_in_gggag(x1, x2, x3, x4, x5)  =  pD_in_gggag(x1, x2, x3, x5)
U5_gggag(x1, x2, x3, x4, x5, x6)  =  U5_gggag(x1, x2, x3, x5, x6)
getleaveC_in_ggga(x1, x2, x3, x4)  =  getleaveC_in_ggga(x1, x2, x3)
getleaveC_out_ggga(x1, x2, x3, x4)  =  getleaveC_out_ggga(x1, x2, x3, x4)
U2_ggga(x1, x2, x3, x4, x5, x6)  =  U2_ggga(x1, x2, x3, x4, x6)
U6_gggag(x1, x2, x3, x4, x5, x6)  =  U6_gggag(x1, x2, x3, x4, x5, x6)
pD_out_gggag(x1, x2, x3, x4, x5)  =  pD_out_gggag(x1, x2, x3, x4, x5)
pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)
U4_ggaagga(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_ggaagga(x1, x2, x3, x6, x7, x9)
SAMELEAVESA_IN_GG(x1, x2)  =  SAMELEAVESA_IN_GG(x1, x2)
U1_GG(x1, x2, x3, x4, x5)  =  U1_GG(x1, x2, x3, x4, x5)
PB_IN_GGAAGGA(x1, x2, x3, x4, x5, x6, x7)  =  PB_IN_GGAAGGA(x1, x2, x5, x6)
U3_GGAAGGA(x1, x2, x3, x4, x5, x6)  =  U3_GGAAGGA(x1, x2, x3, x4, x6)
PD_IN_GGGAG(x1, x2, x3, x4, x5)  =  PD_IN_GGGAG(x1, x2, x3, x5)
U5_GGGAG(x1, x2, x3, x4, x5, x6)  =  U5_GGGAG(x1, x2, x3, x5, x6)
GETLEAVEC_IN_GGGA(x1, x2, x3, x4)  =  GETLEAVEC_IN_GGGA(x1, x2, x3)
U2_GGGA(x1, x2, x3, x4, x5, x6)  =  U2_GGGA(x1, x2, x3, x4, x6)
U6_GGGAG(x1, x2, x3, x4, x5, x6)  =  U6_GGGAG(x1, x2, x3, x4, x5, x6)
U4_GGAAGGA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_GGAAGGA(x1, x2, x3, x6, x7, x9)

We have to consider all (P,R,Pi)-chains

(4) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

SAMELEAVESA_IN_GG(tree(T11, T12), tree(T13, T14)) → U1_GG(T11, T12, T13, T14, pB_in_ggaagga(T11, T12, X15, X16, T13, T14, X17))
SAMELEAVESA_IN_GG(tree(T11, T12), tree(T13, T14)) → PB_IN_GGAAGGA(T11, T12, X15, X16, T13, T14, X17)
PB_IN_GGAAGGA(leaf(T23), T24, T23, T24, T13, T14, X17) → U3_GGAAGGA(T23, T24, T13, T14, X17, pD_in_gggag(T13, T14, T23, X17, T24))
PB_IN_GGAAGGA(leaf(T23), T24, T23, T24, T13, T14, X17) → PD_IN_GGGAG(T13, T14, T23, X17, T24)
PD_IN_GGGAG(T13, T14, T23, T29, T24) → U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_in_ggga(T13, T14, T23, T29))
PD_IN_GGGAG(T13, T14, T23, T29, T24) → GETLEAVEC_IN_GGGA(T13, T14, T23, T29)
GETLEAVEC_IN_GGGA(tree(T52, T53), T54, T55, X63) → U2_GGGA(T52, T53, T54, T55, X63, getleaveC_in_ggga(T52, tree(T53, T54), T55, X63))
GETLEAVEC_IN_GGGA(tree(T52, T53), T54, T55, X63) → GETLEAVEC_IN_GGGA(T52, tree(T53, T54), T55, X63)
U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → U6_GGGAG(T13, T14, T23, T29, T24, sameleavesA_in_gg(T24, T29))
U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → SAMELEAVESA_IN_GG(T24, T29)
PB_IN_GGAAGGA(tree(T70, T71), T72, X89, X90, T13, T14, X17) → U4_GGAAGGA(T70, T71, T72, X89, X90, T13, T14, X17, pB_in_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17))
PB_IN_GGAAGGA(tree(T70, T71), T72, X89, X90, T13, T14, X17) → PB_IN_GGAAGGA(T70, tree(T71, T72), X89, X90, T13, T14, X17)

The TRS R consists of the following rules:

sameleavesA_in_gg(leaf(T6), leaf(T6)) → sameleavesA_out_gg(leaf(T6), leaf(T6))
sameleavesA_in_gg(tree(T11, T12), tree(T13, T14)) → U1_gg(T11, T12, T13, T14, pB_in_ggaagga(T11, T12, X15, X16, T13, T14, X17))
pB_in_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17) → U3_ggaagga(T23, T24, T13, T14, X17, pD_in_gggag(T13, T14, T23, X17, T24))
pD_in_gggag(T13, T14, T23, T29, T24) → U5_gggag(T13, T14, T23, T29, T24, getleaveC_in_ggga(T13, T14, T23, T29))
getleaveC_in_ggga(leaf(T42), T43, T42, T43) → getleaveC_out_ggga(leaf(T42), T43, T42, T43)
getleaveC_in_ggga(tree(T52, T53), T54, T55, X63) → U2_ggga(T52, T53, T54, T55, X63, getleaveC_in_ggga(T52, tree(T53, T54), T55, X63))
U2_ggga(T52, T53, T54, T55, X63, getleaveC_out_ggga(T52, tree(T53, T54), T55, X63)) → getleaveC_out_ggga(tree(T52, T53), T54, T55, X63)
U5_gggag(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → U6_gggag(T13, T14, T23, T29, T24, sameleavesA_in_gg(T24, T29))
U6_gggag(T13, T14, T23, T29, T24, sameleavesA_out_gg(T24, T29)) → pD_out_gggag(T13, T14, T23, T29, T24)
U3_ggaagga(T23, T24, T13, T14, X17, pD_out_gggag(T13, T14, T23, X17, T24)) → pB_out_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17)
pB_in_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17) → U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_in_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17))
U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_out_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17)) → pB_out_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17)
U1_gg(T11, T12, T13, T14, pB_out_ggaagga(T11, T12, X15, X16, T13, T14, X17)) → sameleavesA_out_gg(tree(T11, T12), tree(T13, T14))

The argument filtering Pi contains the following mapping:
sameleavesA_in_gg(x1, x2)  =  sameleavesA_in_gg(x1, x2)
leaf(x1)  =  leaf(x1)
sameleavesA_out_gg(x1, x2)  =  sameleavesA_out_gg(x1, x2)
tree(x1, x2)  =  tree(x1, x2)
U1_gg(x1, x2, x3, x4, x5)  =  U1_gg(x1, x2, x3, x4, x5)
pB_in_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_in_ggaagga(x1, x2, x5, x6)
U3_ggaagga(x1, x2, x3, x4, x5, x6)  =  U3_ggaagga(x1, x2, x3, x4, x6)
pD_in_gggag(x1, x2, x3, x4, x5)  =  pD_in_gggag(x1, x2, x3, x5)
U5_gggag(x1, x2, x3, x4, x5, x6)  =  U5_gggag(x1, x2, x3, x5, x6)
getleaveC_in_ggga(x1, x2, x3, x4)  =  getleaveC_in_ggga(x1, x2, x3)
getleaveC_out_ggga(x1, x2, x3, x4)  =  getleaveC_out_ggga(x1, x2, x3, x4)
U2_ggga(x1, x2, x3, x4, x5, x6)  =  U2_ggga(x1, x2, x3, x4, x6)
U6_gggag(x1, x2, x3, x4, x5, x6)  =  U6_gggag(x1, x2, x3, x4, x5, x6)
pD_out_gggag(x1, x2, x3, x4, x5)  =  pD_out_gggag(x1, x2, x3, x4, x5)
pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)
U4_ggaagga(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_ggaagga(x1, x2, x3, x6, x7, x9)
SAMELEAVESA_IN_GG(x1, x2)  =  SAMELEAVESA_IN_GG(x1, x2)
U1_GG(x1, x2, x3, x4, x5)  =  U1_GG(x1, x2, x3, x4, x5)
PB_IN_GGAAGGA(x1, x2, x3, x4, x5, x6, x7)  =  PB_IN_GGAAGGA(x1, x2, x5, x6)
U3_GGAAGGA(x1, x2, x3, x4, x5, x6)  =  U3_GGAAGGA(x1, x2, x3, x4, x6)
PD_IN_GGGAG(x1, x2, x3, x4, x5)  =  PD_IN_GGGAG(x1, x2, x3, x5)
U5_GGGAG(x1, x2, x3, x4, x5, x6)  =  U5_GGGAG(x1, x2, x3, x5, x6)
GETLEAVEC_IN_GGGA(x1, x2, x3, x4)  =  GETLEAVEC_IN_GGGA(x1, x2, x3)
U2_GGGA(x1, x2, x3, x4, x5, x6)  =  U2_GGGA(x1, x2, x3, x4, x6)
U6_GGGAG(x1, x2, x3, x4, x5, x6)  =  U6_GGGAG(x1, x2, x3, x4, x5, x6)
U4_GGAAGGA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_GGAAGGA(x1, x2, x3, x6, x7, x9)

We have to consider all (P,R,Pi)-chains

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 6 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

GETLEAVEC_IN_GGGA(tree(T52, T53), T54, T55, X63) → GETLEAVEC_IN_GGGA(T52, tree(T53, T54), T55, X63)

The TRS R consists of the following rules:

sameleavesA_in_gg(leaf(T6), leaf(T6)) → sameleavesA_out_gg(leaf(T6), leaf(T6))
sameleavesA_in_gg(tree(T11, T12), tree(T13, T14)) → U1_gg(T11, T12, T13, T14, pB_in_ggaagga(T11, T12, X15, X16, T13, T14, X17))
pB_in_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17) → U3_ggaagga(T23, T24, T13, T14, X17, pD_in_gggag(T13, T14, T23, X17, T24))
pD_in_gggag(T13, T14, T23, T29, T24) → U5_gggag(T13, T14, T23, T29, T24, getleaveC_in_ggga(T13, T14, T23, T29))
getleaveC_in_ggga(leaf(T42), T43, T42, T43) → getleaveC_out_ggga(leaf(T42), T43, T42, T43)
getleaveC_in_ggga(tree(T52, T53), T54, T55, X63) → U2_ggga(T52, T53, T54, T55, X63, getleaveC_in_ggga(T52, tree(T53, T54), T55, X63))
U2_ggga(T52, T53, T54, T55, X63, getleaveC_out_ggga(T52, tree(T53, T54), T55, X63)) → getleaveC_out_ggga(tree(T52, T53), T54, T55, X63)
U5_gggag(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → U6_gggag(T13, T14, T23, T29, T24, sameleavesA_in_gg(T24, T29))
U6_gggag(T13, T14, T23, T29, T24, sameleavesA_out_gg(T24, T29)) → pD_out_gggag(T13, T14, T23, T29, T24)
U3_ggaagga(T23, T24, T13, T14, X17, pD_out_gggag(T13, T14, T23, X17, T24)) → pB_out_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17)
pB_in_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17) → U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_in_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17))
U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_out_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17)) → pB_out_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17)
U1_gg(T11, T12, T13, T14, pB_out_ggaagga(T11, T12, X15, X16, T13, T14, X17)) → sameleavesA_out_gg(tree(T11, T12), tree(T13, T14))

The argument filtering Pi contains the following mapping:
sameleavesA_in_gg(x1, x2)  =  sameleavesA_in_gg(x1, x2)
leaf(x1)  =  leaf(x1)
sameleavesA_out_gg(x1, x2)  =  sameleavesA_out_gg(x1, x2)
tree(x1, x2)  =  tree(x1, x2)
U1_gg(x1, x2, x3, x4, x5)  =  U1_gg(x1, x2, x3, x4, x5)
pB_in_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_in_ggaagga(x1, x2, x5, x6)
U3_ggaagga(x1, x2, x3, x4, x5, x6)  =  U3_ggaagga(x1, x2, x3, x4, x6)
pD_in_gggag(x1, x2, x3, x4, x5)  =  pD_in_gggag(x1, x2, x3, x5)
U5_gggag(x1, x2, x3, x4, x5, x6)  =  U5_gggag(x1, x2, x3, x5, x6)
getleaveC_in_ggga(x1, x2, x3, x4)  =  getleaveC_in_ggga(x1, x2, x3)
getleaveC_out_ggga(x1, x2, x3, x4)  =  getleaveC_out_ggga(x1, x2, x3, x4)
U2_ggga(x1, x2, x3, x4, x5, x6)  =  U2_ggga(x1, x2, x3, x4, x6)
U6_gggag(x1, x2, x3, x4, x5, x6)  =  U6_gggag(x1, x2, x3, x4, x5, x6)
pD_out_gggag(x1, x2, x3, x4, x5)  =  pD_out_gggag(x1, x2, x3, x4, x5)
pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)
U4_ggaagga(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_ggaagga(x1, x2, x3, x6, x7, x9)
GETLEAVEC_IN_GGGA(x1, x2, x3, x4)  =  GETLEAVEC_IN_GGGA(x1, x2, x3)

We have to consider all (P,R,Pi)-chains

(8) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(9) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

GETLEAVEC_IN_GGGA(tree(T52, T53), T54, T55, X63) → GETLEAVEC_IN_GGGA(T52, tree(T53, T54), T55, X63)

R is empty.
The argument filtering Pi contains the following mapping:
tree(x1, x2)  =  tree(x1, x2)
GETLEAVEC_IN_GGGA(x1, x2, x3, x4)  =  GETLEAVEC_IN_GGGA(x1, x2, x3)

We have to consider all (P,R,Pi)-chains

(10) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(11) Obligation:

Q DP problem:
The TRS P consists of the following rules:

GETLEAVEC_IN_GGGA(tree(T52, T53), T54, T55) → GETLEAVEC_IN_GGGA(T52, tree(T53, T54), T55)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(12) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• GETLEAVEC_IN_GGGA(tree(T52, T53), T54, T55) → GETLEAVEC_IN_GGGA(T52, tree(T53, T54), T55)
  The graph contains the following edges 1 > 1, 3 >= 3

(13) YES

(14) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

SAMELEAVESA_IN_GG(tree(T11, T12), tree(T13, T14)) → PB_IN_GGAAGGA(T11, T12, X15, X16, T13, T14, X17)
PB_IN_GGAAGGA(leaf(T23), T24, T23, T24, T13, T14, X17) → PD_IN_GGGAG(T13, T14, T23, X17, T24)
PD_IN_GGGAG(T13, T14, T23, T29, T24) → U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_in_ggga(T13, T14, T23, T29))
U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → SAMELEAVESA_IN_GG(T24, T29)
PB_IN_GGAAGGA(tree(T70, T71), T72, X89, X90, T13, T14, X17) → PB_IN_GGAAGGA(T70, tree(T71, T72), X89, X90, T13, T14, X17)

The TRS R consists of the following rules:

sameleavesA_in_gg(leaf(T6), leaf(T6)) → sameleavesA_out_gg(leaf(T6), leaf(T6))
sameleavesA_in_gg(tree(T11, T12), tree(T13, T14)) → U1_gg(T11, T12, T13, T14, pB_in_ggaagga(T11, T12, X15, X16, T13, T14, X17))
pB_in_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17) → U3_ggaagga(T23, T24, T13, T14, X17, pD_in_gggag(T13, T14, T23, X17, T24))
pD_in_gggag(T13, T14, T23, T29, T24) → U5_gggag(T13, T14, T23, T29, T24, getleaveC_in_ggga(T13, T14, T23, T29))
getleaveC_in_ggga(leaf(T42), T43, T42, T43) → getleaveC_out_ggga(leaf(T42), T43, T42, T43)
getleaveC_in_ggga(tree(T52, T53), T54, T55, X63) → U2_ggga(T52, T53, T54, T55, X63, getleaveC_in_ggga(T52, tree(T53, T54), T55, X63))
U2_ggga(T52, T53, T54, T55, X63, getleaveC_out_ggga(T52, tree(T53, T54), T55, X63)) → getleaveC_out_ggga(tree(T52, T53), T54, T55, X63)
U5_gggag(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → U6_gggag(T13, T14, T23, T29, T24, sameleavesA_in_gg(T24, T29))
U6_gggag(T13, T14, T23, T29, T24, sameleavesA_out_gg(T24, T29)) → pD_out_gggag(T13, T14, T23, T29, T24)
U3_ggaagga(T23, T24, T13, T14, X17, pD_out_gggag(T13, T14, T23, X17, T24)) → pB_out_ggaagga(leaf(T23), T24, T23, T24, T13, T14, X17)
pB_in_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17) → U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_in_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17))
U4_ggaagga(T70, T71, T72, X89, X90, T13, T14, X17, pB_out_ggaagga(T70, tree(T71, T72), X89, X90, T13, T14, X17)) → pB_out_ggaagga(tree(T70, T71), T72, X89, X90, T13, T14, X17)
U1_gg(T11, T12, T13, T14, pB_out_ggaagga(T11, T12, X15, X16, T13, T14, X17)) → sameleavesA_out_gg(tree(T11, T12), tree(T13, T14))

The argument filtering Pi contains the following mapping:
sameleavesA_in_gg(x1, x2)  =  sameleavesA_in_gg(x1, x2)
leaf(x1)  =  leaf(x1)
sameleavesA_out_gg(x1, x2)  =  sameleavesA_out_gg(x1, x2)
tree(x1, x2)  =  tree(x1, x2)
U1_gg(x1, x2, x3, x4, x5)  =  U1_gg(x1, x2, x3, x4, x5)
pB_in_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_in_ggaagga(x1, x2, x5, x6)
U3_ggaagga(x1, x2, x3, x4, x5, x6)  =  U3_ggaagga(x1, x2, x3, x4, x6)
pD_in_gggag(x1, x2, x3, x4, x5)  =  pD_in_gggag(x1, x2, x3, x5)
U5_gggag(x1, x2, x3, x4, x5, x6)  =  U5_gggag(x1, x2, x3, x5, x6)
getleaveC_in_ggga(x1, x2, x3, x4)  =  getleaveC_in_ggga(x1, x2, x3)
getleaveC_out_ggga(x1, x2, x3, x4)  =  getleaveC_out_ggga(x1, x2, x3, x4)
U2_ggga(x1, x2, x3, x4, x5, x6)  =  U2_ggga(x1, x2, x3, x4, x6)
U6_gggag(x1, x2, x3, x4, x5, x6)  =  U6_gggag(x1, x2, x3, x4, x5, x6)
pD_out_gggag(x1, x2, x3, x4, x5)  =  pD_out_gggag(x1, x2, x3, x4, x5)
pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)  =  pB_out_ggaagga(x1, x2, x3, x4, x5, x6, x7)
U4_ggaagga(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_ggaagga(x1, x2, x3, x6, x7, x9)
SAMELEAVESA_IN_GG(x1, x2)  =  SAMELEAVESA_IN_GG(x1, x2)
PB_IN_GGAAGGA(x1, x2, x3, x4, x5, x6, x7)  =  PB_IN_GGAAGGA(x1, x2, x5, x6)
PD_IN_GGGAG(x1, x2, x3, x4, x5)  =  PD_IN_GGGAG(x1, x2, x3, x5)
U5_GGGAG(x1, x2, x3, x4, x5, x6)  =  U5_GGGAG(x1, x2, x3, x5, x6)

We have to consider all (P,R,Pi)-chains

(15) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(16) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

SAMELEAVESA_IN_GG(tree(T11, T12), tree(T13, T14)) → PB_IN_GGAAGGA(T11, T12, X15, X16, T13, T14, X17)
PB_IN_GGAAGGA(leaf(T23), T24, T23, T24, T13, T14, X17) → PD_IN_GGGAG(T13, T14, T23, X17, T24)
PD_IN_GGGAG(T13, T14, T23, T29, T24) → U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_in_ggga(T13, T14, T23, T29))
U5_GGGAG(T13, T14, T23, T29, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → SAMELEAVESA_IN_GG(T24, T29)
PB_IN_GGAAGGA(tree(T70, T71), T72, X89, X90, T13, T14, X17) → PB_IN_GGAAGGA(T70, tree(T71, T72), X89, X90, T13, T14, X17)

The TRS R consists of the following rules:

getleaveC_in_ggga(leaf(T42), T43, T42, T43) → getleaveC_out_ggga(leaf(T42), T43, T42, T43)
getleaveC_in_ggga(tree(T52, T53), T54, T55, X63) → U2_ggga(T52, T53, T54, T55, X63, getleaveC_in_ggga(T52, tree(T53, T54), T55, X63))
U2_ggga(T52, T53, T54, T55, X63, getleaveC_out_ggga(T52, tree(T53, T54), T55, X63)) → getleaveC_out_ggga(tree(T52, T53), T54, T55, X63)

The argument filtering Pi contains the following mapping:
leaf(x1)  =  leaf(x1)
tree(x1, x2)  =  tree(x1, x2)
getleaveC_in_ggga(x1, x2, x3, x4)  =  getleaveC_in_ggga(x1, x2, x3)
getleaveC_out_ggga(x1, x2, x3, x4)  =  getleaveC_out_ggga(x1, x2, x3, x4)
U2_ggga(x1, x2, x3, x4, x5, x6)  =  U2_ggga(x1, x2, x3, x4, x6)
SAMELEAVESA_IN_GG(x1, x2)  =  SAMELEAVESA_IN_GG(x1, x2)
PB_IN_GGAAGGA(x1, x2, x3, x4, x5, x6, x7)  =  PB_IN_GGAAGGA(x1, x2, x5, x6)
PD_IN_GGGAG(x1, x2, x3, x4, x5)  =  PD_IN_GGGAG(x1, x2, x3, x5)
U5_GGGAG(x1, x2, x3, x4, x5, x6)  =  U5_GGGAG(x1, x2, x3, x5, x6)

We have to consider all (P,R,Pi)-chains

(17) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(18) Obligation:

Q DP problem:
The TRS P consists of the following rules:

SAMELEAVESA_IN_GG(tree(T11, T12), tree(T13, T14)) → PB_IN_GGAAGGA(T11, T12, T13, T14)
PB_IN_GGAAGGA(leaf(T23), T24, T13, T14) → PD_IN_GGGAG(T13, T14, T23, T24)
PD_IN_GGGAG(T13, T14, T23, T24) → U5_GGGAG(T13, T14, T23, T24, getleaveC_in_ggga(T13, T14, T23))
U5_GGGAG(T13, T14, T23, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → SAMELEAVESA_IN_GG(T24, T29)
PB_IN_GGAAGGA(tree(T70, T71), T72, T13, T14) → PB_IN_GGAAGGA(T70, tree(T71, T72), T13, T14)

The TRS R consists of the following rules:

getleaveC_in_ggga(leaf(T42), T43, T42) → getleaveC_out_ggga(leaf(T42), T43, T42, T43)
getleaveC_in_ggga(tree(T52, T53), T54, T55) → U2_ggga(T52, T53, T54, T55, getleaveC_in_ggga(T52, tree(T53, T54), T55))
U2_ggga(T52, T53, T54, T55, getleaveC_out_ggga(T52, tree(T53, T54), T55, X63)) → getleaveC_out_ggga(tree(T52, T53), T54, T55, X63)

The set Q consists of the following terms:

getleaveC_in_ggga(x0, x1, x2)
U2_ggga(x0, x1, x2, x3, x4)

We have to consider all (P,Q,R)-chains.

(19) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].

The following pairs can be oriented strictly and are deleted.

U5_GGGAG(T13, T14, T23, T24, getleaveC_out_ggga(T13, T14, T23, T29)) → SAMELEAVESA_IN_GG(T24, T29)

The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(PB_IN_GGAAGGA(x₁, x₂, x₃, x₄)) = x₁ + x₂   
POL(PD_IN_GGGAG(x₁, x₂, x₃, x₄)) = 1 + x₃ + x₄   
POL(SAMELEAVESA_IN_GG(x₁, x₂)) = x₁   
POL(U2_ggga(x₁, x₂, x₃, x₄, x₅)) = 0   
POL(U5_GGGAG(x₁, x₂, x₃, x₄, x₅)) = 1 + x₃ + x₄   
POL(getleaveC_in_ggga(x₁, x₂, x₃)) = 0   
POL(getleaveC_out_ggga(x₁, x₂, x₃, x₄)) = 0   
POL(leaf(x₁)) = 1 + x₁   
POL(tree(x₁, x₂)) = x₁ + x₂   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none

(20) Obligation:

Q DP problem:
The TRS P consists of the following rules:

SAMELEAVESA_IN_GG(tree(T11, T12), tree(T13, T14)) → PB_IN_GGAAGGA(T11, T12, T13, T14)
PB_IN_GGAAGGA(leaf(T23), T24, T13, T14) → PD_IN_GGGAG(T13, T14, T23, T24)
PD_IN_GGGAG(T13, T14, T23, T24) → U5_GGGAG(T13, T14, T23, T24, getleaveC_in_ggga(T13, T14, T23))
PB_IN_GGAAGGA(tree(T70, T71), T72, T13, T14) → PB_IN_GGAAGGA(T70, tree(T71, T72), T13, T14)

The TRS R consists of the following rules:

getleaveC_in_ggga(leaf(T42), T43, T42) → getleaveC_out_ggga(leaf(T42), T43, T42, T43)
getleaveC_in_ggga(tree(T52, T53), T54, T55) → U2_ggga(T52, T53, T54, T55, getleaveC_in_ggga(T52, tree(T53, T54), T55))
U2_ggga(T52, T53, T54, T55, getleaveC_out_ggga(T52, tree(T53, T54), T55, X63)) → getleaveC_out_ggga(tree(T52, T53), T54, T55, X63)

The set Q consists of the following terms:

getleaveC_in_ggga(x0, x1, x2)
U2_ggga(x0, x1, x2, x3, x4)

We have to consider all (P,Q,R)-chains.

(21) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.

(22) Obligation:

Q DP problem:
The TRS P consists of the following rules:

PB_IN_GGAAGGA(tree(T70, T71), T72, T13, T14) → PB_IN_GGAAGGA(T70, tree(T71, T72), T13, T14)

The TRS R consists of the following rules:

getleaveC_in_ggga(leaf(T42), T43, T42) → getleaveC_out_ggga(leaf(T42), T43, T42, T43)
getleaveC_in_ggga(tree(T52, T53), T54, T55) → U2_ggga(T52, T53, T54, T55, getleaveC_in_ggga(T52, tree(T53, T54), T55))
U2_ggga(T52, T53, T54, T55, getleaveC_out_ggga(T52, tree(T53, T54), T55, X63)) → getleaveC_out_ggga(tree(T52, T53), T54, T55, X63)

The set Q consists of the following terms:

getleaveC_in_ggga(x0, x1, x2)
U2_ggga(x0, x1, x2, x3, x4)

We have to consider all (P,Q,R)-chains.

(23) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(24) Obligation:

Q DP problem:
The TRS P consists of the following rules:

PB_IN_GGAAGGA(tree(T70, T71), T72, T13, T14) → PB_IN_GGAAGGA(T70, tree(T71, T72), T13, T14)

R is empty.
The set Q consists of the following terms:

getleaveC_in_ggga(x0, x1, x2)
U2_ggga(x0, x1, x2, x3, x4)

We have to consider all (P,Q,R)-chains.

(25) QReductionProof (EQUIVALENT transformation)

We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].

getleaveC_in_ggga(x0, x1, x2)
U2_ggga(x0, x1, x2, x3, x4)

(26) Obligation:

Q DP problem:
The TRS P consists of the following rules:

PB_IN_GGAAGGA(tree(T70, T71), T72, T13, T14) → PB_IN_GGAAGGA(T70, tree(T71, T72), T13, T14)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(27) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• PB_IN_GGAAGGA(tree(T70, T71), T72, T13, T14) → PB_IN_GGAAGGA(T70, tree(T71, T72), T13, T14)
  The graph contains the following edges 1 > 1, 3 >= 3, 4 >= 4

(28) YES