NO
Problem 1:
Infeasibility Problem:
[(VAR vNonEmpty x n h t m pid st1 in2 st2 in3 st3 vNonEmpty x6 x3 x5)
(STRATEGY CONTEXTSENSITIVE
(app 1 2)
(empty 1)
(fstsplit 1 2)
(head 1)
(length 1)
(leq 1 2)
(mapf 1 2)
(ring 1 2 3 4 5 6)
(sndsplit 1 2)
(tail 1)
(0)
(cons 1 2)
(f 1 2)
(fSNonEmpty)
(false)
(nil)
(s 1)
(three)
(true)
(two)
)
(RULES
app(cons(h,t),x) -> cons(h,app(t,x))
app(nil,x) -> x
empty(cons(h,t)) -> false
empty(nil) -> true
fstsplit(0,x) -> nil
fstsplit(s(n),cons(h,t)) -> cons(h,fstsplit(n,t))
fstsplit(s(n),nil) -> nil
head(cons(h,t)) -> h
length(cons(h,t)) -> s(length(t))
length(nil) -> 0
leq(0,m) -> true
leq(s(n),0) -> false
leq(s(n),s(m)) -> leq(n,m)
mapf(pid,cons(h,t)) -> app(f(pid,h),mapf(pid,t))
mapf(pid,nil) -> nil
ring(st1,in2,st2,in3,st3,m) -> ring(sndsplit(m,st1),cons(fstsplit(m,st1),in2),st2,in3,st3,m) | empty(fstsplit(m,st1)) ->* false
ring(st1,in2,st2,in3,st3,m) -> ring(st1,tail(in2),sndsplit(m,app(mapf(two,head(in2)),st2)),cons(fstsplit(m,app(mapf(two,head(in2)),st2)),in3),st3,m) | leq(m,length(st2)) ->* false, empty(fstsplit(m,app(mapf(two,head(in2)),st2))) ->* false
ring(st1,in2,st2,in3,st3,m) -> ring(st1,tail(in2),st2,in3,st3,m) | empty(mapf(two,head(in2))) ->* true
ring(st1,in2,st2,in3,st3,m) -> ring(st1,in2,sndsplit(m,st2),cons(fstsplit(m,st2),in3),st3,m) | leq(m,length(st2)) ->* true, empty(fstsplit(m,st2)) ->* false
ring(st1,in2,st2,in3,st3,m) -> ring(st1,in2,st2,tail(in3),sndsplit(m,app(mapf(three,head(in3)),st3)),m) | leq(m,length(st3)) ->* false, empty(fstsplit(m,app(mapf(three,head(in3)),st3))) ->* false
ring(st1,in2,st2,in3,st3,m) -> ring(st1,in2,st2,tail(in3),st3,m) | empty(mapf(three,head(in3))) ->* true
ring(st1,in2,st2,in3,st3,m) -> ring(st1,in2,st2,in3,sndsplit(m,st3),m) | leq(m,length(st3)) ->* true, empty(fstsplit(m,st3)) ->* false
sndsplit(0,x) -> x
sndsplit(s(n),cons(h,t)) -> sndsplit(n,t)
sndsplit(s(n),nil) -> nil
tail(cons(h,t)) -> t
)
]
Infeasibility Conditions:
leq(x6,length(x3)) ->* true, empty(fstsplit(x6,x3)) ->* false, leq(x6,length(x5)) ->* true, empty(fstsplit(x6,x5)) ->* false
Problem 1:
Obtaining a proof using Prover9:
-> Prover9 Output:
============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 3266023 was started by sandbox2 on z024.star.cs.uiowa.edu,
Tue Jul 30 08:52:40 2024
The command was "./prover9 -f /tmp/prover93266016-0.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file /tmp/prover93266016-0.in
assign(max_seconds,20).
formulas(assumptions).
->_s0(x1,y) -> ->_s0(app(x1,x2),app(y,x2)) # label(congruence).
->_s0(x2,y) -> ->_s0(app(x1,x2),app(x1,y)) # label(congruence).
->_s0(x1,y) -> ->_s0(empty(x1),empty(y)) # label(congruence).
->_s0(x1,y) -> ->_s0(fstsplit(x1,x2),fstsplit(y,x2)) # label(congruence).
->_s0(x2,y) -> ->_s0(fstsplit(x1,x2),fstsplit(x1,y)) # label(congruence).
->_s0(x1,y) -> ->_s0(head(x1),head(y)) # label(congruence).
->_s0(x1,y) -> ->_s0(length(x1),length(y)) # label(congruence).
->_s0(x1,y) -> ->_s0(leq(x1,x2),leq(y,x2)) # label(congruence).
->_s0(x2,y) -> ->_s0(leq(x1,x2),leq(x1,y)) # label(congruence).
->_s0(x1,y) -> ->_s0(mapf(x1,x2),mapf(y,x2)) # label(congruence).
->_s0(x2,y) -> ->_s0(mapf(x1,x2),mapf(x1,y)) # label(congruence).
->_s0(x1,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(y,x2,x3,x4,x5,x6)) # label(congruence).
->_s0(x2,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,y,x3,x4,x5,x6)) # label(congruence).
->_s0(x3,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,y,x4,x5,x6)) # label(congruence).
->_s0(x4,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,y,x5,x6)) # label(congruence).
->_s0(x5,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,x4,y,x6)) # label(congruence).
->_s0(x6,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,x4,x5,y)) # label(congruence).
->_s0(x1,y) -> ->_s0(sndsplit(x1,x2),sndsplit(y,x2)) # label(congruence).
->_s0(x2,y) -> ->_s0(sndsplit(x1,x2),sndsplit(x1,y)) # label(congruence).
->_s0(x1,y) -> ->_s0(tail(x1),tail(y)) # label(congruence).
->_s0(x1,y) -> ->_s0(cons(x1,x2),cons(y,x2)) # label(congruence).
->_s0(x2,y) -> ->_s0(cons(x1,x2),cons(x1,y)) # label(congruence).
->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence).
->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence).
->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence).
->_s0(app(cons(x3,x4),x1),cons(x3,app(x4,x1))) # label(replacement).
->_s0(app(nil,x1),x1) # label(replacement).
->_s0(empty(cons(x3,x4)),false) # label(replacement).
->_s0(empty(nil),true) # label(replacement).
->_s0(fstsplit(0,x1),nil) # label(replacement).
->_s0(fstsplit(s(x2),cons(x3,x4)),cons(x3,fstsplit(x2,x4))) # label(replacement).
->_s0(fstsplit(s(x2),nil),nil) # label(replacement).
->_s0(head(cons(x3,x4)),x3) # label(replacement).
->_s0(length(cons(x3,x4)),s(length(x4))) # label(replacement).
->_s0(length(nil),0) # label(replacement).
->_s0(leq(0,x5),true) # label(replacement).
->_s0(leq(s(x2),0),false) # label(replacement).
->_s0(leq(s(x2),s(x5)),leq(x2,x5)) # label(replacement).
->_s0(mapf(x6,cons(x3,x4)),app(f(x6,x3),mapf(x6,x4))) # label(replacement).
->_s0(mapf(x6,nil),nil) # label(replacement).
->*_s0(empty(fstsplit(x5,x7)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(sndsplit(x5,x7),cons(fstsplit(x5,x7),x8),x9,x10,x11,x5)) # label(replacement).
->*_s0(leq(x5,length(x9)),false) & ->*_s0(empty(fstsplit(x5,app(mapf(two,head(x8)),x9))),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,tail(x8),sndsplit(x5,app(mapf(two,head(x8)),x9)),cons(fstsplit(x5,app(mapf(two,head(x8)),x9)),x10),x11,x5)) # label(replacement).
->*_s0(empty(mapf(two,head(x8))),true) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,tail(x8),x9,x10,x11,x5)) # label(replacement).
->*_s0(leq(x5,length(x9)),true) & ->*_s0(empty(fstsplit(x5,x9)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,sndsplit(x5,x9),cons(fstsplit(x5,x9),x10),x11,x5)) # label(replacement).
->*_s0(leq(x5,length(x11)),false) & ->*_s0(empty(fstsplit(x5,app(mapf(three,head(x10)),x11))),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,tail(x10),sndsplit(x5,app(mapf(three,head(x10)),x11)),x5)) # label(replacement).
->*_s0(empty(mapf(three,head(x10))),true) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,tail(x10),x11,x5)) # label(replacement).
->*_s0(leq(x5,length(x11)),true) & ->*_s0(empty(fstsplit(x5,x11)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,x10,sndsplit(x5,x11),x5)) # label(replacement).
->_s0(sndsplit(0,x1),x1) # label(replacement).
->_s0(sndsplit(s(x2),cons(x3,x4)),sndsplit(x2,x4)) # label(replacement).
->_s0(sndsplit(s(x2),nil),nil) # label(replacement).
->_s0(tail(cons(x3,x4)),x4) # label(replacement).
->*_s0(x,x) # label(reflexivity).
->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity).
end_of_list.
formulas(goals).
(exists x13 exists x14 exists x15 (->*_s0(leq(x13,length(x14)),true) & ->*_s0(empty(fstsplit(x13,x14)),false) & ->*_s0(leq(x13,length(x15)),true) & ->*_s0(empty(fstsplit(x13,x15)),false))) # label(goal).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 ->_s0(x1,y) -> ->_s0(app(x1,x2),app(y,x2)) # label(congruence) # label(non_clause). [assumption].
2 ->_s0(x2,y) -> ->_s0(app(x1,x2),app(x1,y)) # label(congruence) # label(non_clause). [assumption].
3 ->_s0(x1,y) -> ->_s0(empty(x1),empty(y)) # label(congruence) # label(non_clause). [assumption].
4 ->_s0(x1,y) -> ->_s0(fstsplit(x1,x2),fstsplit(y,x2)) # label(congruence) # label(non_clause). [assumption].
5 ->_s0(x2,y) -> ->_s0(fstsplit(x1,x2),fstsplit(x1,y)) # label(congruence) # label(non_clause). [assumption].
6 ->_s0(x1,y) -> ->_s0(head(x1),head(y)) # label(congruence) # label(non_clause). [assumption].
7 ->_s0(x1,y) -> ->_s0(length(x1),length(y)) # label(congruence) # label(non_clause). [assumption].
8 ->_s0(x1,y) -> ->_s0(leq(x1,x2),leq(y,x2)) # label(congruence) # label(non_clause). [assumption].
9 ->_s0(x2,y) -> ->_s0(leq(x1,x2),leq(x1,y)) # label(congruence) # label(non_clause). [assumption].
10 ->_s0(x1,y) -> ->_s0(mapf(x1,x2),mapf(y,x2)) # label(congruence) # label(non_clause). [assumption].
11 ->_s0(x2,y) -> ->_s0(mapf(x1,x2),mapf(x1,y)) # label(congruence) # label(non_clause). [assumption].
12 ->_s0(x1,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(y,x2,x3,x4,x5,x6)) # label(congruence) # label(non_clause). [assumption].
13 ->_s0(x2,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,y,x3,x4,x5,x6)) # label(congruence) # label(non_clause). [assumption].
14 ->_s0(x3,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,y,x4,x5,x6)) # label(congruence) # label(non_clause). [assumption].
15 ->_s0(x4,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,y,x5,x6)) # label(congruence) # label(non_clause). [assumption].
16 ->_s0(x5,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,x4,y,x6)) # label(congruence) # label(non_clause). [assumption].
17 ->_s0(x6,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,x4,x5,y)) # label(congruence) # label(non_clause). [assumption].
18 ->_s0(x1,y) -> ->_s0(sndsplit(x1,x2),sndsplit(y,x2)) # label(congruence) # label(non_clause). [assumption].
19 ->_s0(x2,y) -> ->_s0(sndsplit(x1,x2),sndsplit(x1,y)) # label(congruence) # label(non_clause). [assumption].
20 ->_s0(x1,y) -> ->_s0(tail(x1),tail(y)) # label(congruence) # label(non_clause). [assumption].
21 ->_s0(x1,y) -> ->_s0(cons(x1,x2),cons(y,x2)) # label(congruence) # label(non_clause). [assumption].
22 ->_s0(x2,y) -> ->_s0(cons(x1,x2),cons(x1,y)) # label(congruence) # label(non_clause). [assumption].
23 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption].
24 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption].
25 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption].
26 ->*_s0(empty(fstsplit(x5,x7)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(sndsplit(x5,x7),cons(fstsplit(x5,x7),x8),x9,x10,x11,x5)) # label(replacement) # label(non_clause). [assumption].
27 ->*_s0(leq(x5,length(x9)),false) & ->*_s0(empty(fstsplit(x5,app(mapf(two,head(x8)),x9))),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,tail(x8),sndsplit(x5,app(mapf(two,head(x8)),x9)),cons(fstsplit(x5,app(mapf(two,head(x8)),x9)),x10),x11,x5)) # label(replacement) # label(non_clause). [assumption].
28 ->*_s0(empty(mapf(two,head(x8))),true) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,tail(x8),x9,x10,x11,x5)) # label(replacement) # label(non_clause). [assumption].
29 ->*_s0(leq(x5,length(x9)),true) & ->*_s0(empty(fstsplit(x5,x9)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,sndsplit(x5,x9),cons(fstsplit(x5,x9),x10),x11,x5)) # label(replacement) # label(non_clause). [assumption].
30 ->*_s0(leq(x5,length(x11)),false) & ->*_s0(empty(fstsplit(x5,app(mapf(three,head(x10)),x11))),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,tail(x10),sndsplit(x5,app(mapf(three,head(x10)),x11)),x5)) # label(replacement) # label(non_clause). [assumption].
31 ->*_s0(empty(mapf(three,head(x10))),true) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,tail(x10),x11,x5)) # label(replacement) # label(non_clause). [assumption].
32 ->*_s0(leq(x5,length(x11)),true) & ->*_s0(empty(fstsplit(x5,x11)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,x10,sndsplit(x5,x11),x5)) # label(replacement) # label(non_clause). [assumption].
33 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption].
34 (exists x13 exists x14 exists x15 (->*_s0(leq(x13,length(x14)),true) & ->*_s0(empty(fstsplit(x13,x14)),false) & ->*_s0(leq(x13,length(x15)),true) & ->*_s0(empty(fstsplit(x13,x15)),false))) # label(goal) # label(non_clause) # label(goal). [goal].
============================== end of process non-clausal formulas ===
============================== PROCESS INITIAL CLAUSES ===============
% Clauses before input processing:
formulas(usable).
end_of_list.
formulas(sos).
-->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence). [clausify(1)].
-->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence). [clausify(2)].
-->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)].
-->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence). [clausify(4)].
-->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence). [clausify(5)].
-->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence). [clausify(6)].
-->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence). [clausify(7)].
-->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence). [clausify(8)].
-->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)].
-->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence). [clausify(10)].
-->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence). [clausify(11)].
-->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence). [clausify(12)].
-->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence). [clausify(13)].
-->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence). [clausify(14)].
-->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence). [clausify(15)].
-->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence). [clausify(16)].
-->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence). [clausify(17)].
-->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence). [clausify(18)].
-->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence). [clausify(19)].
-->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence). [clausify(20)].
-->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence). [clausify(21)].
-->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence). [clausify(22)].
-->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(23)].
-->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(24)].
-->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(25)].
->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement). [assumption].
->_s0(app(nil,x),x) # label(replacement). [assumption].
->_s0(empty(cons(x,y)),false) # label(replacement). [assumption].
->_s0(empty(nil),true) # label(replacement). [assumption].
->_s0(fstsplit(0,x),nil) # label(replacement). [assumption].
->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption].
->_s0(fstsplit(s(x),nil),nil) # label(replacement). [assumption].
->_s0(head(cons(x,y)),x) # label(replacement). [assumption].
->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption].
->_s0(length(nil),0) # label(replacement). [assumption].
->_s0(leq(0,x),true) # label(replacement). [assumption].
->_s0(leq(s(x),0),false) # label(replacement). [assumption].
->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption].
->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement). [assumption].
->_s0(mapf(x,nil),nil) # label(replacement). [assumption].
-->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement). [clausify(26)].
-->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement). [clausify(27)].
-->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement). [clausify(28)].
-->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement). [clausify(29)].
-->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement). [clausify(30)].
-->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement). [clausify(31)].
-->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement). [clausify(32)].
->_s0(sndsplit(0,x),x) # label(replacement). [assumption].
->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement). [assumption].
->_s0(sndsplit(s(x),nil),nil) # label(replacement). [assumption].
->_s0(tail(cons(x,y)),y) # label(replacement). [assumption].
->*_s0(x,x) # label(reflexivity). [assumption].
-->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)].
-->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal). [deny(34)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
No predicates eliminated.
============================== end predicate elimination =============
Auto_denials:
% copying label goal to answer in negative clause
Term ordering decisions:
Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]).
Function symbol precedence: function_order([ nil, false, true, 0, two, three, cons, fstsplit, mapf, sndsplit, app, leq, f, empty, s, head, length, tail, ring ]).
After inverse_order: (no changes).
Unfolding symbols: (none).
Auto_inference settings:
% set(neg_binary_resolution). % (HNE depth_diff=-26)
% clear(ordered_res). % (HNE depth_diff=-26)
% set(ur_resolution). % (HNE depth_diff=-26)
% set(ur_resolution) -> set(pos_ur_resolution).
% set(ur_resolution) -> set(neg_ur_resolution).
Auto_process settings:
% set(unit_deletion). % (Horn set with negative nonunits)
kept: 35 -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence). [clausify(1)].
kept: 36 -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence). [clausify(2)].
kept: 37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)].
kept: 38 -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence). [clausify(4)].
kept: 39 -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence). [clausify(5)].
kept: 40 -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence). [clausify(6)].
kept: 41 -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence). [clausify(7)].
kept: 42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence). [clausify(8)].
kept: 43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)].
kept: 44 -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence). [clausify(10)].
kept: 45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence). [clausify(11)].
kept: 46 -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence). [clausify(12)].
kept: 47 -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence). [clausify(13)].
kept: 48 -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence). [clausify(14)].
kept: 49 -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence). [clausify(15)].
kept: 50 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence). [clausify(16)].
kept: 51 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence). [clausify(17)].
kept: 52 -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence). [clausify(18)].
kept: 53 -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence). [clausify(19)].
kept: 54 -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence). [clausify(20)].
kept: 55 -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence). [clausify(21)].
kept: 56 -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence). [clausify(22)].
kept: 57 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(23)].
kept: 58 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(24)].
kept: 59 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(25)].
kept: 60 ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement). [assumption].
kept: 61 ->_s0(app(nil,x),x) # label(replacement). [assumption].
kept: 62 ->_s0(empty(cons(x,y)),false) # label(replacement). [assumption].
kept: 63 ->_s0(empty(nil),true) # label(replacement). [assumption].
kept: 64 ->_s0(fstsplit(0,x),nil) # label(replacement). [assumption].
kept: 65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption].
kept: 66 ->_s0(fstsplit(s(x),nil),nil) # label(replacement). [assumption].
kept: 67 ->_s0(head(cons(x,y)),x) # label(replacement). [assumption].
kept: 68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption].
kept: 69 ->_s0(length(nil),0) # label(replacement). [assumption].
kept: 70 ->_s0(leq(0,x),true) # label(replacement). [assumption].
kept: 71 ->_s0(leq(s(x),0),false) # label(replacement). [assumption].
kept: 72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption].
kept: 73 ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement). [assumption].
kept: 74 ->_s0(mapf(x,nil),nil) # label(replacement). [assumption].
kept: 75 -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement). [clausify(26)].
kept: 76 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement). [clausify(27)].
kept: 77 -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement). [clausify(28)].
kept: 78 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement). [clausify(29)].
kept: 79 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement). [clausify(30)].
kept: 80 -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement). [clausify(31)].
kept: 81 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement). [clausify(32)].
kept: 82 ->_s0(sndsplit(0,x),x) # label(replacement). [assumption].
kept: 83 ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement). [assumption].
kept: 84 ->_s0(sndsplit(s(x),nil),nil) # label(replacement). [assumption].
kept: 85 ->_s0(tail(cons(x,y)),y) # label(replacement). [assumption].
kept: 86 ->*_s0(x,x) # label(reflexivity). [assumption].
kept: 87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)].
kept: 88 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal) # answer(goal). [deny(34)].
============================== end of process initial clauses ========
============================== CLAUSES FOR SEARCH ====================
% Clauses after input processing:
formulas(usable).
end_of_list.
formulas(sos).
35 -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence). [clausify(1)].
36 -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence). [clausify(2)].
37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)].
38 -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence). [clausify(4)].
39 -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence). [clausify(5)].
40 -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence). [clausify(6)].
41 -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence). [clausify(7)].
42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence). [clausify(8)].
43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)].
44 -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence). [clausify(10)].
45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence). [clausify(11)].
46 -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence). [clausify(12)].
47 -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence). [clausify(13)].
48 -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence). [clausify(14)].
49 -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence). [clausify(15)].
50 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence). [clausify(16)].
51 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence). [clausify(17)].
52 -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence). [clausify(18)].
53 -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence). [clausify(19)].
54 -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence). [clausify(20)].
55 -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence). [clausify(21)].
56 -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence). [clausify(22)].
57 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(23)].
58 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(24)].
59 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(25)].
60 ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement). [assumption].
61 ->_s0(app(nil,x),x) # label(replacement). [assumption].
62 ->_s0(empty(cons(x,y)),false) # label(replacement). [assumption].
63 ->_s0(empty(nil),true) # label(replacement). [assumption].
64 ->_s0(fstsplit(0,x),nil) # label(replacement). [assumption].
65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption].
66 ->_s0(fstsplit(s(x),nil),nil) # label(replacement). [assumption].
67 ->_s0(head(cons(x,y)),x) # label(replacement). [assumption].
68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption].
69 ->_s0(length(nil),0) # label(replacement). [assumption].
70 ->_s0(leq(0,x),true) # label(replacement). [assumption].
71 ->_s0(leq(s(x),0),false) # label(replacement). [assumption].
72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption].
73 ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement). [assumption].
74 ->_s0(mapf(x,nil),nil) # label(replacement). [assumption].
75 -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement). [clausify(26)].
76 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement). [clausify(27)].
77 -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement). [clausify(28)].
78 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement). [clausify(29)].
79 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement). [clausify(30)].
80 -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement). [clausify(31)].
81 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement). [clausify(32)].
82 ->_s0(sndsplit(0,x),x) # label(replacement). [assumption].
83 ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement). [assumption].
84 ->_s0(sndsplit(s(x),nil),nil) # label(replacement). [assumption].
85 ->_s0(tail(cons(x,y)),y) # label(replacement). [assumption].
86 ->*_s0(x,x) # label(reflexivity). [assumption].
87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)].
88 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal) # answer(goal). [deny(34)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== end of clauses for search =============
============================== SEARCH ================================
% Starting search at 0.01 seconds.
given #1 (I,wt=10): 35 -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence). [clausify(1)].
given #2 (I,wt=10): 36 -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence). [clausify(2)].
given #3 (I,wt=8): 37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)].
given #4 (I,wt=10): 38 -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence). [clausify(4)].
given #5 (I,wt=10): 39 -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence). [clausify(5)].
given #6 (I,wt=8): 40 -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence). [clausify(6)].
given #7 (I,wt=8): 41 -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence). [clausify(7)].
given #8 (I,wt=10): 42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence). [clausify(8)].
given #9 (I,wt=10): 43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)].
given #10 (I,wt=10): 44 -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence). [clausify(10)].
given #11 (I,wt=10): 45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence). [clausify(11)].
given #12 (I,wt=18): 46 -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence). [clausify(12)].
given #13 (I,wt=18): 47 -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence). [clausify(13)].
given #14 (I,wt=18): 48 -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence). [clausify(14)].
given #15 (I,wt=18): 49 -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence). [clausify(15)].
given #16 (I,wt=18): 50 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence). [clausify(16)].
given #17 (I,wt=18): 51 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence). [clausify(17)].
given #18 (I,wt=10): 52 -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence). [clausify(18)].
given #19 (I,wt=10): 53 -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence). [clausify(19)].
given #20 (I,wt=8): 54 -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence). [clausify(20)].
given #21 (I,wt=10): 55 -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence). [clausify(21)].
given #22 (I,wt=10): 56 -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence). [clausify(22)].
given #23 (I,wt=10): 57 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(23)].
given #24 (I,wt=10): 58 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(24)].
given #25 (I,wt=8): 59 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(25)].
given #26 (I,wt=11): 60 ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement). [assumption].
given #27 (I,wt=5): 61 ->_s0(app(nil,x),x) # label(replacement). [assumption].
given #28 (I,wt=6): 62 ->_s0(empty(cons(x,y)),false) # label(replacement). [assumption].
given #29 (I,wt=4): 63 ->_s0(empty(nil),true) # label(replacement). [assumption].
given #30 (I,wt=5): 64 ->_s0(fstsplit(0,x),nil) # label(replacement). [assumption].
given #31 (I,wt=12): 65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption].
given #32 (I,wt=6): 66 ->_s0(fstsplit(s(x),nil),nil) # label(replacement). [assumption].
given #33 (I,wt=6): 67 ->_s0(head(cons(x,y)),x) # label(replacement). [assumption].
given #34 (I,wt=8): 68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption].
given #35 (I,wt=4): 69 ->_s0(length(nil),0) # label(replacement). [assumption].
given #36 (I,wt=5): 70 ->_s0(leq(0,x),true) # label(replacement). [assumption].
given #37 (I,wt=6): 71 ->_s0(leq(s(x),0),false) # label(replacement). [assumption].
given #38 (I,wt=9): 72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption].
given #39 (I,wt=13): 73 ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement). [assumption].
given #40 (I,wt=5): 74 ->_s0(mapf(x,nil),nil) # label(replacement). [assumption].
given #41 (I,wt=27): 75 -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement). [clausify(26)].
given #42 (I,wt=49): 76 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement). [clausify(27)].
given #43 (I,wt=23): 77 -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement). [clausify(28)].
given #44 (I,wt=33): 78 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement). [clausify(29)].
given #45 (I,wt=40): 79 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement). [clausify(30)].
given #46 (I,wt=23): 80 -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement). [clausify(31)].
given #47 (I,wt=29): 81 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement). [clausify(32)].
given #48 (I,wt=5): 82 ->_s0(sndsplit(0,x),x) # label(replacement). [assumption].
given #49 (I,wt=10): 83 ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement). [assumption].
given #50 (I,wt=6): 84 ->_s0(sndsplit(s(x),nil),nil) # label(replacement). [assumption].
given #51 (I,wt=6): 85 ->_s0(tail(cons(x,y)),y) # label(replacement). [assumption].
given #52 (I,wt=3): 86 ->*_s0(x,x) # label(reflexivity). [assumption].
given #53 (I,wt=9): 87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)].
given #54 (I,wt=24): 88 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal) # answer(goal). [deny(34)].
given #55 (A,wt=13): 89 ->_s0(s(app(cons(x,y),z)),s(cons(x,app(y,z)))). [ur(59,a,60,a)].
given #56 (T,wt=4): 573 ->*_s0(length(nil),0). [ur(87,a,69,a,b,86,a)].
given #57 (T,wt=4): 579 ->*_s0(empty(nil),true). [ur(87,a,63,a,b,86,a)].
given #58 (T,wt=5): 567 ->*_s0(sndsplit(0,x),x). [ur(87,a,82,a,b,86,a)].
given #59 (T,wt=5): 568 ->*_s0(mapf(x,nil),nil). [ur(87,a,74,a,b,86,a)].
given #60 (A,wt=15): 90 ->_s0(f(x,app(cons(y,z),u)),f(x,cons(y,app(z,u)))). [ur(58,a,60,a)].
given #61 (T,wt=5): 572 ->*_s0(leq(0,x),true). [ur(87,a,70,a,b,86,a)].
given #62 (T,wt=5): 578 ->*_s0(fstsplit(0,x),nil). [ur(87,a,64,a,b,86,a)].
given #63 (T,wt=5): 581 ->*_s0(app(nil,x),x). [ur(87,a,61,a,b,86,a)].
given #64 (T,wt=6): 164 ->_s0(s(empty(nil)),s(true)). [ur(59,a,63,a)].
given #65 (A,wt=15): 91 ->_s0(f(app(cons(x,y),z),u),f(cons(x,app(y,z)),u)). [ur(57,a,60,a)].
given #66 (F,wt=12): 652 -->*_s0(empty(fstsplit(0,x)),false) | -->*_s0(empty(fstsplit(0,y)),false) # answer(goal). [resolve(572,a,88,c),unit_del(a,572)].
given #67 (T,wt=6): 169 ->_s0(tail(empty(nil)),tail(true)). [ur(54,a,63,a)].
given #68 (T,wt=6): 182 ->_s0(length(empty(nil)),length(true)). [ur(41,a,63,a)].
given #69 (T,wt=6): 183 ->_s0(head(empty(nil)),head(true)). [ur(40,a,63,a)].
given #70 (T,wt=6): 186 ->_s0(empty(empty(nil)),empty(true)). [ur(37,a,63,a)].
given #71 (A,wt=15): 92 ->_s0(cons(x,app(cons(y,z),u)),cons(x,cons(y,app(z,u)))). [ur(56,a,60,a)].
given #72 (T,wt=6): 314 ->_s0(s(length(nil)),s(0)). [ur(59,a,69,a)].
given #73 (T,wt=6): 319 ->_s0(tail(length(nil)),tail(0)). [ur(54,a,69,a)].
given #74 (T,wt=6): 332 ->_s0(length(length(nil)),length(0)). [ur(41,a,69,a)].
given #75 (T,wt=6): 333 ->_s0(head(length(nil)),head(0)). [ur(40,a,69,a)].
given #76 (A,wt=15): 93 ->_s0(cons(app(cons(x,y),z),u),cons(cons(x,app(y,z)),u)). [ur(55,a,60,a)].
given #77 (T,wt=6): 336 ->_s0(empty(length(nil)),empty(0)). [ur(37,a,69,a)].
given #78 (T,wt=6): 564 ->*_s0(tail(cons(x,y)),y). [ur(87,a,85,a,b,86,a)].
given #79 (T,wt=6): 565 ->*_s0(sndsplit(s(x),nil),nil). [ur(87,a,84,a,b,86,a)].
given #80 (T,wt=6): 571 ->*_s0(leq(s(x),0),false). [ur(87,a,71,a,b,86,a)].
given #81 (A,wt=13): 94 ->_s0(tail(app(cons(x,y),z)),tail(cons(x,app(y,z)))). [ur(54,a,60,a)].
given #82 (T,wt=6): 575 ->*_s0(head(cons(x,y)),x). [ur(87,a,67,a,b,86,a)].
given #83 (T,wt=6): 576 ->*_s0(fstsplit(s(x),nil),nil). [ur(87,a,66,a,b,86,a)].
given #84 (T,wt=6): 580 ->*_s0(empty(cons(x,y)),false). [ur(87,a,62,a,b,86,a)].
given #85 (T,wt=6): 610 ->*_s0(sndsplit(0,length(nil)),0). [ur(87,a,82,a,b,573,a)].
given #86 (A,wt=15): 95 ->_s0(sndsplit(x,app(cons(y,z),u)),sndsplit(x,cons(y,app(z,u)))). [ur(53,a,60,a)].
given #87 (T,wt=6): 612 ->*_s0(app(nil,length(nil)),0). [ur(87,a,61,a,b,573,a)].
given #88 (T,wt=6): 614 ->*_s0(sndsplit(0,empty(nil)),true). [ur(87,a,82,a,b,579,a)].
given #89 (T,wt=6): 616 ->*_s0(app(nil,empty(nil)),true). [ur(87,a,61,a,b,579,a)].
given #90 (T,wt=6): 666 ->*_s0(s(empty(nil)),s(true)). [ur(87,a,164,a,b,86,a)].
given #91 (A,wt=15): 96 ->_s0(sndsplit(app(cons(x,y),z),u),sndsplit(cons(x,app(y,z)),u)). [ur(52,a,60,a)].
given #92 (T,wt=6): 718 ->*_s0(tail(empty(nil)),tail(true)). [ur(87,a,169,a,b,86,a)].
given #93 (T,wt=6): 744 ->*_s0(length(empty(nil)),length(true)). [ur(87,a,182,a,b,86,a)].
given #94 (T,wt=6): 770 ->*_s0(head(empty(nil)),head(true)). [ur(87,a,183,a,b,86,a)].
given #95 (T,wt=6): 796 ->*_s0(empty(empty(nil)),empty(true)). [ur(87,a,186,a,b,86,a)].
given #96 (A,wt=23): 97 ->_s0(ring(x,y,z,u,w,app(cons(v5,v6),v7)),ring(x,y,z,u,w,cons(v5,app(v6,v7)))). [ur(51,a,60,a)].
given #97 (T,wt=6): 848 ->*_s0(s(length(nil)),s(0)). [ur(87,a,314,a,b,86,a)].
given #98 (T,wt=6): 874 ->*_s0(tail(length(nil)),tail(0)). [ur(87,a,319,a,b,86,a)].
given #99 (T,wt=6): 900 ->*_s0(length(length(nil)),length(0)). [ur(87,a,332,a,b,86,a)].
given #100 (T,wt=6): 926 ->*_s0(head(length(nil)),head(0)). [ur(87,a,333,a,b,86,a)].
given #101 (A,wt=23): 98 ->_s0(ring(x,y,z,u,app(cons(w,v5),v6),v7),ring(x,y,z,u,cons(w,app(v5,v6)),v7)). [ur(50,a,60,a)].
given #102 (T,wt=6): 978 ->*_s0(empty(length(nil)),empty(0)). [ur(87,a,336,a,b,86,a)].
given #103 (T,wt=7): 114 ->_s0(s(app(nil,x)),s(x)). [ur(59,a,61,a)].
given #104 (T,wt=7): 119 ->_s0(tail(app(nil,x)),tail(x)). [ur(54,a,61,a)].
given #105 (T,wt=7): 132 ->_s0(length(app(nil,x)),length(x)). [ur(41,a,61,a)].
given #106 (A,wt=23): 99 ->_s0(ring(x,y,z,app(cons(u,w),v5),v6,v7),ring(x,y,z,cons(u,app(w,v5)),v6,v7)). [ur(49,a,60,a)].
given #107 (T,wt=6): 1280 ->*_s0(length(app(nil,nil)),0). [ur(87,a,132,a,b,573,a)].
given #108 (T,wt=7): 133 ->_s0(head(app(nil,x)),head(x)). [ur(40,a,61,a)].
given #109 (T,wt=7): 136 ->_s0(empty(app(nil,x)),empty(x)). [ur(37,a,61,a)].
given #110 (T,wt=6): 1370 ->*_s0(empty(app(nil,nil)),true). [ur(87,a,136,a,b,579,a)].
given #111 (A,wt=23): 100 ->_s0(ring(x,y,app(cons(z,u),w),v5,v6,v7),ring(x,y,cons(z,app(u,w)),v5,v6,v7)). [ur(48,a,60,a)].
given #112 (T,wt=7): 189 ->_s0(s(fstsplit(0,x)),s(nil)). [ur(59,a,64,a)].
given #113 (T,wt=7): 194 ->_s0(tail(fstsplit(0,x)),tail(nil)). [ur(54,a,64,a)].
given #114 (T,wt=7): 207 ->_s0(length(fstsplit(0,x)),length(nil)). [ur(41,a,64,a)].
given #115 (T,wt=6): 1480 ->*_s0(length(fstsplit(0,x)),0). [ur(87,a,207,a,b,573,a)].
given #116 (A,wt=23): 101 ->_s0(ring(x,app(cons(y,z),u),w,v5,v6,v7),ring(x,cons(y,app(z,u)),w,v5,v6,v7)). [ur(47,a,60,a)].
given #117 (T,wt=7): 208 ->_s0(head(fstsplit(0,x)),head(nil)). [ur(40,a,64,a)].
given #118 (T,wt=7): 211 ->_s0(empty(fstsplit(0,x)),empty(nil)). [ur(37,a,64,a)].
given #119 (T,wt=6): 1564 ->*_s0(empty(fstsplit(0,x)),true). [ur(87,a,211,a,b,579,a)].
given #120 (T,wt=7): 339 ->_s0(s(leq(0,x)),s(true)). [ur(59,a,70,a)].
given #121 (A,wt=23): 102 ->_s0(ring(app(cons(x,y),z),u,w,v5,v6,v7),ring(cons(x,app(y,z)),u,w,v5,v6,v7)). [ur(46,a,60,a)].
given #122 (T,wt=7): 344 ->_s0(tail(leq(0,x)),tail(true)). [ur(54,a,70,a)].
given #123 (T,wt=7): 357 ->_s0(length(leq(0,x)),length(true)). [ur(41,a,70,a)].
given #124 (T,wt=7): 358 ->_s0(head(leq(0,x)),head(true)). [ur(40,a,70,a)].
given #125 (T,wt=7): 361 ->_s0(empty(leq(0,x)),empty(true)). [ur(37,a,70,a)].
given #126 (A,wt=15): 103 ->_s0(mapf(x,app(cons(y,z),u)),mapf(x,cons(y,app(z,u)))). [ur(45,a,60,a)].
given #127 (T,wt=7): 439 ->_s0(s(mapf(x,nil)),s(nil)). [ur(59,a,74,a)].
given #128 (T,wt=7): 444 ->_s0(tail(mapf(x,nil)),tail(nil)). [ur(54,a,74,a)].
given #129 (T,wt=7): 457 ->_s0(length(mapf(x,nil)),length(nil)). [ur(41,a,74,a)].
given #130 (T,wt=6): 1830 ->*_s0(length(mapf(x,nil)),0). [ur(87,a,457,a,b,573,a)].
given #131 (A,wt=15): 104 ->_s0(mapf(app(cons(x,y),z),u),mapf(cons(x,app(y,z)),u)). [ur(44,a,60,a)].
given #132 (T,wt=7): 458 ->_s0(head(mapf(x,nil)),head(nil)). [ur(40,a,74,a)].
given #133 (T,wt=7): 461 ->_s0(empty(mapf(x,nil)),empty(nil)). [ur(37,a,74,a)].
given #134 (T,wt=6): 1914 ->*_s0(empty(mapf(x,nil)),true). [ur(87,a,461,a,b,579,a)].
given #135 (T,wt=7): 464 ->_s0(s(sndsplit(0,x)),s(x)). [ur(59,a,82,a)].
given #136 (A,wt=15): 105 ->_s0(leq(x,app(cons(y,z),u)),leq(x,cons(y,app(z,u)))). [ur(43,a,60,a)].
given #137 (T,wt=7): 469 ->_s0(tail(sndsplit(0,x)),tail(x)). [ur(54,a,82,a)].
given #138 (T,wt=7): 482 ->_s0(length(sndsplit(0,x)),length(x)). [ur(41,a,82,a)].
given #139 (T,wt=6): 2034 ->*_s0(length(sndsplit(0,nil)),0). [ur(87,a,482,a,b,573,a)].
given #140 (T,wt=7): 483 ->_s0(head(sndsplit(0,x)),head(x)). [ur(40,a,82,a)].
given #141 (A,wt=15): 106 ->_s0(leq(app(cons(x,y),z),u),leq(cons(x,app(y,z)),u)). [ur(42,a,60,a)].
given #142 (T,wt=7): 486 ->_s0(empty(sndsplit(0,x)),empty(x)). [ur(37,a,82,a)].
given #143 (T,wt=6): 2128 ->*_s0(empty(sndsplit(0,nil)),true). [ur(87,a,486,a,b,579,a)].
given #144 (T,wt=7): 609 ->*_s0(tail(cons(x,length(nil))),0). [ur(87,a,85,a,b,573,a)].
given #145 (T,wt=7): 611 ->*_s0(head(cons(length(nil),x)),0). [ur(87,a,67,a,b,573,a)].
given #146 (A,wt=13): 107 ->_s0(length(app(cons(x,y),z)),length(cons(x,app(y,z)))). [ur(41,a,60,a)].
given #147 (T,wt=7): 613 ->*_s0(tail(cons(x,empty(nil))),true). [ur(87,a,85,a,b,579,a)].
given #148 (T,wt=7): 615 ->*_s0(head(cons(empty(nil),x)),true). [ur(87,a,67,a,b,579,a)].
given #149 (T,wt=7): 619 ->*_s0(sndsplit(0,sndsplit(0,x)),x). [ur(87,a,82,a,b,567,a)].
given #150 (T,wt=7): 621 ->*_s0(app(nil,sndsplit(0,x)),x). [ur(87,a,61,a,b,567,a)].
given #151 (A,wt=13): 108 ->_s0(head(app(cons(x,y),z)),head(cons(x,app(y,z)))). [ur(40,a,60,a)].
given #152 (T,wt=7): 623 ->*_s0(sndsplit(0,mapf(x,nil)),nil). [ur(87,a,82,a,b,568,a)].
given #153 (T,wt=7): 625 ->*_s0(app(nil,mapf(x,nil)),nil). [ur(87,a,61,a,b,568,a)].
given #154 (T,wt=7): 654 ->*_s0(sndsplit(0,leq(0,x)),true). [ur(87,a,82,a,b,572,a)].
given #155 (T,wt=7): 655 ->*_s0(leq(s(0),s(x)),true). [ur(87,a,72,a,b,572,a)].
given #156 (A,wt=15): 109 ->_s0(fstsplit(x,app(cons(y,z),u)),fstsplit(x,cons(y,app(z,u)))). [ur(39,a,60,a)].
given #157 (T,wt=7): 657 ->*_s0(app(nil,leq(0,x)),true). [ur(87,a,61,a,b,572,a)].
given #158 (T,wt=7): 659 ->*_s0(sndsplit(0,fstsplit(0,x)),nil). [ur(87,a,82,a,b,578,a)].
given #159 (T,wt=7): 661 ->*_s0(app(nil,fstsplit(0,x)),nil). [ur(87,a,61,a,b,578,a)].
given #160 (T,wt=7): 663 ->*_s0(sndsplit(0,app(nil,x)),x). [ur(87,a,82,a,b,581,a)].
given #161 (A,wt=15): 110 ->_s0(fstsplit(app(cons(x,y),z),u),fstsplit(cons(x,app(y,z)),u)). [ur(38,a,60,a)].
given #162 (T,wt=7): 665 ->*_s0(app(nil,app(nil,x)),x). [ur(87,a,61,a,b,581,a)].
given #163 (T,wt=7): 1176 ->*_s0(length(cons(x,nil)),s(0)). [ur(87,a,68,a,b,848,a)].
given #164 (T,wt=7): 1223 ->*_s0(s(app(nil,x)),s(x)). [ur(87,a,114,a,b,86,a)].
given #165 (T,wt=7): 1252 ->*_s0(tail(app(nil,x)),tail(x)). [ur(87,a,119,a,b,86,a)].
given #166 (A,wt=13): 111 ->_s0(empty(app(cons(x,y),z)),empty(cons(x,app(y,z)))). [ur(37,a,60,a)].
given #167 (T,wt=7): 1281 ->*_s0(length(app(nil,x)),length(x)). [ur(87,a,132,a,b,86,a)].
given #168 (T,wt=7): 1341 ->*_s0(head(app(nil,x)),head(x)). [ur(87,a,133,a,b,86,a)].
given #169 (T,wt=7): 1371 ->*_s0(empty(app(nil,x)),empty(x)). [ur(87,a,136,a,b,86,a)].
given #170 (T,wt=7): 1428 ->*_s0(s(fstsplit(0,x)),s(nil)). [ur(87,a,189,a,b,86,a)].
given #171 (A,wt=15): 112 ->_s0(app(x,app(cons(y,z),u)),app(x,cons(y,app(z,u)))). [ur(36,a,60,a)].
given #172 (T,wt=7): 1454 ->*_s0(tail(fstsplit(0,x)),tail(nil)). [ur(87,a,194,a,b,86,a)].
given #173 (T,wt=7): 1481 ->*_s0(length(fstsplit(0,x)),length(nil)). [ur(87,a,207,a,b,86,a)].
given #174 (T,wt=7): 1538 ->*_s0(head(fstsplit(0,x)),head(nil)). [ur(87,a,208,a,b,86,a)].
given #175 (T,wt=7): 1565 ->*_s0(empty(fstsplit(0,x)),empty(nil)). [ur(87,a,211,a,b,86,a)].
given #176 (A,wt=15): 113 ->_s0(app(app(cons(x,y),z),u),app(cons(x,app(y,z)),u)). [ur(35,a,60,a)].
given #177 (T,wt=7): 1596 ->*_s0(s(leq(0,x)),s(true)). [ur(87,a,339,a,b,86,a)].
given #178 (T,wt=7): 1648 ->*_s0(tail(leq(0,x)),tail(true)). [ur(87,a,344,a,b,86,a)].
given #179 (T,wt=7): 1674 ->*_s0(length(leq(0,x)),length(true)). [ur(87,a,357,a,b,86,a)].
given #180 (T,wt=7): 1700 ->*_s0(head(leq(0,x)),head(true)). [ur(87,a,358,a,b,86,a)].
given #181 (A,wt=9): 115 ->_s0(f(x,app(nil,y)),f(x,y)). [ur(58,a,61,a)].
given #182 (T,wt=7): 1726 ->*_s0(empty(leq(0,x)),empty(true)). [ur(87,a,361,a,b,86,a)].
given #183 (T,wt=7): 1778 ->*_s0(s(mapf(x,nil)),s(nil)). [ur(87,a,439,a,b,86,a)].
given #184 (T,wt=7): 1804 ->*_s0(tail(mapf(x,nil)),tail(nil)). [ur(87,a,444,a,b,86,a)].
given #185 (T,wt=7): 1831 ->*_s0(length(mapf(x,nil)),length(nil)). [ur(87,a,457,a,b,86,a)].
given #186 (A,wt=9): 116 ->_s0(f(app(nil,x),y),f(x,y)). [ur(57,a,61,a)].
given #187 (T,wt=7): 1888 ->*_s0(head(mapf(x,nil)),head(nil)). [ur(87,a,458,a,b,86,a)].
given #188 (T,wt=7): 1915 ->*_s0(empty(mapf(x,nil)),empty(nil)). [ur(87,a,461,a,b,86,a)].
given #189 (T,wt=7): 1948 ->*_s0(s(sndsplit(0,x)),s(x)). [ur(87,a,464,a,b,86,a)].
given #190 (T,wt=7): 2003 ->*_s0(tail(sndsplit(0,x)),tail(x)). [ur(87,a,469,a,b,86,a)].
given #191 (A,wt=9): 117 ->_s0(cons(x,app(nil,y)),cons(x,y)). [ur(56,a,61,a)].
given #192 (T,wt=7): 2035 ->*_s0(length(sndsplit(0,x)),length(x)). [ur(87,a,482,a,b,86,a)].
given #193 (T,wt=7): 2070 ->*_s0(head(sndsplit(0,x)),head(x)). [ur(87,a,483,a,b,86,a)].
given #194 (T,wt=7): 2129 ->*_s0(empty(sndsplit(0,x)),empty(x)). [ur(87,a,486,a,b,86,a)].
given #195 (T,wt=8): 139 ->_s0(s(empty(cons(x,y))),s(false)). [ur(59,a,62,a)].
given #196 (A,wt=9): 118 ->_s0(cons(app(nil,x),y),cons(x,y)). [ur(55,a,61,a)].
given #197 (T,wt=8): 144 ->_s0(tail(empty(cons(x,y))),tail(false)). [ur(54,a,62,a)].
given #198 (T,wt=8): 157 ->_s0(length(empty(cons(x,y))),length(false)). [ur(41,a,62,a)].
given #199 (T,wt=8): 158 ->_s0(head(empty(cons(x,y))),head(false)). [ur(40,a,62,a)].
given #200 (T,wt=8): 161 ->_s0(empty(empty(cons(x,y))),empty(false)). [ur(37,a,62,a)].
given #201 (A,wt=9): 120 ->_s0(sndsplit(x,app(nil,y)),sndsplit(x,y)). [ur(53,a,61,a)].
given #202 (T,wt=8): 165 ->_s0(f(x,empty(nil)),f(x,true)). [ur(58,a,63,a)].
given #203 (T,wt=8): 166 ->_s0(f(empty(nil),x),f(true,x)). [ur(57,a,63,a)].
given #204 (T,wt=8): 167 ->_s0(cons(x,empty(nil)),cons(x,true)). [ur(56,a,63,a)].
given #205 (T,wt=8): 168 ->_s0(cons(empty(nil),x),cons(true,x)). [ur(55,a,63,a)].
given #206 (A,wt=9): 121 ->_s0(sndsplit(app(nil,x),y),sndsplit(x,y)). [ur(52,a,61,a)].
given #207 (T,wt=7): 2950 ->*_s0(sndsplit(app(nil,0),x),x). [ur(87,a,121,a,b,567,a)].
given #208 (T,wt=8): 170 ->_s0(sndsplit(x,empty(nil)),sndsplit(x,true)). [ur(53,a,63,a)].
given #209 (T,wt=8): 171 ->_s0(sndsplit(empty(nil),x),sndsplit(true,x)). [ur(52,a,63,a)].
given #210 (T,wt=8): 178 ->_s0(mapf(x,empty(nil)),mapf(x,true)). [ur(45,a,63,a)].
given #211 (A,wt=17): 122 ->_s0(ring(x,y,z,u,w,app(nil,v5)),ring(x,y,z,u,w,v5)). [ur(51,a,61,a)].
given #212 (T,wt=8): 179 ->_s0(mapf(empty(nil),x),mapf(true,x)). [ur(44,a,63,a)].
given #213 (T,wt=8): 180 ->_s0(leq(x,empty(nil)),leq(x,true)). [ur(43,a,63,a)].
given #214 (T,wt=8): 181 ->_s0(leq(empty(nil),x),leq(true,x)). [ur(42,a,63,a)].
given #215 (T,wt=8): 184 ->_s0(fstsplit(x,empty(nil)),fstsplit(x,true)). [ur(39,a,63,a)].
given #216 (A,wt=17): 123 ->_s0(ring(x,y,z,u,app(nil,w),v5),ring(x,y,z,u,w,v5)). [ur(50,a,61,a)].
given #217 (T,wt=8): 185 ->_s0(fstsplit(empty(nil),x),fstsplit(true,x)). [ur(38,a,63,a)].
given #218 (T,wt=8): 187 ->_s0(app(x,empty(nil)),app(x,true)). [ur(36,a,63,a)].
given #219 (T,wt=8): 188 ->_s0(app(empty(nil),x),app(true,x)). [ur(35,a,63,a)].
given #220 (T,wt=8): 239 ->_s0(s(fstsplit(s(x),nil)),s(nil)). [ur(59,a,66,a)].
given #221 (A,wt=17): 124 ->_s0(ring(x,y,z,app(nil,u),w,v5),ring(x,y,z,u,w,v5)). [ur(49,a,61,a)].
given #222 (T,wt=8): 244 ->_s0(tail(fstsplit(s(x),nil)),tail(nil)). [ur(54,a,66,a)].
given #223 (T,wt=8): 257 ->_s0(length(fstsplit(s(x),nil)),length(nil)). [ur(41,a,66,a)].
given #224 (T,wt=7): 3375 ->*_s0(length(fstsplit(s(x),nil)),0). [ur(87,a,257,a,b,573,a)].
given #225 (T,wt=8): 258 ->_s0(head(fstsplit(s(x),nil)),head(nil)). [ur(40,a,66,a)].
given #226 (A,wt=17): 125 ->_s0(ring(x,y,app(nil,z),u,w,v5),ring(x,y,z,u,w,v5)). [ur(48,a,61,a)].
given #227 (T,wt=8): 261 ->_s0(empty(fstsplit(s(x),nil)),empty(nil)). [ur(37,a,66,a)].
given #228 (T,wt=7): 3460 ->*_s0(empty(fstsplit(s(x),nil)),true). [ur(87,a,261,a,b,579,a)].
given #229 (T,wt=8): 264 ->_s0(s(head(cons(x,y))),s(x)). [ur(59,a,67,a)].
given #230 (T,wt=8): 269 ->_s0(tail(head(cons(x,y))),tail(x)). [ur(54,a,67,a)].
given #231 (A,wt=17): 126 ->_s0(ring(x,app(nil,y),z,u,w,v5),ring(x,y,z,u,w,v5)). [ur(47,a,61,a)].
given #232 (T,wt=8): 282 ->_s0(length(head(cons(x,y))),length(x)). [ur(41,a,67,a)].
given #233 (T,wt=7): 3601 ->*_s0(length(head(cons(nil,x))),0). [ur(87,a,282,a,b,573,a)].
given #234 (T,wt=8): 283 ->_s0(head(head(cons(x,y))),head(x)). [ur(40,a,67,a)].
given #235 (T,wt=8): 286 ->_s0(empty(head(cons(x,y))),empty(x)). [ur(37,a,67,a)].
given #236 (A,wt=17): 127 ->_s0(ring(app(nil,x),y,z,u,w,v5),ring(x,y,z,u,w,v5)). [ur(46,a,61,a)].
given #237 (T,wt=7): 3684 ->*_s0(empty(head(cons(nil,x))),true). [ur(87,a,286,a,b,579,a)].
given #238 (T,wt=8): 315 ->_s0(f(x,length(nil)),f(x,0)). [ur(58,a,69,a)].
given #239 (T,wt=8): 316 ->_s0(f(length(nil),x),f(0,x)). [ur(57,a,69,a)].
given #240 (T,wt=8): 317 ->_s0(cons(x,length(nil)),cons(x,0)). [ur(56,a,69,a)].
given #241 (A,wt=9): 128 ->_s0(mapf(x,app(nil,y)),mapf(x,y)). [ur(45,a,61,a)].
given #242 (T,wt=7): 3822 ->*_s0(mapf(x,app(nil,nil)),nil). [ur(87,a,128,a,b,568,a)].
given #243 (T,wt=8): 318 ->_s0(cons(length(nil),x),cons(0,x)). [ur(55,a,69,a)].
given #244 (T,wt=8): 320 ->_s0(sndsplit(x,length(nil)),sndsplit(x,0)). [ur(53,a,69,a)].
given #245 (T,wt=8): 321 ->_s0(sndsplit(length(nil),x),sndsplit(0,x)). [ur(52,a,69,a)].
given #246 (A,wt=9): 129 ->_s0(mapf(app(nil,x),y),mapf(x,y)). [ur(44,a,61,a)].
given #247 (T,wt=6): 3913 ->*_s0(sndsplit(length(nil),x),x). [ur(87,a,321,a,b,567,a)].
given #248 (T,wt=7): 3911 ->*_s0(sndsplit(length(nil),empty(nil)),true). [ur(87,a,321,a,b,614,a)].
given #249 (T,wt=7): 3912 ->*_s0(sndsplit(length(nil),length(nil)),0). [ur(87,a,321,a,b,610,a)].
given #250 (T,wt=8): 328 ->_s0(mapf(x,length(nil)),mapf(x,0)). [ur(45,a,69,a)].
given #251 (A,wt=9): 130 ->_s0(leq(x,app(nil,y)),leq(x,y)). [ur(43,a,61,a)].
given #252 (T,wt=8): 329 ->_s0(mapf(length(nil),x),mapf(0,x)). [ur(44,a,69,a)].
given #253 (T,wt=8): 330 ->_s0(leq(x,length(nil)),leq(x,0)). [ur(43,a,69,a)].
given #254 (T,wt=7): 4067 ->*_s0(leq(s(x),length(nil)),false). [ur(87,a,330,a,b,571,a)].
given #255 (T,wt=8): 331 ->_s0(leq(length(nil),x),leq(0,x)). [ur(42,a,69,a)].
given #256 (A,wt=9): 131 ->_s0(leq(app(nil,x),y),leq(x,y)). [ur(42,a,61,a)].
given #257 (T,wt=6): 4100 ->*_s0(leq(length(nil),x),true). [ur(87,a,331,a,b,572,a)].
given #258 (T,wt=7): 4129 ->*_s0(leq(app(nil,0),x),true). [ur(87,a,131,a,b,572,a)].
given #259 (T,wt=8): 334 ->_s0(fstsplit(x,length(nil)),fstsplit(x,0)). [ur(39,a,69,a)].
given #260 (T,wt=8): 335 ->_s0(fstsplit(length(nil),x),fstsplit(0,x)). [ur(38,a,69,a)].
given #261 (A,wt=9): 134 ->_s0(fstsplit(x,app(nil,y)),fstsplit(x,y)). [ur(39,a,61,a)].
given #262 (F,wt=14): 4157 -->*_s0(empty(fstsplit(length(nil),x)),false) | -->*_s0(empty(fstsplit(length(nil),y)),false) # answer(goal). [resolve(4100,a,88,c),unit_del(a,4100)].
given #263 (F,wt=16): 4164 -->*_s0(empty(fstsplit(app(nil,0),x)),false) | -->*_s0(empty(fstsplit(app(nil,0),y)),false) # answer(goal). [resolve(4129,a,88,c),unit_del(a,4129)].
given #264 (T,wt=6): 4197 ->*_s0(fstsplit(length(nil),x),nil). [ur(87,a,335,a,b,578,a)].
given #265 (T,wt=8): 337 ->_s0(app(x,length(nil)),app(x,0)). [ur(36,a,69,a)].
given #266 (T,wt=8): 338 ->_s0(app(length(nil),x),app(0,x)). [ur(35,a,69,a)].
given #267 (T,wt=8): 364 ->_s0(s(leq(s(x),0)),s(false)). [ur(59,a,71,a)].
given #268 (A,wt=9): 135 ->_s0(fstsplit(app(nil,x),y),fstsplit(x,y)). [ur(38,a,61,a)].
given #269 (T,wt=7): 4334 ->*_s0(fstsplit(app(nil,0),x),nil). [ur(87,a,135,a,b,578,a)].
given #270 (T,wt=8): 369 ->_s0(tail(leq(s(x),0)),tail(false)). [ur(54,a,71,a)].
given #271 (T,wt=8): 382 ->_s0(length(leq(s(x),0)),length(false)). [ur(41,a,71,a)].
given #272 (T,wt=8): 383 ->_s0(head(leq(s(x),0)),head(false)). [ur(40,a,71,a)].
given #273 (A,wt=9): 137 ->_s0(app(x,app(nil,y)),app(x,y)). [ur(36,a,61,a)].
given #274 (T,wt=8): 386 ->_s0(empty(leq(s(x),0)),empty(false)). [ur(37,a,71,a)].
given #275 (T,wt=8): 514 ->_s0(s(sndsplit(s(x),nil)),s(nil)). [ur(59,a,84,a)].
given #276 (T,wt=8): 519 ->_s0(tail(sndsplit(s(x),nil)),tail(nil)). [ur(54,a,84,a)].
given #277 (T,wt=8): 532 ->_s0(length(sndsplit(s(x),nil)),length(nil)). [ur(41,a,84,a)].
given #278 (A,wt=9): 138 ->_s0(app(app(nil,x),y),app(x,y)). [ur(35,a,61,a)].
given #279 (T,wt=7): 4549 ->*_s0(length(sndsplit(s(x),nil)),0). [ur(87,a,532,a,b,573,a)].
given #280 (T,wt=7): 4583 ->*_s0(app(app(nil,nil),x),x). [ur(87,a,138,a,b,581,a)].
given #281 (T,wt=8): 533 ->_s0(head(sndsplit(s(x),nil)),head(nil)). [ur(40,a,84,a)].
given #282 (T,wt=8): 536 ->_s0(empty(sndsplit(s(x),nil)),empty(nil)). [ur(37,a,84,a)].
given #283 (A,wt=10): 140 ->_s0(f(x,empty(cons(y,z))),f(x,false)). [ur(58,a,62,a)].
given #284 (T,wt=7): 4649 ->*_s0(empty(sndsplit(s(x),nil)),true). [ur(87,a,536,a,b,579,a)].
given #285 (T,wt=8): 539 ->_s0(s(tail(cons(x,y))),s(y)). [ur(59,a,85,a)].
given #286 (T,wt=8): 544 ->_s0(tail(tail(cons(x,y))),tail(y)). [ur(54,a,85,a)].
given #287 (T,wt=8): 557 ->_s0(length(tail(cons(x,y))),length(y)). [ur(41,a,85,a)].
given #288 (A,wt=10): 141 ->_s0(f(empty(cons(x,y)),z),f(false,z)). [ur(57,a,62,a)].
given #289 (T,wt=7): 4793 ->*_s0(length(tail(cons(x,nil))),0). [ur(87,a,557,a,b,573,a)].
given #290 (T,wt=8): 558 ->_s0(head(tail(cons(x,y))),head(y)). [ur(40,a,85,a)].
given #291 (T,wt=8): 561 ->_s0(empty(tail(cons(x,y))),empty(y)). [ur(37,a,85,a)].
given #292 (T,wt=7): 4905 ->*_s0(empty(tail(cons(x,nil))),true). [ur(87,a,561,a,b,579,a)].
given #293 (A,wt=10): 142 ->_s0(cons(x,empty(cons(y,z))),cons(x,false)). [ur(56,a,62,a)].
given #294 (T,wt=8): 574 ->*_s0(length(cons(x,y)),s(length(y))). [ur(87,a,68,a,b,86,a)].
given #295 (T,wt=8): 617 ->*_s0(tail(cons(x,sndsplit(0,y))),y). [ur(87,a,85,a,b,567,a)].
given #296 (T,wt=8): 618 ->*_s0(sndsplit(s(0),cons(x,y)),y). [ur(87,a,83,a,b,567,a)].
given #297 (T,wt=8): 620 ->*_s0(head(cons(sndsplit(0,x),y)),x). [ur(87,a,67,a,b,567,a)].
given #298 (A,wt=10): 143 ->_s0(cons(empty(cons(x,y)),z),cons(false,z)). [ur(55,a,62,a)].
given #299 (T,wt=8): 622 ->*_s0(tail(cons(x,mapf(y,nil))),nil). [ur(87,a,85,a,b,568,a)].
given #300 (T,wt=8): 624 ->*_s0(head(cons(mapf(x,nil),y)),nil). [ur(87,a,67,a,b,568,a)].
given #301 (T,wt=8): 653 ->*_s0(tail(cons(x,leq(0,y))),true). [ur(87,a,85,a,b,572,a)].
given #302 (T,wt=8): 656 ->*_s0(head(cons(leq(0,x),y)),true). [ur(87,a,67,a,b,572,a)].
given #303 (A,wt=10): 145 ->_s0(sndsplit(x,empty(cons(y,z))),sndsplit(x,false)). [ur(53,a,62,a)].
given #304 (T,wt=8): 658 ->*_s0(tail(cons(x,fstsplit(0,y))),nil). [ur(87,a,85,a,b,578,a)].
given #305 (T,wt=8): 660 ->*_s0(head(cons(fstsplit(0,x),y)),nil). [ur(87,a,67,a,b,578,a)].
given #306 (T,wt=8): 662 ->*_s0(tail(cons(x,app(nil,y))),y). [ur(87,a,85,a,b,581,a)].
given #307 (T,wt=8): 664 ->*_s0(head(cons(app(nil,x),y)),x). [ur(87,a,67,a,b,581,a)].
given #308 (A,wt=10): 146 ->_s0(sndsplit(empty(cons(x,y)),z),sndsplit(false,z)). [ur(52,a,62,a)].
given #309 (T,wt=8): 667 ->_s0(s(s(empty(nil))),s(s(true))). [ur(59,a,164,a)].
given #310 (T,wt=8): 672 ->_s0(tail(s(empty(nil))),tail(s(true))). [ur(54,a,164,a)].
given #311 (T,wt=8): 685 ->_s0(length(s(empty(nil))),length(s(true))). [ur(41,a,164,a)].
given #312 (T,wt=8): 686 ->_s0(head(s(empty(nil))),head(s(true))). [ur(40,a,164,a)].
given #313 (A,wt=18): 147 ->_s0(ring(x,y,z,u,w,empty(cons(v5,v6))),ring(x,y,z,u,w,false)). [ur(51,a,62,a)].
given #314 (T,wt=8): 689 ->_s0(empty(s(empty(nil))),empty(s(true))). [ur(37,a,164,a)].
given #315 (T,wt=8): 719 ->_s0(s(tail(empty(nil))),s(tail(true))). [ur(59,a,169,a)].
given #316 (T,wt=8): 724 ->_s0(tail(tail(empty(nil))),tail(tail(true))). [ur(54,a,169,a)].
given #317 (T,wt=8): 737 ->_s0(length(tail(empty(nil))),length(tail(true))). [ur(41,a,169,a)].
given #318 (A,wt=18): 148 ->_s0(ring(x,y,z,u,empty(cons(w,v5)),v6),ring(x,y,z,u,false,v6)). [ur(50,a,62,a)].
given #319 (T,wt=8): 738 ->_s0(head(tail(empty(nil))),head(tail(true))). [ur(40,a,169,a)].
given #320 (T,wt=8): 741 ->_s0(empty(tail(empty(nil))),empty(tail(true))). [ur(37,a,169,a)].
given #321 (T,wt=8): 745 ->_s0(s(length(empty(nil))),s(length(true))). [ur(59,a,182,a)].
given #322 (T,wt=8): 750 ->_s0(tail(length(empty(nil))),tail(length(true))). [ur(54,a,182,a)].
given #323 (A,wt=18): 149 ->_s0(ring(x,y,z,empty(cons(u,w)),v5,v6),ring(x,y,z,false,v5,v6)). [ur(49,a,62,a)].
given #324 (T,wt=8): 763 ->_s0(length(length(empty(nil))),length(length(true))). [ur(41,a,182,a)].
given #325 (T,wt=8): 764 ->_s0(head(length(empty(nil))),head(length(true))). [ur(40,a,182,a)].
given #326 (T,wt=8): 767 ->_s0(empty(length(empty(nil))),empty(length(true))). [ur(37,a,182,a)].
given #327 (T,wt=8): 771 ->_s0(s(head(empty(nil))),s(head(true))). [ur(59,a,183,a)].
given #328 (A,wt=18): 150 ->_s0(ring(x,y,empty(cons(z,u)),w,v5,v6),ring(x,y,false,w,v5,v6)). [ur(48,a,62,a)].
given #329 (T,wt=8): 776 ->_s0(tail(head(empty(nil))),tail(head(true))). [ur(54,a,183,a)].
given #330 (T,wt=8): 789 ->_s0(length(head(empty(nil))),length(head(true))). [ur(41,a,183,a)].
given #331 (T,wt=8): 790 ->_s0(head(head(empty(nil))),head(head(true))). [ur(40,a,183,a)].
given #332 (T,wt=8): 793 ->_s0(empty(head(empty(nil))),empty(head(true))). [ur(37,a,183,a)].
given #333 (A,wt=18): 151 ->_s0(ring(x,empty(cons(y,z)),u,w,v5,v6),ring(x,false,u,w,v5,v6)). [ur(47,a,62,a)].
given #334 (T,wt=8): 797 ->_s0(s(empty(empty(nil))),s(empty(true))). [ur(59,a,186,a)].
given #335 (T,wt=8): 802 ->_s0(tail(empty(empty(nil))),tail(empty(true))). [ur(54,a,186,a)].
given #336 (T,wt=8): 815 ->_s0(length(empty(empty(nil))),length(empty(true))). [ur(41,a,186,a)].
given #337 (T,wt=8): 816 ->_s0(head(empty(empty(nil))),head(empty(true))). [ur(40,a,186,a)].
given #338 (A,wt=18): 152 ->_s0(ring(empty(cons(x,y)),z,u,w,v5,v6),ring(false,z,u,w,v5,v6)). [ur(46,a,62,a)].
given #339 (T,wt=8): 819 ->_s0(empty(empty(empty(nil))),empty(empty(true))). [ur(37,a,186,a)].
given #340 (T,wt=8): 849 ->_s0(s(s(length(nil))),s(s(0))). [ur(59,a,314,a)].
given #341 (T,wt=8): 854 ->_s0(tail(s(length(nil))),tail(s(0))). [ur(54,a,314,a)].
given #342 (T,wt=8): 867 ->_s0(length(s(length(nil))),length(s(0))). [ur(41,a,314,a)].
given #343 (A,wt=10): 153 ->_s0(mapf(x,empty(cons(y,z))),mapf(x,false)). [ur(45,a,62,a)].
given #344 (T,wt=8): 868 ->_s0(head(s(length(nil))),head(s(0))). [ur(40,a,314,a)].
given #345 (T,wt=8): 871 ->_s0(empty(s(length(nil))),empty(s(0))). [ur(37,a,314,a)].
given #346 (T,wt=8): 875 ->_s0(s(tail(length(nil))),s(tail(0))). [ur(59,a,319,a)].
given #347 (T,wt=8): 880 ->_s0(tail(tail(length(nil))),tail(tail(0))). [ur(54,a,319,a)].
given #348 (A,wt=10): 154 ->_s0(mapf(empty(cons(x,y)),z),mapf(false,z)). [ur(44,a,62,a)].
given #349 (T,wt=8): 893 ->_s0(length(tail(length(nil))),length(tail(0))). [ur(41,a,319,a)].
given #350 (T,wt=8): 894 ->_s0(head(tail(length(nil))),head(tail(0))). [ur(40,a,319,a)].
given #351 (T,wt=8): 897 ->_s0(empty(tail(length(nil))),empty(tail(0))). [ur(37,a,319,a)].
given #352 (T,wt=8): 901 ->_s0(s(length(length(nil))),s(length(0))). [ur(59,a,332,a)].
given #353 (A,wt=10): 155 ->_s0(leq(x,empty(cons(y,z))),leq(x,false)). [ur(43,a,62,a)].
given #354 (T,wt=8): 906 ->_s0(tail(length(length(nil))),tail(length(0))). [ur(54,a,332,a)].
given #355 (T,wt=8): 919 ->_s0(length(length(length(nil))),length(length(0))). [ur(41,a,332,a)].
given #356 (T,wt=8): 920 ->_s0(head(length(length(nil))),head(length(0))). [ur(40,a,332,a)].
given #357 (T,wt=8): 923 ->_s0(empty(length(length(nil))),empty(length(0))). [ur(37,a,332,a)].
given #358 (A,wt=10): 156 ->_s0(leq(empty(cons(x,y)),z),leq(false,z)). [ur(42,a,62,a)].
given #359 (T,wt=8): 927 ->_s0(s(head(length(nil))),s(head(0))). [ur(59,a,333,a)].
given #360 (T,wt=8): 932 ->_s0(tail(head(length(nil))),tail(head(0))). [ur(54,a,333,a)].
given #361 (T,wt=8): 945 ->_s0(length(head(length(nil))),length(head(0))). [ur(41,a,333,a)].
given #362 (T,wt=8): 946 ->_s0(head(head(length(nil))),head(head(0))). [ur(40,a,333,a)].
given #363 (A,wt=10): 159 ->_s0(fstsplit(x,empty(cons(y,z))),fstsplit(x,false)). [ur(39,a,62,a)].
given #364 (T,wt=8): 949 ->_s0(empty(head(length(nil))),empty(head(0))). [ur(37,a,333,a)].
given #365 (T,wt=8): 979 ->_s0(s(empty(length(nil))),s(empty(0))). [ur(59,a,336,a)].
given #366 (T,wt=8): 984 ->_s0(tail(empty(length(nil))),tail(empty(0))). [ur(54,a,336,a)].
given #367 (T,wt=8): 997 ->_s0(length(empty(length(nil))),length(empty(0))). [ur(41,a,336,a)].
given #368 (A,wt=10): 160 ->_s0(fstsplit(empty(cons(x,y)),z),fstsplit(false,z)). [ur(38,a,62,a)].
given #369 (T,wt=8): 998 ->_s0(head(empty(length(nil))),head(empty(0))). [ur(40,a,336,a)].
given #370 (T,wt=8): 1001 ->_s0(empty(empty(length(nil))),empty(empty(0))). [ur(37,a,336,a)].
given #371 (T,wt=8): 1005 ->*_s0(sndsplit(0,tail(cons(x,y))),y). [ur(87,a,82,a,b,564,a)].
given #372 (T,wt=8): 1007 ->*_s0(app(nil,tail(cons(x,y))),y). [ur(87,a,61,a,b,564,a)].
given #373 (A,wt=10): 162 ->_s0(app(x,empty(cons(y,z))),app(x,false)). [ur(36,a,62,a)].
given #374 (T,wt=8): 1010 ->*_s0(sndsplit(0,sndsplit(s(x),nil)),nil). [ur(87,a,82,a,b,565,a)].
given #375 (T,wt=8): 1012 ->*_s0(app(nil,sndsplit(s(x),nil)),nil). [ur(87,a,61,a,b,565,a)].
given #376 (T,wt=8): 1014 ->*_s0(sndsplit(0,leq(s(x),0)),false). [ur(87,a,82,a,b,571,a)].
given #377 (T,wt=8): 1015 ->*_s0(leq(s(s(x)),s(0)),false). [ur(87,a,72,a,b,571,a)].
given #378 (A,wt=10): 163 ->_s0(app(empty(cons(x,y)),z),app(false,z)). [ur(35,a,62,a)].
given #379 (T,wt=8): 1017 ->*_s0(app(nil,leq(s(x),0)),false). [ur(87,a,61,a,b,571,a)].
given #380 (T,wt=8): 1046 ->*_s0(sndsplit(0,head(cons(x,y))),x). [ur(87,a,82,a,b,575,a)].
given #381 (T,wt=8): 1048 ->*_s0(app(nil,head(cons(x,y))),x). [ur(87,a,61,a,b,575,a)].
given #382 (T,wt=8): 1050 ->*_s0(sndsplit(0,fstsplit(s(x),nil)),nil). [ur(87,a,82,a,b,576,a)].
given #383 (A,wt=16): 172 ->_s0(ring(x,y,z,u,w,empty(nil)),ring(x,y,z,u,w,true)). [ur(51,a,63,a)].
given #384 (T,wt=8): 1052 ->*_s0(app(nil,fstsplit(s(x),nil)),nil). [ur(87,a,61,a,b,576,a)].
given #385 (T,wt=8): 1054 ->*_s0(sndsplit(0,empty(cons(x,y))),false). [ur(87,a,82,a,b,580,a)].
given #386 (T,wt=8): 1056 ->*_s0(app(nil,empty(cons(x,y))),false). [ur(87,a,61,a,b,580,a)].
given #387 (T,wt=8): 1059 ->*_s0(sndsplit(0,sndsplit(0,length(nil))),0). [ur(87,a,82,a,b,610,a)].
given #388 (A,wt=16): 173 ->_s0(ring(x,y,z,u,empty(nil),w),ring(x,y,z,u,true,w)). [ur(50,a,63,a)].
given #389 (T,wt=8): 1061 ->*_s0(app(nil,sndsplit(0,length(nil))),0). [ur(87,a,61,a,b,610,a)].
given #390 (T,wt=8): 1090 ->*_s0(sndsplit(0,app(nil,length(nil))),0). [ur(87,a,82,a,b,612,a)].
given #391 (T,wt=8): 1092 ->*_s0(app(nil,app(nil,length(nil))),0). [ur(87,a,61,a,b,612,a)].
given #392 (T,wt=8): 1095 ->*_s0(sndsplit(0,sndsplit(0,empty(nil))),true). [ur(87,a,82,a,b,614,a)].
given #393 (A,wt=16): 174 ->_s0(ring(x,y,z,empty(nil),u,w),ring(x,y,z,true,u,w)). [ur(49,a,63,a)].
given #394 (T,wt=8): 1097 ->*_s0(app(nil,sndsplit(0,empty(nil))),true). [ur(87,a,61,a,b,614,a)].
given #395 (T,wt=8): 1099 ->*_s0(sndsplit(0,app(nil,empty(nil))),true). [ur(87,a,82,a,b,616,a)].
given #396 (T,wt=8): 1101 ->*_s0(app(nil,app(nil,empty(nil))),true). [ur(87,a,61,a,b,616,a)].
given #397 (T,wt=8): 1103 ->*_s0(sndsplit(0,s(empty(nil))),s(true)). [ur(87,a,82,a,b,666,a)].
given #398 (A,wt=16): 175 ->_s0(ring(x,y,empty(nil),z,u,w),ring(x,y,true,z,u,w)). [ur(48,a,63,a)].
given #399 (T,wt=8): 1105 ->*_s0(app(nil,s(empty(nil))),s(true)). [ur(87,a,61,a,b,666,a)].
given #400 (T,wt=8): 1133 ->*_s0(sndsplit(0,tail(empty(nil))),tail(true)). [ur(87,a,82,a,b,718,a)].
given #401 (T,wt=8): 1135 ->*_s0(app(nil,tail(empty(nil))),tail(true)). [ur(87,a,61,a,b,718,a)].
given #402 (T,wt=8): 1137 ->*_s0(sndsplit(0,length(empty(nil))),length(true)). [ur(87,a,82,a,b,744,a)].
given #403 (A,wt=16): 176 ->_s0(ring(x,empty(nil),y,z,u,w),ring(x,true,y,z,u,w)). [ur(47,a,63,a)].
given #404 (T,wt=8): 1139 ->*_s0(app(nil,length(empty(nil))),length(true)). [ur(87,a,61,a,b,744,a)].
given #405 (T,wt=8): 1141 ->*_s0(sndsplit(0,head(empty(nil))),head(true)). [ur(87,a,82,a,b,770,a)].
given #406 (T,wt=8): 1143 ->*_s0(app(nil,head(empty(nil))),head(true)). [ur(87,a,61,a,b,770,a)].
given #407 (T,wt=8): 1145 ->*_s0(sndsplit(0,empty(empty(nil))),empty(true)). [ur(87,a,82,a,b,796,a)].
given #408 (A,wt=16): 177 ->_s0(ring(empty(nil),x,y,z,u,w),ring(true,x,y,z,u,w)). [ur(46,a,63,a)].
given #409 (T,wt=8): 1147 ->*_s0(app(nil,empty(empty(nil))),empty(true)). [ur(87,a,61,a,b,796,a)].
given #410 (T,wt=8): 1175 ->*_s0(sndsplit(0,s(length(nil))),s(0)). [ur(87,a,82,a,b,848,a)].
given #411 (T,wt=8): 1178 ->*_s0(app(nil,s(length(nil))),s(0)). [ur(87,a,61,a,b,848,a)].
given #412 (T,wt=8): 1180 ->*_s0(sndsplit(0,tail(length(nil))),tail(0)). [ur(87,a,82,a,b,874,a)].
given #413 (A,wt=9): 190 ->_s0(f(x,fstsplit(0,y)),f(x,nil)). [ur(58,a,64,a)].
given #414 (T,wt=8): 1182 ->*_s0(app(nil,tail(length(nil))),tail(0)). [ur(87,a,61,a,b,874,a)].
given #415 (T,wt=8): 1184 ->*_s0(sndsplit(0,length(length(nil))),length(0)). [ur(87,a,82,a,b,900,a)].
given #416 (T,wt=8): 1186 ->*_s0(app(nil,length(length(nil))),length(0)). [ur(87,a,61,a,b,900,a)].
given #417 (T,wt=8): 1188 ->*_s0(sndsplit(0,head(length(nil))),head(0)). [ur(87,a,82,a,b,926,a)].
given #418 (A,wt=9): 191 ->_s0(f(fstsplit(0,x),y),f(nil,y)). [ur(57,a,64,a)].
given #419 (T,wt=8): 1190 ->*_s0(app(nil,head(length(nil))),head(0)). [ur(87,a,61,a,b,926,a)].
given #420 (T,wt=8): 1218 ->*_s0(sndsplit(0,empty(length(nil))),empty(0)). [ur(87,a,82,a,b,978,a)].
given #421 (T,wt=8): 1220 ->*_s0(app(nil,empty(length(nil))),empty(0)). [ur(87,a,61,a,b,978,a)].
given #422 (T,wt=8): 1221 ->*_s0(s(app(nil,length(nil))),s(0)). [ur(87,a,114,a,b,848,a)].
given #423 (A,wt=9): 192 ->_s0(cons(x,fstsplit(0,y)),cons(x,nil)). [ur(56,a,64,a)].
given #424 (T,wt=8): 1222 ->*_s0(s(app(nil,empty(nil))),s(true)). [ur(87,a,114,a,b,666,a)].
given #425 (T,wt=8): 1249 ->*_s0(tail(app(nil,length(nil))),tail(0)). [ur(87,a,119,a,b,874,a)].
given #426 (T,wt=8): 1250 ->*_s0(tail(app(nil,empty(nil))),tail(true)). [ur(87,a,119,a,b,718,a)].
given #427 (T,wt=8): 1251 ->*_s0(tail(app(nil,cons(x,y))),y). [ur(87,a,119,a,b,564,a)].
given #428 (A,wt=9): 193 ->_s0(cons(fstsplit(0,x),y),cons(nil,y)). [ur(55,a,64,a)].
given #429 (T,wt=8): 1278 ->*_s0(length(app(nil,length(nil))),length(0)). [ur(87,a,132,a,b,900,a)].
given #430 (T,wt=8): 1279 ->*_s0(length(app(nil,empty(nil))),length(true)). [ur(87,a,132,a,b,744,a)].
given #431 (T,wt=8): 1333 ->*_s0(length(app(nil,app(nil,nil))),0). [ur(87,a,132,a,b,1280,a)].
given #432 (T,wt=8): 1335 ->*_s0(sndsplit(0,length(app(nil,nil))),0). [ur(87,a,82,a,b,1280,a)].
given #433 (A,wt=9): 195 ->_s0(sndsplit(x,fstsplit(0,y)),sndsplit(x,nil)). [ur(53,a,64,a)].
given #434 (T,wt=8): 1337 ->*_s0(app(nil,length(app(nil,nil))),0). [ur(87,a,61,a,b,1280,a)].
given #435 (T,wt=8): 1338 ->*_s0(head(app(nil,length(nil))),head(0)). [ur(87,a,133,a,b,926,a)].
given #436 (T,wt=8): 1339 ->*_s0(head(app(nil,empty(nil))),head(true)). [ur(87,a,133,a,b,770,a)].
given #437 (T,wt=8): 1340 ->*_s0(head(app(nil,cons(x,y))),x). [ur(87,a,133,a,b,575,a)].
given #438 (A,wt=9): 196 ->_s0(sndsplit(fstsplit(0,x),y),sndsplit(nil,y)). [ur(52,a,64,a)].
given #439 (T,wt=8): 1367 ->*_s0(empty(app(nil,length(nil))),empty(0)). [ur(87,a,136,a,b,978,a)].
given #440 (T,wt=8): 1368 ->*_s0(empty(app(nil,empty(nil))),empty(true)). [ur(87,a,136,a,b,796,a)].
given #441 (T,wt=8): 1369 ->*_s0(empty(app(nil,cons(x,y))),false). [ur(87,a,136,a,b,580,a)].
given #442 (T,wt=8): 1397 ->*_s0(empty(app(nil,app(nil,nil))),true). [ur(87,a,136,a,b,1370,a)].
given #443 (A,wt=17): 197 ->_s0(ring(x,y,z,u,w,fstsplit(0,v5)),ring(x,y,z,u,w,nil)). [ur(51,a,64,a)].
given #444 (T,wt=8): 1399 ->*_s0(sndsplit(0,empty(app(nil,nil))),true). [ur(87,a,82,a,b,1370,a)].
given #445 (T,wt=8): 1401 ->*_s0(app(nil,empty(app(nil,nil))),true). [ur(87,a,61,a,b,1370,a)].
given #446 (T,wt=8): 1507 ->*_s0(length(app(nil,fstsplit(0,x))),0). [ur(87,a,132,a,b,1480,a)].
given #447 (T,wt=8): 1509 ->*_s0(sndsplit(0,length(fstsplit(0,x))),0). [ur(87,a,82,a,b,1480,a)].
given #448 (A,wt=17): 198 ->_s0(ring(x,y,z,u,fstsplit(0,w),v5),ring(x,y,z,u,nil,v5)). [ur(50,a,64,a)].
given #449 (T,wt=8): 1511 ->*_s0(app(nil,length(fstsplit(0,x))),0). [ur(87,a,61,a,b,1480,a)].
given #450 (T,wt=8): 1591 ->*_s0(empty(app(nil,fstsplit(0,x))),true). [ur(87,a,136,a,b,1564,a)].
given #451 (T,wt=8): 1593 ->*_s0(sndsplit(0,empty(fstsplit(0,x))),true). [ur(87,a,82,a,b,1564,a)].
given #452 (T,wt=8): 1595 ->*_s0(app(nil,empty(fstsplit(0,x))),true). [ur(87,a,61,a,b,1564,a)].
given #453 (A,wt=17): 199 ->_s0(ring(x,y,z,fstsplit(0,u),w,v5),ring(x,y,z,nil,w,v5)). [ur(49,a,64,a)].
given #454 (T,wt=8): 1857 ->*_s0(length(app(nil,mapf(x,nil))),0). [ur(87,a,132,a,b,1830,a)].
given #455 (T,wt=8): 1859 ->*_s0(sndsplit(0,length(mapf(x,nil))),0). [ur(87,a,82,a,b,1830,a)].
given #456 (T,wt=8): 1861 ->*_s0(app(nil,length(mapf(x,nil))),0). [ur(87,a,61,a,b,1830,a)].
given #457 (T,wt=8): 1941 ->*_s0(empty(app(nil,mapf(x,nil))),true). [ur(87,a,136,a,b,1914,a)].
given #458 (A,wt=17): 200 ->_s0(ring(x,y,fstsplit(0,z),u,w,v5),ring(x,y,nil,u,w,v5)). [ur(48,a,64,a)].
given #459 (T,wt=8): 1943 ->*_s0(sndsplit(0,empty(mapf(x,nil))),true). [ur(87,a,82,a,b,1914,a)].
given #460 (T,wt=8): 1945 ->*_s0(app(nil,empty(mapf(x,nil))),true). [ur(87,a,61,a,b,1914,a)].
given #461 (T,wt=8): 1946 ->*_s0(s(sndsplit(0,length(nil))),s(0)). [ur(87,a,464,a,b,848,a)].
given #462 (T,wt=8): 1947 ->*_s0(s(sndsplit(0,empty(nil))),s(true)). [ur(87,a,464,a,b,666,a)].
given #463 (A,wt=17): 201 ->_s0(ring(x,fstsplit(0,y),z,u,w,v5),ring(x,nil,z,u,w,v5)). [ur(47,a,64,a)].
given #464 (T,wt=8): 2000 ->*_s0(tail(sndsplit(0,length(nil))),tail(0)). [ur(87,a,469,a,b,874,a)].
given #465 (T,wt=8): 2001 ->*_s0(tail(sndsplit(0,empty(nil))),tail(true)). [ur(87,a,469,a,b,718,a)].
given #466 (T,wt=8): 2002 ->*_s0(tail(sndsplit(0,cons(x,y))),y). [ur(87,a,469,a,b,564,a)].
given #467 (T,wt=8): 2029 ->*_s0(length(sndsplit(0,mapf(x,nil))),0). [ur(87,a,482,a,b,1830,a)].
given #468 (A,wt=17): 202 ->_s0(ring(fstsplit(0,x),y,z,u,w,v5),ring(nil,y,z,u,w,v5)). [ur(46,a,64,a)].
given #469 (T,wt=8): 2030 ->*_s0(length(sndsplit(0,fstsplit(0,x))),0). [ur(87,a,482,a,b,1480,a)].
given #470 (T,wt=8): 2031 ->*_s0(length(sndsplit(0,app(nil,nil))),0). [ur(87,a,482,a,b,1280,a)].
given #471 (T,wt=8): 2032 ->*_s0(length(sndsplit(0,length(nil))),length(0)). [ur(87,a,482,a,b,900,a)].
given #472 (T,wt=8): 2033 ->*_s0(length(sndsplit(0,empty(nil))),length(true)). [ur(87,a,482,a,b,744,a)].
given #473 (A,wt=9): 203 ->_s0(mapf(x,fstsplit(0,y)),mapf(x,nil)). [ur(45,a,64,a)].
given #474 (T,wt=7): 7829 ->*_s0(mapf(x,fstsplit(0,y)),nil). [ur(87,a,203,a,b,568,a)].
given #475 (T,wt=8): 2061 ->*_s0(length(sndsplit(0,sndsplit(0,nil))),0). [ur(87,a,482,a,b,2034,a)].
given #476 (T,wt=8): 2062 ->*_s0(length(app(nil,sndsplit(0,nil))),0). [ur(87,a,132,a,b,2034,a)].
given #477 (T,wt=8): 2064 ->*_s0(sndsplit(0,length(sndsplit(0,nil))),0). [ur(87,a,82,a,b,2034,a)].
given #478 (A,wt=9): 204 ->_s0(mapf(fstsplit(0,x),y),mapf(nil,y)). [ur(44,a,64,a)].
given #479 (T,wt=8): 2066 ->*_s0(app(nil,length(sndsplit(0,nil))),0). [ur(87,a,61,a,b,2034,a)].
given #480 (T,wt=8): 2067 ->*_s0(head(sndsplit(0,length(nil))),head(0)). [ur(87,a,483,a,b,926,a)].
given #481 (T,wt=8): 2068 ->*_s0(head(sndsplit(0,empty(nil))),head(true)). [ur(87,a,483,a,b,770,a)].
given #482 (T,wt=8): 2069 ->*_s0(head(sndsplit(0,cons(x,y))),x). [ur(87,a,483,a,b,575,a)].
given #483 (A,wt=9): 205 ->_s0(leq(x,fstsplit(0,y)),leq(x,nil)). [ur(43,a,64,a)].
given #484 (T,wt=8): 2122 ->*_s0(empty(sndsplit(0,mapf(x,nil))),true). [ur(87,a,486,a,b,1914,a)].
given #485 (T,wt=8): 2123 ->*_s0(empty(sndsplit(0,fstsplit(0,x))),true). [ur(87,a,486,a,b,1564,a)].
given #486 (T,wt=8): 2124 ->*_s0(empty(sndsplit(0,app(nil,nil))),true). [ur(87,a,486,a,b,1370,a)].
given #487 (T,wt=8): 2125 ->*_s0(empty(sndsplit(0,length(nil))),empty(0)). [ur(87,a,486,a,b,978,a)].
given #488 (A,wt=9): 206 ->_s0(leq(fstsplit(0,x),y),leq(nil,y)). [ur(42,a,64,a)].
given #489 (T,wt=8): 2126 ->*_s0(empty(sndsplit(0,empty(nil))),empty(true)). [ur(87,a,486,a,b,796,a)].
given #490 (T,wt=8): 2127 ->*_s0(empty(sndsplit(0,cons(x,y))),false). [ur(87,a,486,a,b,580,a)].
given #491 (T,wt=8): 2155 ->*_s0(empty(sndsplit(0,sndsplit(0,nil))),true). [ur(87,a,486,a,b,2128,a)].
given #492 (T,wt=8): 2156 ->*_s0(empty(app(nil,sndsplit(0,nil))),true). [ur(87,a,136,a,b,2128,a)].
given #493 (A,wt=9): 209 ->_s0(fstsplit(x,fstsplit(0,y)),fstsplit(x,nil)). [ur(39,a,64,a)].
given #494 (T,wt=8): 2158 ->*_s0(sndsplit(0,empty(sndsplit(0,nil))),true). [ur(87,a,82,a,b,2128,a)].
given #495 (T,wt=8): 2160 ->*_s0(app(nil,empty(sndsplit(0,nil))),true). [ur(87,a,61,a,b,2128,a)].
given #496 (T,wt=8): 2222 ->*_s0(head(app(cons(x,y),z)),x). [ur(87,a,108,a,b,575,a)].
given #497 (T,wt=8): 2360 ->*_s0(empty(app(cons(x,y),z)),false). [ur(87,a,111,a,b,580,a)].
given #498 (A,wt=9): 210 ->_s0(fstsplit(fstsplit(0,x),y),fstsplit(nil,y)). [ur(38,a,64,a)].
given #499 (T,wt=8): 2656 ->*_s0(s(empty(cons(x,y))),s(false)). [ur(87,a,139,a,b,86,a)].
NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.12 sec).
given #500 (T,wt=8): 2708 ->*_s0(tail(empty(cons(x,y))),tail(false)). [ur(87,a,144,a,b,86,a)].
given #501 (T,wt=8): 2734 ->*_s0(length(empty(cons(x,y))),length(false)). [ur(87,a,157,a,b,86,a)].
given #502 (T,wt=8): 2760 ->*_s0(head(empty(cons(x,y))),head(false)). [ur(87,a,158,a,b,86,a)].
given #503 (A,wt=9): 212 ->_s0(app(x,fstsplit(0,y)),app(x,nil)). [ur(36,a,64,a)].
given #504 (T,wt=8): 2786 ->*_s0(empty(empty(cons(x,y))),empty(false)). [ur(87,a,161,a,b,86,a)].
given #505 (T,wt=8): 2812 ->*_s0(sndsplit(s(x),app(nil,nil)),nil). [ur(87,a,120,a,b,565,a)].
given #506 (T,wt=8): 2839 ->*_s0(f(x,empty(nil)),f(x,true)). [ur(87,a,165,a,b,86,a)].
given #507 (T,wt=8): 2865 ->*_s0(f(empty(nil),x),f(true,x)). [ur(87,a,166,a,b,86,a)].
given #508 (A,wt=9): 213 ->_s0(app(fstsplit(0,x),y),app(nil,y)). [ur(35,a,64,a)].
given #509 (T,wt=7): 8265 ->*_s0(app(fstsplit(0,x),y),y). [ur(87,a,213,a,b,581,a)].
given #510 (T,wt=8): 2891 ->*_s0(cons(x,empty(nil)),cons(x,true)). [ur(87,a,167,a,b,86,a)].
given #511 (T,wt=8): 2917 ->*_s0(cons(empty(nil),x),cons(true,x)). [ur(87,a,168,a,b,86,a)].
given #512 (T,wt=8): 2948 ->*_s0(sndsplit(app(nil,0),empty(nil)),true). [ur(87,a,121,a,b,614,a)].
given #513 (A,wt=14): 214 ->_s0(s(fstsplit(s(x),cons(y,z))),s(cons(y,fstsplit(x,z)))). [ur(59,a,65,a)].
given #514 (T,wt=8): 2949 ->*_s0(sndsplit(app(nil,0),length(nil)),0). [ur(87,a,121,a,b,610,a)].
given #515 (T,wt=8): 2951 ->*_s0(sndsplit(app(nil,s(x)),nil),nil). [ur(87,a,121,a,b,565,a)].
given #516 (T,wt=8): 2985 ->*_s0(sndsplit(x,empty(nil)),sndsplit(x,true)). [ur(87,a,170,a,b,86,a)].
given #517 (T,wt=8): 3011 ->*_s0(sndsplit(empty(nil),x),sndsplit(true,x)). [ur(87,a,171,a,b,86,a)].
given #518 (A,wt=16): 215 ->_s0(f(x,fstsplit(s(y),cons(z,u))),f(x,cons(z,fstsplit(y,u)))). [ur(58,a,65,a)].
given #519 (T,wt=8): 3037 ->*_s0(mapf(x,empty(nil)),mapf(x,true)). [ur(87,a,178,a,b,86,a)].
given #520 (T,wt=8): 3089 ->*_s0(mapf(empty(nil),x),mapf(true,x)). [ur(87,a,179,a,b,86,a)].
given #521 (T,wt=8): 3115 ->*_s0(leq(x,empty(nil)),leq(x,true)). [ur(87,a,180,a,b,86,a)].
given #522 (T,wt=8): 3141 ->*_s0(leq(empty(nil),x),leq(true,x)). [ur(87,a,181,a,b,86,a)].
given #523 (A,wt=16): 216 ->_s0(f(fstsplit(s(x),cons(y,z)),u),f(cons(y,fstsplit(x,z)),u)). [ur(57,a,65,a)].
given #524 (T,wt=8): 3167 ->*_s0(fstsplit(x,empty(nil)),fstsplit(x,true)). [ur(87,a,184,a,b,86,a)].
given #525 (T,wt=8): 3219 ->*_s0(fstsplit(empty(nil),x),fstsplit(true,x)). [ur(87,a,185,a,b,86,a)].
given #526 (T,wt=8): 3245 ->*_s0(app(x,empty(nil)),app(x,true)). [ur(87,a,187,a,b,86,a)].
given #527 (T,wt=8): 3271 ->*_s0(app(empty(nil),x),app(true,x)). [ur(87,a,188,a,b,86,a)].
given #528 (A,wt=16): 217 ->_s0(cons(x,fstsplit(s(y),cons(z,u))),cons(x,cons(z,fstsplit(y,u)))). [ur(56,a,65,a)].
given #529 (T,wt=8): 3297 ->*_s0(s(fstsplit(s(x),nil)),s(nil)). [ur(87,a,239,a,b,86,a)].
given #530 (T,wt=8): 3349 ->*_s0(tail(fstsplit(s(x),nil)),tail(nil)). [ur(87,a,244,a,b,86,a)].
given #531 (T,wt=8): 3376 ->*_s0(length(fstsplit(s(x),nil)),length(nil)). [ur(87,a,257,a,b,86,a)].
given #532 (T,wt=8): 3408 ->*_s0(head(fstsplit(s(x),nil)),head(nil)). [ur(87,a,258,a,b,86,a)].
given #533 (A,wt=16): 218 ->_s0(cons(fstsplit(s(x),cons(y,z)),u),cons(cons(y,fstsplit(x,z)),u)). [ur(55,a,65,a)].
given #534 (T,wt=8): 3461 ->*_s0(empty(fstsplit(s(x),nil)),empty(nil)). [ur(87,a,261,a,b,86,a)].
given #535 (T,wt=8): 3500 ->*_s0(s(head(cons(x,y))),s(x)). [ur(87,a,264,a,b,86,a)].
given #536 (T,wt=8): 3536 ->*_s0(tail(head(cons(x,y))),tail(x)). [ur(87,a,269,a,b,86,a)].
given #537 (T,wt=8): 3602 ->*_s0(length(head(cons(x,y))),length(x)). [ur(87,a,282,a,b,86,a)].
given #538 (A,wt=14): 219 ->_s0(tail(fstsplit(s(x),cons(y,z))),tail(cons(y,fstsplit(x,z)))). [ur(54,a,65,a)].
given #539 (T,wt=8): 3645 ->*_s0(head(head(cons(x,y))),head(x)). [ur(87,a,283,a,b,86,a)].
given #540 (T,wt=8): 3685 ->*_s0(empty(head(cons(x,y))),empty(x)). [ur(87,a,286,a,b,86,a)].
given #541 (T,wt=8): 3744 ->*_s0(f(x,length(nil)),f(x,0)). [ur(87,a,315,a,b,86,a)].
given #542 (T,wt=8): 3770 ->*_s0(f(length(nil),x),f(0,x)). [ur(87,a,316,a,b,86,a)].
given #543 (A,wt=16): 220 ->_s0(sndsplit(x,fstsplit(s(y),cons(z,u))),sndsplit(x,cons(z,fstsplit(y,u)))). [ur(53,a,65,a)].
given #544 (T,wt=8): 3796 ->*_s0(cons(x,length(nil)),cons(x,0)). [ur(87,a,317,a,b,86,a)].
given #545 (T,wt=8): 3854 ->*_s0(cons(length(nil),x),cons(0,x)). [ur(87,a,318,a,b,86,a)].
given #546 (T,wt=8): 3880 ->*_s0(sndsplit(x,length(nil)),sndsplit(x,0)). [ur(87,a,320,a,b,86,a)].
given #547 (T,wt=8): 3906 ->*_s0(sndsplit(length(nil),app(nil,x)),x). [ur(87,a,321,a,b,663,a)].
given #548 (A,wt=16): 221 ->_s0(sndsplit(fstsplit(s(x),cons(y,z)),u),sndsplit(cons(y,fstsplit(x,z)),u)). [ur(52,a,65,a)].
given #549 (T,wt=8): 3907 ->*_s0(sndsplit(length(nil),fstsplit(0,x)),nil). [ur(87,a,321,a,b,659,a)].
given #550 (T,wt=8): 3908 ->*_s0(sndsplit(length(nil),leq(0,x)),true). [ur(87,a,321,a,b,654,a)].
given #551 (T,wt=8): 3909 ->*_s0(sndsplit(length(nil),mapf(x,nil)),nil). [ur(87,a,321,a,b,623,a)].
given #552 (T,wt=8): 3910 ->*_s0(sndsplit(length(nil),sndsplit(0,x)),x). [ur(87,a,321,a,b,619,a)].
given #553 (A,wt=24): 222 ->_s0(ring(x,y,z,u,w,fstsplit(s(v5),cons(v6,v7))),ring(x,y,z,u,w,cons(v6,fstsplit(v5,v7)))). [ur(51,a,65,a)].
given #554 (T,wt=8): 3914 ->*_s0(sndsplit(length(nil),x),sndsplit(0,x)). [ur(87,a,321,a,b,86,a)].
given #555 (T,wt=8): 3966 ->*_s0(sndsplit(app(nil,length(nil)),x),x). [ur(87,a,121,a,b,3913,a)].
given #556 (T,wt=8): 3970 ->*_s0(sndsplit(0,sndsplit(length(nil),x)),x). [ur(87,a,82,a,b,3913,a)].
given #557 (T,wt=8): 3972 ->*_s0(app(nil,sndsplit(length(nil),x)),x). [ur(87,a,61,a,b,3913,a)].
given #558 (A,wt=24): 223 ->_s0(ring(x,y,z,u,fstsplit(s(w),cons(v5,v6)),v7),ring(x,y,z,u,cons(v5,fstsplit(w,v6)),v7)). [ur(50,a,65,a)].
given #559 (T,wt=8): 3987 ->*_s0(mapf(x,length(nil)),mapf(x,0)). [ur(87,a,328,a,b,86,a)].
given #560 (T,wt=8): 4014 ->*_s0(leq(s(x),app(nil,0)),false). [ur(87,a,130,a,b,571,a)].
given #561 (T,wt=8): 4041 ->*_s0(mapf(length(nil),x),mapf(0,x)). [ur(87,a,329,a,b,86,a)].
given #562 (T,wt=8): 4068 ->*_s0(leq(x,length(nil)),leq(x,0)). [ur(87,a,330,a,b,86,a)].
given #563 (A,wt=24): 224 ->_s0(ring(x,y,z,fstsplit(s(u),cons(w,v5)),v6,v7),ring(x,y,z,cons(w,fstsplit(u,v5)),v6,v7)). [ur(49,a,65,a)].
given #564 (T,wt=8): 4101 ->*_s0(leq(length(nil),x),leq(0,x)). [ur(87,a,331,a,b,86,a)].
given #565 (T,wt=8): 4130 ->*_s0(leq(app(nil,s(x)),0),false). [ur(87,a,131,a,b,571,a)].
given #566 (T,wt=8): 4158 ->*_s0(leq(app(nil,length(nil)),x),true). [ur(87,a,131,a,b,4100,a)].
given #567 (T,wt=8): 4160 ->*_s0(sndsplit(0,leq(length(nil),x)),true). [ur(87,a,82,a,b,4100,a)].
given #568 (A,wt=24): 225 ->_s0(ring(x,y,fstsplit(s(z),cons(u,w)),v5,v6,v7),ring(x,y,cons(u,fstsplit(z,w)),v5,v6,v7)). [ur(48,a,65,a)].
Low Water (keep): wt=24.000, iters=8863
given #569 (F,wt=18): 9004 -->*_s0(empty(fstsplit(app(nil,length(nil)),x)),false) | -->*_s0(empty(fstsplit(app(nil,length(nil)),y)),false) # answer(goal). [resolve(4158,a,88,c),unit_del(a,4158)].
given #570 (T,wt=8): 4161 ->*_s0(leq(s(length(nil)),s(x)),true). [ur(87,a,72,a,b,4100,a)].
given #571 (T,wt=8): 4163 ->*_s0(app(nil,leq(length(nil),x)),true). [ur(87,a,61,a,b,4100,a)].
given #572 (T,wt=8): 4171 ->*_s0(fstsplit(x,length(nil)),fstsplit(x,0)). [ur(87,a,334,a,b,86,a)].
given #573 (T,wt=8): 4198 ->*_s0(fstsplit(length(nil),x),fstsplit(0,x)). [ur(87,a,335,a,b,86,a)].
given #574 (A,wt=24): 226 ->_s0(ring(x,fstsplit(s(y),cons(z,u)),w,v5,v6,v7),ring(x,cons(z,fstsplit(y,u)),w,v5,v6,v7)). [ur(47,a,65,a)].
given #575 (T,wt=8): 4224 ->*_s0(fstsplit(s(x),app(nil,nil)),nil). [ur(87,a,134,a,b,576,a)].
given #576 (T,wt=8): 4252 ->*_s0(sndsplit(0,fstsplit(length(nil),x)),nil). [ur(87,a,82,a,b,4197,a)].
given #577 (T,wt=8): 4254 ->*_s0(app(nil,fstsplit(length(nil),x)),nil). [ur(87,a,61,a,b,4197,a)].
given #578 (T,wt=8): 4255 ->*_s0(app(x,length(nil)),app(x,0)). [ur(87,a,337,a,b,86,a)].
given #579 (A,wt=24): 227 ->_s0(ring(fstsplit(s(x),cons(y,z)),u,w,v5,v6,v7),ring(cons(y,fstsplit(x,z)),u,w,v5,v6,v7)). [ur(46,a,65,a)].
given #580 (T,wt=8): 4281 ->*_s0(app(length(nil),x),app(0,x)). [ur(87,a,338,a,b,86,a)].
given #581 (T,wt=8): 4307 ->*_s0(s(leq(s(x),0)),s(false)). [ur(87,a,364,a,b,86,a)].
given #582 (T,wt=8): 4333 ->*_s0(fstsplit(app(nil,length(nil)),x),nil). [ur(87,a,135,a,b,4197,a)].
given #583 (T,wt=8): 4335 ->*_s0(fstsplit(app(nil,s(x)),nil),nil). [ur(87,a,135,a,b,576,a)].
given #584 (A,wt=16): 228 ->_s0(mapf(x,fstsplit(s(y),cons(z,u))),mapf(x,cons(z,fstsplit(y,u)))). [ur(45,a,65,a)].
given #585 (T,wt=8): 4367 ->*_s0(tail(leq(s(x),0)),tail(false)). [ur(87,a,369,a,b,86,a)].
given #586 (T,wt=8): 4393 ->*_s0(length(leq(s(x),0)),length(false)). [ur(87,a,382,a,b,86,a)].
given #587 (T,wt=8): 4419 ->*_s0(head(leq(s(x),0)),head(false)). [ur(87,a,383,a,b,86,a)].
given #588 (T,wt=8): 4471 ->*_s0(empty(leq(s(x),0)),empty(false)). [ur(87,a,386,a,b,86,a)].
given #589 (A,wt=16): 229 ->_s0(mapf(fstsplit(s(x),cons(y,z)),u),mapf(cons(y,fstsplit(x,z)),u)). [ur(44,a,65,a)].
given #590 (T,wt=8): 4497 ->*_s0(s(sndsplit(s(x),nil)),s(nil)). [ur(87,a,514,a,b,86,a)].
given #591 (T,wt=8): 4523 ->*_s0(tail(sndsplit(s(x),nil)),tail(nil)). [ur(87,a,519,a,b,86,a)].
given #592 (T,wt=8): 4550 ->*_s0(length(sndsplit(s(x),nil)),length(nil)). [ur(87,a,532,a,b,86,a)].
given #593 (T,wt=8): 4581 ->*_s0(app(app(nil,nil),empty(nil)),true). [ur(87,a,138,a,b,616,a)].
given #594 (A,wt=16): 230 ->_s0(leq(x,fstsplit(s(y),cons(z,u))),leq(x,cons(z,fstsplit(y,u)))). [ur(43,a,65,a)].
given #595 (T,wt=8): 4582 ->*_s0(app(app(nil,nil),length(nil)),0). [ur(87,a,138,a,b,612,a)].
given #596 (T,wt=8): 4623 ->*_s0(head(sndsplit(s(x),nil)),head(nil)). [ur(87,a,533,a,b,86,a)].
given #597 (T,wt=8): 4650 ->*_s0(empty(sndsplit(s(x),nil)),empty(nil)). [ur(87,a,536,a,b,86,a)].
given #598 (T,wt=8): 4716 ->*_s0(s(tail(cons(x,y))),s(y)). [ur(87,a,539,a,b,86,a)].
given #599 (A,wt=16): 231 ->_s0(leq(fstsplit(s(x),cons(y,z)),u),leq(cons(y,fstsplit(x,z)),u)). [ur(42,a,65,a)].
given #600 (T,wt=8): 4752 ->*_s0(tail(tail(cons(x,y))),tail(y)). [ur(87,a,544,a,b,86,a)].
given #601 (T,wt=8): 4794 ->*_s0(length(tail(cons(x,y))),length(y)). [ur(87,a,557,a,b,86,a)].
given #602 (T,wt=8): 4864 ->*_s0(head(tail(cons(x,y))),head(y)). [ur(87,a,558,a,b,86,a)].
given #603 (T,wt=8): 4906 ->*_s0(empty(tail(cons(x,y))),empty(y)). [ur(87,a,561,a,b,86,a)].
given #604 (A,wt=14): 232 ->_s0(length(fstsplit(s(x),cons(y,z))),length(cons(y,fstsplit(x,z)))). [ur(41,a,65,a)].
given #605 (T,wt=8): 5109 ->*_s0(tail(app(cons(x,nil),y)),y). [ur(87,a,94,a,b,662,a)].
given #606 (T,wt=8): 5149 ->*_s0(s(s(empty(nil))),s(s(true))). [ur(87,a,667,a,b,86,a)].
given #607 (T,wt=8): 5175 ->*_s0(tail(s(empty(nil))),tail(s(true))). [ur(87,a,672,a,b,86,a)].
given #608 (T,wt=8): 5201 ->*_s0(length(s(empty(nil))),length(s(true))). [ur(87,a,685,a,b,86,a)].
given #609 (A,wt=14): 233 ->_s0(head(fstsplit(s(x),cons(y,z))),head(cons(y,fstsplit(x,z)))). [ur(40,a,65,a)].
given #610 (T,wt=8): 5227 ->*_s0(head(s(empty(nil))),head(s(true))). [ur(87,a,686,a,b,86,a)].
given #611 (T,wt=8): 5279 ->*_s0(empty(s(empty(nil))),empty(s(true))). [ur(87,a,689,a,b,86,a)].
given #612 (T,wt=8): 5305 ->*_s0(s(tail(empty(nil))),s(tail(true))). [ur(87,a,719,a,b,86,a)].
given #613 (T,wt=8): 5331 ->*_s0(tail(tail(empty(nil))),tail(tail(true))). [ur(87,a,724,a,b,86,a)].
given #614 (A,wt=16): 234 ->_s0(fstsplit(x,fstsplit(s(y),cons(z,u))),fstsplit(x,cons(z,fstsplit(y,u)))). [ur(39,a,65,a)].
given #615 (T,wt=8): 5357 ->*_s0(length(tail(empty(nil))),length(tail(true))). [ur(87,a,737,a,b,86,a)].
given #616 (T,wt=8): 5409 ->*_s0(head(tail(empty(nil))),head(tail(true))). [ur(87,a,738,a,b,86,a)].
given #617 (T,wt=8): 5435 ->*_s0(empty(tail(empty(nil))),empty(tail(true))). [ur(87,a,741,a,b,86,a)].
given #618 (T,wt=8): 5461 ->*_s0(s(length(empty(nil))),s(length(true))). [ur(87,a,745,a,b,86,a)].
given #619 (A,wt=16): 235 ->_s0(fstsplit(fstsplit(s(x),cons(y,z)),u),fstsplit(cons(y,fstsplit(x,z)),u)). [ur(38,a,65,a)].
given #620 (T,wt=8): 5487 ->*_s0(tail(length(empty(nil))),tail(length(true))). [ur(87,a,750,a,b,86,a)].
given #621 (T,wt=8): 5539 ->*_s0(length(length(empty(nil))),length(length(true))). [ur(87,a,763,a,b,86,a)].
given #622 (T,wt=8): 5565 ->*_s0(head(length(empty(nil))),head(length(true))). [ur(87,a,764,a,b,86,a)].
given #623 (T,wt=8): 5591 ->*_s0(empty(length(empty(nil))),empty(length(true))). [ur(87,a,767,a,b,86,a)].
given #624 (A,wt=14): 236 ->_s0(empty(fstsplit(s(x),cons(y,z))),empty(cons(y,fstsplit(x,z)))). [ur(37,a,65,a)].
given #625 (T,wt=8): 5617 ->*_s0(s(head(empty(nil))),s(head(true))). [ur(87,a,771,a,b,86,a)].
given #626 (T,wt=8): 5669 ->*_s0(tail(head(empty(nil))),tail(head(true))). [ur(87,a,776,a,b,86,a)].
given #627 (T,wt=8): 5695 ->*_s0(length(head(empty(nil))),length(head(true))). [ur(87,a,789,a,b,86,a)].
given #628 (T,wt=8): 5721 ->*_s0(head(head(empty(nil))),head(head(true))). [ur(87,a,790,a,b,86,a)].
given #629 (A,wt=16): 237 ->_s0(app(x,fstsplit(s(y),cons(z,u))),app(x,cons(z,fstsplit(y,u)))). [ur(36,a,65,a)].
given #630 (T,wt=8): 5747 ->*_s0(empty(head(empty(nil))),empty(head(true))). [ur(87,a,793,a,b,86,a)].
given #631 (T,wt=8): 5799 ->*_s0(s(empty(empty(nil))),s(empty(true))). [ur(87,a,797,a,b,86,a)].
given #632 (T,wt=8): 5825 ->*_s0(tail(empty(empty(nil))),tail(empty(true))). [ur(87,a,802,a,b,86,a)].
given #633 (T,wt=8): 5851 ->*_s0(length(empty(empty(nil))),length(empty(true))). [ur(87,a,815,a,b,86,a)].
given #634 (A,wt=16): 238 ->_s0(app(fstsplit(s(x),cons(y,z)),u),app(cons(y,fstsplit(x,z)),u)). [ur(35,a,65,a)].
given #635 (T,wt=8): 5877 ->*_s0(head(empty(empty(nil))),head(empty(true))). [ur(87,a,816,a,b,86,a)].
given #636 (T,wt=8): 5929 ->*_s0(empty(empty(empty(nil))),empty(empty(true))). [ur(87,a,819,a,b,86,a)].
given #637 (T,wt=8): 5955 ->*_s0(s(s(length(nil))),s(s(0))). [ur(87,a,849,a,b,86,a)].
given #638 (T,wt=8): 5981 ->*_s0(tail(s(length(nil))),tail(s(0))). [ur(87,a,854,a,b,86,a)].
given #639 (A,wt=10): 240 ->_s0(f(x,fstsplit(s(y),nil)),f(x,nil)). [ur(58,a,66,a)].
given #640 (T,wt=8): 6007 ->*_s0(length(s(length(nil))),length(s(0))). [ur(87,a,867,a,b,86,a)].
given #641 (T,wt=8): 6059 ->*_s0(head(s(length(nil))),head(s(0))). [ur(87,a,868,a,b,86,a)].
given #642 (T,wt=8): 6085 ->*_s0(empty(s(length(nil))),empty(s(0))). [ur(87,a,871,a,b,86,a)].
given #643 (T,wt=8): 6111 ->*_s0(s(tail(length(nil))),s(tail(0))). [ur(87,a,875,a,b,86,a)].
given #644 (A,wt=10): 241 ->_s0(f(fstsplit(s(x),nil),y),f(nil,y)). [ur(57,a,66,a)].
given #645 (T,wt=8): 6137 ->*_s0(tail(tail(length(nil))),tail(tail(0))). [ur(87,a,880,a,b,86,a)].
given #646 (T,wt=8): 6189 ->*_s0(length(tail(length(nil))),length(tail(0))). [ur(87,a,893,a,b,86,a)].
given #647 (T,wt=8): 6215 ->*_s0(head(tail(length(nil))),head(tail(0))). [ur(87,a,894,a,b,86,a)].
given #648 (T,wt=8): 6241 ->*_s0(empty(tail(length(nil))),empty(tail(0))). [ur(87,a,897,a,b,86,a)].
given #649 (A,wt=10): 242 ->_s0(cons(x,fstsplit(s(y),nil)),cons(x,nil)). [ur(56,a,66,a)].
given #650 (T,wt=8): 6267 ->*_s0(s(length(length(nil))),s(length(0))). [ur(87,a,901,a,b,86,a)].
given #651 (T,wt=8): 6319 ->*_s0(tail(length(length(nil))),tail(length(0))). [ur(87,a,906,a,b,86,a)].
given #652 (T,wt=8): 6345 ->*_s0(length(length(length(nil))),length(length(0))). [ur(87,a,919,a,b,86,a)].
given #653 (T,wt=8): 6371 ->*_s0(head(length(length(nil))),head(length(0))). [ur(87,a,920,a,b,86,a)].
given #654 (A,wt=10): 243 ->_s0(cons(fstsplit(s(x),nil),y),cons(nil,y)). [ur(55,a,66,a)].
given #655 (T,wt=8): 6397 ->*_s0(empty(length(length(nil))),empty(length(0))). [ur(87,a,923,a,b,86,a)].
given #656 (T,wt=8): 6449 ->*_s0(s(head(length(nil))),s(head(0))). [ur(87,a,927,a,b,86,a)].
given #657 (T,wt=8): 6475 ->*_s0(tail(head(length(nil))),tail(head(0))). [ur(87,a,932,a,b,86,a)].
given #658 (T,wt=8): 6501 ->*_s0(length(head(length(nil))),length(head(0))). [ur(87,a,945,a,b,86,a)].
given #659 (A,wt=10): 245 ->_s0(sndsplit(x,fstsplit(s(y),nil)),sndsplit(x,nil)). [ur(53,a,66,a)].
given #660 (T,wt=8): 6527 ->*_s0(head(head(length(nil))),head(head(0))). [ur(87,a,946,a,b,86,a)].
given #661 (T,wt=8): 6579 ->*_s0(empty(head(length(nil))),empty(head(0))). [ur(87,a,949,a,b,86,a)].
given #662 (T,wt=8): 6605 ->*_s0(s(empty(length(nil))),s(empty(0))). [ur(87,a,979,a,b,86,a)].
given #663 (T,wt=8): 6631 ->*_s0(tail(empty(length(nil))),tail(empty(0))). [ur(87,a,984,a,b,86,a)].
given #664 (A,wt=10): 246 ->_s0(sndsplit(fstsplit(s(x),nil),y),sndsplit(nil,y)). [ur(52,a,66,a)].
given #665 (T,wt=8): 6657 ->*_s0(length(empty(length(nil))),length(empty(0))). [ur(87,a,997,a,b,86,a)].
given #666 (T,wt=8): 6709 ->*_s0(head(empty(length(nil))),head(empty(0))). [ur(87,a,998,a,b,86,a)].
given #667 (T,wt=8): 6735 ->*_s0(empty(empty(length(nil))),empty(empty(0))). [ur(87,a,1001,a,b,86,a)].
given #668 (T,wt=8): 7388 ->*_s0(sndsplit(s(x),fstsplit(0,y)),nil). [ur(87,a,195,a,b,565,a)].
given #669 (A,wt=18): 247 ->_s0(ring(x,y,z,u,w,fstsplit(s(v5),nil)),ring(x,y,z,u,w,nil)). [ur(51,a,66,a)].
given #670 (T,wt=8): 8055 ->*_s0(fstsplit(s(x),fstsplit(0,y)),nil). [ur(87,a,209,a,b,576,a)].
given #671 (T,wt=8): 8263 ->*_s0(app(fstsplit(0,x),empty(nil)),true). [ur(87,a,213,a,b,616,a)].
given #672 (T,wt=8): 8264 ->*_s0(app(fstsplit(0,x),length(nil)),0). [ur(87,a,213,a,b,612,a)].
given #673 (T,wt=9): 340 ->_s0(f(x,leq(0,y)),f(x,true)). [ur(58,a,70,a)].
given #674 (A,wt=18): 248 ->_s0(ring(x,y,z,u,fstsplit(s(w),nil),v5),ring(x,y,z,u,nil,v5)). [ur(50,a,66,a)].
given #675 (T,wt=9): 341 ->_s0(f(leq(0,x),y),f(true,y)). [ur(57,a,70,a)].
given #676 (T,wt=9): 342 ->_s0(cons(x,leq(0,y)),cons(x,true)). [ur(56,a,70,a)].
given #677 (T,wt=9): 343 ->_s0(cons(leq(0,x),y),cons(true,y)). [ur(55,a,70,a)].
given #678 (T,wt=9): 345 ->_s0(sndsplit(x,leq(0,y)),sndsplit(x,true)). [ur(53,a,70,a)].
given #679 (A,wt=18): 249 ->_s0(ring(x,y,z,fstsplit(s(u),nil),w,v5),ring(x,y,z,nil,w,v5)). [ur(49,a,66,a)].
given #680 (T,wt=9): 346 ->_s0(sndsplit(leq(0,x),y),sndsplit(true,y)). [ur(52,a,70,a)].
given #681 (T,wt=9): 353 ->_s0(mapf(x,leq(0,y)),mapf(x,true)). [ur(45,a,70,a)].
given #682 (T,wt=9): 354 ->_s0(mapf(leq(0,x),y),mapf(true,y)). [ur(44,a,70,a)].
given #683 (T,wt=9): 355 ->_s0(leq(x,leq(0,y)),leq(x,true)). [ur(43,a,70,a)].
given #684 (A,wt=18): 250 ->_s0(ring(x,y,fstsplit(s(z),nil),u,w,v5),ring(x,y,nil,u,w,v5)). [ur(48,a,66,a)].
given #685 (T,wt=9): 356 ->_s0(leq(leq(0,x),y),leq(true,y)). [ur(42,a,70,a)].
given #686 (T,wt=9): 359 ->_s0(fstsplit(x,leq(0,y)),fstsplit(x,true)). [ur(39,a,70,a)].
given #687 (T,wt=9): 360 ->_s0(fstsplit(leq(0,x),y),fstsplit(true,y)). [ur(38,a,70,a)].
given #688 (T,wt=9): 362 ->_s0(app(x,leq(0,y)),app(x,true)). [ur(36,a,70,a)].
given #689 (A,wt=18): 251 ->_s0(ring(x,fstsplit(s(y),nil),z,u,w,v5),ring(x,nil,z,u,w,v5)). [ur(47,a,66,a)].
given #690 (T,wt=9): 363 ->_s0(app(leq(0,x),y),app(true,y)). [ur(35,a,70,a)].
given #691 (T,wt=9): 440 ->_s0(f(x,mapf(y,nil)),f(x,nil)). [ur(58,a,74,a)].
given #692 (T,wt=9): 441 ->_s0(f(mapf(x,nil),y),f(nil,y)). [ur(57,a,74,a)].
given #693 (T,wt=9): 442 ->_s0(cons(x,mapf(y,nil)),cons(x,nil)). [ur(56,a,74,a)].
given #694 (A,wt=18): 252 ->_s0(ring(fstsplit(s(x),nil),y,z,u,w,v5),ring(nil,y,z,u,w,v5)). [ur(46,a,66,a)].
given #695 (T,wt=9): 443 ->_s0(cons(mapf(x,nil),y),cons(nil,y)). [ur(55,a,74,a)].
given #696 (T,wt=9): 445 ->_s0(sndsplit(x,mapf(y,nil)),sndsplit(x,nil)). [ur(53,a,74,a)].
given #697 (T,wt=8): 10861 ->*_s0(sndsplit(s(x),mapf(y,nil)),nil). [ur(87,a,445,a,b,565,a)].
given #698 (T,wt=9): 446 ->_s0(sndsplit(mapf(x,nil),y),sndsplit(nil,y)). [ur(52,a,74,a)].
given #699 (A,wt=10): 253 ->_s0(mapf(x,fstsplit(s(y),nil)),mapf(x,nil)). [ur(45,a,66,a)].
given #700 (T,wt=8): 10924 ->*_s0(mapf(x,fstsplit(s(y),nil)),nil). [ur(87,a,253,a,b,568,a)].
given #701 (T,wt=9): 453 ->_s0(mapf(x,mapf(y,nil)),mapf(x,nil)). [ur(45,a,74,a)].
given #702 (T,wt=7): 10958 ->*_s0(mapf(x,mapf(y,nil)),nil). [ur(87,a,453,a,b,568,a)].
given #703 (T,wt=9): 454 ->_s0(mapf(mapf(x,nil),y),mapf(nil,y)). [ur(44,a,74,a)].
given #704 (A,wt=10): 254 ->_s0(mapf(fstsplit(s(x),nil),y),mapf(nil,y)). [ur(44,a,66,a)].
given #705 (T,wt=9): 455 ->_s0(leq(x,mapf(y,nil)),leq(x,nil)). [ur(43,a,74,a)].
given #706 (T,wt=9): 456 ->_s0(leq(mapf(x,nil),y),leq(nil,y)). [ur(42,a,74,a)].
given #707 (T,wt=9): 459 ->_s0(fstsplit(x,mapf(y,nil)),fstsplit(x,nil)). [ur(39,a,74,a)].
given #708 (T,wt=8): 11105 ->*_s0(fstsplit(s(x),mapf(y,nil)),nil). [ur(87,a,459,a,b,576,a)].
given #709 (A,wt=10): 255 ->_s0(leq(x,fstsplit(s(y),nil)),leq(x,nil)). [ur(43,a,66,a)].
given #710 (T,wt=9): 460 ->_s0(fstsplit(mapf(x,nil),y),fstsplit(nil,y)). [ur(38,a,74,a)].
given #711 (T,wt=9): 462 ->_s0(app(x,mapf(y,nil)),app(x,nil)). [ur(36,a,74,a)].
given #712 (T,wt=9): 463 ->_s0(app(mapf(x,nil),y),app(nil,y)). [ur(35,a,74,a)].
given #713 (T,wt=7): 11261 ->*_s0(app(mapf(x,nil),y),y). [ur(87,a,463,a,b,581,a)].
given #714 (A,wt=10): 256 ->_s0(leq(fstsplit(s(x),nil),y),leq(nil,y)). [ur(42,a,66,a)].
given #715 (T,wt=8): 11259 ->*_s0(app(mapf(x,nil),empty(nil)),true). [ur(87,a,463,a,b,616,a)].
given #716 (T,wt=8): 11260 ->*_s0(app(mapf(x,nil),length(nil)),0). [ur(87,a,463,a,b,612,a)].
given #717 (T,wt=9): 465 ->_s0(f(x,sndsplit(0,y)),f(x,y)). [ur(58,a,82,a)].
given #718 (T,wt=9): 466 ->_s0(f(sndsplit(0,x),y),f(x,y)). [ur(57,a,82,a)].
given #719 (A,wt=10): 259 ->_s0(fstsplit(x,fstsplit(s(y),nil)),fstsplit(x,nil)). [ur(39,a,66,a)].
given #720 (T,wt=9): 467 ->_s0(cons(x,sndsplit(0,y)),cons(x,y)). [ur(56,a,82,a)].
given #721 (T,wt=9): 468 ->_s0(cons(sndsplit(0,x),y),cons(x,y)). [ur(55,a,82,a)].
given #722 (T,wt=9): 470 ->_s0(sndsplit(x,sndsplit(0,y)),sndsplit(x,y)). [ur(53,a,82,a)].
given #723 (T,wt=8): 11496 ->*_s0(sndsplit(s(x),sndsplit(0,nil)),nil). [ur(87,a,470,a,b,565,a)].
given #724 (A,wt=10): 260 ->_s0(fstsplit(fstsplit(s(x),nil),y),fstsplit(nil,y)). [ur(38,a,66,a)].
given #725 (T,wt=9): 471 ->_s0(sndsplit(sndsplit(0,x),y),sndsplit(x,y)). [ur(52,a,82,a)].
given #726 (T,wt=7): 11618 ->*_s0(sndsplit(sndsplit(0,0),x),x). [ur(87,a,471,a,b,567,a)].
given #727 (T,wt=8): 11566 ->*_s0(sndsplit(sndsplit(0,length(nil)),x),x). [ur(87,a,471,a,b,3913,a)].
given #728 (T,wt=8): 11616 ->*_s0(sndsplit(sndsplit(0,0),empty(nil)),true). [ur(87,a,471,a,b,614,a)].
given #729 (A,wt=10): 262 ->_s0(app(x,fstsplit(s(y),nil)),app(x,nil)). [ur(36,a,66,a)].
given #730 (T,wt=8): 11617 ->*_s0(sndsplit(sndsplit(0,0),length(nil)),0). [ur(87,a,471,a,b,610,a)].
given #731 (T,wt=8): 11619 ->*_s0(sndsplit(sndsplit(0,s(x)),nil),nil). [ur(87,a,471,a,b,565,a)].
given #732 (T,wt=9): 478 ->_s0(mapf(x,sndsplit(0,y)),mapf(x,y)). [ur(45,a,82,a)].
given #733 (T,wt=7): 11724 ->*_s0(mapf(x,sndsplit(0,nil)),nil). [ur(87,a,478,a,b,568,a)].
given #734 (A,wt=10): 263 ->_s0(app(fstsplit(s(x),nil),y),app(nil,y)). [ur(35,a,66,a)].
given #735 (T,wt=8): 11797 ->*_s0(app(fstsplit(s(x),nil),y),y). [ur(87,a,263,a,b,581,a)].
given #736 (T,wt=9): 479 ->_s0(mapf(sndsplit(0,x),y),mapf(x,y)). [ur(44,a,82,a)].
given #737 (T,wt=9): 480 ->_s0(leq(x,sndsplit(0,y)),leq(x,y)). [ur(43,a,82,a)].
given #738 (T,wt=8): 11871 ->*_s0(leq(s(x),sndsplit(0,0)),false). [ur(87,a,480,a,b,571,a)].
given #739 (A,wt=10): 265 ->_s0(f(x,head(cons(y,z))),f(x,y)). [ur(58,a,67,a)].
given #740 (T,wt=9): 481 ->_s0(leq(sndsplit(0,x),y),leq(x,y)). [ur(42,a,82,a)].
given #741 (T,wt=7): 11949 ->*_s0(leq(sndsplit(0,0),x),true). [ur(87,a,481,a,b,572,a)].
given #742 (T,wt=8): 11941 ->*_s0(leq(sndsplit(0,length(nil)),x),true). [ur(87,a,481,a,b,4100,a)].
Low Water (keep): wt=13.000, iters=8037
Low Water (keep): wt=12.000, iters=6968
given #743 (T,wt=8): 11950 ->*_s0(leq(sndsplit(0,s(x)),0),false). [ur(87,a,481,a,b,571,a)].
given #744 (A,wt=10): 266 ->_s0(f(head(cons(x,y)),z),f(x,z)). [ur(57,a,67,a)].
given #745 (F,wt=16): 11977 -->*_s0(empty(fstsplit(sndsplit(0,0),x)),false) | -->*_s0(empty(fstsplit(sndsplit(0,0),y)),false) # answer(goal). [resolve(11949,a,88,c),unit_del(a,11949)].
given #746 (F,wt=18): 11985 -->*_s0(empty(fstsplit(sndsplit(0,length(nil)),x)),false) | -->*_s0(empty(fstsplit(sndsplit(0,length(nil)),y)),false) # answer(goal). [resolve(11941,a,88,c),unit_del(a,11941)].
given #747 (T,wt=9): 484 ->_s0(fstsplit(x,sndsplit(0,y)),fstsplit(x,y)). [ur(39,a,82,a)].
given #748 (T,wt=8): 12013 ->*_s0(fstsplit(s(x),sndsplit(0,nil)),nil). [ur(87,a,484,a,b,576,a)].
given #749 (T,wt=9): 485 ->_s0(fstsplit(sndsplit(0,x),y),fstsplit(x,y)). [ur(38,a,82,a)].
given #750 (T,wt=7): 12058 ->*_s0(fstsplit(sndsplit(0,0),x),nil). [ur(87,a,485,a,b,578,a)].
given #751 (A,wt=10): 267 ->_s0(cons(x,head(cons(y,z))),cons(x,y)). [ur(56,a,67,a)].
given #752 (T,wt=8): 12054 ->*_s0(fstsplit(sndsplit(0,length(nil)),x),nil). [ur(87,a,485,a,b,4197,a)].
given #753 (T,wt=8): 12059 ->*_s0(fstsplit(sndsplit(0,s(x)),nil),nil). [ur(87,a,485,a,b,576,a)].
given #754 (T,wt=9): 487 ->_s0(app(x,sndsplit(0,y)),app(x,y)). [ur(36,a,82,a)].
given #755 (T,wt=9): 488 ->_s0(app(sndsplit(0,x),y),app(x,y)). [ur(35,a,82,a)].
given #756 (A,wt=10): 268 ->_s0(cons(head(cons(x,y)),z),cons(x,z)). [ur(55,a,67,a)].
given #757 (T,wt=7): 12217 ->*_s0(app(sndsplit(0,nil),x),x). [ur(87,a,488,a,b,581,a)].
given #758 (T,wt=8): 12215 ->*_s0(app(sndsplit(0,nil),empty(nil)),true). [ur(87,a,488,a,b,616,a)].
given #759 (T,wt=8): 12216 ->*_s0(app(sndsplit(0,nil),length(nil)),0). [ur(87,a,488,a,b,612,a)].
given #760 (T,wt=9): 570 ->*_s0(leq(s(x),s(y)),leq(x,y)). [ur(87,a,72,a,b,86,a)].
given #761 (A,wt=10): 270 ->_s0(sndsplit(x,head(cons(y,z))),sndsplit(x,y)). [ur(53,a,67,a)].
given #762 (T,wt=9): 1004 ->*_s0(tail(cons(x,tail(cons(y,z)))),z). [ur(87,a,85,a,b,564,a)].
given #763 (T,wt=9): 1006 ->*_s0(head(cons(tail(cons(x,y)),z)),y). [ur(87,a,67,a,b,564,a)].
given #764 (T,wt=9): 1008 ->*_s0(tail(cons(x,sndsplit(s(y),nil))),nil). [ur(87,a,85,a,b,565,a)].
given #765 (T,wt=9): 1009 ->*_s0(sndsplit(s(s(x)),cons(y,nil)),nil). [ur(87,a,83,a,b,565,a)].
given #766 (A,wt=10): 271 ->_s0(sndsplit(head(cons(x,y)),z),sndsplit(x,z)). [ur(52,a,67,a)].
given #767 (T,wt=8): 12474 ->*_s0(sndsplit(head(cons(0,x)),y),y). [ur(87,a,271,a,b,567,a)].
given #768 (T,wt=9): 1011 ->*_s0(head(cons(sndsplit(s(x),nil),y)),nil). [ur(87,a,67,a,b,565,a)].
given #769 (T,wt=9): 1013 ->*_s0(tail(cons(x,leq(s(y),0))),false). [ur(87,a,85,a,b,571,a)].
given #770 (T,wt=9): 1016 ->*_s0(head(cons(leq(s(x),0),y)),false). [ur(87,a,67,a,b,571,a)].
given #771 (A,wt=18): 272 ->_s0(ring(x,y,z,u,w,head(cons(v5,v6))),ring(x,y,z,u,w,v5)). [ur(51,a,67,a)].
given #772 (T,wt=9): 1045 ->*_s0(tail(cons(x,head(cons(y,z)))),y). [ur(87,a,85,a,b,575,a)].
given #773 (T,wt=9): 1047 ->*_s0(head(cons(head(cons(x,y)),z)),x). [ur(87,a,67,a,b,575,a)].
given #774 (T,wt=9): 1049 ->*_s0(tail(cons(x,fstsplit(s(y),nil))),nil). [ur(87,a,85,a,b,576,a)].
given #775 (T,wt=9): 1051 ->*_s0(head(cons(fstsplit(s(x),nil),y)),nil). [ur(87,a,67,a,b,576,a)].
given #776 (A,wt=18): 273 ->_s0(ring(x,y,z,u,head(cons(w,v5)),v6),ring(x,y,z,u,w,v6)). [ur(50,a,67,a)].
given #777 (T,wt=9): 1053 ->*_s0(tail(cons(x,empty(cons(y,z)))),false). [ur(87,a,85,a,b,580,a)].
given #778 (T,wt=9): 1055 ->*_s0(head(cons(empty(cons(x,y)),z)),false). [ur(87,a,67,a,b,580,a)].
given #779 (T,wt=9): 1057 ->*_s0(tail(cons(x,sndsplit(0,length(nil)))),0). [ur(87,a,85,a,b,610,a)].
given #780 (T,wt=9): 1058 ->*_s0(sndsplit(s(0),cons(x,length(nil))),0). [ur(87,a,83,a,b,610,a)].
given #781 (A,wt=18): 274 ->_s0(ring(x,y,z,head(cons(u,w)),v5,v6),ring(x,y,z,u,v5,v6)). [ur(49,a,67,a)].
given #782 (T,wt=9): 1060 ->*_s0(head(cons(sndsplit(0,length(nil)),x)),0). [ur(87,a,67,a,b,610,a)].
given #783 (T,wt=9): 1089 ->*_s0(tail(cons(x,app(nil,length(nil)))),0). [ur(87,a,85,a,b,612,a)].
given #784 (T,wt=9): 1091 ->*_s0(head(cons(app(nil,length(nil)),x)),0). [ur(87,a,67,a,b,612,a)].
given #785 (T,wt=9): 1093 ->*_s0(tail(cons(x,sndsplit(0,empty(nil)))),true). [ur(87,a,85,a,b,614,a)].
given #786 (A,wt=18): 275 ->_s0(ring(x,y,head(cons(z,u)),w,v5,v6),ring(x,y,z,w,v5,v6)). [ur(48,a,67,a)].
given #787 (T,wt=9): 1094 ->*_s0(sndsplit(s(0),cons(x,empty(nil))),true). [ur(87,a,83,a,b,614,a)].
given #788 (T,wt=9): 1096 ->*_s0(head(cons(sndsplit(0,empty(nil)),x)),true). [ur(87,a,67,a,b,614,a)].
given #789 (T,wt=9): 1098 ->*_s0(tail(cons(x,app(nil,empty(nil)))),true). [ur(87,a,85,a,b,616,a)].
given #790 (T,wt=9): 1100 ->*_s0(head(cons(app(nil,empty(nil)),x)),true). [ur(87,a,67,a,b,616,a)].
given #791 (A,wt=18): 276 ->_s0(ring(x,head(cons(y,z)),u,w,v5,v6),ring(x,y,u,w,v5,v6)). [ur(47,a,67,a)].
given #792 (T,wt=9): 1102 ->*_s0(tail(cons(x,s(empty(nil)))),s(true)). [ur(87,a,85,a,b,666,a)].
given #793 (T,wt=9): 1104 ->*_s0(head(cons(s(empty(nil)),x)),s(true)). [ur(87,a,67,a,b,666,a)].
given #794 (T,wt=9): 1132 ->*_s0(tail(cons(x,tail(empty(nil)))),tail(true)). [ur(87,a,85,a,b,718,a)].
given #795 (T,wt=9): 1134 ->*_s0(head(cons(tail(empty(nil)),x)),tail(true)). [ur(87,a,67,a,b,718,a)].
given #796 (A,wt=18): 277 ->_s0(ring(head(cons(x,y)),z,u,w,v5,v6),ring(x,z,u,w,v5,v6)). [ur(46,a,67,a)].
given #797 (T,wt=9): 1136 ->*_s0(tail(cons(x,length(empty(nil)))),length(true)). [ur(87,a,85,a,b,744,a)].
given #798 (T,wt=9): 1138 ->*_s0(head(cons(length(empty(nil)),x)),length(true)). [ur(87,a,67,a,b,744,a)].
given #799 (T,wt=9): 1140 ->*_s0(tail(cons(x,head(empty(nil)))),head(true)). [ur(87,a,85,a,b,770,a)].
given #800 (T,wt=9): 1142 ->*_s0(head(cons(head(empty(nil)),x)),head(true)). [ur(87,a,67,a,b,770,a)].
given #801 (A,wt=10): 278 ->_s0(mapf(x,head(cons(y,z))),mapf(x,y)). [ur(45,a,67,a)].
given #802 (T,wt=8): 12789 ->*_s0(mapf(x,head(cons(nil,y))),nil). [ur(87,a,278,a,b,568,a)].
given #803 (T,wt=9): 1144 ->*_s0(tail(cons(x,empty(empty(nil)))),empty(true)). [ur(87,a,85,a,b,796,a)].
given #804 (T,wt=9): 1146 ->*_s0(head(cons(empty(empty(nil)),x)),empty(true)). [ur(87,a,67,a,b,796,a)].
given #805 (T,wt=9): 1174 ->*_s0(tail(cons(x,s(length(nil)))),s(0)). [ur(87,a,85,a,b,848,a)].
given #806 (A,wt=10): 279 ->_s0(mapf(head(cons(x,y)),z),mapf(x,z)). [ur(44,a,67,a)].
given #807 (T,wt=9): 1177 ->*_s0(head(cons(s(length(nil)),x)),s(0)). [ur(87,a,67,a,b,848,a)].
given #808 (T,wt=9): 1179 ->*_s0(tail(cons(x,tail(length(nil)))),tail(0)). [ur(87,a,85,a,b,874,a)].
given #809 (T,wt=9): 1181 ->*_s0(head(cons(tail(length(nil)),x)),tail(0)). [ur(87,a,67,a,b,874,a)].
given #810 (T,wt=9): 1183 ->*_s0(tail(cons(x,length(length(nil)))),length(0)). [ur(87,a,85,a,b,900,a)].
given #811 (A,wt=10): 280 ->_s0(leq(x,head(cons(y,z))),leq(x,y)). [ur(43,a,67,a)].
given #812 (T,wt=9): 1185 ->*_s0(head(cons(length(length(nil)),x)),length(0)). [ur(87,a,67,a,b,900,a)].
given #813 (T,wt=9): 1187 ->*_s0(tail(cons(x,head(length(nil)))),head(0)). [ur(87,a,85,a,b,926,a)].
given #814 (T,wt=9): 1189 ->*_s0(head(cons(head(length(nil)),x)),head(0)). [ur(87,a,67,a,b,926,a)].
given #815 (T,wt=9): 1217 ->*_s0(tail(cons(x,empty(length(nil)))),empty(0)). [ur(87,a,85,a,b,978,a)].
given #816 (A,wt=10): 281 ->_s0(leq(head(cons(x,y)),z),leq(x,z)). [ur(42,a,67,a)].
given #817 (T,wt=8): 12985 ->*_s0(leq(head(cons(0,x)),y),true). [ur(87,a,281,a,b,572,a)].
given #818 (T,wt=9): 1219 ->*_s0(head(cons(empty(length(nil)),x)),empty(0)). [ur(87,a,67,a,b,978,a)].
given #819 (T,wt=9): 1224 ->_s0(s(s(app(nil,x))),s(s(x))). [ur(59,a,114,a)].
given #820 (T,wt=9): 1229 ->_s0(tail(s(app(nil,x))),tail(s(x))). [ur(54,a,114,a)].
given #821 (A,wt=10): 284 ->_s0(fstsplit(x,head(cons(y,z))),fstsplit(x,y)). [ur(39,a,67,a)].
given #822 (F,wt=18): 13008 -->*_s0(empty(fstsplit(head(cons(0,x)),y)),false) | -->*_s0(empty(fstsplit(head(cons(0,x)),z)),false) # answer(goal). [resolve(12985,a,88,c),unit_del(a,12985)].
given #823 (T,wt=9): 1242 ->_s0(length(s(app(nil,x))),length(s(x))). [ur(41,a,114,a)].
given #824 (T,wt=9): 1243 ->_s0(head(s(app(nil,x))),head(s(x))). [ur(40,a,114,a)].
given #825 (T,wt=9): 1246 ->_s0(empty(s(app(nil,x))),empty(s(x))). [ur(37,a,114,a)].
given #826 (T,wt=9): 1253 ->_s0(s(tail(app(nil,x))),s(tail(x))). [ur(59,a,119,a)].
given #827 (A,wt=10): 285 ->_s0(fstsplit(head(cons(x,y)),z),fstsplit(x,z)). [ur(38,a,67,a)].
given #828 (T,wt=8): 13153 ->*_s0(fstsplit(head(cons(0,x)),y),nil). [ur(87,a,285,a,b,578,a)].
given #829 (T,wt=9): 1258 ->_s0(tail(tail(app(nil,x))),tail(tail(x))). [ur(54,a,119,a)].
given #830 (T,wt=9): 1271 ->_s0(length(tail(app(nil,x))),length(tail(x))). [ur(41,a,119,a)].
given #831 (T,wt=9): 1272 ->_s0(head(tail(app(nil,x))),head(tail(x))). [ur(40,a,119,a)].
given #832 (A,wt=10): 287 ->_s0(app(x,head(cons(y,z))),app(x,y)). [ur(36,a,67,a)].
given #833 (T,wt=9): 1275 ->_s0(empty(tail(app(nil,x))),empty(tail(x))). [ur(37,a,119,a)].
given #834 (T,wt=9): 1282 ->_s0(s(length(app(nil,x))),s(length(x))). [ur(59,a,132,a)].
given #835 (T,wt=8): 13321 ->*_s0(s(length(app(nil,nil))),s(0)). [ur(87,a,1282,a,b,848,a)].
given #836 (T,wt=9): 1287 ->_s0(tail(length(app(nil,x))),tail(length(x))). [ur(54,a,132,a)].
given #837 (A,wt=10): 288 ->_s0(app(head(cons(x,y)),z),app(x,z)). [ur(35,a,67,a)].
given #838 (T,wt=8): 13354 ->*_s0(tail(length(app(nil,nil))),tail(0)). [ur(87,a,1287,a,b,874,a)].
given #839 (T,wt=8): 13430 ->*_s0(app(head(cons(nil,x)),y),y). [ur(87,a,288,a,b,581,a)].
given #840 (T,wt=9): 1300 ->_s0(length(length(app(nil,x))),length(length(x))). [ur(41,a,132,a)].
given #841 (T,wt=8): 13471 ->*_s0(length(length(app(nil,nil))),length(0)). [ur(87,a,1300,a,b,900,a)].
given #842 (A,wt=10): 289 ->_s0(s(length(cons(x,y))),s(s(length(y)))). [ur(59,a,68,a)].
given #843 (T,wt=9): 1301 ->_s0(head(length(app(nil,x))),head(length(x))). [ur(40,a,132,a)].
given #844 (T,wt=8): 13524 ->*_s0(head(length(app(nil,nil))),head(0)). [ur(87,a,1301,a,b,926,a)].
given #845 (T,wt=9): 1304 ->_s0(empty(length(app(nil,x))),empty(length(x))). [ur(37,a,132,a)].
given #846 (T,wt=8): 13556 ->*_s0(empty(length(app(nil,nil))),empty(0)). [ur(87,a,1304,a,b,978,a)].
given #847 (A,wt=12): 290 ->_s0(f(x,length(cons(y,z))),f(x,s(length(z)))). [ur(58,a,68,a)].
given #848 (T,wt=9): 1334 ->*_s0(tail(cons(x,length(app(nil,nil)))),0). [ur(87,a,85,a,b,1280,a)].
given #849 (T,wt=9): 1336 ->*_s0(head(cons(length(app(nil,nil)),x)),0). [ur(87,a,67,a,b,1280,a)].
given #850 (T,wt=9): 1342 ->_s0(s(head(app(nil,x))),s(head(x))). [ur(59,a,133,a)].
given #851 (T,wt=9): 1347 ->_s0(tail(head(app(nil,x))),tail(head(x))). [ur(54,a,133,a)].
given #852 (A,wt=12): 291 ->_s0(f(length(cons(x,y)),z),f(s(length(y)),z)). [ur(57,a,68,a)].
given #853 (T,wt=9): 1360 ->_s0(length(head(app(nil,x))),length(head(x))). [ur(41,a,133,a)].
given #854 (T,wt=9): 1361 ->_s0(head(head(app(nil,x))),head(head(x))). [ur(40,a,133,a)].
given #855 (T,wt=9): 1364 ->_s0(empty(head(app(nil,x))),empty(head(x))). [ur(37,a,133,a)].
given #856 (T,wt=9): 1372 ->_s0(s(empty(app(nil,x))),s(empty(x))). [ur(59,a,136,a)].
given #857 (A,wt=12): 292 ->_s0(cons(x,length(cons(y,z))),cons(x,s(length(z)))). [ur(56,a,68,a)].
given #858 (T,wt=8): 13766 ->*_s0(s(empty(app(nil,nil))),s(true)). [ur(87,a,1372,a,b,666,a)].
given #859 (T,wt=9): 1377 ->_s0(tail(empty(app(nil,x))),tail(empty(x))). [ur(54,a,136,a)].
given #860 (T,wt=8): 13821 ->*_s0(tail(empty(app(nil,nil))),tail(true)). [ur(87,a,1377,a,b,718,a)].
given #861 (T,wt=9): 1390 ->_s0(length(empty(app(nil,x))),length(empty(x))). [ur(41,a,136,a)].
given #862 (A,wt=12): 293 ->_s0(cons(length(cons(x,y)),z),cons(s(length(y)),z)). [ur(55,a,68,a)].
given #863 (T,wt=8): 13854 ->*_s0(length(empty(app(nil,nil))),length(true)). [ur(87,a,1390,a,b,744,a)].
given #864 (T,wt=9): 1391 ->_s0(head(empty(app(nil,x))),head(empty(x))). [ur(40,a,136,a)].
given #865 (T,wt=8): 13909 ->*_s0(head(empty(app(nil,nil))),head(true)). [ur(87,a,1391,a,b,770,a)].
given #866 (T,wt=9): 1394 ->_s0(empty(empty(app(nil,x))),empty(empty(x))). [ur(37,a,136,a)].
given #867 (A,wt=10): 294 ->_s0(tail(length(cons(x,y))),tail(s(length(y)))). [ur(54,a,68,a)].
given #868 (T,wt=8): 13942 ->*_s0(empty(empty(app(nil,nil))),empty(true)). [ur(87,a,1394,a,b,796,a)].
given #869 (T,wt=9): 1398 ->*_s0(tail(cons(x,empty(app(nil,nil)))),true). [ur(87,a,85,a,b,1370,a)].
given #870 (T,wt=9): 1400 ->*_s0(head(cons(empty(app(nil,nil)),x)),true). [ur(87,a,67,a,b,1370,a)].
given #871 (T,wt=9): 1429 ->_s0(s(s(fstsplit(0,x))),s(s(nil))). [ur(59,a,189,a)].
given #872 (A,wt=12): 295 ->_s0(sndsplit(x,length(cons(y,z))),sndsplit(x,s(length(z)))). [ur(53,a,68,a)].
given #873 (T,wt=9): 1434 ->_s0(tail(s(fstsplit(0,x))),tail(s(nil))). [ur(54,a,189,a)].
given #874 (T,wt=9): 1447 ->_s0(length(s(fstsplit(0,x))),length(s(nil))). [ur(41,a,189,a)].
given #875 (T,wt=9): 1448 ->_s0(head(s(fstsplit(0,x))),head(s(nil))). [ur(40,a,189,a)].
given #876 (T,wt=9): 1451 ->_s0(empty(s(fstsplit(0,x))),empty(s(nil))). [ur(37,a,189,a)].
given #877 (A,wt=12): 296 ->_s0(sndsplit(length(cons(x,y)),z),sndsplit(s(length(y)),z)). [ur(52,a,68,a)].
given #878 (T,wt=8): 14143 ->*_s0(sndsplit(length(cons(x,y)),nil),nil). [ur(87,a,296,a,b,565,a)].
given #879 (T,wt=9): 1455 ->_s0(s(tail(fstsplit(0,x))),s(tail(nil))). [ur(59,a,194,a)].
given #880 (T,wt=9): 1460 ->_s0(tail(tail(fstsplit(0,x))),tail(tail(nil))). [ur(54,a,194,a)].
given #881 (T,wt=9): 1473 ->_s0(length(tail(fstsplit(0,x))),length(tail(nil))). [ur(41,a,194,a)].
given #882 (A,wt=20): 297 ->_s0(ring(x,y,z,u,w,length(cons(v5,v6))),ring(x,y,z,u,w,s(length(v6)))). [ur(51,a,68,a)].
given #883 (T,wt=9): 1474 ->_s0(head(tail(fstsplit(0,x))),head(tail(nil))). [ur(40,a,194,a)].
given #884 (T,wt=9): 1477 ->_s0(empty(tail(fstsplit(0,x))),empty(tail(nil))). [ur(37,a,194,a)].
given #885 (T,wt=9): 1482 ->_s0(s(length(fstsplit(0,x))),s(length(nil))). [ur(59,a,207,a)].
given #886 (T,wt=8): 14274 ->*_s0(s(length(fstsplit(0,x))),s(0)). [ur(87,a,1482,a,b,848,a)].
given #887 (A,wt=20): 298 ->_s0(ring(x,y,z,u,length(cons(w,v5)),v6),ring(x,y,z,u,s(length(v5)),v6)). [ur(50,a,68,a)].
given #888 (T,wt=9): 1487 ->_s0(tail(length(fstsplit(0,x))),tail(length(nil))). [ur(54,a,207,a)].
given #889 (T,wt=8): 14305 ->*_s0(tail(length(fstsplit(0,x))),tail(0)). [ur(87,a,1487,a,b,874,a)].
given #890 (T,wt=9): 1500 ->_s0(length(length(fstsplit(0,x))),length(length(nil))). [ur(41,a,207,a)].
given #891 (T,wt=8): 14335 ->*_s0(length(length(fstsplit(0,x))),length(0)). [ur(87,a,1500,a,b,900,a)].
given #892 (A,wt=20): 299 ->_s0(ring(x,y,z,length(cons(u,w)),v5,v6),ring(x,y,z,s(length(w)),v5,v6)). [ur(49,a,68,a)].
given #893 (T,wt=9): 1501 ->_s0(head(length(fstsplit(0,x))),head(length(nil))). [ur(40,a,207,a)].
given #894 (T,wt=8): 14365 ->*_s0(head(length(fstsplit(0,x))),head(0)). [ur(87,a,1501,a,b,926,a)].
given #895 (T,wt=9): 1504 ->_s0(empty(length(fstsplit(0,x))),empty(length(nil))). [ur(37,a,207,a)].
given #896 (T,wt=8): 14395 ->*_s0(empty(length(fstsplit(0,x))),empty(0)). [ur(87,a,1504,a,b,978,a)].
given #897 (A,wt=20): 300 ->_s0(ring(x,y,length(cons(z,u)),w,v5,v6),ring(x,y,s(length(u)),w,v5,v6)). [ur(48,a,68,a)].
given #898 (T,wt=9): 1508 ->*_s0(tail(cons(x,length(fstsplit(0,y)))),0). [ur(87,a,85,a,b,1480,a)].
given #899 (T,wt=9): 1510 ->*_s0(head(cons(length(fstsplit(0,x)),y)),0). [ur(87,a,67,a,b,1480,a)].
given #900 (T,wt=9): 1539 ->_s0(s(head(fstsplit(0,x))),s(head(nil))). [ur(59,a,208,a)].
given #901 (T,wt=9): 1544 ->_s0(tail(head(fstsplit(0,x))),tail(head(nil))). [ur(54,a,208,a)].
given #902 (A,wt=20): 301 ->_s0(ring(x,length(cons(y,z)),u,w,v5,v6),ring(x,s(length(z)),u,w,v5,v6)). [ur(47,a,68,a)].
given #903 (T,wt=9): 1557 ->_s0(length(head(fstsplit(0,x))),length(head(nil))). [ur(41,a,208,a)].
given #904 (T,wt=9): 1558 ->_s0(head(head(fstsplit(0,x))),head(head(nil))). [ur(40,a,208,a)].
given #905 (T,wt=9): 1561 ->_s0(empty(head(fstsplit(0,x))),empty(head(nil))). [ur(37,a,208,a)].
given #906 (T,wt=9): 1566 ->_s0(s(empty(fstsplit(0,x))),s(empty(nil))). [ur(59,a,211,a)].
given #907 (A,wt=20): 302 ->_s0(ring(length(cons(x,y)),z,u,w,v5,v6),ring(s(length(y)),z,u,w,v5,v6)). [ur(46,a,68,a)].
given #908 (T,wt=8): 14541 ->*_s0(s(empty(fstsplit(0,x))),s(true)). [ur(87,a,1566,a,b,666,a)].
given #909 (T,wt=9): 1571 ->_s0(tail(empty(fstsplit(0,x))),tail(empty(nil))). [ur(54,a,211,a)].
given #910 (T,wt=8): 14571 ->*_s0(tail(empty(fstsplit(0,x))),tail(true)). [ur(87,a,1571,a,b,718,a)].
given #911 (T,wt=9): 1584 ->_s0(length(empty(fstsplit(0,x))),length(empty(nil))). [ur(41,a,211,a)].
given #912 (A,wt=12): 303 ->_s0(mapf(x,length(cons(y,z))),mapf(x,s(length(z)))). [ur(45,a,68,a)].
given #913 (T,wt=8): 14601 ->*_s0(length(empty(fstsplit(0,x))),length(true)). [ur(87,a,1584,a,b,744,a)].
given #914 (T,wt=9): 1585 ->_s0(head(empty(fstsplit(0,x))),head(empty(nil))). [ur(40,a,211,a)].
given #915 (T,wt=8): 14653 ->*_s0(head(empty(fstsplit(0,x))),head(true)). [ur(87,a,1585,a,b,770,a)].
given #916 (T,wt=9): 1588 ->_s0(empty(empty(fstsplit(0,x))),empty(empty(nil))). [ur(37,a,211,a)].
given #917 (A,wt=12): 304 ->_s0(mapf(length(cons(x,y)),z),mapf(s(length(y)),z)). [ur(44,a,68,a)].
given #918 (T,wt=8): 14683 ->*_s0(empty(empty(fstsplit(0,x))),empty(true)). [ur(87,a,1588,a,b,796,a)].
given #919 (T,wt=9): 1592 ->*_s0(tail(cons(x,empty(fstsplit(0,y)))),true). [ur(87,a,85,a,b,1564,a)].
given #920 (T,wt=9): 1594 ->*_s0(head(cons(empty(fstsplit(0,x)),y)),true). [ur(87,a,67,a,b,1564,a)].
given #921 (T,wt=9): 1597 ->_s0(s(s(leq(0,x))),s(s(true))). [ur(59,a,339,a)].
given #922 (A,wt=12): 305 ->_s0(leq(x,length(cons(y,z))),leq(x,s(length(z)))). [ur(43,a,68,a)].
given #923 (T,wt=9): 1602 ->_s0(tail(s(leq(0,x))),tail(s(true))). [ur(54,a,339,a)].
given #924 (T,wt=9): 1615 ->_s0(length(s(leq(0,x))),length(s(true))). [ur(41,a,339,a)].
given #925 (T,wt=9): 1616 ->_s0(head(s(leq(0,x))),head(s(true))). [ur(40,a,339,a)].
given #926 (T,wt=9): 1619 ->_s0(empty(s(leq(0,x))),empty(s(true))). [ur(37,a,339,a)].
given #927 (A,wt=12): 306 ->_s0(leq(length(cons(x,y)),z),leq(s(length(y)),z)). [ur(42,a,68,a)].
given #928 (T,wt=8): 14882 ->*_s0(leq(length(cons(x,y)),0),false). [ur(87,a,306,a,b,571,a)].
given #929 (T,wt=9): 1649 ->_s0(s(tail(leq(0,x))),s(tail(true))). [ur(59,a,344,a)].
given #930 (T,wt=9): 1654 ->_s0(tail(tail(leq(0,x))),tail(tail(true))). [ur(54,a,344,a)].
given #931 (T,wt=9): 1667 ->_s0(length(tail(leq(0,x))),length(tail(true))). [ur(41,a,344,a)].
given #932 (A,wt=10): 307 ->_s0(length(length(cons(x,y))),length(s(length(y)))). [ur(41,a,68,a)].
given #933 (T,wt=9): 1668 ->_s0(head(tail(leq(0,x))),head(tail(true))). [ur(40,a,344,a)].
given #934 (T,wt=9): 1671 ->_s0(empty(tail(leq(0,x))),empty(tail(true))). [ur(37,a,344,a)].
given #935 (T,wt=9): 1675 ->_s0(s(length(leq(0,x))),s(length(true))). [ur(59,a,357,a)].
given #936 (T,wt=9): 1680 ->_s0(tail(length(leq(0,x))),tail(length(true))). [ur(54,a,357,a)].
given #937 (A,wt=10): 308 ->_s0(head(length(cons(x,y))),head(s(length(y)))). [ur(40,a,68,a)].
given #938 (T,wt=9): 1693 ->_s0(length(length(leq(0,x))),length(length(true))). [ur(41,a,357,a)].
given #939 (T,wt=9): 1694 ->_s0(head(length(leq(0,x))),head(length(true))). [ur(40,a,357,a)].
given #940 (T,wt=9): 1697 ->_s0(empty(length(leq(0,x))),empty(length(true))). [ur(37,a,357,a)].
given #941 (T,wt=9): 1701 ->_s0(s(head(leq(0,x))),s(head(true))). [ur(59,a,358,a)].
given #942 (A,wt=12): 309 ->_s0(fstsplit(x,length(cons(y,z))),fstsplit(x,s(length(z)))). [ur(39,a,68,a)].
given #943 (T,wt=9): 1706 ->_s0(tail(head(leq(0,x))),tail(head(true))). [ur(54,a,358,a)].
given #944 (T,wt=9): 1719 ->_s0(length(head(leq(0,x))),length(head(true))). [ur(41,a,358,a)].
given #945 (T,wt=9): 1720 ->_s0(head(head(leq(0,x))),head(head(true))). [ur(40,a,358,a)].
given #946 (T,wt=9): 1723 ->_s0(empty(head(leq(0,x))),empty(head(true))). [ur(37,a,358,a)].
given #947 (A,wt=12): 310 ->_s0(fstsplit(length(cons(x,y)),z),fstsplit(s(length(y)),z)). [ur(38,a,68,a)].
given #948 (T,wt=8): 15283 ->*_s0(fstsplit(length(cons(x,y)),nil),nil). [ur(87,a,310,a,b,576,a)].
given #949 (T,wt=9): 1727 ->_s0(s(empty(leq(0,x))),s(empty(true))). [ur(59,a,361,a)].
given #950 (T,wt=9): 1732 ->_s0(tail(empty(leq(0,x))),tail(empty(true))). [ur(54,a,361,a)].
given #951 (T,wt=9): 1745 ->_s0(length(empty(leq(0,x))),length(empty(true))). [ur(41,a,361,a)].
given #952 (A,wt=10): 311 ->_s0(empty(length(cons(x,y))),empty(s(length(y)))). [ur(37,a,68,a)].
given #953 (T,wt=9): 1746 ->_s0(head(empty(leq(0,x))),head(empty(true))). [ur(40,a,361,a)].
given #954 (T,wt=9): 1749 ->_s0(empty(empty(leq(0,x))),empty(empty(true))). [ur(37,a,361,a)].
given #955 (T,wt=9): 1779 ->_s0(s(s(mapf(x,nil))),s(s(nil))). [ur(59,a,439,a)].
given #956 (T,wt=9): 1784 ->_s0(tail(s(mapf(x,nil))),tail(s(nil))). [ur(54,a,439,a)].
given #957 (A,wt=12): 312 ->_s0(app(x,length(cons(y,z))),app(x,s(length(z)))). [ur(36,a,68,a)].
given #958 (T,wt=9): 1797 ->_s0(length(s(mapf(x,nil))),length(s(nil))). [ur(41,a,439,a)].
given #959 (T,wt=9): 1798 ->_s0(head(s(mapf(x,nil))),head(s(nil))). [ur(40,a,439,a)].
given #960 (T,wt=9): 1801 ->_s0(empty(s(mapf(x,nil))),empty(s(nil))). [ur(37,a,439,a)].
given #961 (T,wt=9): 1805 ->_s0(s(tail(mapf(x,nil))),s(tail(nil))). [ur(59,a,444,a)].
given #962 (A,wt=12): 313 ->_s0(app(length(cons(x,y)),z),app(s(length(y)),z)). [ur(35,a,68,a)].
given #963 (T,wt=9): 1810 ->_s0(tail(tail(mapf(x,nil))),tail(tail(nil))). [ur(54,a,444,a)].
given #964 (T,wt=9): 1823 ->_s0(length(tail(mapf(x,nil))),length(tail(nil))). [ur(41,a,444,a)].
given #965 (T,wt=9): 1824 ->_s0(head(tail(mapf(x,nil))),head(tail(nil))). [ur(40,a,444,a)].
given #966 (T,wt=9): 1827 ->_s0(empty(tail(mapf(x,nil))),empty(tail(nil))). [ur(37,a,444,a)].
given #967 (A,wt=16): 322 ->_s0(ring(x,y,z,u,w,length(nil)),ring(x,y,z,u,w,0)). [ur(51,a,69,a)].
given #968 (T,wt=9): 1832 ->_s0(s(length(mapf(x,nil))),s(length(nil))). [ur(59,a,457,a)].
given #969 (T,wt=8): 15637 ->*_s0(s(length(mapf(x,nil))),s(0)). [ur(87,a,1832,a,b,848,a)].
given #970 (T,wt=9): 1837 ->_s0(tail(length(mapf(x,nil))),tail(length(nil))). [ur(54,a,457,a)].
given #971 (T,wt=8): 15668 ->*_s0(tail(length(mapf(x,nil))),tail(0)). [ur(87,a,1837,a,b,874,a)].
given #972 (A,wt=16): 323 ->_s0(ring(x,y,z,u,length(nil),w),ring(x,y,z,u,0,w)). [ur(50,a,69,a)].
given #973 (T,wt=9): 1850 ->_s0(length(length(mapf(x,nil))),length(length(nil))). [ur(41,a,457,a)].
given #974 (T,wt=8): 15698 ->*_s0(length(length(mapf(x,nil))),length(0)). [ur(87,a,1850,a,b,900,a)].
given #975 (T,wt=9): 1851 ->_s0(head(length(mapf(x,nil))),head(length(nil))). [ur(40,a,457,a)].
given #976 (T,wt=8): 15728 ->*_s0(head(length(mapf(x,nil))),head(0)). [ur(87,a,1851,a,b,926,a)].
given #977 (A,wt=16): 324 ->_s0(ring(x,y,z,length(nil),u,w),ring(x,y,z,0,u,w)). [ur(49,a,69,a)].
given #978 (T,wt=9): 1854 ->_s0(empty(length(mapf(x,nil))),empty(length(nil))). [ur(37,a,457,a)].
given #979 (T,wt=8): 15758 ->*_s0(empty(length(mapf(x,nil))),empty(0)). [ur(87,a,1854,a,b,978,a)].
given #980 (T,wt=9): 1858 ->*_s0(tail(cons(x,length(mapf(y,nil)))),0). [ur(87,a,85,a,b,1830,a)].
given #981 (T,wt=9): 1860 ->*_s0(head(cons(length(mapf(x,nil)),y)),0). [ur(87,a,67,a,b,1830,a)].
given #982 (A,wt=16): 325 ->_s0(ring(x,y,length(nil),z,u,w),ring(x,y,0,z,u,w)). [ur(48,a,69,a)].
given #983 (T,wt=9): 1889 ->_s0(s(head(mapf(x,nil))),s(head(nil))). [ur(59,a,458,a)].
given #984 (T,wt=9): 1894 ->_s0(tail(head(mapf(x,nil))),tail(head(nil))). [ur(54,a,458,a)].
given #985 (T,wt=9): 1907 ->_s0(length(head(mapf(x,nil))),length(head(nil))). [ur(41,a,458,a)].
given #986 (T,wt=9): 1908 ->_s0(head(head(mapf(x,nil))),head(head(nil))). [ur(40,a,458,a)].
given #987 (A,wt=16): 326 ->_s0(ring(x,length(nil),y,z,u,w),ring(x,0,y,z,u,w)). [ur(47,a,69,a)].
given #988 (T,wt=9): 1911 ->_s0(empty(head(mapf(x,nil))),empty(head(nil))). [ur(37,a,458,a)].
given #989 (T,wt=9): 1916 ->_s0(s(empty(mapf(x,nil))),s(empty(nil))). [ur(59,a,461,a)].
given #990 (T,wt=8): 15904 ->*_s0(s(empty(mapf(x,nil))),s(true)). [ur(87,a,1916,a,b,666,a)].
given #991 (T,wt=9): 1921 ->_s0(tail(empty(mapf(x,nil))),tail(empty(nil))). [ur(54,a,461,a)].
given #992 (A,wt=16): 327 ->_s0(ring(length(nil),x,y,z,u,w),ring(0,x,y,z,u,w)). [ur(46,a,69,a)].
given #993 (T,wt=8): 15934 ->*_s0(tail(empty(mapf(x,nil))),tail(true)). [ur(87,a,1921,a,b,718,a)].
given #994 (T,wt=9): 1934 ->_s0(length(empty(mapf(x,nil))),length(empty(nil))). [ur(41,a,461,a)].
given #995 (T,wt=8): 15964 ->*_s0(length(empty(mapf(x,nil))),length(true)). [ur(87,a,1934,a,b,744,a)].
given #996 (T,wt=9): 1935 ->_s0(head(empty(mapf(x,nil))),head(empty(nil))). [ur(40,a,461,a)].
given #997 (A,wt=17): 347 ->_s0(ring(x,y,z,u,w,leq(0,v5)),ring(x,y,z,u,w,true)). [ur(51,a,70,a)].
given #998 (T,wt=8): 15994 ->*_s0(head(empty(mapf(x,nil))),head(true)). [ur(87,a,1935,a,b,770,a)].
given #999 (T,wt=9): 1938 ->_s0(empty(empty(mapf(x,nil))),empty(empty(nil))). [ur(37,a,461,a)].
given #1000 (T,wt=8): 16024 ->*_s0(empty(empty(mapf(x,nil))),empty(true)). [ur(87,a,1938,a,b,796,a)].
given #1001 (T,wt=9): 1942 ->*_s0(tail(cons(x,empty(mapf(y,nil)))),true). [ur(87,a,85,a,b,1914,a)].
given #1002 (A,wt=17): 348 ->_s0(ring(x,y,z,u,leq(0,w),v5),ring(x,y,z,u,true,v5)). [ur(50,a,70,a)].
given #1003 (T,wt=9): 1944 ->*_s0(head(cons(empty(mapf(x,nil)),y)),true). [ur(87,a,67,a,b,1914,a)].
given #1004 (T,wt=9): 1949 ->_s0(s(s(sndsplit(0,x))),s(s(x))). [ur(59,a,464,a)].
given #1005 (T,wt=9): 1954 ->_s0(tail(s(sndsplit(0,x))),tail(s(x))). [ur(54,a,464,a)].
given #1006 (T,wt=9): 1967 ->_s0(length(s(sndsplit(0,x))),length(s(x))). [ur(41,a,464,a)].
given #1007 (A,wt=17): 349 ->_s0(ring(x,y,z,leq(0,u),w,v5),ring(x,y,z,true,w,v5)). [ur(49,a,70,a)].
given #1008 (T,wt=9): 1968 ->_s0(head(s(sndsplit(0,x))),head(s(x))). [ur(40,a,464,a)].
given #1009 (T,wt=9): 1971 ->_s0(empty(s(sndsplit(0,x))),empty(s(x))). [ur(37,a,464,a)].
given #1010 (T,wt=9): 2004 ->_s0(s(tail(sndsplit(0,x))),s(tail(x))). [ur(59,a,469,a)].
given #1011 (T,wt=9): 2009 ->_s0(tail(tail(sndsplit(0,x))),tail(tail(x))). [ur(54,a,469,a)].
given #1012 (A,wt=17): 350 ->_s0(ring(x,y,leq(0,z),u,w,v5),ring(x,y,true,u,w,v5)). [ur(48,a,70,a)].
given #1013 (T,wt=9): 2022 ->_s0(length(tail(sndsplit(0,x))),length(tail(x))). [ur(41,a,469,a)].
given #1014 (T,wt=9): 2023 ->_s0(head(tail(sndsplit(0,x))),head(tail(x))). [ur(40,a,469,a)].
given #1015 (T,wt=9): 2026 ->_s0(empty(tail(sndsplit(0,x))),empty(tail(x))). [ur(37,a,469,a)].
given #1016 (T,wt=9): 2036 ->_s0(s(length(sndsplit(0,x))),s(length(x))). [ur(59,a,482,a)].
given #1017 (A,wt=17): 351 ->_s0(ring(x,leq(0,y),z,u,w,v5),ring(x,true,z,u,w,v5)). [ur(47,a,70,a)].
given #1018 (T,wt=8): 16288 ->*_s0(s(length(sndsplit(0,nil))),s(0)). [ur(87,a,2036,a,b,848,a)].
given #1019 (T,wt=9): 2041 ->_s0(tail(length(sndsplit(0,x))),tail(length(x))). [ur(54,a,482,a)].
given #1020 (T,wt=8): 16311 ->*_s0(tail(length(sndsplit(0,nil))),tail(0)). [ur(87,a,2041,a,b,874,a)].
given #1021 (T,wt=9): 2054 ->_s0(length(length(sndsplit(0,x))),length(length(x))). [ur(41,a,482,a)].
given #1022 (A,wt=17): 352 ->_s0(ring(leq(0,x),y,z,u,w,v5),ring(true,y,z,u,w,v5)). [ur(46,a,70,a)].
given #1023 (T,wt=8): 16333 ->*_s0(length(length(sndsplit(0,nil))),length(0)). [ur(87,a,2054,a,b,900,a)].
given #1024 (T,wt=9): 2055 ->_s0(head(length(sndsplit(0,x))),head(length(x))). [ur(40,a,482,a)].
given #1025 (T,wt=8): 16355 ->*_s0(head(length(sndsplit(0,nil))),head(0)). [ur(87,a,2055,a,b,926,a)].
given #1026 (T,wt=9): 2058 ->_s0(empty(length(sndsplit(0,x))),empty(length(x))). [ur(37,a,482,a)].
given #1027 (A,wt=10): 365 ->_s0(f(x,leq(s(y),0)),f(x,false)). [ur(58,a,71,a)].
given #1028 (T,wt=8): 16377 ->*_s0(empty(length(sndsplit(0,nil))),empty(0)). [ur(87,a,2058,a,b,978,a)].
given #1029 (T,wt=9): 2063 ->*_s0(tail(cons(x,length(sndsplit(0,nil)))),0). [ur(87,a,85,a,b,2034,a)].
given #1030 (T,wt=9): 2065 ->*_s0(head(cons(length(sndsplit(0,nil)),x)),0). [ur(87,a,67,a,b,2034,a)].
given #1031 (T,wt=9): 2071 ->_s0(s(head(sndsplit(0,x))),s(head(x))). [ur(59,a,483,a)].
given #1032 (A,wt=10): 366 ->_s0(f(leq(s(x),0),y),f(false,y)). [ur(57,a,71,a)].
given #1033 (T,wt=9): 2076 ->_s0(tail(head(sndsplit(0,x))),tail(head(x))). [ur(54,a,483,a)].
given #1034 (T,wt=9): 2089 ->_s0(length(head(sndsplit(0,x))),length(head(x))). [ur(41,a,483,a)].
given #1035 (T,wt=9): 2090 ->_s0(head(head(sndsplit(0,x))),head(head(x))). [ur(40,a,483,a)].
given #1036 (T,wt=9): 2093 ->_s0(empty(head(sndsplit(0,x))),empty(head(x))). [ur(37,a,483,a)].
given #1037 (A,wt=10): 367 ->_s0(cons(x,leq(s(y),0)),cons(x,false)). [ur(56,a,71,a)].
given #1038 (T,wt=9): 2130 ->_s0(s(empty(sndsplit(0,x))),s(empty(x))). [ur(59,a,486,a)].
given #1039 (T,wt=8): 16487 ->*_s0(s(empty(sndsplit(0,nil))),s(true)). [ur(87,a,2130,a,b,666,a)].
given #1040 (T,wt=9): 2135 ->_s0(tail(empty(sndsplit(0,x))),tail(empty(x))). [ur(54,a,486,a)].
given #1041 (T,wt=8): 16510 ->*_s0(tail(empty(sndsplit(0,nil))),tail(true)). [ur(87,a,2135,a,b,718,a)].
given #1042 (A,wt=10): 368 ->_s0(cons(leq(s(x),0),y),cons(false,y)). [ur(55,a,71,a)].
given #1043 (T,wt=9): 2148 ->_s0(length(empty(sndsplit(0,x))),length(empty(x))). [ur(41,a,486,a)].
given #1044 (T,wt=8): 16541 ->*_s0(length(empty(sndsplit(0,nil))),length(true)). [ur(87,a,2148,a,b,744,a)].
given #1045 (T,wt=9): 2149 ->_s0(head(empty(sndsplit(0,x))),head(empty(x))). [ur(40,a,486,a)].
given #1046 (T,wt=8): 16564 ->*_s0(head(empty(sndsplit(0,nil))),head(true)). [ur(87,a,2149,a,b,770,a)].
given #1047 (A,wt=10): 370 ->_s0(sndsplit(x,leq(s(y),0)),sndsplit(x,false)). [ur(53,a,71,a)].
given #1048 (T,wt=9): 2152 ->_s0(empty(empty(sndsplit(0,x))),empty(empty(x))). [ur(37,a,486,a)].
given #1049 (T,wt=8): 16597 ->*_s0(empty(empty(sndsplit(0,nil))),empty(true)). [ur(87,a,2152,a,b,796,a)].
given #1050 (T,wt=9): 2157 ->*_s0(tail(cons(x,empty(sndsplit(0,nil)))),true). [ur(87,a,85,a,b,2128,a)].
given #1051 (T,wt=9): 2159 ->*_s0(head(cons(empty(sndsplit(0,nil)),x)),true). [ur(87,a,67,a,b,2128,a)].
given #1052 (A,wt=10): 371 ->_s0(sndsplit(leq(s(x),0),y),sndsplit(false,y)). [ur(52,a,71,a)].
given #1053 (T,wt=9): 2161 ->*_s0(tail(sndsplit(0,cons(x,length(nil)))),0). [ur(87,a,469,a,b,609,a)].
given #1054 (T,wt=9): 2162 ->*_s0(tail(app(nil,cons(x,length(nil)))),0). [ur(87,a,119,a,b,609,a)].
given #1055 (T,wt=9): 2164 ->*_s0(sndsplit(0,tail(cons(x,length(nil)))),0). [ur(87,a,82,a,b,609,a)].
given #1056 (T,wt=9): 2166 ->*_s0(app(nil,tail(cons(x,length(nil)))),0). [ur(87,a,61,a,b,609,a)].
given #1057 (A,wt=18): 372 ->_s0(ring(x,y,z,u,w,leq(s(v5),0)),ring(x,y,z,u,w,false)). [ur(51,a,71,a)].
given #1058 (T,wt=9): 2167 ->*_s0(head(sndsplit(0,cons(length(nil),x))),0). [ur(87,a,483,a,b,611,a)].
given #1059 (T,wt=9): 2168 ->*_s0(head(app(nil,cons(length(nil),x))),0). [ur(87,a,133,a,b,611,a)].
given #1060 (T,wt=9): 2170 ->*_s0(sndsplit(0,head(cons(length(nil),x))),0). [ur(87,a,82,a,b,611,a)].
given #1061 (T,wt=9): 2172 ->*_s0(app(nil,head(cons(length(nil),x))),0). [ur(87,a,61,a,b,611,a)].
given #1062 (A,wt=18): 373 ->_s0(ring(x,y,z,u,leq(s(w),0),v5),ring(x,y,z,u,false,v5)). [ur(50,a,71,a)].
given #1063 (T,wt=9): 2199 ->*_s0(tail(sndsplit(0,cons(x,empty(nil)))),true). [ur(87,a,469,a,b,613,a)].
given #1064 (T,wt=9): 2200 ->*_s0(tail(app(nil,cons(x,empty(nil)))),true). [ur(87,a,119,a,b,613,a)].
given #1065 (T,wt=9): 2202 ->*_s0(sndsplit(0,tail(cons(x,empty(nil)))),true). [ur(87,a,82,a,b,613,a)].
given #1066 (T,wt=9): 2204 ->*_s0(app(nil,tail(cons(x,empty(nil)))),true). [ur(87,a,61,a,b,613,a)].
given #1067 (A,wt=18): 374 ->_s0(ring(x,y,z,leq(s(u),0),w,v5),ring(x,y,z,false,w,v5)). [ur(49,a,71,a)].
given #1068 (T,wt=9): 2205 ->*_s0(head(sndsplit(0,cons(empty(nil),x))),true). [ur(87,a,483,a,b,615,a)].
given #1069 (T,wt=9): 2206 ->*_s0(head(app(nil,cons(empty(nil),x))),true). [ur(87,a,133,a,b,615,a)].
given #1070 (T,wt=9): 2208 ->*_s0(sndsplit(0,head(cons(empty(nil),x))),true). [ur(87,a,82,a,b,615,a)].
given #1071 (T,wt=9): 2210 ->*_s0(app(nil,head(cons(empty(nil),x))),true). [ur(87,a,61,a,b,615,a)].
given #1072 (A,wt=18): 375 ->_s0(ring(x,y,leq(s(z),0),u,w,v5),ring(x,y,false,u,w,v5)). [ur(48,a,71,a)].
given #1073 (T,wt=9): 2213 ->*_s0(sndsplit(0,sndsplit(0,sndsplit(0,x))),x). [ur(87,a,82,a,b,619,a)].
given #1074 (T,wt=9): 2215 ->*_s0(app(nil,sndsplit(0,sndsplit(0,x))),x). [ur(87,a,61,a,b,619,a)].
given #1075 (T,wt=9): 2217 ->*_s0(sndsplit(0,app(nil,sndsplit(0,x))),x). [ur(87,a,82,a,b,621,a)].
given #1076 (T,wt=9): 2219 ->*_s0(app(nil,app(nil,sndsplit(0,x))),x). [ur(87,a,61,a,b,621,a)].
given #1077 (A,wt=18): 376 ->_s0(ring(x,leq(s(y),0),z,u,w,v5),ring(x,false,z,u,w,v5)). [ur(47,a,71,a)].
given #1078 (T,wt=9): 2220 ->*_s0(head(app(cons(empty(nil),x),y)),true). [ur(87,a,108,a,b,615,a)].
given #1079 (T,wt=9): 2221 ->*_s0(head(app(cons(length(nil),x),y)),0). [ur(87,a,108,a,b,611,a)].
given #1080 (T,wt=9): 2251 ->*_s0(sndsplit(0,sndsplit(0,mapf(x,nil))),nil). [ur(87,a,82,a,b,623,a)].
given #1081 (T,wt=9): 2253 ->*_s0(app(nil,sndsplit(0,mapf(x,nil))),nil). [ur(87,a,61,a,b,623,a)].
given #1082 (A,wt=18): 377 ->_s0(ring(leq(s(x),0),y,z,u,w,v5),ring(false,y,z,u,w,v5)). [ur(46,a,71,a)].
given #1083 (T,wt=9): 2255 ->*_s0(sndsplit(0,app(nil,mapf(x,nil))),nil). [ur(87,a,82,a,b,625,a)].
given #1084 (T,wt=9): 2257 ->*_s0(app(nil,app(nil,mapf(x,nil))),nil). [ur(87,a,61,a,b,625,a)].
given #1085 (T,wt=9): 2260 ->*_s0(sndsplit(0,sndsplit(0,leq(0,x))),true). [ur(87,a,82,a,b,654,a)].
given #1086 (T,wt=9): 2262 ->*_s0(app(nil,sndsplit(0,leq(0,x))),true). [ur(87,a,61,a,b,654,a)].
given #1087 (A,wt=10): 378 ->_s0(mapf(x,leq(s(y),0)),mapf(x,false)). [ur(45,a,71,a)].
given #1088 (T,wt=9): 2264 ->*_s0(sndsplit(0,leq(s(0),s(x))),true). [ur(87,a,82,a,b,655,a)].
given #1089 (T,wt=9): 2265 ->*_s0(leq(s(s(0)),s(s(x))),true). [ur(87,a,72,a,b,655,a)].
given #1090 (T,wt=9): 2267 ->*_s0(app(nil,leq(s(0),s(x))),true). [ur(87,a,61,a,b,655,a)].
given #1091 (T,wt=9): 2295 ->*_s0(sndsplit(0,app(nil,leq(0,x))),true). [ur(87,a,82,a,b,657,a)].
given #1092 (A,wt=10): 379 ->_s0(mapf(leq(s(x),0),y),mapf(false,y)). [ur(44,a,71,a)].
given #1093 (T,wt=9): 2297 ->*_s0(app(nil,app(nil,leq(0,x))),true). [ur(87,a,61,a,b,657,a)].
given #1094 (T,wt=9): 2300 ->*_s0(sndsplit(0,sndsplit(0,fstsplit(0,x))),nil). [ur(87,a,82,a,b,659,a)].
given #1095 (T,wt=9): 2302 ->*_s0(app(nil,sndsplit(0,fstsplit(0,x))),nil). [ur(87,a,61,a,b,659,a)].
given #1096 (T,wt=9): 2304 ->*_s0(sndsplit(0,app(nil,fstsplit(0,x))),nil). [ur(87,a,82,a,b,661,a)].
given #1097 (A,wt=10): 380 ->_s0(leq(x,leq(s(y),0)),leq(x,false)). [ur(43,a,71,a)].
given #1098 (T,wt=9): 2306 ->*_s0(app(nil,app(nil,fstsplit(0,x))),nil). [ur(87,a,61,a,b,661,a)].
given #1099 (T,wt=9): 2309 ->*_s0(sndsplit(0,sndsplit(0,app(nil,x))),x). [ur(87,a,82,a,b,663,a)].
given #1100 (T,wt=9): 2311 ->*_s0(app(nil,sndsplit(0,app(nil,x))),x). [ur(87,a,61,a,b,663,a)].
given #1101 (T,wt=9): 2339 ->*_s0(sndsplit(0,app(nil,app(nil,x))),x). [ur(87,a,82,a,b,665,a)].
given #1102 (A,wt=10): 381 ->_s0(leq(leq(s(x),0),y),leq(false,y)). [ur(42,a,71,a)].
given #1103 (T,wt=9): 2341 ->*_s0(app(nil,app(nil,app(nil,x))),x). [ur(87,a,61,a,b,665,a)].
given #1104 (T,wt=9): 2342 ->*_s0(length(sndsplit(0,cons(x,nil))),s(0)). [ur(87,a,482,a,b,1176,a)].
given #1105 (T,wt=9): 2343 ->*_s0(length(app(nil,cons(x,nil))),s(0)). [ur(87,a,132,a,b,1176,a)].
given #1106 (T,wt=9): 2345 ->*_s0(sndsplit(0,length(cons(x,nil))),s(0)). [ur(87,a,82,a,b,1176,a)].
given #1107 (A,wt=10): 384 ->_s0(fstsplit(x,leq(s(y),0)),fstsplit(x,false)). [ur(39,a,71,a)].
given #1108 (T,wt=9): 2347 ->*_s0(app(nil,length(cons(x,nil))),s(0)). [ur(87,a,61,a,b,1176,a)].
given #1109 (T,wt=9): 2348 ->*_s0(s(sndsplit(0,app(nil,x))),s(x)). [ur(87,a,464,a,b,1223,a)].
given #1110 (T,wt=9): 2349 ->*_s0(s(app(nil,app(nil,x))),s(x)). [ur(87,a,114,a,b,1223,a)].
given #1111 (T,wt=9): 2351 ->*_s0(sndsplit(0,s(app(nil,x))),s(x)). [ur(87,a,82,a,b,1223,a)].
given #1112 (A,wt=10): 385 ->_s0(fstsplit(leq(s(x),0),y),fstsplit(false,y)). [ur(38,a,71,a)].
given #1113 (T,wt=9): 2353 ->*_s0(app(nil,s(app(nil,x))),s(x)). [ur(87,a,61,a,b,1223,a)].
given #1114 (T,wt=9): 2354 ->*_s0(tail(sndsplit(0,app(nil,x))),tail(x)). [ur(87,a,469,a,b,1252,a)].
given #1115 (T,wt=9): 2355 ->*_s0(tail(app(nil,app(nil,x))),tail(x)). [ur(87,a,119,a,b,1252,a)].
given #1116 (T,wt=9): 2357 ->*_s0(sndsplit(0,tail(app(nil,x))),tail(x)). [ur(87,a,82,a,b,1252,a)].
given #1117 (A,wt=10): 387 ->_s0(app(x,leq(s(y),0)),app(x,false)). [ur(36,a,71,a)].
given #1118 (T,wt=9): 2359 ->*_s0(app(nil,tail(app(nil,x))),tail(x)). [ur(87,a,61,a,b,1252,a)].
given #1119 (T,wt=9): 2387 ->*_s0(length(sndsplit(0,app(nil,x))),length(x)). [ur(87,a,482,a,b,1281,a)].
given #1120 (T,wt=9): 2388 ->*_s0(length(app(nil,app(nil,x))),length(x)). [ur(87,a,132,a,b,1281,a)].
given #1121 (T,wt=9): 2390 ->*_s0(sndsplit(0,length(app(nil,x))),length(x)). [ur(87,a,82,a,b,1281,a)].
given #1122 (A,wt=10): 388 ->_s0(app(leq(s(x),0),y),app(false,y)). [ur(35,a,71,a)].
given #1123 (T,wt=9): 2392 ->*_s0(app(nil,length(app(nil,x))),length(x)). [ur(87,a,61,a,b,1281,a)].
given #1124 (T,wt=9): 2393 ->*_s0(head(sndsplit(0,app(nil,x))),head(x)). [ur(87,a,483,a,b,1341,a)].
given #1125 (T,wt=9): 2394 ->*_s0(head(app(nil,app(nil,x))),head(x)). [ur(87,a,133,a,b,1341,a)].
given #1126 (T,wt=9): 2396 ->*_s0(sndsplit(0,head(app(nil,x))),head(x)). [ur(87,a,82,a,b,1341,a)].
given #1127 (A,wt=11): 389 ->_s0(s(leq(s(x),s(y))),s(leq(x,y))). [ur(59,a,72,a)].
given #1128 (T,wt=9): 2398 ->*_s0(app(nil,head(app(nil,x))),head(x)). [ur(87,a,61,a,b,1341,a)].
given #1129 (T,wt=9): 2399 ->*_s0(empty(sndsplit(0,app(nil,x))),empty(x)). [ur(87,a,486,a,b,1371,a)].
given #1130 (T,wt=9): 2400 ->*_s0(empty(app(nil,app(nil,x))),empty(x)). [ur(87,a,136,a,b,1371,a)].
given #1131 (T,wt=9): 2402 ->*_s0(sndsplit(0,empty(app(nil,x))),empty(x)). [ur(87,a,82,a,b,1371,a)].
given #1132 (A,wt=13): 390 ->_s0(f(x,leq(s(y),s(z))),f(x,leq(y,z))). [ur(58,a,72,a)].
given #1133 (T,wt=9): 2404 ->*_s0(app(nil,empty(app(nil,x))),empty(x)). [ur(87,a,61,a,b,1371,a)].
given #1134 (T,wt=9): 2405 ->*_s0(s(sndsplit(0,fstsplit(0,x))),s(nil)). [ur(87,a,464,a,b,1428,a)].
given #1135 (T,wt=9): 2406 ->*_s0(s(app(nil,fstsplit(0,x))),s(nil)). [ur(87,a,114,a,b,1428,a)].
given #1136 (T,wt=9): 2408 ->*_s0(sndsplit(0,s(fstsplit(0,x))),s(nil)). [ur(87,a,82,a,b,1428,a)].
given #1137 (A,wt=13): 391 ->_s0(f(leq(s(x),s(y)),z),f(leq(x,y),z)). [ur(57,a,72,a)].
given #1138 (T,wt=9): 2410 ->*_s0(app(nil,s(fstsplit(0,x))),s(nil)). [ur(87,a,61,a,b,1428,a)].
given #1139 (T,wt=9): 2438 ->*_s0(tail(sndsplit(0,fstsplit(0,x))),tail(nil)). [ur(87,a,469,a,b,1454,a)].
given #1140 (T,wt=9): 2439 ->*_s0(tail(app(nil,fstsplit(0,x))),tail(nil)). [ur(87,a,119,a,b,1454,a)].
given #1141 (T,wt=9): 2441 ->*_s0(sndsplit(0,tail(fstsplit(0,x))),tail(nil)). [ur(87,a,82,a,b,1454,a)].
given #1142 (A,wt=13): 392 ->_s0(cons(x,leq(s(y),s(z))),cons(x,leq(y,z))). [ur(56,a,72,a)].
given #1143 (T,wt=9): 2443 ->*_s0(app(nil,tail(fstsplit(0,x))),tail(nil)). [ur(87,a,61,a,b,1454,a)].
given #1144 (T,wt=9): 2444 ->*_s0(length(sndsplit(0,fstsplit(0,x))),length(nil)). [ur(87,a,482,a,b,1481,a)].
given #1145 (T,wt=9): 2445 ->*_s0(length(app(nil,fstsplit(0,x))),length(nil)). [ur(87,a,132,a,b,1481,a)].
given #1146 (T,wt=9): 2447 ->*_s0(sndsplit(0,length(fstsplit(0,x))),length(nil)). [ur(87,a,82,a,b,1481,a)].
given #1147 (A,wt=13): 393 ->_s0(cons(leq(s(x),s(y)),z),cons(leq(x,y),z)). [ur(55,a,72,a)].
given #1148 (T,wt=9): 2449 ->*_s0(app(nil,length(fstsplit(0,x))),length(nil)). [ur(87,a,61,a,b,1481,a)].
given #1149 (T,wt=9): 2450 ->*_s0(head(sndsplit(0,fstsplit(0,x))),head(nil)). [ur(87,a,483,a,b,1538,a)].
given #1150 (T,wt=9): 2451 ->*_s0(head(app(nil,fstsplit(0,x))),head(nil)). [ur(87,a,133,a,b,1538,a)].
given #1151 (T,wt=9): 2453 ->*_s0(sndsplit(0,head(fstsplit(0,x))),head(nil)). [ur(87,a,82,a,b,1538,a)].
given #1152 (A,wt=11): 394 ->_s0(tail(leq(s(x),s(y))),tail(leq(x,y))). [ur(54,a,72,a)].
given #1153 (T,wt=9): 2455 ->*_s0(app(nil,head(fstsplit(0,x))),head(nil)). [ur(87,a,61,a,b,1538,a)].
given #1154 (T,wt=9): 2456 ->*_s0(empty(sndsplit(0,fstsplit(0,x))),empty(nil)). [ur(87,a,486,a,b,1565,a)].
given #1155 (T,wt=9): 2457 ->*_s0(empty(app(nil,fstsplit(0,x))),empty(nil)). [ur(87,a,136,a,b,1565,a)].
given #1156 (T,wt=9): 2459 ->*_s0(sndsplit(0,empty(fstsplit(0,x))),empty(nil)). [ur(87,a,82,a,b,1565,a)].
given #1157 (A,wt=13): 395 ->_s0(sndsplit(x,leq(s(y),s(z))),sndsplit(x,leq(y,z))). [ur(53,a,72,a)].
given #1158 (T,wt=9): 2461 ->*_s0(app(nil,empty(fstsplit(0,x))),empty(nil)). [ur(87,a,61,a,b,1565,a)].
given #1159 (T,wt=9): 2488 ->*_s0(s(sndsplit(0,leq(0,x))),s(true)). [ur(87,a,464,a,b,1596,a)].
given #1160 (T,wt=9): 2489 ->*_s0(s(app(nil,leq(0,x))),s(true)). [ur(87,a,114,a,b,1596,a)].
given #1161 (T,wt=9): 2491 ->*_s0(sndsplit(0,s(leq(0,x))),s(true)). [ur(87,a,82,a,b,1596,a)].
given #1162 (A,wt=13): 396 ->_s0(sndsplit(leq(s(x),s(y)),z),sndsplit(leq(x,y),z)). [ur(52,a,72,a)].
given #1163 (T,wt=9): 2493 ->*_s0(app(nil,s(leq(0,x))),s(true)). [ur(87,a,61,a,b,1596,a)].
given #1164 (T,wt=9): 2494 ->*_s0(tail(sndsplit(0,leq(0,x))),tail(true)). [ur(87,a,469,a,b,1648,a)].
given #1165 (T,wt=9): 2495 ->*_s0(tail(app(nil,leq(0,x))),tail(true)). [ur(87,a,119,a,b,1648,a)].
given #1166 (T,wt=9): 2497 ->*_s0(sndsplit(0,tail(leq(0,x))),tail(true)). [ur(87,a,82,a,b,1648,a)].
given #1167 (A,wt=21): 397 ->_s0(ring(x,y,z,u,w,leq(s(v5),s(v6))),ring(x,y,z,u,w,leq(v5,v6))). [ur(51,a,72,a)].
given #1168 (T,wt=9): 2499 ->*_s0(app(nil,tail(leq(0,x))),tail(true)). [ur(87,a,61,a,b,1648,a)].
given #1169 (T,wt=9): 2500 ->*_s0(length(sndsplit(0,leq(0,x))),length(true)). [ur(87,a,482,a,b,1674,a)].
given #1170 (T,wt=9): 2501 ->*_s0(length(app(nil,leq(0,x))),length(true)). [ur(87,a,132,a,b,1674,a)].
given #1171 (T,wt=9): 2503 ->*_s0(sndsplit(0,length(leq(0,x))),length(true)). [ur(87,a,82,a,b,1674,a)].
given #1172 (A,wt=21): 398 ->_s0(ring(x,y,z,u,leq(s(w),s(v5)),v6),ring(x,y,z,u,leq(w,v5),v6)). [ur(50,a,72,a)].
given #1173 (T,wt=9): 2505 ->*_s0(app(nil,length(leq(0,x))),length(true)). [ur(87,a,61,a,b,1674,a)].
given #1174 (T,wt=9): 2506 ->*_s0(head(sndsplit(0,leq(0,x))),head(true)). [ur(87,a,483,a,b,1700,a)].
given #1175 (T,wt=9): 2507 ->*_s0(head(app(nil,leq(0,x))),head(true)). [ur(87,a,133,a,b,1700,a)].
given #1176 (T,wt=9): 2509 ->*_s0(sndsplit(0,head(leq(0,x))),head(true)). [ur(87,a,82,a,b,1700,a)].
given #1177 (A,wt=21): 399 ->_s0(ring(x,y,z,leq(s(u),s(w)),v5,v6),ring(x,y,z,leq(u,w),v5,v6)). [ur(49,a,72,a)].
given #1178 (T,wt=9): 2511 ->*_s0(app(nil,head(leq(0,x))),head(true)). [ur(87,a,61,a,b,1700,a)].
given #1179 (T,wt=9): 2512 ->*_s0(f(x,app(nil,y)),f(x,y)). [ur(87,a,115,a,b,86,a)].
given #1180 (T,wt=9): 2538 ->*_s0(empty(sndsplit(0,leq(0,x))),empty(true)). [ur(87,a,486,a,b,1726,a)].
given #1181 (T,wt=9): 2539 ->*_s0(empty(app(nil,leq(0,x))),empty(true)). [ur(87,a,136,a,b,1726,a)].
given #1182 (A,wt=21): 400 ->_s0(ring(x,y,leq(s(z),s(u)),w,v5,v6),ring(x,y,leq(z,u),w,v5,v6)). [ur(48,a,72,a)].
given #1183 (T,wt=9): 2541 ->*_s0(sndsplit(0,empty(leq(0,x))),empty(true)). [ur(87,a,82,a,b,1726,a)].
given #1184 (T,wt=9): 2543 ->*_s0(app(nil,empty(leq(0,x))),empty(true)). [ur(87,a,61,a,b,1726,a)].
given #1185 (T,wt=9): 2544 ->*_s0(s(sndsplit(0,mapf(x,nil))),s(nil)). [ur(87,a,464,a,b,1778,a)].
given #1186 (T,wt=9): 2545 ->*_s0(s(app(nil,mapf(x,nil))),s(nil)). [ur(87,a,114,a,b,1778,a)].
given #1187 (A,wt=21): 401 ->_s0(ring(x,leq(s(y),s(z)),u,w,v5,v6),ring(x,leq(y,z),u,w,v5,v6)). [ur(47,a,72,a)].
given #1188 (T,wt=9): 2547 ->*_s0(sndsplit(0,s(mapf(x,nil))),s(nil)). [ur(87,a,82,a,b,1778,a)].
given #1189 (T,wt=9): 2549 ->*_s0(app(nil,s(mapf(x,nil))),s(nil)). [ur(87,a,61,a,b,1778,a)].
given #1190 (T,wt=9): 2550 ->*_s0(tail(sndsplit(0,mapf(x,nil))),tail(nil)). [ur(87,a,469,a,b,1804,a)].
given #1191 (T,wt=9): 2551 ->*_s0(tail(app(nil,mapf(x,nil))),tail(nil)). [ur(87,a,119,a,b,1804,a)].
given #1192 (A,wt=21): 402 ->_s0(ring(leq(s(x),s(y)),z,u,w,v5,v6),ring(leq(x,y),z,u,w,v5,v6)). [ur(46,a,72,a)].
given #1193 (T,wt=9): 2553 ->*_s0(sndsplit(0,tail(mapf(x,nil))),tail(nil)). [ur(87,a,82,a,b,1804,a)].
given #1194 (T,wt=9): 2555 ->*_s0(app(nil,tail(mapf(x,nil))),tail(nil)). [ur(87,a,61,a,b,1804,a)].
given #1195 (T,wt=9): 2556 ->*_s0(length(sndsplit(0,mapf(x,nil))),length(nil)). [ur(87,a,482,a,b,1831,a)].
given #1196 (T,wt=9): 2557 ->*_s0(length(app(nil,mapf(x,nil))),length(nil)). [ur(87,a,132,a,b,1831,a)].
given #1197 (A,wt=13): 403 ->_s0(mapf(x,leq(s(y),s(z))),mapf(x,leq(y,z))). [ur(45,a,72,a)].
given #1198 (T,wt=9): 2559 ->*_s0(sndsplit(0,length(mapf(x,nil))),length(nil)). [ur(87,a,82,a,b,1831,a)].
given #1199 (T,wt=9): 2561 ->*_s0(app(nil,length(mapf(x,nil))),length(nil)). [ur(87,a,61,a,b,1831,a)].
given #1200 (T,wt=9): 2562 ->*_s0(f(app(nil,x),y),f(x,y)). [ur(87,a,116,a,b,86,a)].
given #1201 (T,wt=9): 2588 ->*_s0(head(sndsplit(0,mapf(x,nil))),head(nil)). [ur(87,a,483,a,b,1888,a)].
given #1202 (A,wt=13): 404 ->_s0(mapf(leq(s(x),s(y)),z),mapf(leq(x,y),z)). [ur(44,a,72,a)].
given #1203 (T,wt=9): 2589 ->*_s0(head(app(nil,mapf(x,nil))),head(nil)). [ur(87,a,133,a,b,1888,a)].
given #1204 (T,wt=9): 2591 ->*_s0(sndsplit(0,head(mapf(x,nil))),head(nil)). [ur(87,a,82,a,b,1888,a)].
given #1205 (T,wt=9): 2593 ->*_s0(app(nil,head(mapf(x,nil))),head(nil)). [ur(87,a,61,a,b,1888,a)].
given #1206 (T,wt=9): 2594 ->*_s0(empty(sndsplit(0,mapf(x,nil))),empty(nil)). [ur(87,a,486,a,b,1915,a)].
given #1207 (A,wt=13): 405 ->_s0(leq(x,leq(s(y),s(z))),leq(x,leq(y,z))). [ur(43,a,72,a)].
given #1208 (T,wt=9): 2595 ->*_s0(empty(app(nil,mapf(x,nil))),empty(nil)). [ur(87,a,136,a,b,1915,a)].
given #1209 (T,wt=9): 2597 ->*_s0(sndsplit(0,empty(mapf(x,nil))),empty(nil)). [ur(87,a,82,a,b,1915,a)].
given #1210 (T,wt=9): 2599 ->*_s0(app(nil,empty(mapf(x,nil))),empty(nil)). [ur(87,a,61,a,b,1915,a)].
given #1211 (T,wt=9): 2600 ->*_s0(s(sndsplit(0,sndsplit(0,x))),s(x)). [ur(87,a,464,a,b,1948,a)].
given #1212 (A,wt=13): 406 ->_s0(leq(leq(s(x),s(y)),z),leq(leq(x,y),z)). [ur(42,a,72,a)].
given #1213 (T,wt=9): 2601 ->*_s0(s(app(nil,sndsplit(0,x))),s(x)). [ur(87,a,114,a,b,1948,a)].
given #1214 (T,wt=9): 2603 ->*_s0(sndsplit(0,s(sndsplit(0,x))),s(x)). [ur(87,a,82,a,b,1948,a)].
given #1215 (T,wt=9): 2605 ->*_s0(app(nil,s(sndsplit(0,x))),s(x)). [ur(87,a,61,a,b,1948,a)].
given #1216 (T,wt=9): 2606 ->*_s0(tail(sndsplit(0,sndsplit(0,x))),tail(x)). [ur(87,a,469,a,b,2003,a)].
given #1217 (A,wt=11): 407 ->_s0(length(leq(s(x),s(y))),length(leq(x,y))). [ur(41,a,72,a)].
given #1218 (T,wt=9): 2607 ->*_s0(tail(app(nil,sndsplit(0,x))),tail(x)). [ur(87,a,119,a,b,2003,a)].
given #1219 (T,wt=9): 2609 ->*_s0(sndsplit(0,tail(sndsplit(0,x))),tail(x)). [ur(87,a,82,a,b,2003,a)].
given #1220 (T,wt=9): 2611 ->*_s0(app(nil,tail(sndsplit(0,x))),tail(x)). [ur(87,a,61,a,b,2003,a)].
given #1221 (T,wt=9): 2612 ->*_s0(cons(x,app(nil,y)),cons(x,y)). [ur(87,a,117,a,b,86,a)].
given #1222 (A,wt=11): 408 ->_s0(head(leq(s(x),s(y))),head(leq(x,y))). [ur(40,a,72,a)].
given #1223 (T,wt=9): 2638 ->*_s0(length(sndsplit(0,sndsplit(0,x))),length(x)). [ur(87,a,482,a,b,2035,a)].
given #1224 (T,wt=9): 2639 ->*_s0(length(app(nil,sndsplit(0,x))),length(x)). [ur(87,a,132,a,b,2035,a)].
given #1225 (T,wt=9): 2641 ->*_s0(sndsplit(0,length(sndsplit(0,x))),length(x)). [ur(87,a,82,a,b,2035,a)].
given #1226 (T,wt=9): 2643 ->*_s0(app(nil,length(sndsplit(0,x))),length(x)). [ur(87,a,61,a,b,2035,a)].
given #1227 (A,wt=13): 409 ->_s0(fstsplit(x,leq(s(y),s(z))),fstsplit(x,leq(y,z))). [ur(39,a,72,a)].
given #1228 (T,wt=9): 2644 ->*_s0(head(sndsplit(0,sndsplit(0,x))),head(x)). [ur(87,a,483,a,b,2070,a)].
given #1229 (T,wt=9): 2645 ->*_s0(head(app(nil,sndsplit(0,x))),head(x)). [ur(87,a,133,a,b,2070,a)].
given #1230 (T,wt=9): 2647 ->*_s0(sndsplit(0,head(sndsplit(0,x))),head(x)). [ur(87,a,82,a,b,2070,a)].
given #1231 (T,wt=9): 2649 ->*_s0(app(nil,head(sndsplit(0,x))),head(x)). [ur(87,a,61,a,b,2070,a)].
given #1232 (A,wt=13): 410 ->_s0(fstsplit(leq(s(x),s(y)),z),fstsplit(leq(x,y),z)). [ur(38,a,72,a)].
given #1233 (T,wt=9): 2650 ->*_s0(empty(sndsplit(0,sndsplit(0,x))),empty(x)). [ur(87,a,486,a,b,2129,a)].
given #1234 (T,wt=9): 2651 ->*_s0(empty(app(nil,sndsplit(0,x))),empty(x)). [ur(87,a,136,a,b,2129,a)].
given #1235 (T,wt=9): 2653 ->*_s0(sndsplit(0,empty(sndsplit(0,x))),empty(x)). [ur(87,a,82,a,b,2129,a)].
given #1236 (T,wt=9): 2655 ->*_s0(app(nil,empty(sndsplit(0,x))),empty(x)). [ur(87,a,61,a,b,2129,a)].
given #1237 (A,wt=11): 411 ->_s0(empty(leq(s(x),s(y))),empty(leq(x,y))). [ur(37,a,72,a)].
given #1238 (T,wt=9): 2682 ->*_s0(cons(app(nil,x),y),cons(x,y)). [ur(87,a,118,a,b,86,a)].
given #1239 (T,wt=9): 2813 ->*_s0(sndsplit(x,app(nil,y)),sndsplit(x,y)). [ur(87,a,120,a,b,86,a)].
given #1240 (T,wt=9): 2943 ->*_s0(sndsplit(app(nil,0),app(nil,x)),x). [ur(87,a,121,a,b,663,a)].
given #1241 (T,wt=9): 2944 ->*_s0(sndsplit(app(nil,0),fstsplit(0,x)),nil). [ur(87,a,121,a,b,659,a)].
given #1242 (A,wt=13): 412 ->_s0(app(x,leq(s(y),s(z))),app(x,leq(y,z))). [ur(36,a,72,a)].
given #1243 (T,wt=9): 2945 ->*_s0(sndsplit(app(nil,0),leq(0,x)),true). [ur(87,a,121,a,b,654,a)].
given #1244 (T,wt=9): 2946 ->*_s0(sndsplit(app(nil,0),mapf(x,nil)),nil). [ur(87,a,121,a,b,623,a)].
given #1245 (T,wt=9): 2947 ->*_s0(sndsplit(app(nil,0),sndsplit(0,x)),x). [ur(87,a,121,a,b,619,a)].
given #1246 (T,wt=9): 2952 ->*_s0(sndsplit(app(nil,x),y),sndsplit(x,y)). [ur(87,a,121,a,b,86,a)].
given #1247 (A,wt=13): 413 ->_s0(app(leq(s(x),s(y)),z),app(leq(x,y),z)). [ur(35,a,72,a)].
given #1248 (T,wt=9): 2978 ->*_s0(sndsplit(app(nil,app(nil,0)),x),x). [ur(87,a,121,a,b,2950,a)].
given #1249 (T,wt=9): 2982 ->*_s0(sndsplit(0,sndsplit(app(nil,0),x)),x). [ur(87,a,82,a,b,2950,a)].
given #1250 (T,wt=9): 2984 ->*_s0(app(nil,sndsplit(app(nil,0),x)),x). [ur(87,a,61,a,b,2950,a)].
given #1251 (T,wt=9): 3402 ->*_s0(length(sndsplit(0,fstsplit(s(x),nil))),0). [ur(87,a,482,a,b,3375,a)].
given #1252 (A,wt=15): 414 ->_s0(s(mapf(x,cons(y,z))),s(app(f(x,y),mapf(x,z)))). [ur(59,a,73,a)].
given #1253 (T,wt=9): 3403 ->*_s0(length(app(nil,fstsplit(s(x),nil))),0). [ur(87,a,132,a,b,3375,a)].
given #1254 (T,wt=9): 3405 ->*_s0(sndsplit(0,length(fstsplit(s(x),nil))),0). [ur(87,a,82,a,b,3375,a)].
given #1255 (T,wt=9): 3407 ->*_s0(app(nil,length(fstsplit(s(x),nil))),0). [ur(87,a,61,a,b,3375,a)].
given #1256 (T,wt=9): 3487 ->*_s0(empty(sndsplit(0,fstsplit(s(x),nil))),true). [ur(87,a,486,a,b,3460,a)].
given #1257 (A,wt=17): 415 ->_s0(f(x,mapf(y,cons(z,u))),f(x,app(f(y,z),mapf(y,u)))). [ur(58,a,73,a)].
given #1258 (T,wt=9): 3488 ->*_s0(empty(app(nil,fstsplit(s(x),nil))),true). [ur(87,a,136,a,b,3460,a)].
given #1259 (T,wt=9): 3490 ->*_s0(sndsplit(0,empty(fstsplit(s(x),nil))),true). [ur(87,a,82,a,b,3460,a)].
given #1260 (T,wt=9): 3492 ->*_s0(app(nil,empty(fstsplit(s(x),nil))),true). [ur(87,a,61,a,b,3460,a)].
given #1261 (T,wt=9): 3498 ->*_s0(s(head(cons(length(nil),x))),s(0)). [ur(87,a,264,a,b,848,a)].
given #1262 (A,wt=17): 416 ->_s0(f(mapf(x,cons(y,z)),u),f(app(f(x,y),mapf(x,z)),u)). [ur(57,a,73,a)].
given #1263 (T,wt=9): 3499 ->*_s0(s(head(cons(empty(nil),x))),s(true)). [ur(87,a,264,a,b,666,a)].
given #1264 (T,wt=9): 3531 ->*_s0(tail(head(cons(length(nil),x))),tail(0)). [ur(87,a,269,a,b,874,a)].
given #1265 (T,wt=9): 3532 ->*_s0(tail(head(cons(empty(nil),x))),tail(true)). [ur(87,a,269,a,b,718,a)].
given #1266 (T,wt=9): 3535 ->*_s0(tail(head(cons(cons(x,y),z))),y). [ur(87,a,269,a,b,564,a)].
given #1267 (A,wt=17): 417 ->_s0(cons(x,mapf(y,cons(z,u))),cons(x,app(f(y,z),mapf(y,u)))). [ur(56,a,73,a)].
given #1268 (T,wt=9): 3590 ->*_s0(length(head(cons(sndsplit(0,nil),x))),0). [ur(87,a,282,a,b,2034,a)].
given #1269 (T,wt=9): 3592 ->*_s0(length(head(cons(mapf(x,nil),y))),0). [ur(87,a,282,a,b,1830,a)].
given #1270 (T,wt=9): 3595 ->*_s0(length(head(cons(fstsplit(0,x),y))),0). [ur(87,a,282,a,b,1480,a)].
given #1271 (T,wt=9): 3597 ->*_s0(length(head(cons(app(nil,nil),x))),0). [ur(87,a,282,a,b,1280,a)].
given #1272 (A,wt=17): 418 ->_s0(cons(mapf(x,cons(y,z)),u),cons(app(f(x,y),mapf(x,z)),u)). [ur(55,a,73,a)].
given #1273 (T,wt=9): 3599 ->*_s0(length(head(cons(length(nil),x))),length(0)). [ur(87,a,282,a,b,900,a)].
given #1274 (T,wt=9): 3600 ->*_s0(length(head(cons(empty(nil),x))),length(true)). [ur(87,a,282,a,b,744,a)].
given #1275 (T,wt=9): 3628 ->*_s0(length(sndsplit(0,head(cons(nil,x)))),0). [ur(87,a,482,a,b,3601,a)].
given #1276 (T,wt=9): 3630 ->*_s0(length(app(nil,head(cons(nil,x)))),0). [ur(87,a,132,a,b,3601,a)].
given #1277 (A,wt=15): 419 ->_s0(tail(mapf(x,cons(y,z))),tail(app(f(x,y),mapf(x,z)))). [ur(54,a,73,a)].
given #1278 (T,wt=9): 3632 ->*_s0(sndsplit(0,length(head(cons(nil,x)))),0). [ur(87,a,82,a,b,3601,a)].
given #1279 (T,wt=9): 3634 ->*_s0(app(nil,length(head(cons(nil,x)))),0). [ur(87,a,61,a,b,3601,a)].
given #1280 (T,wt=9): 3640 ->*_s0(head(head(cons(length(nil),x))),head(0)). [ur(87,a,283,a,b,926,a)].
given #1281 (T,wt=9): 3641 ->*_s0(head(head(cons(empty(nil),x))),head(true)). [ur(87,a,283,a,b,770,a)].
given #1282 (A,wt=17): 420 ->_s0(sndsplit(x,mapf(y,cons(z,u))),sndsplit(x,app(f(y,z),mapf(y,u)))). [ur(53,a,73,a)].
given #1283 (T,wt=9): 3644 ->*_s0(head(head(cons(cons(x,y),z))),x). [ur(87,a,283,a,b,575,a)].
given #1284 (T,wt=9): 3673 ->*_s0(empty(head(cons(sndsplit(0,nil),x))),true). [ur(87,a,286,a,b,2128,a)].
given #1285 (T,wt=9): 3675 ->*_s0(empty(head(cons(mapf(x,nil),y))),true). [ur(87,a,286,a,b,1914,a)].
given #1286 (T,wt=9): 3678 ->*_s0(empty(head(cons(fstsplit(0,x),y))),true). [ur(87,a,286,a,b,1564,a)].
given #1287 (A,wt=17): 421 ->_s0(sndsplit(mapf(x,cons(y,z)),u),sndsplit(app(f(x,y),mapf(x,z)),u)). [ur(52,a,73,a)].
given #1288 (T,wt=9): 3680 ->*_s0(empty(head(cons(app(nil,nil),x))),true). [ur(87,a,286,a,b,1370,a)].
given #1289 (T,wt=9): 3681 ->*_s0(empty(head(cons(length(nil),x))),empty(0)). [ur(87,a,286,a,b,978,a)].
given #1290 (T,wt=9): 3682 ->*_s0(empty(head(cons(empty(nil),x))),empty(true)). [ur(87,a,286,a,b,796,a)].
given #1291 (T,wt=9): 3683 ->*_s0(empty(head(cons(cons(x,y),z))),false). [ur(87,a,286,a,b,580,a)].
given #1292 (A,wt=25): 422 ->_s0(ring(x,y,z,u,w,mapf(v5,cons(v6,v7))),ring(x,y,z,u,w,app(f(v5,v6),mapf(v5,v7)))). [ur(51,a,73,a)].
given #1293 (T,wt=9): 3737 ->*_s0(empty(sndsplit(0,head(cons(nil,x)))),true). [ur(87,a,486,a,b,3684,a)].
given #1294 (T,wt=9): 3739 ->*_s0(empty(app(nil,head(cons(nil,x)))),true). [ur(87,a,136,a,b,3684,a)].
given #1295 (T,wt=9): 3741 ->*_s0(sndsplit(0,empty(head(cons(nil,x)))),true). [ur(87,a,82,a,b,3684,a)].
given #1296 (T,wt=9): 3743 ->*_s0(app(nil,empty(head(cons(nil,x)))),true). [ur(87,a,61,a,b,3684,a)].
given #1297 (A,wt=25): 423 ->_s0(ring(x,y,z,u,mapf(w,cons(v5,v6)),v7),ring(x,y,z,u,app(f(w,v5),mapf(w,v6)),v7)). [ur(50,a,73,a)].
given #1298 (T,wt=9): 3823 ->*_s0(mapf(x,app(nil,y)),mapf(x,y)). [ur(87,a,128,a,b,86,a)].
given #1299 (T,wt=9): 3849 ->*_s0(mapf(x,app(nil,app(nil,nil))),nil). [ur(87,a,128,a,b,3822,a)].
given #1300 (T,wt=9): 3851 ->*_s0(sndsplit(0,mapf(x,app(nil,nil))),nil). [ur(87,a,82,a,b,3822,a)].
given #1301 (T,wt=9): 3853 ->*_s0(app(nil,mapf(x,app(nil,nil))),nil). [ur(87,a,61,a,b,3822,a)].
given #1302 (A,wt=25): 424 ->_s0(ring(x,y,z,mapf(u,cons(w,v5)),v6,v7),ring(x,y,z,app(f(u,w),mapf(u,v5)),v6,v7)). [ur(49,a,73,a)].
given #1303 (T,wt=9): 3940 ->*_s0(mapf(app(nil,x),y),mapf(x,y)). [ur(87,a,129,a,b,86,a)].
given #1304 (T,wt=9): 3968 ->*_s0(tail(cons(x,sndsplit(length(nil),y))),y). [ur(87,a,85,a,b,3913,a)].
given #1305 (T,wt=9): 3969 ->*_s0(sndsplit(s(length(nil)),cons(x,y)),y). [ur(87,a,83,a,b,3913,a)].
given #1306 (T,wt=9): 3971 ->*_s0(head(cons(sndsplit(length(nil),x),y)),x). [ur(87,a,67,a,b,3913,a)].
given #1307 (A,wt=25): 425 ->_s0(ring(x,y,mapf(z,cons(u,w)),v5,v6,v7),ring(x,y,app(f(z,u),mapf(z,w)),v5,v6,v7)). [ur(48,a,73,a)].
given #1308 (T,wt=9): 3973 ->*_s0(sndsplit(app(nil,length(nil)),empty(nil)),true). [ur(87,a,121,a,b,3911,a)].
given #1309 (T,wt=9): 3974 ->*_s0(sndsplit(length(nil),app(nil,empty(nil))),true). [ur(87,a,120,a,b,3911,a)].
given #1310 (T,wt=9): 3977 ->*_s0(sndsplit(0,sndsplit(length(nil),empty(nil))),true). [ur(87,a,82,a,b,3911,a)].
given #1311 (T,wt=9): 3979 ->*_s0(app(nil,sndsplit(length(nil),empty(nil))),true). [ur(87,a,61,a,b,3911,a)].
given #1312 (A,wt=25): 426 ->_s0(ring(x,mapf(y,cons(z,u)),w,v5,v6,v7),ring(x,app(f(y,z),mapf(y,u)),w,v5,v6,v7)). [ur(47,a,73,a)].
given #1313 (T,wt=9): 3980 ->*_s0(sndsplit(app(nil,length(nil)),length(nil)),0). [ur(87,a,121,a,b,3912,a)].
given #1314 (T,wt=9): 3981 ->*_s0(sndsplit(length(nil),app(nil,length(nil))),0). [ur(87,a,120,a,b,3912,a)].
given #1315 (T,wt=9): 3984 ->*_s0(sndsplit(0,sndsplit(length(nil),length(nil))),0). [ur(87,a,82,a,b,3912,a)].
given #1316 (T,wt=9): 3986 ->*_s0(app(nil,sndsplit(length(nil),length(nil))),0). [ur(87,a,61,a,b,3912,a)].
given #1317 (A,wt=25): 427 ->_s0(ring(mapf(x,cons(y,z)),u,w,v5,v6,v7),ring(app(f(x,y),mapf(x,z)),u,w,v5,v6,v7)). [ur(46,a,73,a)].
given #1318 (T,wt=9): 4013 ->*_s0(leq(s(0),app(nil,s(x))),true). [ur(87,a,130,a,b,655,a)].
given #1319 (T,wt=9): 4015 ->*_s0(leq(x,app(nil,y)),leq(x,y)). [ur(87,a,130,a,b,86,a)].
given #1320 (T,wt=9): 4094 ->*_s0(leq(s(x),app(nil,length(nil))),false). [ur(87,a,130,a,b,4067,a)].
given #1321 (T,wt=9): 4096 ->*_s0(sndsplit(0,leq(s(x),length(nil))),false). [ur(87,a,82,a,b,4067,a)].
given #1322 (A,wt=17): 428 ->_s0(mapf(x,mapf(y,cons(z,u))),mapf(x,app(f(y,z),mapf(y,u)))). [ur(45,a,73,a)].
given #1323 (T,wt=9): 4097 ->*_s0(leq(s(s(x)),s(length(nil))),false). [ur(87,a,72,a,b,4067,a)].
given #1324 (T,wt=9): 4099 ->*_s0(app(nil,leq(s(x),length(nil))),false). [ur(87,a,61,a,b,4067,a)].
given #1325 (T,wt=9): 4127 ->*_s0(leq(app(nil,s(x)),length(nil)),false). [ur(87,a,131,a,b,4067,a)].
given #1326 (T,wt=9): 4128 ->*_s0(leq(app(nil,s(0)),s(x)),true). [ur(87,a,131,a,b,655,a)].
given #1327 (A,wt=17): 429 ->_s0(mapf(mapf(x,cons(y,z)),u),mapf(app(f(x,y),mapf(x,z)),u)). [ur(44,a,73,a)].
given #1328 (T,wt=9): 4131 ->*_s0(leq(app(nil,x),y),leq(x,y)). [ur(87,a,131,a,b,86,a)].
given #1329 (T,wt=9): 4159 ->*_s0(tail(cons(x,leq(length(nil),y))),true). [ur(87,a,85,a,b,4100,a)].
given #1330 (T,wt=9): 4162 ->*_s0(head(cons(leq(length(nil),x),y)),true). [ur(87,a,67,a,b,4100,a)].
given #1331 (T,wt=9): 4165 ->*_s0(leq(app(nil,app(nil,0)),x),true). [ur(87,a,131,a,b,4129,a)].
given #1332 (A,wt=17): 430 ->_s0(leq(x,mapf(y,cons(z,u))),leq(x,app(f(y,z),mapf(y,u)))). [ur(43,a,73,a)].
Low Water (keep): wt=11.000, iters=8253
given #1333 (F,wt=20): 18891 -->*_s0(empty(fstsplit(app(nil,app(nil,0)),x)),false) | -->*_s0(empty(fstsplit(app(nil,app(nil,0)),y)),false) # answer(goal). [resolve(4165,a,88,c),unit_del(a,4165)].
given #1334 (T,wt=9): 4167 ->*_s0(sndsplit(0,leq(app(nil,0),x)),true). [ur(87,a,82,a,b,4129,a)].
given #1335 (T,wt=9): 4168 ->*_s0(leq(s(app(nil,0)),s(x)),true). [ur(87,a,72,a,b,4129,a)].
given #1336 (T,wt=9): 4170 ->*_s0(app(nil,leq(app(nil,0),x)),true). [ur(87,a,61,a,b,4129,a)].
given #1337 (T,wt=9): 4225 ->*_s0(fstsplit(x,app(nil,y)),fstsplit(x,y)). [ur(87,a,134,a,b,86,a)].
given #1338 (A,wt=17): 431 ->_s0(leq(mapf(x,cons(y,z)),u),leq(app(f(x,y),mapf(x,z)),u)). [ur(42,a,73,a)].
given #1339 (T,wt=9): 4251 ->*_s0(tail(cons(x,fstsplit(length(nil),y))),nil). [ur(87,a,85,a,b,4197,a)].
given #1340 (T,wt=9): 4253 ->*_s0(head(cons(fstsplit(length(nil),x),y)),nil). [ur(87,a,67,a,b,4197,a)].
given #1341 (T,wt=9): 4336 ->*_s0(fstsplit(app(nil,x),y),fstsplit(x,y)). [ur(87,a,135,a,b,86,a)].
given #1342 (T,wt=9): 4362 ->*_s0(fstsplit(app(nil,app(nil,0)),x),nil). [ur(87,a,135,a,b,4334,a)].
given #1343 (A,wt=15): 432 ->_s0(length(mapf(x,cons(y,z))),length(app(f(x,y),mapf(x,z)))). [ur(41,a,73,a)].
given #1344 (T,wt=9): 4364 ->*_s0(sndsplit(0,fstsplit(app(nil,0),x)),nil). [ur(87,a,82,a,b,4334,a)].
given #1345 (T,wt=9): 4366 ->*_s0(app(nil,fstsplit(app(nil,0),x)),nil). [ur(87,a,61,a,b,4334,a)].
given #1346 (T,wt=9): 4445 ->*_s0(app(x,app(nil,y)),app(x,y)). [ur(87,a,137,a,b,86,a)].
given #1347 (T,wt=9): 4576 ->*_s0(app(app(nil,nil),app(nil,x)),x). [ur(87,a,138,a,b,665,a)].
given #1348 (A,wt=15): 433 ->_s0(head(mapf(x,cons(y,z))),head(app(f(x,y),mapf(x,z)))). [ur(40,a,73,a)].
given #1349 (T,wt=9): 4577 ->*_s0(app(app(nil,nil),fstsplit(0,x)),nil). [ur(87,a,138,a,b,661,a)].
given #1350 (T,wt=9): 4578 ->*_s0(app(app(nil,nil),leq(0,x)),true). [ur(87,a,138,a,b,657,a)].
given #1351 (T,wt=9): 4579 ->*_s0(app(app(nil,nil),mapf(x,nil)),nil). [ur(87,a,138,a,b,625,a)].
given #1352 (T,wt=9): 4580 ->*_s0(app(app(nil,nil),sndsplit(0,x)),x). [ur(87,a,138,a,b,621,a)].
given #1353 (A,wt=17): 434 ->_s0(fstsplit(x,mapf(y,cons(z,u))),fstsplit(x,app(f(y,z),mapf(y,u)))). [ur(39,a,73,a)].
given #1354 (T,wt=9): 4584 ->*_s0(app(app(nil,x),y),app(x,y)). [ur(87,a,138,a,b,86,a)].
given #1355 (T,wt=9): 4610 ->*_s0(length(sndsplit(0,sndsplit(s(x),nil))),0). [ur(87,a,482,a,b,4549,a)].
given #1356 (T,wt=9): 4612 ->*_s0(length(app(nil,sndsplit(s(x),nil))),0). [ur(87,a,132,a,b,4549,a)].
given #1357 (T,wt=9): 4614 ->*_s0(sndsplit(0,length(sndsplit(s(x),nil))),0). [ur(87,a,82,a,b,4549,a)].
given #1358 (A,wt=17): 435 ->_s0(fstsplit(mapf(x,cons(y,z)),u),fstsplit(app(f(x,y),mapf(x,z)),u)). [ur(38,a,73,a)].
given #1359 (T,wt=9): 4616 ->*_s0(app(nil,length(sndsplit(s(x),nil))),0). [ur(87,a,61,a,b,4549,a)].
given #1360 (T,wt=9): 4617 ->*_s0(app(app(nil,app(nil,nil)),x),x). [ur(87,a,138,a,b,4583,a)].
given #1361 (T,wt=9): 4620 ->*_s0(sndsplit(0,app(app(nil,nil),x)),x). [ur(87,a,82,a,b,4583,a)].
given #1362 (T,wt=9): 4622 ->*_s0(app(nil,app(app(nil,nil),x)),x). [ur(87,a,61,a,b,4583,a)].
given #1363 (A,wt=15): 436 ->_s0(empty(mapf(x,cons(y,z))),empty(app(f(x,y),mapf(x,z)))). [ur(37,a,73,a)].
given #1364 (T,wt=9): 4702 ->*_s0(empty(sndsplit(0,sndsplit(s(x),nil))),true). [ur(87,a,486,a,b,4649,a)].
given #1365 (T,wt=9): 4704 ->*_s0(empty(app(nil,sndsplit(s(x),nil))),true). [ur(87,a,136,a,b,4649,a)].
given #1366 (T,wt=9): 4706 ->*_s0(sndsplit(0,empty(sndsplit(s(x),nil))),true). [ur(87,a,82,a,b,4649,a)].
given #1367 (T,wt=9): 4708 ->*_s0(app(nil,empty(sndsplit(s(x),nil))),true). [ur(87,a,61,a,b,4649,a)].
given #1368 (A,wt=17): 437 ->_s0(app(x,mapf(y,cons(z,u))),app(x,app(f(y,z),mapf(y,u)))). [ur(36,a,73,a)].
given #1369 (T,wt=9): 4714 ->*_s0(s(tail(cons(x,length(nil)))),s(0)). [ur(87,a,539,a,b,848,a)].
given #1370 (T,wt=9): 4715 ->*_s0(s(tail(cons(x,empty(nil)))),s(true)). [ur(87,a,539,a,b,666,a)].
given #1371 (T,wt=9): 4747 ->*_s0(tail(tail(cons(x,length(nil)))),tail(0)). [ur(87,a,544,a,b,874,a)].
given #1372 (T,wt=9): 4748 ->*_s0(tail(tail(cons(x,empty(nil)))),tail(true)). [ur(87,a,544,a,b,718,a)].
given #1373 (A,wt=17): 438 ->_s0(app(mapf(x,cons(y,z)),u),app(app(f(x,y),mapf(x,z)),u)). [ur(35,a,73,a)].
given #1374 (T,wt=9): 4751 ->*_s0(tail(tail(cons(x,cons(y,z)))),z). [ur(87,a,544,a,b,564,a)].
given #1375 (T,wt=9): 4782 ->*_s0(length(tail(cons(x,sndsplit(0,nil)))),0). [ur(87,a,557,a,b,2034,a)].
given #1376 (T,wt=9): 4784 ->*_s0(length(tail(cons(x,mapf(y,nil)))),0). [ur(87,a,557,a,b,1830,a)].
given #1377 (T,wt=9): 4787 ->*_s0(length(tail(cons(x,fstsplit(0,y)))),0). [ur(87,a,557,a,b,1480,a)].
given #1378 (A,wt=17): 447 ->_s0(ring(x,y,z,u,w,mapf(v5,nil)),ring(x,y,z,u,w,nil)). [ur(51,a,74,a)].
given #1379 (T,wt=9): 4789 ->*_s0(length(tail(cons(x,app(nil,nil)))),0). [ur(87,a,557,a,b,1280,a)].
given #1380 (T,wt=9): 4791 ->*_s0(length(tail(cons(x,length(nil)))),length(0)). [ur(87,a,557,a,b,900,a)].
given #1381 (T,wt=9): 4792 ->*_s0(length(tail(cons(x,empty(nil)))),length(true)). [ur(87,a,557,a,b,744,a)].
given #1382 (T,wt=9): 4847 ->*_s0(length(sndsplit(0,tail(cons(x,nil)))),0). [ur(87,a,482,a,b,4793,a)].
given #1383 (A,wt=17): 448 ->_s0(ring(x,y,z,u,mapf(w,nil),v5),ring(x,y,z,u,nil,v5)). [ur(50,a,74,a)].
given #1384 (T,wt=9): 4849 ->*_s0(length(app(nil,tail(cons(x,nil)))),0). [ur(87,a,132,a,b,4793,a)].
given #1385 (T,wt=9): 4851 ->*_s0(sndsplit(0,length(tail(cons(x,nil)))),0). [ur(87,a,82,a,b,4793,a)].
given #1386 (T,wt=9): 4853 ->*_s0(app(nil,length(tail(cons(x,nil)))),0). [ur(87,a,61,a,b,4793,a)].
given #1387 (T,wt=9): 4859 ->*_s0(head(tail(cons(x,length(nil)))),head(0)). [ur(87,a,558,a,b,926,a)].
given #1388 (A,wt=17): 449 ->_s0(ring(x,y,z,mapf(u,nil),w,v5),ring(x,y,z,nil,w,v5)). [ur(49,a,74,a)].
given #1389 (T,wt=9): 4860 ->*_s0(head(tail(cons(x,empty(nil)))),head(true)). [ur(87,a,558,a,b,770,a)].
given #1390 (T,wt=9): 4863 ->*_s0(head(tail(cons(x,cons(y,z)))),y). [ur(87,a,558,a,b,575,a)].
given #1391 (T,wt=9): 4894 ->*_s0(empty(tail(cons(x,sndsplit(0,nil)))),true). [ur(87,a,561,a,b,2128,a)].
given #1392 (T,wt=9): 4896 ->*_s0(empty(tail(cons(x,mapf(y,nil)))),true). [ur(87,a,561,a,b,1914,a)].
given #1393 (A,wt=17): 450 ->_s0(ring(x,y,mapf(z,nil),u,w,v5),ring(x,y,nil,u,w,v5)). [ur(48,a,74,a)].
given #1394 (T,wt=9): 4899 ->*_s0(empty(tail(cons(x,fstsplit(0,y)))),true). [ur(87,a,561,a,b,1564,a)].
given #1395 (T,wt=9): 4901 ->*_s0(empty(tail(cons(x,app(nil,nil)))),true). [ur(87,a,561,a,b,1370,a)].
given #1396 (T,wt=9): 4902 ->*_s0(empty(tail(cons(x,length(nil)))),empty(0)). [ur(87,a,561,a,b,978,a)].
given #1397 (T,wt=9): 4903 ->*_s0(empty(tail(cons(x,empty(nil)))),empty(true)). [ur(87,a,561,a,b,796,a)].
given #1398 (A,wt=17): 451 ->_s0(ring(x,mapf(y,nil),z,u,w,v5),ring(x,nil,z,u,w,v5)). [ur(47,a,74,a)].
given #1399 (T,wt=9): 4904 ->*_s0(empty(tail(cons(x,cons(y,z)))),false). [ur(87,a,561,a,b,580,a)].
given #1400 (T,wt=9): 4933 ->*_s0(empty(sndsplit(0,tail(cons(x,nil)))),true). [ur(87,a,486,a,b,4905,a)].
given #1401 (T,wt=9): 4935 ->*_s0(empty(app(nil,tail(cons(x,nil)))),true). [ur(87,a,136,a,b,4905,a)].
given #1402 (T,wt=9): 4937 ->*_s0(sndsplit(0,empty(tail(cons(x,nil)))),true). [ur(87,a,82,a,b,4905,a)].
given #1403 (A,wt=17): 452 ->_s0(ring(mapf(x,nil),y,z,u,w,v5),ring(nil,y,z,u,w,v5)). [ur(46,a,74,a)].
given #1404 (T,wt=9): 4939 ->*_s0(app(nil,empty(tail(cons(x,nil)))),true). [ur(87,a,61,a,b,4905,a)].
given #1405 (T,wt=9): 5060 ->*_s0(sndsplit(length(nil),empty(cons(x,y))),false). [ur(87,a,145,a,b,3913,a)].
given #1406 (T,wt=9): 6761 ->*_s0(sndsplit(length(nil),tail(cons(x,y))),y). [ur(87,a,321,a,b,1005,a)].
given #1407 (T,wt=9): 6800 ->*_s0(sndsplit(length(nil),sndsplit(s(x),nil)),nil). [ur(87,a,321,a,b,1010,a)].
given #1408 (A,wt=17): 472 ->_s0(ring(x,y,z,u,w,sndsplit(0,v5)),ring(x,y,z,u,w,v5)). [ur(51,a,82,a)].
given #1409 (T,wt=9): 6812 ->*_s0(sndsplit(length(nil),leq(s(x),0)),false). [ur(87,a,321,a,b,1014,a)].
given #1410 (T,wt=9): 6857 ->*_s0(sndsplit(length(nil),head(cons(x,y))),x). [ur(87,a,321,a,b,1046,a)].
given #1411 (T,wt=9): 6869 ->*_s0(sndsplit(length(nil),fstsplit(s(x),nil)),nil). [ur(87,a,321,a,b,1050,a)].
given #1412 (T,wt=9): 6916 ->*_s0(sndsplit(length(nil),sndsplit(0,length(nil))),0). [ur(87,a,321,a,b,1059,a)].
given #1413 (A,wt=17): 473 ->_s0(ring(x,y,z,u,sndsplit(0,w),v5),ring(x,y,z,u,w,v5)). [ur(50,a,82,a)].
given #1414 (T,wt=9): 6965 ->*_s0(sndsplit(length(nil),sndsplit(0,empty(nil))),true). [ur(87,a,321,a,b,1095,a)].
given #1415 (T,wt=9): 7014 ->*_s0(sndsplit(length(nil),s(empty(nil))),s(true)). [ur(87,a,321,a,b,1103,a)].
given #1416 (T,wt=9): 7052 ->*_s0(sndsplit(length(nil),tail(empty(nil))),tail(true)). [ur(87,a,321,a,b,1133,a)].
given #1417 (T,wt=9): 7064 ->*_s0(sndsplit(length(nil),length(empty(nil))),length(true)). [ur(87,a,321,a,b,1137,a)].
given #1418 (A,wt=17): 474 ->_s0(ring(x,y,z,sndsplit(0,u),w,v5),ring(x,y,z,u,w,v5)). [ur(49,a,82,a)].
given #1419 (T,wt=9): 7102 ->*_s0(sndsplit(length(nil),head(empty(nil))),head(true)). [ur(87,a,321,a,b,1141,a)].
given #1420 (T,wt=9): 7114 ->*_s0(sndsplit(length(nil),empty(empty(nil))),empty(true)). [ur(87,a,321,a,b,1145,a)].
given #1421 (T,wt=9): 7152 ->*_s0(sndsplit(length(nil),s(length(nil))),s(0)). [ur(87,a,321,a,b,1175,a)].
given #1422 (T,wt=9): 7164 ->*_s0(sndsplit(length(nil),tail(length(nil))),tail(0)). [ur(87,a,321,a,b,1180,a)].
given #1423 (A,wt=17): 475 ->_s0(ring(x,y,sndsplit(0,z),u,w,v5),ring(x,y,z,u,w,v5)). [ur(48,a,82,a)].
given #1424 (T,wt=9): 7172 ->*_s0(f(x,fstsplit(0,y)),f(x,nil)). [ur(87,a,190,a,b,86,a)].
given #1425 (T,wt=9): 7202 ->*_s0(sndsplit(length(nil),length(length(nil))),length(0)). [ur(87,a,321,a,b,1184,a)].
given #1426 (T,wt=9): 7214 ->*_s0(sndsplit(length(nil),head(length(nil))),head(0)). [ur(87,a,321,a,b,1188,a)].
given #1427 (T,wt=9): 7222 ->*_s0(f(fstsplit(0,x),y),f(nil,y)). [ur(87,a,191,a,b,86,a)].
given #1428 (A,wt=17): 476 ->_s0(ring(x,sndsplit(0,y),z,u,w,v5),ring(x,y,z,u,w,v5)). [ur(47,a,82,a)].
given #1429 (T,wt=9): 7252 ->*_s0(sndsplit(length(nil),empty(length(nil))),empty(0)). [ur(87,a,321,a,b,1218,a)].
given #1430 (T,wt=9): 7272 ->*_s0(cons(x,fstsplit(0,y)),cons(x,nil)). [ur(87,a,192,a,b,86,a)].
given #1431 (T,wt=9): 7330 ->*_s0(cons(fstsplit(0,x),y),cons(nil,y)). [ur(87,a,193,a,b,86,a)].
given #1432 (T,wt=9): 7380 ->*_s0(sndsplit(length(nil),length(app(nil,nil))),0). [ur(87,a,321,a,b,1335,a)].
given #1433 (A,wt=17): 477 ->_s0(ring(sndsplit(0,x),y,z,u,w,v5),ring(x,y,z,u,w,v5)). [ur(46,a,82,a)].
given #1434 (T,wt=9): 7389 ->*_s0(sndsplit(x,fstsplit(0,y)),sndsplit(x,nil)). [ur(87,a,195,a,b,86,a)].
given #1435 (T,wt=9): 7443 ->*_s0(sndsplit(fstsplit(0,x),y),sndsplit(nil,y)). [ur(87,a,196,a,b,86,a)].
given #1436 (T,wt=9): 7527 ->*_s0(sndsplit(length(nil),empty(app(nil,nil))),true). [ur(87,a,321,a,b,1399,a)].
given #1437 (T,wt=9): 7547 ->*_s0(sndsplit(length(nil),length(fstsplit(0,x))),0). [ur(87,a,321,a,b,1509,a)].
given #1438 (A,wt=12): 489 ->_s0(s(sndsplit(s(x),cons(y,z))),s(sndsplit(x,z))). [ur(59,a,83,a)].
given #1439 (T,wt=9): 7593 ->*_s0(sndsplit(length(nil),empty(fstsplit(0,x))),true). [ur(87,a,321,a,b,1593,a)].
given #1440 (T,wt=9): 7639 ->*_s0(sndsplit(length(nil),length(mapf(x,nil))),0). [ur(87,a,321,a,b,1859,a)].
given #1441 (T,wt=9): 7685 ->*_s0(sndsplit(length(nil),empty(mapf(x,nil))),true). [ur(87,a,321,a,b,1943,a)].
given #1442 (T,wt=9): 7830 ->*_s0(mapf(x,fstsplit(0,y)),mapf(x,nil)). [ur(87,a,203,a,b,86,a)].
given #1443 (A,wt=14): 490 ->_s0(f(x,sndsplit(s(y),cons(z,u))),f(x,sndsplit(y,u))). [ur(58,a,83,a)].
given #1444 (T,wt=9): 7856 ->*_s0(mapf(x,app(nil,fstsplit(0,y))),nil). [ur(87,a,128,a,b,7829,a)].
given #1445 (T,wt=9): 7858 ->*_s0(sndsplit(0,mapf(x,fstsplit(0,y))),nil). [ur(87,a,82,a,b,7829,a)].
given #1446 (T,wt=9): 7860 ->*_s0(app(nil,mapf(x,fstsplit(0,y))),nil). [ur(87,a,61,a,b,7829,a)].
given #1447 (T,wt=9): 7877 ->*_s0(sndsplit(length(nil),length(sndsplit(0,nil))),0). [ur(87,a,321,a,b,2064,a)].
given #1448 (A,wt=14): 491 ->_s0(f(sndsplit(s(x),cons(y,z)),u),f(sndsplit(x,z),u)). [ur(57,a,83,a)].
given #1449 (T,wt=9): 7885 ->*_s0(mapf(fstsplit(0,x),y),mapf(nil,y)). [ur(87,a,204,a,b,86,a)].
given #1450 (T,wt=9): 7939 ->*_s0(leq(x,fstsplit(0,y)),leq(x,nil)). [ur(87,a,205,a,b,86,a)].
given #1451 (T,wt=9): 7997 ->*_s0(leq(fstsplit(0,x),y),leq(nil,y)). [ur(87,a,206,a,b,86,a)].
given #1452 (T,wt=9): 8056 ->*_s0(fstsplit(x,fstsplit(0,y)),fstsplit(x,nil)). [ur(87,a,209,a,b,86,a)].
given #1453 (A,wt=14): 492 ->_s0(cons(x,sndsplit(s(y),cons(z,u))),cons(x,sndsplit(y,u))). [ur(56,a,83,a)].
given #1454 (T,wt=9): 8082 ->*_s0(sndsplit(length(nil),empty(sndsplit(0,nil))),true). [ur(87,a,321,a,b,2158,a)].
given #1455 (T,wt=9): 8110 ->*_s0(fstsplit(fstsplit(0,x),y),fstsplit(nil,y)). [ur(87,a,210,a,b,86,a)].
given #1456 (T,wt=9): 8168 ->*_s0(app(x,fstsplit(0,y)),app(x,nil)). [ur(87,a,212,a,b,86,a)].
given #1457 (T,wt=9): 8209 ->*_s0(f(length(nil),empty(nil)),f(0,true)). [ur(87,a,316,a,b,2839,a)].
given #1458 (A,wt=14): 493 ->_s0(cons(sndsplit(s(x),cons(y,z)),u),cons(sndsplit(x,z),u)). [ur(55,a,83,a)].
given #1459 (T,wt=9): 8211 ->*_s0(f(empty(nil),empty(nil)),f(true,true)). [ur(87,a,166,a,b,2839,a)].
given #1460 (T,wt=9): 8220 ->*_s0(f(empty(nil),length(nil)),f(true,0)). [ur(87,a,315,a,b,2865,a)].
given #1461 (T,wt=9): 8258 ->*_s0(app(fstsplit(0,x),app(nil,y)),y). [ur(87,a,213,a,b,665,a)].
given #1462 (T,wt=9): 8259 ->*_s0(app(fstsplit(0,x),fstsplit(0,y)),nil). [ur(87,a,213,a,b,661,a)].
given #1463 (A,wt=12): 494 ->_s0(tail(sndsplit(s(x),cons(y,z))),tail(sndsplit(x,z))). [ur(54,a,83,a)].
given #1464 (T,wt=9): 8260 ->*_s0(app(fstsplit(0,x),leq(0,y)),true). [ur(87,a,213,a,b,657,a)].
given #1465 (T,wt=9): 8261 ->*_s0(app(fstsplit(0,x),mapf(y,nil)),nil). [ur(87,a,213,a,b,625,a)].
given #1466 (T,wt=9): 8262 ->*_s0(app(fstsplit(0,x),sndsplit(0,y)),y). [ur(87,a,213,a,b,621,a)].
given #1467 (T,wt=9): 8266 ->*_s0(app(fstsplit(0,x),y),app(nil,y)). [ur(87,a,213,a,b,86,a)].
given #1468 (A,wt=14): 495 ->_s0(sndsplit(x,sndsplit(s(y),cons(z,u))),sndsplit(x,sndsplit(y,u))). [ur(53,a,83,a)].
given #1469 (T,wt=9): 8292 ->*_s0(app(app(nil,fstsplit(0,x)),y),y). [ur(87,a,138,a,b,8265,a)].
given #1470 (T,wt=9): 8295 ->*_s0(sndsplit(0,app(fstsplit(0,x),y)),y). [ur(87,a,82,a,b,8265,a)].
given #1471 (T,wt=9): 8297 ->*_s0(app(nil,app(fstsplit(0,x),y)),y). [ur(87,a,61,a,b,8265,a)].
given #1472 (T,wt=9): 8298 ->*_s0(cons(length(nil),empty(nil)),cons(0,true)). [ur(87,a,318,a,b,2891,a)].
given #1473 (A,wt=14): 496 ->_s0(sndsplit(sndsplit(s(x),cons(y,z)),u),sndsplit(sndsplit(x,z),u)). [ur(52,a,83,a)].
given #1474 (T,wt=9): 8300 ->*_s0(cons(empty(nil),empty(nil)),cons(true,true)). [ur(87,a,168,a,b,2891,a)].
given #1475 (T,wt=9): 8309 ->*_s0(cons(empty(nil),length(nil)),cons(true,0)). [ur(87,a,317,a,b,2917,a)].
given #1476 (T,wt=9): 8366 ->*_s0(sndsplit(length(nil),empty(nil)),sndsplit(0,true)). [ur(87,a,321,a,b,2985,a)].
given #1477 (T,wt=9): 8368 ->*_s0(sndsplit(empty(nil),empty(nil)),sndsplit(true,true)). [ur(87,a,171,a,b,2985,a)].
given #1478 (A,wt=22): 497 ->_s0(ring(x,y,z,u,w,sndsplit(s(v5),cons(v6,v7))),ring(x,y,z,u,w,sndsplit(v5,v7))). [ur(51,a,83,a)].
given #1479 (T,wt=9): 8378 ->*_s0(sndsplit(empty(nil),length(nil)),sndsplit(true,0)). [ur(87,a,320,a,b,3011,a)].
given #1480 (T,wt=9): 8416 ->*_s0(mapf(length(nil),empty(nil)),mapf(0,true)). [ur(87,a,329,a,b,3037,a)].
given #1481 (T,wt=9): 8418 ->*_s0(mapf(empty(nil),empty(nil)),mapf(true,true)). [ur(87,a,179,a,b,3037,a)].
given #1482 (T,wt=9): 8427 ->*_s0(mapf(empty(nil),length(nil)),mapf(true,0)). [ur(87,a,328,a,b,3089,a)].
given #1483 (A,wt=22): 498 ->_s0(ring(x,y,z,u,sndsplit(s(w),cons(v5,v6)),v7),ring(x,y,z,u,sndsplit(w,v6),v7)). [ur(50,a,83,a)].
given #1484 (T,wt=9): 8437 ->*_s0(leq(length(nil),empty(nil)),leq(0,true)). [ur(87,a,331,a,b,3115,a)].
given #1485 (T,wt=9): 8439 ->*_s0(leq(empty(nil),empty(nil)),leq(true,true)). [ur(87,a,181,a,b,3115,a)].
given #1486 (T,wt=9): 8449 ->*_s0(leq(empty(nil),length(nil)),leq(true,0)). [ur(87,a,330,a,b,3141,a)].
given #1487 (T,wt=9): 8487 ->*_s0(fstsplit(length(nil),empty(nil)),fstsplit(0,true)). [ur(87,a,335,a,b,3167,a)].
given #1488 (A,wt=22): 499 ->_s0(ring(x,y,z,sndsplit(s(u),cons(w,v5)),v6,v7),ring(x,y,z,sndsplit(u,v5),v6,v7)). [ur(49,a,83,a)].
given #1489 (T,wt=9): 8489 ->*_s0(fstsplit(empty(nil),empty(nil)),fstsplit(true,true)). [ur(87,a,185,a,b,3167,a)].
given #1490 (T,wt=9): 8498 ->*_s0(fstsplit(empty(nil),length(nil)),fstsplit(true,0)). [ur(87,a,334,a,b,3219,a)].
given #1491 (T,wt=9): 8508 ->*_s0(app(length(nil),empty(nil)),app(0,true)). [ur(87,a,338,a,b,3245,a)].
given #1492 (T,wt=9): 8510 ->*_s0(app(empty(nil),empty(nil)),app(true,true)). [ur(87,a,188,a,b,3245,a)].
given #1493 (A,wt=22): 500 ->_s0(ring(x,y,sndsplit(s(z),cons(u,w)),v5,v6,v7),ring(x,y,sndsplit(z,w),v5,v6,v7)). [ur(48,a,83,a)].
given #1494 (T,wt=9): 8519 ->*_s0(app(empty(nil),length(nil)),app(true,0)). [ur(87,a,337,a,b,3271,a)].
given #1495 (T,wt=9): 8647 ->*_s0(tail(fstsplit(s(0),cons(x,y))),nil). [ur(87,a,219,a,b,658,a)].
given #1496 (T,wt=9): 8691 ->*_s0(f(length(nil),length(nil)),f(0,0)). [ur(87,a,316,a,b,3744,a)].
given #1497 (T,wt=9): 8743 ->*_s0(cons(length(nil),length(nil)),cons(0,0)). [ur(87,a,318,a,b,3796,a)].
given #1498 (A,wt=22): 501 ->_s0(ring(x,sndsplit(s(y),cons(z,u)),w,v5,v6,v7),ring(x,sndsplit(y,u),w,v5,v6,v7)). [ur(47,a,83,a)].
given #1499 (T,wt=9): 8766 ->*_s0(sndsplit(length(nil),length(nil)),sndsplit(0,0)). [ur(87,a,321,a,b,3880,a)].
given #1500 (T,wt=9): 8886 ->*_s0(sndsplit(length(nil),sndsplit(length(nil),x)),x). [ur(87,a,321,a,b,3970,a)].
given #1501 (T,wt=9): 8925 ->*_s0(mapf(length(nil),length(nil)),mapf(0,0)). [ur(87,a,329,a,b,3987,a)].
given #1502 (T,wt=9): 8951 ->*_s0(leq(length(nil),length(nil)),leq(0,0)). [ur(87,a,331,a,b,4068,a)].
given #1503 (A,wt=22): 502 ->_s0(ring(sndsplit(s(x),cons(y,z)),u,w,v5,v6,v7),ring(sndsplit(x,z),u,w,v5,v6,v7)). [ur(46,a,83,a)].
given #1504 (T,wt=9): 9011 ->*_s0(sndsplit(length(nil),leq(length(nil),x)),true). [ur(87,a,321,a,b,4160,a)].
given #1505 (T,wt=9): 9031 ->*_s0(fstsplit(length(nil),length(nil)),fstsplit(0,0)). [ur(87,a,335,a,b,4171,a)].
given #1506 (T,wt=9): 9082 ->*_s0(sndsplit(length(nil),fstsplit(length(nil),x)),nil). [ur(87,a,321,a,b,4252,a)].
given #1507 (T,wt=9): 9095 ->*_s0(app(length(nil),length(nil)),app(0,0)). [ur(87,a,338,a,b,4255,a)].
given #1508 (A,wt=14): 503 ->_s0(mapf(x,sndsplit(s(y),cons(z,u))),mapf(x,sndsplit(y,u))). [ur(45,a,83,a)].
given #1509 (T,wt=9): 9459 ->*_s0(head(fstsplit(s(x),cons(y,z))),y). [ur(87,a,233,a,b,575,a)].
given #1510 (T,wt=9): 9576 ->*_s0(length(cons(x,empty(nil))),s(length(true))). [ur(87,a,68,a,b,5461,a)].
given #1511 (T,wt=9): 9639 ->*_s0(empty(fstsplit(s(x),cons(y,z))),false). [ur(87,a,236,a,b,580,a)].
given #1512 (T,wt=9): 9975 ->*_s0(length(cons(x,length(nil))),s(length(0))). [ur(87,a,68,a,b,6267,a)].
given #1513 (A,wt=14): 504 ->_s0(mapf(sndsplit(s(x),cons(y,z)),u),mapf(sndsplit(x,z),u)). [ur(44,a,83,a)].
given #1514 (F,wt=23): 19832 -->*_s0(leq(s(x),length(y)),true) | -->*_s0(empty(fstsplit(s(x),y)),false) | -->*_s0(leq(s(x),length(cons(z,u))),true) # answer(goal). [resolve(9639,a,88,d)].
given #1515 (F,wt=18): 19838 -->*_s0(leq(s(x),length(cons(y,z))),true) | -->*_s0(leq(s(x),length(cons(u,w))),true) # answer(goal). [resolve(19832,b,9639,a)].
given #1516 (F,wt=26): 19837 -->*_s0(empty(fstsplit(s(x),y)),false) | -->*_s0(leq(s(x),length(cons(z,u))),true) | -->_s0(leq(s(x),length(y)),w) | -->*_s0(w,true) # answer(goal). [resolve(19832,a,87,c)].
============================== PROOF =================================
% Proof 1 at 0.26 (+ 0.03) seconds: goal.
% Length of proof is 29.
% Level of proof is 6.
% Maximum clause weight is 26.000.
% Given clauses 1516.
3 ->_s0(x1,y) -> ->_s0(empty(x1),empty(y)) # label(congruence) # label(non_clause). [assumption].
8 ->_s0(x1,y) -> ->_s0(leq(x1,x2),leq(y,x2)) # label(congruence) # label(non_clause). [assumption].
9 ->_s0(x2,y) -> ->_s0(leq(x1,x2),leq(x1,y)) # label(congruence) # label(non_clause). [assumption].
33 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption].
34 (exists x13 exists x14 exists x15 (->*_s0(leq(x13,length(x14)),true) & ->*_s0(empty(fstsplit(x13,x14)),false) & ->*_s0(leq(x13,length(x15)),true) & ->*_s0(empty(fstsplit(x13,x15)),false))) # label(goal) # label(non_clause) # label(goal). [goal].
37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)].
42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence). [clausify(8)].
43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)].
61 ->_s0(app(nil,x),x) # label(replacement). [assumption].
62 ->_s0(empty(cons(x,y)),false) # label(replacement). [assumption].
65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption].
68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption].
70 ->_s0(leq(0,x),true) # label(replacement). [assumption].
72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption].
86 ->*_s0(x,x) # label(reflexivity). [assumption].
87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)].
88 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal) # answer(goal). [deny(34)].
131 ->_s0(leq(app(nil,x),y),leq(x,y)). [ur(42,a,61,a)].
236 ->_s0(empty(fstsplit(s(x),cons(y,z))),empty(cons(y,fstsplit(x,z)))). [ur(37,a,65,a)].
305 ->_s0(leq(x,length(cons(y,z))),leq(x,s(length(z)))). [ur(43,a,68,a)].
572 ->*_s0(leq(0,x),true). [ur(87,a,70,a,b,86,a)].
580 ->*_s0(empty(cons(x,y)),false). [ur(87,a,62,a,b,86,a)].
4129 ->*_s0(leq(app(nil,0),x),true). [ur(87,a,131,a,b,572,a)].
4168 ->*_s0(leq(s(app(nil,0)),s(x)),true). [ur(87,a,72,a,b,4129,a)].
9639 ->*_s0(empty(fstsplit(s(x),cons(y,z))),false). [ur(87,a,236,a,b,580,a)].
18914 ->*_s0(leq(s(app(nil,0)),length(cons(x,y))),true). [ur(87,a,305,a,b,4168,a)].
19832 -->*_s0(leq(s(x),length(y)),true) | -->*_s0(empty(fstsplit(s(x),y)),false) | -->*_s0(leq(s(x),length(cons(z,u))),true) # answer(goal). [resolve(9639,a,88,d)].
19837 -->*_s0(empty(fstsplit(s(x),y)),false) | -->*_s0(leq(s(x),length(cons(z,u))),true) | -->_s0(leq(s(x),length(y)),w) | -->*_s0(w,true) # answer(goal). [resolve(19832,a,87,c)].
20023 $F # answer(goal). [ur(19837,a,9639,a,c,305,a,d,4168,a),unit_del(a,18914)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=1516. Generated=26621. Kept=19988. proofs=1.
Usable=1516. Sos=18290. Demods=0. Limbo=182, Disabled=54. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=1342. Back_subsumed=0.
Sos_limit_deleted=5290. Sos_displaced=0. Sos_removed=0.
New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
Demod_attempts=0. Demod_rewrites=0.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=252. Nonunit_bsub_feature_tests=87.
Megabytes=37.83.
User_CPU=0.26, System_CPU=0.03, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
Exiting with 1 proof.
Process 3266023 exit (max_proofs) Tue Jul 30 08:52:40 2024
The problem is feasible.