NO

Problem 1: 

Infeasibility Problem:
[(VAR vNonEmpty x n h t m pid st1 in2 st2 in3 st3 vNonEmpty x6 x3 x2)
(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, empty(mapf(two,head(x2))) ->* true

Problem 1: 

Obtaining a proof using Prover9:

 -> Prover9 Output:
============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 3268716 was started by sandbox on z002.star.cs.uiowa.edu,
Tue Jul 30 09:06:55 2024
The command was "./prover9 -f /tmp/prover93268709-0.in".
============================== end of head ===========================

============================== INPUT =================================

% Reading from file /tmp/prover93268709-0.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(empty(mapf(two,head(x15))),true))) # 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(empty(mapf(two,head(x15))),true))) # 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(empty(mapf(two,head(z))),true) # 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(empty(mapf(two,head(z))),true) # 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(empty(mapf(two,head(z))),true) # 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=19): 88 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(empty(mapf(two,head(z))),true) # 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 (F,wt=22): 583 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(empty(mapf(two,head(z))),true) | -->_s0(leq(x,length(y)),u) | -->*_s0(u,true) # answer(goal).  [resolve(88,a,87,c)].

given #57 (F,wt=13): 614 -->*_s0(empty(fstsplit(0,x)),false) | -->*_s0(empty(mapf(two,head(y))),true) # answer(goal).  [resolve(583,c,70,a),unit_del(c,86)].

given #58 (F,wt=16): 619 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(fstsplit(0,y)),z) | -->*_s0(z,false) # answer(goal).  [resolve(614,a,87,c)].

given #59 (F,wt=13): 624 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(fstsplit(0,y)),false) # answer(goal).  [resolve(619,c,86,a)].

given #60 (T,wt=4): 573 ->*_s0(length(nil),0).  [ur(87,a,69,a,b,86,a)].

given #61 (T,wt=4): 579 ->*_s0(empty(nil),true).  [ur(87,a,63,a,b,86,a)].

given #62 (T,wt=5): 567 ->*_s0(sndsplit(0,x),x).  [ur(87,a,82,a,b,86,a)].

given #63 (T,wt=5): 568 ->*_s0(mapf(x,nil),nil).  [ur(87,a,74,a,b,86,a)].

given #64 (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 #65 (F,wt=15): 635 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(fstsplit(0,y)),sndsplit(0,false)) # answer(goal).  [resolve(567,a,619,c)].

given #66 (F,wt=16): 620 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),z) | -->*_s0(z,true) # answer(goal).  [resolve(614,b,87,c)].

given #67 (F,wt=13): 677 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),true) # answer(goal).  [resolve(620,c,86,a)].

given #68 (F,wt=14): 674 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),empty(nil)) # answer(goal).  [resolve(620,c,579,a)].

given #69 (T,wt=5): 572 ->*_s0(leq(0,x),true).  [ur(87,a,70,a,b,86,a)].

given #70 (T,wt=5): 578 ->*_s0(fstsplit(0,x),nil).  [ur(87,a,64,a,b,86,a)].

given #71 (T,wt=5): 581 ->*_s0(app(nil,x),x).  [ur(87,a,61,a,b,86,a)].

given #72 (T,wt=6): 164 ->_s0(s(empty(nil)),s(true)).  [ur(59,a,63,a)].

given #73 (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 #74 (F,wt=12): 680 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(mapf(two,head(y)),nil) # answer(goal).  [resolve(674,b,37,b)].

given #75 (F,wt=15): 675 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),sndsplit(0,true)) # answer(goal).  [resolve(620,c,567,a)].

given #76 (F,wt=15): 681 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),leq(0,z)) # answer(goal).  [resolve(572,a,620,c)].

given #77 (F,wt=15): 692 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),app(nil,true)) # answer(goal).  [resolve(581,a,620,c)].

given #78 (T,wt=6): 169 ->_s0(tail(empty(nil)),tail(true)).  [ur(54,a,63,a)].

given #79 (T,wt=6): 182 ->_s0(length(empty(nil)),length(true)).  [ur(41,a,63,a)].

given #80 (T,wt=6): 183 ->_s0(head(empty(nil)),head(true)).  [ur(40,a,63,a)].

given #81 (T,wt=6): 186 ->_s0(empty(empty(nil)),empty(true)).  [ur(37,a,63,a)].

given #82 (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 #83 (F,wt=15): 693 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(fstsplit(0,y)),app(nil,false)) # answer(goal).  [resolve(581,a,619,c)].

given #84 (F,wt=15): 751 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),z) | -->*_s0(z,false) # answer(goal).  [resolve(680,a,87,c)].

given #85 (F,wt=12): 890 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),false) # answer(goal).  [resolve(751,c,86,a)].

given #86 (F,wt=14): 887 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),app(nil,false)) # answer(goal).  [resolve(751,c,581,a)].

given #87 (T,wt=6): 314 ->_s0(s(length(nil)),s(0)).  [ur(59,a,69,a)].

given #88 (T,wt=6): 319 ->_s0(tail(length(nil)),tail(0)).  [ur(54,a,69,a)].

given #89 (T,wt=6): 332 ->_s0(length(length(nil)),length(0)).  [ur(41,a,69,a)].

given #90 (T,wt=6): 333 ->_s0(head(length(nil)),head(0)).  [ur(40,a,69,a)].

given #91 (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 #92 (F,wt=14): 888 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),sndsplit(0,false)) # answer(goal).  [resolve(751,c,567,a)].

given #93 (F,wt=15): 886 -->_s0(mapf(two,head(x)),nil) | -->*_s0(empty(y),false) | -->_s0(fstsplit(0,z),y) # answer(goal).  [resolve(751,b,37,b)].

given #94 (F,wt=10): 1022 -->_s0(mapf(two,head(x)),nil) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(886,c,64,a)].

given #95 (F,wt=13): 1024 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),y) | -->*_s0(y,false) # answer(goal).  [resolve(1022,b,87,c)].

given #96 (T,wt=6): 336 ->_s0(empty(length(nil)),empty(0)).  [ur(37,a,69,a)].

given #97 (T,wt=6): 564 ->*_s0(tail(cons(x,y)),y).  [ur(87,a,85,a,b,86,a)].

given #98 (T,wt=6): 565 ->*_s0(sndsplit(s(x),nil),nil).  [ur(87,a,84,a,b,86,a)].

given #99 (T,wt=6): 571 ->*_s0(leq(s(x),0),false).  [ur(87,a,71,a,b,86,a)].

given #100 (A,wt=13): 94 ->_s0(tail(app(cons(x,y),z)),tail(cons(x,app(y,z)))).  [ur(54,a,60,a)].

given #101 (F,wt=9): 1025 -->_s0(mapf(two,head(x)),nil) | -->*_s0(true,false) # answer(goal).  [resolve(1024,b,63,a)].

given #102 (F,wt=10): 1030 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),false) # answer(goal).  [resolve(1024,c,86,a)].

given #103 (F,wt=12): 1027 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),app(nil,false)) # answer(goal).  [resolve(1024,c,581,a)].

given #104 (F,wt=12): 1028 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),sndsplit(0,false)) # answer(goal).  [resolve(1024,c,567,a)].

given #105 (T,wt=6): 575 ->*_s0(head(cons(x,y)),x).  [ur(87,a,67,a,b,86,a)].

given #106 (T,wt=6): 576 ->*_s0(fstsplit(s(x),nil),nil).  [ur(87,a,66,a,b,86,a)].

given #107 (T,wt=6): 580 ->*_s0(empty(cons(x,y)),false).  [ur(87,a,62,a,b,86,a)].

given #108 (T,wt=6): 627 ->*_s0(sndsplit(0,length(nil)),0).  [ur(87,a,82,a,b,573,a)].

given #109 (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 #110 (F,wt=12): 1106 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->*_s0(y,false) # answer(goal).  [resolve(1025,b,87,c)].

given #111 (F,wt=9): 1167 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,false) # answer(goal).  [resolve(1106,c,86,a)].

given #112 (F,wt=11): 1160 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,false)) # answer(goal).  [resolve(1106,c,581,a)].

given #113 (F,wt=11): 1164 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,false)) # answer(goal).  [resolve(1106,c,567,a)].

given #114 (T,wt=6): 629 ->*_s0(app(nil,length(nil)),0).  [ur(87,a,61,a,b,573,a)].

given #115 (T,wt=6): 632 ->*_s0(sndsplit(0,empty(nil)),true).  [ur(87,a,82,a,b,579,a)].

given #116 (T,wt=6): 634 ->*_s0(app(nil,empty(nil)),true).  [ur(87,a,61,a,b,579,a)].

given #117 (T,wt=6): 699 ->*_s0(s(empty(nil)),s(true)).  [ur(87,a,164,a,b,86,a)].

given #118 (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 #119 (F,wt=12): 1161 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(cons(y,z))) # answer(goal).  [resolve(1106,c,580,a)].

given #120 (F,wt=12): 1162 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(false,y))) # answer(goal).  [resolve(1106,c,575,a)].

given #121 (F,wt=12): 1163 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(s(y),0)) # answer(goal).  [resolve(1106,c,571,a)].

given #122 (F,wt=12): 1165 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,false))) # answer(goal).  [resolve(1106,c,564,a)].

given #123 (T,wt=6): 755 ->*_s0(tail(empty(nil)),tail(true)).  [ur(87,a,169,a,b,86,a)].

given #124 (T,wt=6): 781 ->*_s0(length(empty(nil)),length(true)).  [ur(87,a,182,a,b,86,a)].

given #125 (T,wt=6): 807 ->*_s0(head(empty(nil)),head(true)).  [ur(87,a,183,a,b,86,a)].

given #126 (T,wt=6): 833 ->*_s0(empty(empty(nil)),empty(true)).  [ur(87,a,186,a,b,86,a)].

given #127 (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 #128 (F,wt=13): 1026 -->_s0(mapf(two,head(x)),nil) | -->*_s0(empty(y),false) | -->_s0(nil,y) # answer(goal).  [resolve(1024,b,37,b)].

given #129 (F,wt=11): 1257 -->_s0(mapf(two,head(x)),nil) | -->_s0(nil,cons(y,z)) # answer(goal).  [resolve(1026,b,580,a)].

given #130 (F,wt=13): 1057 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),tail(cons(y,false))) # answer(goal).  [resolve(564,a,1024,c)].

given #131 (F,wt=13): 1071 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),leq(s(y),0)) # answer(goal).  [resolve(571,a,1024,c)].

given #132 (T,wt=6): 891 ->*_s0(s(length(nil)),s(0)).  [ur(87,a,314,a,b,86,a)].

given #133 (T,wt=6): 917 ->*_s0(tail(length(nil)),tail(0)).  [ur(87,a,319,a,b,86,a)].

given #134 (T,wt=6): 943 ->*_s0(length(length(nil)),length(0)).  [ur(87,a,332,a,b,86,a)].

given #135 (T,wt=6): 969 ->*_s0(head(length(nil)),head(0)).  [ur(87,a,333,a,b,86,a)].

given #136 (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 #137 (F,wt=13): 1107 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),head(cons(false,y))) # answer(goal).  [resolve(575,a,1024,c)].

given #138 (F,wt=13): 1120 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),empty(cons(y,z))) # answer(goal).  [resolve(580,a,1024,c)].

given #139 (F,wt=13): 1121 -->_s0(mapf(two,head(x)),nil) | -->_s0(fstsplit(0,y),cons(z,u)) # answer(goal).  [resolve(580,a,886,b)].

given #140 (F,wt=15): 1023 -->_s0(mapf(two,head(x)),nil) | -->*_s0(empty(fstsplit(y,z)),false) | -->_s0(0,y) # answer(goal).  [resolve(886,c,38,b)].

given #141 (T,wt=6): 1031 ->*_s0(empty(length(nil)),empty(0)).  [ur(87,a,336,a,b,86,a)].

given #142 (T,wt=7): 114 ->_s0(s(app(nil,x)),s(x)).  [ur(59,a,61,a)].

given #143 (T,wt=7): 119 ->_s0(tail(app(nil,x)),tail(x)).  [ur(54,a,61,a)].

given #144 (T,wt=7): 132 ->_s0(length(app(nil,x)),length(x)).  [ur(41,a,61,a)].

given #145 (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 #146 (F,wt=15): 1058 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),tail(cons(z,false))) # answer(goal).  [resolve(564,a,751,c)].

given #147 (F,wt=15): 1072 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),leq(s(z),0)) # answer(goal).  [resolve(571,a,751,c)].

given #148 (F,wt=15): 1108 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),head(cons(false,z))) # answer(goal).  [resolve(575,a,751,c)].

given #149 (F,wt=15): 1122 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),empty(cons(z,u))) # answer(goal).  [resolve(580,a,751,c)].

given #150 (T,wt=6): 1366 ->*_s0(length(app(nil,nil)),0).  [ur(87,a,132,a,b,573,a)].

given #151 (T,wt=7): 133 ->_s0(head(app(nil,x)),head(x)).  [ur(40,a,61,a)].

given #152 (T,wt=7): 136 ->_s0(empty(app(nil,x)),empty(x)).  [ur(37,a,61,a)].

given #153 (T,wt=6): 1456 ->*_s0(empty(app(nil,nil)),true).  [ur(87,a,136,a,b,579,a)].

given #154 (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 #155 (F,wt=15): 1166 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,z) | -->*_s0(z,false) # answer(goal).  [resolve(1106,c,87,c)].

given #156 (F,wt=12): 1597 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,false) # answer(goal).  [resolve(1166,d,86,a)].

given #157 (F,wt=13): 1557 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,length(nil)) | -->*_s0(0,false) # answer(goal).  [resolve(1166,c,69,a)].

given #158 (F,wt=14): 1546 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,y)) | -->*_s0(y,false) # answer(goal).  [resolve(1166,c,82,a)].

given #159 (T,wt=7): 189 ->_s0(s(fstsplit(0,x)),s(nil)).  [ur(59,a,64,a)].

given #160 (T,wt=7): 194 ->_s0(tail(fstsplit(0,x)),tail(nil)).  [ur(54,a,64,a)].

given #161 (T,wt=7): 207 ->_s0(length(fstsplit(0,x)),length(nil)).  [ur(41,a,64,a)].

given #162 (T,wt=6): 1661 ->*_s0(length(fstsplit(0,x)),0).  [ur(87,a,207,a,b,573,a)].

given #163 (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 #164 (F,wt=13): 1599 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,app(nil,false))) # answer(goal).  [resolve(1546,c,581,a)].

given #165 (F,wt=13): 1603 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,sndsplit(0,false))) # answer(goal).  [resolve(1546,c,567,a)].

given #166 (F,wt=14): 1554 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,mapf(y,nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(1166,c,74,a)].

given #167 (F,wt=14): 1562 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,fstsplit(0,y)) | -->*_s0(nil,false) # answer(goal).  [resolve(1166,c,64,a)].

given #168 (T,wt=7): 208 ->_s0(head(fstsplit(0,x)),head(nil)).  [ur(40,a,64,a)].

given #169 (T,wt=7): 211 ->_s0(empty(fstsplit(0,x)),empty(nil)).  [ur(37,a,64,a)].

given #170 (T,wt=6): 1750 ->*_s0(empty(fstsplit(0,x)),true).  [ur(87,a,211,a,b,579,a)].

given #171 (T,wt=7): 339 ->_s0(s(leq(0,x)),s(true)).  [ur(59,a,70,a)].

given #172 (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 #173 (F,wt=11): 1749 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(211,a,619,b)].

given #174 (F,wt=14): 1563 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,y)) | -->*_s0(y,false) # answer(goal).  [resolve(1166,c,61,a)].

given #175 (F,wt=13): 1840 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,app(nil,false))) # answer(goal).  [resolve(1563,c,581,a)].

given #176 (F,wt=13): 1844 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,sndsplit(0,false))) # answer(goal).  [resolve(1563,c,567,a)].

given #177 (T,wt=7): 344 ->_s0(tail(leq(0,x)),tail(true)).  [ur(54,a,70,a)].

given #178 (T,wt=7): 357 ->_s0(length(leq(0,x)),length(true)).  [ur(41,a,70,a)].

given #179 (T,wt=7): 358 ->_s0(head(leq(0,x)),head(true)).  [ur(40,a,70,a)].

given #180 (T,wt=7): 361 ->_s0(empty(leq(0,x)),empty(true)).  [ur(37,a,70,a)].

given #181 (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 #182 (F,wt=14): 1590 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,app(nil,false)) # answer(goal).  [resolve(1166,d,581,a)].

given #183 (F,wt=14): 1594 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,sndsplit(0,false)) # answer(goal).  [resolve(1166,d,567,a)].

given #184 (F,wt=14): 1600 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,empty(cons(y,z)))) # answer(goal).  [resolve(1546,c,580,a)].

given #185 (F,wt=14): 1601 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,head(cons(false,y)))) # answer(goal).  [resolve(1546,c,575,a)].

given #186 (T,wt=7): 439 ->_s0(s(mapf(x,nil)),s(nil)).  [ur(59,a,74,a)].

given #187 (T,wt=7): 444 ->_s0(tail(mapf(x,nil)),tail(nil)).  [ur(54,a,74,a)].

given #188 (T,wt=7): 457 ->_s0(length(mapf(x,nil)),length(nil)).  [ur(41,a,74,a)].

given #189 (T,wt=6): 2046 ->*_s0(length(mapf(x,nil)),0).  [ur(87,a,457,a,b,573,a)].

given #190 (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 #191 (F,wt=14): 1602 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,leq(s(y),0))) # answer(goal).  [resolve(1546,c,571,a)].

given #192 (F,wt=14): 1604 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,tail(cons(y,false)))) # answer(goal).  [resolve(1546,c,564,a)].

given #193 (F,wt=14): 1838 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),y) | -->*_s0(y,true) # answer(goal).  [resolve(1749,a,87,c)].

given #194 (F,wt=11): 2118 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),true) # answer(goal).  [resolve(1838,c,86,a)].

given #195 (T,wt=7): 458 ->_s0(head(mapf(x,nil)),head(nil)).  [ur(40,a,74,a)].

given #196 (T,wt=7): 461 ->_s0(empty(mapf(x,nil)),empty(nil)).  [ur(37,a,74,a)].

given #197 (T,wt=6): 2147 ->*_s0(empty(mapf(x,nil)),true).  [ur(87,a,461,a,b,579,a)].

given #198 (T,wt=7): 464 ->_s0(s(sndsplit(0,x)),s(x)).  [ur(59,a,82,a)].

given #199 (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 #200 (F,wt=12): 2112 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),empty(nil)) # answer(goal).  [resolve(1838,c,579,a)].

given #201 (F,wt=13): 2111 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),app(nil,true)) # answer(goal).  [resolve(1838,c,581,a)].

given #202 (F,wt=13): 2114 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),leq(0,y)) # answer(goal).  [resolve(1838,c,572,a)].

given #203 (F,wt=13): 2115 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),sndsplit(0,true)) # answer(goal).  [resolve(1838,c,567,a)].

given #204 (T,wt=7): 469 ->_s0(tail(sndsplit(0,x)),tail(x)).  [ur(54,a,82,a)].

given #205 (T,wt=7): 482 ->_s0(length(sndsplit(0,x)),length(x)).  [ur(41,a,82,a)].

given #206 (T,wt=6): 2278 ->*_s0(length(sndsplit(0,nil)),0).  [ur(87,a,482,a,b,573,a)].

given #207 (T,wt=7): 483 ->_s0(head(sndsplit(0,x)),head(x)).  [ur(40,a,82,a)].

given #208 (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 #209 (F,wt=14): 1839 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(nil),y) | -->*_s0(y,false) # answer(goal).  [resolve(1749,b,87,c)].

given #210 (F,wt=10): 2369 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(true,false) # answer(goal).  [resolve(1839,b,63,a)].

given #211 (F,wt=11): 2378 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(nil),false) # answer(goal).  [resolve(1839,c,86,a)].

given #212 (F,wt=13): 2371 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(nil),app(nil,false)) # answer(goal).  [resolve(1839,c,581,a)].

given #213 (T,wt=7): 486 ->_s0(empty(sndsplit(0,x)),empty(x)).  [ur(37,a,82,a)].

given #214 (T,wt=6): 2390 ->*_s0(empty(sndsplit(0,nil)),true).  [ur(87,a,486,a,b,579,a)].

given #215 (T,wt=7): 626 ->*_s0(tail(cons(x,length(nil))),0).  [ur(87,a,85,a,b,573,a)].

given #216 (T,wt=7): 628 ->*_s0(head(cons(length(nil),x)),0).  [ur(87,a,67,a,b,573,a)].

given #217 (A,wt=13): 107 ->_s0(length(app(cons(x,y),z)),length(cons(x,app(y,z)))).  [ur(41,a,60,a)].

given #218 (F,wt=13): 2375 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(nil),sndsplit(0,false)) # answer(goal).  [resolve(1839,c,567,a)].

given #219 (F,wt=13): 2379 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),y) | -->*_s0(y,true) # answer(goal).  [resolve(2369,a,87,c)].

given #220 (F,wt=10): 2481 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),true) # answer(goal).  [resolve(2379,c,86,a)].

given #221 (F,wt=11): 2475 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),empty(nil)) # answer(goal).  [resolve(2379,c,579,a)].

given #222 (T,wt=7): 631 ->*_s0(tail(cons(x,empty(nil))),true).  [ur(87,a,85,a,b,579,a)].

given #223 (T,wt=7): 633 ->*_s0(head(cons(empty(nil),x)),true).  [ur(87,a,67,a,b,579,a)].

given #224 (T,wt=7): 639 ->*_s0(sndsplit(0,sndsplit(0,x)),x).  [ur(87,a,82,a,b,567,a)].

given #225 (T,wt=7): 641 ->*_s0(app(nil,sndsplit(0,x)),x).  [ur(87,a,61,a,b,567,a)].

given #226 (A,wt=13): 108 ->_s0(head(app(cons(x,y),z)),head(cons(x,app(y,z)))).  [ur(40,a,60,a)].

given #227 (F,wt=12): 2474 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),app(nil,true)) # answer(goal).  [resolve(2379,c,581,a)].

given #228 (F,wt=12): 2477 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),leq(0,y)) # answer(goal).  [resolve(2379,c,572,a)].

given #229 (F,wt=12): 2478 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),sndsplit(0,true)) # answer(goal).  [resolve(2379,c,567,a)].

given #230 (F,wt=13): 2380 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(true,y) | -->*_s0(y,false) # answer(goal).  [resolve(2369,b,87,c)].

given #231 (T,wt=7): 643 ->*_s0(sndsplit(0,mapf(x,nil)),nil).  [ur(87,a,82,a,b,568,a)].

given #232 (T,wt=7): 645 ->*_s0(app(nil,mapf(x,nil)),nil).  [ur(87,a,61,a,b,568,a)].

given #233 (T,wt=7): 684 ->*_s0(sndsplit(0,leq(0,x)),true).  [ur(87,a,82,a,b,572,a)].

given #234 (T,wt=7): 685 ->*_s0(leq(s(0),s(x)),true).  [ur(87,a,72,a,b,572,a)].

given #235 (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 #236 (F,wt=10): 2577 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(true,false) # answer(goal).  [resolve(2380,c,86,a)].

given #237 (F,wt=12): 2570 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(true,app(nil,false)) # answer(goal).  [resolve(2380,c,581,a)].

given #238 (F,wt=12): 2574 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(true,sndsplit(0,false)) # answer(goal).  [resolve(2380,c,567,a)].

given #239 (F,wt=13): 2467 -->*_s0(true,false) | -->*_s0(empty(x),true) | -->_s0(mapf(two,head(y)),x) # answer(goal).  [resolve(2379,b,37,b)].

given #240 (T,wt=7): 687 ->*_s0(app(nil,leq(0,x)),true).  [ur(87,a,61,a,b,572,a)].

given #241 (T,wt=7): 689 ->*_s0(sndsplit(0,fstsplit(0,x)),nil).  [ur(87,a,82,a,b,578,a)].

given #242 (T,wt=7): 691 ->*_s0(app(nil,fstsplit(0,x)),nil).  [ur(87,a,61,a,b,578,a)].

given #243 (T,wt=7): 696 ->*_s0(sndsplit(0,app(nil,x)),x).  [ur(87,a,82,a,b,581,a)].

given #244 (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 #245 (F,wt=11): 2636 -->*_s0(true,false) | -->_s0(mapf(two,head(x)),sndsplit(0,nil)) # answer(goal).  [resolve(2467,b,2390,a)].

given #246 (F,wt=11): 2637 -->*_s0(true,false) | -->_s0(mapf(two,head(x)),mapf(y,nil)) # answer(goal).  [resolve(2467,b,2147,a)].

given #247 (F,wt=7): 2706 -->*_s0(true,false) | -->_s0(head(x),nil) # answer(goal).  [resolve(2637,b,45,b)].

given #248 (F,wt=3): 2708 -->*_s0(true,false) # answer(goal).  [resolve(2706,b,67,a)].

given #249 (T,wt=7): 698 ->*_s0(app(nil,app(nil,x)),x).  [ur(87,a,61,a,b,581,a)].

given #250 (T,wt=7): 1261 ->*_s0(length(cons(x,nil)),s(0)).  [ur(87,a,68,a,b,891,a)].

given #251 (T,wt=7): 1309 ->*_s0(s(app(nil,x)),s(x)).  [ur(87,a,114,a,b,86,a)].

given #252 (T,wt=7): 1338 ->*_s0(tail(app(nil,x)),tail(x)).  [ur(87,a,119,a,b,86,a)].

given #253 (A,wt=13): 111 ->_s0(empty(app(cons(x,y),z)),empty(cons(x,app(y,z)))).  [ur(37,a,60,a)].

given #254 (F,wt=3): 2719 -->_s0(true,false) # answer(goal).  [ur(87,b,86,a,c,2708,a)].

given #255 (F,wt=5): 2713 -->_s0(true,app(nil,false)) # answer(goal).  [ur(87,b,581,a,c,2708,a)].

given #256 (F,wt=5): 2717 -->_s0(true,sndsplit(0,false)) # answer(goal).  [ur(87,b,567,a,c,2708,a)].

given #257 (F,wt=6): 2709 -->_s0(true,x) | -->*_s0(x,false) # answer(goal).  [resolve(2708,a,87,c)].

given #258 (T,wt=7): 1367 ->*_s0(length(app(nil,x)),length(x)).  [ur(87,a,132,a,b,86,a)].

given #259 (T,wt=7): 1427 ->*_s0(head(app(nil,x)),head(x)).  [ur(87,a,133,a,b,86,a)].

given #260 (T,wt=7): 1457 ->*_s0(empty(app(nil,x)),empty(x)).  [ur(87,a,136,a,b,86,a)].

given #261 (T,wt=7): 1607 ->*_s0(s(fstsplit(0,x)),s(nil)).  [ur(87,a,189,a,b,86,a)].

given #262 (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 #263 (F,wt=6): 2714 -->_s0(true,empty(cons(x,y))) # answer(goal).  [ur(87,b,580,a,c,2708,a)].

given #264 (F,wt=6): 2715 -->_s0(true,head(cons(false,x))) # answer(goal).  [ur(87,b,575,a,c,2708,a)].

given #265 (F,wt=6): 2716 -->_s0(true,leq(s(x),0)) # answer(goal).  [ur(87,b,571,a,c,2708,a)].

given #266 (F,wt=6): 2718 -->_s0(true,tail(cons(x,false))) # answer(goal).  [ur(87,b,564,a,c,2708,a)].

given #267 (T,wt=7): 1634 ->*_s0(tail(fstsplit(0,x)),tail(nil)).  [ur(87,a,194,a,b,86,a)].

given #268 (T,wt=7): 1662 ->*_s0(length(fstsplit(0,x)),length(nil)).  [ur(87,a,207,a,b,86,a)].

given #269 (T,wt=7): 1723 ->*_s0(head(fstsplit(0,x)),head(nil)).  [ur(87,a,208,a,b,86,a)].

given #270 (T,wt=7): 1751 ->*_s0(empty(fstsplit(0,x)),empty(nil)).  [ur(87,a,211,a,b,86,a)].

given #271 (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 #272 (F,wt=7): 2710 -->_s0(true,sndsplit(0,app(nil,false))) # answer(goal).  [ur(87,b,696,a,c,2708,a)].

given #273 (F,wt=7): 2711 -->_s0(true,app(nil,sndsplit(0,false))) # answer(goal).  [ur(87,b,641,a,c,2708,a)].

given #274 (F,wt=7): 2712 -->_s0(true,sndsplit(0,sndsplit(0,false))) # answer(goal).  [ur(87,b,639,a,c,2708,a)].

given #275 (F,wt=7): 2734 -->_s0(true,app(nil,app(nil,false))) # answer(goal).  [ur(87,b,698,a,c,2708,a)].

given #276 (T,wt=7): 1785 ->*_s0(s(leq(0,x)),s(true)).  [ur(87,a,339,a,b,86,a)].

given #277 (T,wt=7): 1848 ->*_s0(tail(leq(0,x)),tail(true)).  [ur(87,a,344,a,b,86,a)].

given #278 (T,wt=7): 1875 ->*_s0(length(leq(0,x)),length(true)).  [ur(87,a,357,a,b,86,a)].

given #279 (T,wt=7): 1902 ->*_s0(head(leq(0,x)),head(true)).  [ur(87,a,358,a,b,86,a)].

given #280 (A,wt=9): 115 ->_s0(f(x,app(nil,y)),f(x,y)).  [ur(58,a,61,a)].

given #281 (F,wt=9): 2781 -->_s0(true,x) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal).  [resolve(2709,b,87,c)].

given #282 (F,wt=6): 3052 -->_s0(true,x) | -->_s0(x,false) # answer(goal).  [resolve(2781,c,86,a)].

given #283 (F,wt=7): 3008 -->_s0(true,length(nil)) | -->*_s0(0,false) # answer(goal).  [resolve(2781,b,69,a)].

given #284 (F,wt=8): 2971 -->_s0(true,empty(app(cons(x,y),z))) # answer(goal).  [resolve(2781,b,111,a),unit_del(b,580)].

given #285 (T,wt=7): 1929 ->*_s0(empty(leq(0,x)),empty(true)).  [ur(87,a,361,a,b,86,a)].

given #286 (T,wt=7): 1992 ->*_s0(s(mapf(x,nil)),s(nil)).  [ur(87,a,439,a,b,86,a)].

given #287 (T,wt=7): 2019 ->*_s0(tail(mapf(x,nil)),tail(nil)).  [ur(87,a,444,a,b,86,a)].

given #288 (T,wt=7): 2047 ->*_s0(length(mapf(x,nil)),length(nil)).  [ur(87,a,457,a,b,86,a)].

given #289 (A,wt=9): 116 ->_s0(f(app(nil,x),y),f(x,y)).  [ur(57,a,61,a)].

given #290 (F,wt=8): 2997 -->_s0(true,sndsplit(0,x)) | -->*_s0(x,false) # answer(goal).  [resolve(2781,b,82,a)].

given #291 (F,wt=8): 3005 -->_s0(true,mapf(x,nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(2781,b,74,a)].

given #292 (F,wt=8): 3013 -->_s0(true,fstsplit(0,x)) | -->*_s0(nil,false) # answer(goal).  [resolve(2781,b,64,a)].

given #293 (F,wt=8): 3014 -->_s0(true,app(nil,x)) | -->*_s0(x,false) # answer(goal).  [resolve(2781,b,61,a)].

given #294 (T,wt=7): 2121 ->*_s0(head(mapf(x,nil)),head(nil)).  [ur(87,a,458,a,b,86,a)].

given #295 (T,wt=7): 2148 ->*_s0(empty(mapf(x,nil)),empty(nil)).  [ur(87,a,461,a,b,86,a)].

given #296 (T,wt=7): 2185 ->*_s0(s(sndsplit(0,x)),s(x)).  [ur(87,a,464,a,b,86,a)].

given #297 (T,wt=7): 2246 ->*_s0(tail(sndsplit(0,x)),tail(x)).  [ur(87,a,469,a,b,86,a)].

given #298 (A,wt=9): 117 ->_s0(cons(x,app(nil,y)),cons(x,y)).  [ur(56,a,61,a)].

given #299 (F,wt=8): 3045 -->_s0(true,x) | -->_s0(x,app(nil,false)) # answer(goal).  [resolve(2781,c,581,a)].

given #300 (F,wt=8): 3049 -->_s0(true,x) | -->_s0(x,sndsplit(0,false)) # answer(goal).  [resolve(2781,c,567,a)].

given #301 (F,wt=8): 3053 -->_s0(true,empty(sndsplit(0,cons(x,y)))) # answer(goal).  [ur(2781,b,486,a,c,580,a)].

given #302 (F,wt=8): 3054 -->_s0(true,head(sndsplit(0,cons(false,x)))) # answer(goal).  [ur(2781,b,483,a,c,575,a)].

given #303 (T,wt=7): 2279 ->*_s0(length(sndsplit(0,x)),length(x)).  [ur(87,a,482,a,b,86,a)].

given #304 (T,wt=7): 2315 ->*_s0(head(sndsplit(0,x)),head(x)).  [ur(87,a,483,a,b,86,a)].

given #305 (T,wt=7): 2391 ->*_s0(empty(sndsplit(0,x)),empty(x)).  [ur(87,a,486,a,b,86,a)].

given #306 (T,wt=8): 139 ->_s0(s(empty(cons(x,y))),s(false)).  [ur(59,a,62,a)].

given #307 (A,wt=9): 118 ->_s0(cons(app(nil,x),y),cons(x,y)).  [ur(55,a,61,a)].

given #308 (F,wt=8): 3055 -->_s0(true,tail(sndsplit(0,cons(x,false)))) # answer(goal).  [ur(2781,b,469,a,c,564,a)].

given #309 (F,wt=8): 3056 -->_s0(true,empty(app(nil,cons(x,y)))) # answer(goal).  [ur(2781,b,136,a,c,580,a)].

given #310 (F,wt=8): 3057 -->_s0(true,head(app(nil,cons(false,x)))) # answer(goal).  [ur(2781,b,133,a,c,575,a)].

given #311 (F,wt=8): 3058 -->_s0(true,tail(app(nil,cons(x,false)))) # answer(goal).  [ur(2781,b,119,a,c,564,a)].

given #312 (T,wt=8): 144 ->_s0(tail(empty(cons(x,y))),tail(false)).  [ur(54,a,62,a)].

given #313 (T,wt=8): 157 ->_s0(length(empty(cons(x,y))),length(false)).  [ur(41,a,62,a)].

given #314 (T,wt=8): 158 ->_s0(head(empty(cons(x,y))),head(false)).  [ur(40,a,62,a)].

given #315 (T,wt=8): 161 ->_s0(empty(empty(cons(x,y))),empty(false)).  [ur(37,a,62,a)].

given #316 (A,wt=9): 120 ->_s0(sndsplit(x,app(nil,y)),sndsplit(x,y)).  [ur(53,a,61,a)].

given #317 (F,wt=8): 3059 -->_s0(true,head(app(cons(false,x),y))) # answer(goal).  [ur(2781,b,108,a,c,575,a)].

given #318 (F,wt=8): 3064 -->_s0(true,tail(cons(x,app(nil,false)))) # answer(goal).  [ur(2781,b,85,a,c,581,a)].

given #319 (F,wt=8): 3068 -->_s0(true,tail(cons(x,sndsplit(0,false)))) # answer(goal).  [ur(2781,b,85,a,c,567,a)].

given #320 (F,wt=8): 3072 -->_s0(true,sndsplit(s(0),cons(x,false))) # answer(goal).  [ur(2781,b,83,a,c,567,a)].

given #321 (T,wt=8): 165 ->_s0(f(x,empty(nil)),f(x,true)).  [ur(58,a,63,a)].

given #322 (T,wt=8): 166 ->_s0(f(empty(nil),x),f(true,x)).  [ur(57,a,63,a)].

given #323 (T,wt=8): 167 ->_s0(cons(x,empty(nil)),cons(x,true)).  [ur(56,a,63,a)].

given #324 (T,wt=8): 168 ->_s0(cons(empty(nil),x),cons(true,x)).  [ur(55,a,63,a)].

given #325 (A,wt=9): 121 ->_s0(sndsplit(app(nil,x),y),sndsplit(x,y)).  [ur(52,a,61,a)].

given #326 (F,wt=7): 3527 -->_s0(true,sndsplit(app(nil,0),false)) # answer(goal).  [resolve(121,a,3049,b)].

given #327 (F,wt=8): 3077 -->_s0(true,sndsplit(0,empty(cons(x,y)))) # answer(goal).  [ur(2781,b,82,a,c,580,a)].

given #328 (F,wt=8): 3078 -->_s0(true,sndsplit(0,head(cons(false,x)))) # answer(goal).  [ur(2781,b,82,a,c,575,a)].

given #329 (F,wt=8): 3079 -->_s0(true,sndsplit(0,leq(s(x),0))) # answer(goal).  [ur(2781,b,82,a,c,571,a)].

given #330 (T,wt=7): 3536 ->*_s0(sndsplit(app(nil,0),x),x).  [ur(87,a,121,a,b,567,a)].

given #331 (T,wt=8): 170 ->_s0(sndsplit(x,empty(nil)),sndsplit(x,true)).  [ur(53,a,63,a)].

given #332 (T,wt=8): 171 ->_s0(sndsplit(empty(nil),x),sndsplit(true,x)).  [ur(52,a,63,a)].

given #333 (T,wt=8): 178 ->_s0(mapf(x,empty(nil)),mapf(x,true)).  [ur(45,a,63,a)].

given #334 (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 #335 (F,wt=8): 3080 -->_s0(true,sndsplit(0,tail(cons(x,false)))) # answer(goal).  [ur(2781,b,82,a,c,564,a)].

given #336 (F,wt=8): 3081 -->_s0(true,leq(s(s(x)),s(0))) # answer(goal).  [ur(2781,b,72,a,c,571,a)].

given #337 (F,wt=8): 3086 -->_s0(true,head(cons(app(nil,false),x))) # answer(goal).  [ur(2781,b,67,a,c,581,a)].

given #338 (F,wt=8): 3090 -->_s0(true,head(cons(sndsplit(0,false),x))) # answer(goal).  [ur(2781,b,67,a,c,567,a)].

given #339 (T,wt=8): 179 ->_s0(mapf(empty(nil),x),mapf(true,x)).  [ur(44,a,63,a)].

given #340 (T,wt=8): 180 ->_s0(leq(x,empty(nil)),leq(x,true)).  [ur(43,a,63,a)].

given #341 (T,wt=8): 181 ->_s0(leq(empty(nil),x),leq(true,x)).  [ur(42,a,63,a)].

given #342 (T,wt=8): 184 ->_s0(fstsplit(x,empty(nil)),fstsplit(x,true)).  [ur(39,a,63,a)].

given #343 (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 #344 (F,wt=8): 3096 -->_s0(true,app(nil,empty(cons(x,y)))) # answer(goal).  [ur(2781,b,61,a,c,580,a)].

given #345 (F,wt=8): 3097 -->_s0(true,app(nil,head(cons(false,x)))) # answer(goal).  [ur(2781,b,61,a,c,575,a)].

given #346 (F,wt=8): 3098 -->_s0(true,app(nil,leq(s(x),0))) # answer(goal).  [ur(2781,b,61,a,c,571,a)].

given #347 (F,wt=8): 3099 -->_s0(true,app(nil,tail(cons(x,false)))) # answer(goal).  [ur(2781,b,61,a,c,564,a)].

given #348 (T,wt=8): 185 ->_s0(fstsplit(empty(nil),x),fstsplit(true,x)).  [ur(38,a,63,a)].

given #349 (T,wt=8): 187 ->_s0(app(x,empty(nil)),app(x,true)).  [ur(36,a,63,a)].

given #350 (T,wt=8): 188 ->_s0(app(empty(nil),x),app(true,x)).  [ur(35,a,63,a)].

given #351 (T,wt=8): 239 ->_s0(s(fstsplit(s(x),nil)),s(nil)).  [ur(59,a,66,a)].

given #352 (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 #353 (F,wt=8): 3207 -->_s0(true,app(nil,x)) | -->_s0(x,false) # answer(goal).  [resolve(3045,b,36,b)].

given #354 (F,wt=8): 3208 -->_s0(true,app(x,false)) | -->_s0(x,nil) # answer(goal).  [resolve(3045,b,35,b)].

given #355 (F,wt=7): 3968 -->_s0(true,app(sndsplit(0,nil),false)) # answer(goal).  [resolve(3208,b,82,a)].

given #356 (F,wt=7): 3969 -->_s0(true,app(mapf(x,nil),false)) # answer(goal).  [resolve(3208,b,74,a)].

given #357 (T,wt=8): 244 ->_s0(tail(fstsplit(s(x),nil)),tail(nil)).  [ur(54,a,66,a)].

given #358 (T,wt=8): 257 ->_s0(length(fstsplit(s(x),nil)),length(nil)).  [ur(41,a,66,a)].

given #359 (T,wt=7): 4002 ->*_s0(length(fstsplit(s(x),nil)),0).  [ur(87,a,257,a,b,573,a)].

given #360 (T,wt=8): 258 ->_s0(head(fstsplit(s(x),nil)),head(nil)).  [ur(40,a,66,a)].

given #361 (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 #362 (F,wt=7): 3972 -->_s0(true,app(fstsplit(0,x),false)) # answer(goal).  [resolve(3208,b,64,a)].

given #363 (F,wt=7): 3973 -->_s0(true,app(app(nil,nil),false)) # answer(goal).  [resolve(3208,b,61,a)].

given #364 (F,wt=8): 3209 -->_s0(true,sndsplit(0,x)) | -->_s0(x,false) # answer(goal).  [resolve(3049,b,53,b)].

given #365 (F,wt=8): 3210 -->_s0(true,sndsplit(x,false)) | -->_s0(x,0) # answer(goal).  [resolve(3049,b,52,b)].

given #366 (T,wt=8): 261 ->_s0(empty(fstsplit(s(x),nil)),empty(nil)).  [ur(37,a,66,a)].

given #367 (T,wt=7): 4094 ->*_s0(empty(fstsplit(s(x),nil)),true).  [ur(87,a,261,a,b,579,a)].

given #368 (T,wt=8): 264 ->_s0(s(head(cons(x,y))),s(x)).  [ur(59,a,67,a)].

given #369 (T,wt=8): 269 ->_s0(tail(head(cons(x,y))),tail(x)).  [ur(54,a,67,a)].

given #370 (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 #371 (F,wt=6): 4091 -->_s0(true,sndsplit(length(nil),false)) # answer(goal).  [resolve(3210,b,69,a)].

given #372 (F,wt=7): 4090 -->_s0(true,sndsplit(sndsplit(0,0),false)) # answer(goal).  [resolve(3210,b,82,a)].

given #373 (F,wt=8): 3966 -->_s0(true,app(tail(cons(x,nil)),false)) # answer(goal).  [resolve(3208,b,85,a)].

given #374 (F,wt=8): 3967 -->_s0(true,app(sndsplit(s(x),nil),false)) # answer(goal).  [resolve(3208,b,84,a)].

given #375 (T,wt=8): 282 ->_s0(length(head(cons(x,y))),length(x)).  [ur(41,a,67,a)].

given #376 (T,wt=7): 4243 ->*_s0(length(head(cons(nil,x))),0).  [ur(87,a,282,a,b,573,a)].

given #377 (T,wt=8): 283 ->_s0(head(head(cons(x,y))),head(x)).  [ur(40,a,67,a)].

given #378 (T,wt=8): 286 ->_s0(empty(head(cons(x,y))),empty(x)).  [ur(37,a,67,a)].

given #379 (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 #380 (F,wt=8): 3970 -->_s0(true,app(head(cons(nil,x)),false)) # answer(goal).  [resolve(3208,b,67,a)].

given #381 (F,wt=8): 3971 -->_s0(true,app(fstsplit(s(x),nil),false)) # answer(goal).  [resolve(3208,b,66,a)].

given #382 (F,wt=8): 4089 -->_s0(true,sndsplit(tail(cons(x,0)),false)) # answer(goal).  [resolve(3210,b,85,a)].

given #383 (F,wt=8): 4092 -->_s0(true,sndsplit(head(cons(0,x)),false)) # answer(goal).  [resolve(3210,b,67,a)].

given #384 (T,wt=7): 4329 ->*_s0(empty(head(cons(nil,x))),true).  [ur(87,a,286,a,b,579,a)].

given #385 (T,wt=8): 315 ->_s0(f(x,length(nil)),f(x,0)).  [ur(58,a,69,a)].

given #386 (T,wt=8): 316 ->_s0(f(length(nil),x),f(0,x)).  [ur(57,a,69,a)].

given #387 (T,wt=8): 317 ->_s0(cons(x,length(nil)),cons(x,0)).  [ur(56,a,69,a)].

given #388 (A,wt=9): 128 ->_s0(mapf(x,app(nil,y)),mapf(x,y)).  [ur(45,a,61,a)].

given #389 (F,wt=9): 2948 -->_s0(true,empty(length(nil))) | -->*_s0(empty(0),false) # answer(goal).  [resolve(2781,b,336,a)].

given #390 (F,wt=9): 2949 -->_s0(true,head(length(nil))) | -->*_s0(head(0),false) # answer(goal).  [resolve(2781,b,333,a)].

given #391 (F,wt=9): 2950 -->_s0(true,length(length(nil))) | -->*_s0(length(0),false) # answer(goal).  [resolve(2781,b,332,a)].

given #392 (F,wt=9): 2951 -->_s0(true,tail(length(nil))) | -->*_s0(tail(0),false) # answer(goal).  [resolve(2781,b,319,a)].

given #393 (T,wt=7): 4476 ->*_s0(mapf(x,app(nil,nil)),nil).  [ur(87,a,128,a,b,568,a)].

given #394 (T,wt=8): 318 ->_s0(cons(length(nil),x),cons(0,x)).  [ur(55,a,69,a)].

given #395 (T,wt=8): 320 ->_s0(sndsplit(x,length(nil)),sndsplit(x,0)).  [ur(53,a,69,a)].

given #396 (T,wt=8): 321 ->_s0(sndsplit(length(nil),x),sndsplit(0,x)).  [ur(52,a,69,a)].

given #397 (A,wt=9): 129 ->_s0(mapf(app(nil,x),y),mapf(x,y)).  [ur(44,a,61,a)].

given #398 (F,wt=8): 4601 -->_s0(true,sndsplit(length(nil),app(nil,false))) # answer(goal).  [ur(2781,b,321,a,c,696,a)].

given #399 (F,wt=8): 4602 -->_s0(true,sndsplit(length(nil),sndsplit(0,false))) # answer(goal).  [ur(2781,b,321,a,c,639,a)].

given #400 (F,wt=9): 2952 -->_s0(true,s(length(nil))) | -->*_s0(s(0),false) # answer(goal).  [resolve(2781,b,314,a)].

given #401 (F,wt=9): 2958 -->_s0(true,empty(empty(nil))) | -->*_s0(empty(true),false) # answer(goal).  [resolve(2781,b,186,a)].

given #402 (T,wt=6): 4574 ->*_s0(sndsplit(length(nil),x),x).  [ur(87,a,321,a,b,567,a)].

given #403 (T,wt=7): 4572 ->*_s0(sndsplit(length(nil),empty(nil)),true).  [ur(87,a,321,a,b,632,a)].

given #404 (T,wt=7): 4573 ->*_s0(sndsplit(length(nil),length(nil)),0).  [ur(87,a,321,a,b,627,a)].

given #405 (T,wt=8): 328 ->_s0(mapf(x,length(nil)),mapf(x,0)).  [ur(45,a,69,a)].

given #406 (A,wt=9): 130 ->_s0(leq(x,app(nil,y)),leq(x,y)).  [ur(43,a,61,a)].

given #407 (F,wt=8): 4632 -->_s0(true,app(nil,sndsplit(length(nil),false))) # answer(goal).  [resolve(4574,a,3014,b)].

given #408 (F,wt=8): 4633 -->_s0(true,sndsplit(0,sndsplit(length(nil),false))) # answer(goal).  [resolve(4574,a,2997,b)].

given #409 (F,wt=8): 4649 -->_s0(true,sndsplit(app(nil,length(nil)),false)) # answer(goal).  [ur(2781,b,121,a,c,4574,a)].

given #410 (F,wt=8): 4726 -->_s0(true,leq(s(x),app(nil,0))) # answer(goal).  [ur(2781,b,130,a,c,571,a)].

given #411 (T,wt=8): 329 ->_s0(mapf(length(nil),x),mapf(0,x)).  [ur(44,a,69,a)].

given #412 (T,wt=8): 330 ->_s0(leq(x,length(nil)),leq(x,0)).  [ur(43,a,69,a)].

given #413 (T,wt=7): 4756 ->*_s0(leq(s(x),length(nil)),false).  [ur(87,a,330,a,b,571,a)].

given #414 (T,wt=8): 331 ->_s0(leq(length(nil),x),leq(0,x)).  [ur(42,a,69,a)].

given #415 (A,wt=9): 131 ->_s0(leq(app(nil,x),y),leq(x,y)).  [ur(42,a,61,a)].

given #416 (F,wt=7): 4783 -->_s0(true,leq(s(x),length(nil))) # answer(goal).  [ur(2781,b,330,a,c,571,a)].

given #417 (F,wt=8): 4863 -->_s0(true,leq(app(nil,s(x)),0)) # answer(goal).  [ur(2781,b,131,a,c,571,a)].

given #418 (F,wt=9): 2959 -->_s0(true,head(empty(nil))) | -->*_s0(head(true),false) # answer(goal).  [resolve(2781,b,183,a)].

given #419 (F,wt=9): 2960 -->_s0(true,length(empty(nil))) | -->*_s0(length(true),false) # answer(goal).  [resolve(2781,b,182,a)].

given #420 (T,wt=6): 4803 ->*_s0(leq(length(nil),x),true).  [ur(87,a,331,a,b,572,a)].

given #421 (T,wt=7): 4834 ->*_s0(leq(app(nil,0),x),true).  [ur(87,a,131,a,b,572,a)].

given #422 (T,wt=8): 334 ->_s0(fstsplit(x,length(nil)),fstsplit(x,0)).  [ur(39,a,69,a)].

given #423 (T,wt=8): 335 ->_s0(fstsplit(length(nil),x),fstsplit(0,x)).  [ur(38,a,69,a)].

given #424 (A,wt=9): 134 ->_s0(fstsplit(x,app(nil,y)),fstsplit(x,y)).  [ur(39,a,61,a)].

given #425 (F,wt=9): 2961 -->_s0(true,tail(empty(nil))) | -->*_s0(tail(true),false) # answer(goal).  [resolve(2781,b,169,a)].

given #426 (F,wt=9): 2962 -->_s0(true,s(empty(nil))) | -->*_s0(s(true),false) # answer(goal).  [resolve(2781,b,164,a)].

given #427 (F,wt=9): 2994 -->_s0(true,tail(cons(x,y))) | -->*_s0(y,false) # answer(goal).  [resolve(2781,b,85,a)].

given #428 (F,wt=9): 2995 -->_s0(true,sndsplit(s(x),nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(2781,b,84,a)].

given #429 (T,wt=6): 4913 ->*_s0(fstsplit(length(nil),x),nil).  [ur(87,a,335,a,b,578,a)].

given #430 (T,wt=8): 337 ->_s0(app(x,length(nil)),app(x,0)).  [ur(36,a,69,a)].

given #431 (T,wt=8): 338 ->_s0(app(length(nil),x),app(0,x)).  [ur(35,a,69,a)].

given #432 (T,wt=8): 364 ->_s0(s(leq(s(x),0)),s(false)).  [ur(59,a,71,a)].

given #433 (A,wt=9): 135 ->_s0(fstsplit(app(nil,x),y),fstsplit(x,y)).  [ur(38,a,61,a)].

given #434 (F,wt=9): 3010 -->_s0(true,head(cons(x,y))) | -->*_s0(x,false) # answer(goal).  [resolve(2781,b,67,a)].

given #435 (F,wt=9): 3011 -->_s0(true,fstsplit(s(x),nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(2781,b,66,a)].

given #436 (F,wt=9): 3046 -->_s0(true,x) | -->_s0(x,empty(cons(y,z))) # answer(goal).  [resolve(2781,c,580,a)].

given #437 (F,wt=9): 3047 -->_s0(true,x) | -->_s0(x,head(cons(false,y))) # answer(goal).  [resolve(2781,c,575,a)].

given #438 (T,wt=7): 5059 ->*_s0(fstsplit(app(nil,0),x),nil).  [ur(87,a,135,a,b,578,a)].

given #439 (T,wt=8): 369 ->_s0(tail(leq(s(x),0)),tail(false)).  [ur(54,a,71,a)].

given #440 (T,wt=8): 382 ->_s0(length(leq(s(x),0)),length(false)).  [ur(41,a,71,a)].

given #441 (T,wt=8): 383 ->_s0(head(leq(s(x),0)),head(false)).  [ur(40,a,71,a)].

given #442 (A,wt=9): 137 ->_s0(app(x,app(nil,y)),app(x,y)).  [ur(36,a,61,a)].

given #443 (F,wt=9): 3048 -->_s0(true,x) | -->_s0(x,leq(s(y),0)) # answer(goal).  [resolve(2781,c,571,a)].

given #444 (F,wt=9): 3050 -->_s0(true,x) | -->_s0(x,tail(cons(y,false))) # answer(goal).  [resolve(2781,c,564,a)].

given #445 (F,wt=9): 3065 -->_s0(true,tail(cons(x,empty(cons(y,z))))) # answer(goal).  [ur(2781,b,85,a,c,580,a)].

given #446 (F,wt=9): 3066 -->_s0(true,tail(cons(x,head(cons(false,y))))) # answer(goal).  [ur(2781,b,85,a,c,575,a)].

given #447 (T,wt=8): 386 ->_s0(empty(leq(s(x),0)),empty(false)).  [ur(37,a,71,a)].

given #448 (T,wt=8): 514 ->_s0(s(sndsplit(s(x),nil)),s(nil)).  [ur(59,a,84,a)].

given #449 (T,wt=8): 519 ->_s0(tail(sndsplit(s(x),nil)),tail(nil)).  [ur(54,a,84,a)].

given #450 (T,wt=8): 532 ->_s0(length(sndsplit(s(x),nil)),length(nil)).  [ur(41,a,84,a)].

given #451 (A,wt=9): 138 ->_s0(app(app(nil,x),y),app(x,y)).  [ur(35,a,61,a)].

given #452 (F,wt=9): 3067 -->_s0(true,tail(cons(x,leq(s(y),0)))) # answer(goal).  [ur(2781,b,85,a,c,571,a)].

given #453 (F,wt=9): 3069 -->_s0(true,tail(cons(x,tail(cons(y,false))))) # answer(goal).  [ur(2781,b,85,a,c,564,a)].

given #454 (F,wt=9): 3073 -->_s0(true,sndsplit(0,app(nil,app(nil,false)))) # answer(goal).  [ur(2781,b,82,a,c,698,a)].

given #455 (F,wt=9): 3074 -->_s0(true,sndsplit(0,sndsplit(0,app(nil,false)))) # answer(goal).  [ur(2781,b,82,a,c,696,a)].

given #456 (T,wt=7): 5289 ->*_s0(length(sndsplit(s(x),nil)),0).  [ur(87,a,532,a,b,573,a)].

given #457 (T,wt=7): 5324 ->*_s0(app(app(nil,nil),x),x).  [ur(87,a,138,a,b,581,a)].

given #458 (T,wt=8): 533 ->_s0(head(sndsplit(s(x),nil)),head(nil)).  [ur(40,a,84,a)].

given #459 (T,wt=8): 536 ->_s0(empty(sndsplit(s(x),nil)),empty(nil)).  [ur(37,a,84,a)].

given #460 (A,wt=10): 140 ->_s0(f(x,empty(cons(y,z))),f(x,false)).  [ur(58,a,62,a)].

given #461 (F,wt=9): 3075 -->_s0(true,sndsplit(0,app(nil,sndsplit(0,false)))) # answer(goal).  [ur(2781,b,82,a,c,641,a)].

given #462 (F,wt=9): 3076 -->_s0(true,sndsplit(0,sndsplit(0,sndsplit(0,false)))) # answer(goal).  [ur(2781,b,82,a,c,639,a)].

given #463 (F,wt=9): 3087 -->_s0(true,head(cons(empty(cons(x,y)),z))) # answer(goal).  [ur(2781,b,67,a,c,580,a)].

given #464 (F,wt=9): 3088 -->_s0(true,head(cons(head(cons(false,x)),y))) # answer(goal).  [ur(2781,b,67,a,c,575,a)].

given #465 (T,wt=7): 5407 ->*_s0(empty(sndsplit(s(x),nil)),true).  [ur(87,a,536,a,b,579,a)].

given #466 (T,wt=8): 539 ->_s0(s(tail(cons(x,y))),s(y)).  [ur(59,a,85,a)].

given #467 (T,wt=8): 544 ->_s0(tail(tail(cons(x,y))),tail(y)).  [ur(54,a,85,a)].

given #468 (T,wt=8): 557 ->_s0(length(tail(cons(x,y))),length(y)).  [ur(41,a,85,a)].

given #469 (A,wt=10): 141 ->_s0(f(empty(cons(x,y)),z),f(false,z)).  [ur(57,a,62,a)].

given #470 (F,wt=9): 3089 -->_s0(true,head(cons(leq(s(x),0),y))) # answer(goal).  [ur(2781,b,67,a,c,571,a)].

given #471 (F,wt=9): 3091 -->_s0(true,head(cons(tail(cons(x,false)),y))) # answer(goal).  [ur(2781,b,67,a,c,564,a)].

given #472 (F,wt=9): 3092 -->_s0(true,app(nil,app(nil,app(nil,false)))) # answer(goal).  [ur(2781,b,61,a,c,698,a)].

given #473 (F,wt=9): 3093 -->_s0(true,app(nil,sndsplit(0,app(nil,false)))) # answer(goal).  [ur(2781,b,61,a,c,696,a)].

given #474 (T,wt=7): 5559 ->*_s0(length(tail(cons(x,nil))),0).  [ur(87,a,557,a,b,573,a)].

given #475 (T,wt=8): 558 ->_s0(head(tail(cons(x,y))),head(y)).  [ur(40,a,85,a)].

given #476 (T,wt=8): 561 ->_s0(empty(tail(cons(x,y))),empty(y)).  [ur(37,a,85,a)].

given #477 (T,wt=7): 5676 ->*_s0(empty(tail(cons(x,nil))),true).  [ur(87,a,561,a,b,579,a)].

given #478 (A,wt=10): 142 ->_s0(cons(x,empty(cons(y,z))),cons(x,false)).  [ur(56,a,62,a)].

given #479 (F,wt=9): 3094 -->_s0(true,app(nil,app(nil,sndsplit(0,false)))) # answer(goal).  [ur(2781,b,61,a,c,641,a)].

given #480 (F,wt=9): 3095 -->_s0(true,app(nil,sndsplit(0,sndsplit(0,false)))) # answer(goal).  [ur(2781,b,61,a,c,639,a)].

given #481 (F,wt=9): 3564 -->_s0(true,sndsplit(app(nil,0),app(nil,false))) # answer(goal).  [ur(2781,b,121,a,c,696,a)].

given #482 (F,wt=9): 3565 -->_s0(true,sndsplit(app(nil,0),sndsplit(0,false))) # answer(goal).  [ur(2781,b,121,a,c,639,a)].

given #483 (T,wt=8): 574 ->*_s0(length(cons(x,y)),s(length(y))).  [ur(87,a,68,a,b,86,a)].

given #484 (T,wt=8): 637 ->*_s0(tail(cons(x,sndsplit(0,y))),y).  [ur(87,a,85,a,b,567,a)].

given #485 (T,wt=8): 638 ->*_s0(sndsplit(s(0),cons(x,y)),y).  [ur(87,a,83,a,b,567,a)].

given #486 (T,wt=8): 640 ->*_s0(head(cons(sndsplit(0,x),y)),x).  [ur(87,a,67,a,b,567,a)].

given #487 (A,wt=10): 143 ->_s0(cons(empty(cons(x,y)),z),cons(false,z)).  [ur(55,a,62,a)].

given #488 (F,wt=9): 3566 -->_s0(true,app(nil,sndsplit(app(nil,0),false))) # answer(goal).  [resolve(3536,a,3014,b)].

given #489 (F,wt=9): 3567 -->_s0(true,sndsplit(0,sndsplit(app(nil,0),false))) # answer(goal).  [resolve(3536,a,2997,b)].

given #490 (F,wt=9): 3583 -->_s0(true,sndsplit(app(nil,app(nil,0)),false)) # answer(goal).  [ur(2781,b,121,a,c,3536,a)].

given #491 (F,wt=9): 4201 -->_s0(true,tail(head(cons(cons(x,false),y)))) # answer(goal).  [ur(2781,b,269,a,c,564,a)].

given #492 (T,wt=8): 642 ->*_s0(tail(cons(x,mapf(y,nil))),nil).  [ur(87,a,85,a,b,568,a)].

given #493 (T,wt=8): 644 ->*_s0(head(cons(mapf(x,nil),y)),nil).  [ur(87,a,67,a,b,568,a)].

given #494 (T,wt=8): 683 ->*_s0(tail(cons(x,leq(0,y))),true).  [ur(87,a,85,a,b,572,a)].

given #495 (T,wt=8): 686 ->*_s0(head(cons(leq(0,x),y)),true).  [ur(87,a,67,a,b,572,a)].

given #496 (A,wt=10): 145 ->_s0(sndsplit(x,empty(cons(y,z))),sndsplit(x,false)).  [ur(53,a,62,a)].

given #497 (F,wt=9): 4314 -->_s0(true,head(head(cons(cons(false,x),y)))) # answer(goal).  [ur(2781,b,283,a,c,575,a)].

given #498 (F,wt=9): 4356 -->_s0(true,empty(head(cons(cons(x,y),z)))) # answer(goal).  [ur(2781,b,286,a,c,580,a)].

given #499 (F,wt=9): 4634 -->_s0(true,x) | -->_s0(x,sndsplit(length(nil),false)) # answer(goal).  [resolve(4574,a,2781,c)].

NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 27 (0.00 of 0.11 sec).

given #500 (F,wt=9): 4650 -->_s0(true,tail(cons(x,sndsplit(length(nil),false)))) # answer(goal).  [ur(2781,b,85,a,c,4574,a)].

given #501 (T,wt=8): 688 ->*_s0(tail(cons(x,fstsplit(0,y))),nil).  [ur(87,a,85,a,b,578,a)].

given #502 (T,wt=8): 690 ->*_s0(head(cons(fstsplit(0,x),y)),nil).  [ur(87,a,67,a,b,578,a)].

given #503 (T,wt=8): 695 ->*_s0(tail(cons(x,app(nil,y))),y).  [ur(87,a,85,a,b,581,a)].

given #504 (T,wt=8): 697 ->*_s0(head(cons(app(nil,x),y)),x).  [ur(87,a,67,a,b,581,a)].

given #505 (A,wt=10): 146 ->_s0(sndsplit(empty(cons(x,y)),z),sndsplit(false,z)).  [ur(52,a,62,a)].

given #506 (F,wt=8): 5965 -->_s0(true,tail(app(cons(x,nil),false))) # answer(goal).  [ur(2781,b,94,a,c,695,a)].

given #507 (F,wt=9): 4651 -->_s0(true,sndsplit(s(length(nil)),cons(x,false))) # answer(goal).  [ur(2781,b,83,a,c,4574,a)].

given #508 (F,wt=9): 4652 -->_s0(true,head(cons(sndsplit(length(nil),false),x))) # answer(goal).  [ur(2781,b,67,a,c,4574,a)].

given #509 (F,wt=9): 4784 -->_s0(true,app(nil,leq(s(x),length(nil)))) # answer(goal).  [resolve(4756,a,3014,b)].

given #510 (T,wt=8): 700 ->_s0(s(s(empty(nil))),s(s(true))).  [ur(59,a,164,a)].

given #511 (T,wt=8): 705 ->_s0(tail(s(empty(nil))),tail(s(true))).  [ur(54,a,164,a)].

given #512 (T,wt=8): 718 ->_s0(length(s(empty(nil))),length(s(true))).  [ur(41,a,164,a)].

given #513 (T,wt=8): 719 ->_s0(head(s(empty(nil))),head(s(true))).  [ur(40,a,164,a)].

given #514 (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 #515 (F,wt=9): 4785 -->_s0(true,sndsplit(0,leq(s(x),length(nil)))) # answer(goal).  [resolve(4756,a,2997,b)].

given #516 (F,wt=9): 4797 -->_s0(true,leq(s(x),app(nil,length(nil)))) # answer(goal).  [ur(2781,b,130,a,c,4756,a)].

given #517 (F,wt=9): 4799 -->_s0(true,leq(s(s(x)),s(length(nil)))) # answer(goal).  [ur(2781,b,72,a,c,4756,a)].

given #518 (F,wt=9): 4862 -->_s0(true,leq(app(nil,s(x)),length(nil))) # answer(goal).  [ur(2781,b,131,a,c,4756,a)].

given #519 (T,wt=8): 722 ->_s0(empty(s(empty(nil))),empty(s(true))).  [ur(37,a,164,a)].

given #520 (T,wt=8): 756 ->_s0(s(tail(empty(nil))),s(tail(true))).  [ur(59,a,169,a)].

given #521 (T,wt=8): 761 ->_s0(tail(tail(empty(nil))),tail(tail(true))).  [ur(54,a,169,a)].

given #522 (T,wt=8): 774 ->_s0(length(tail(empty(nil))),length(tail(true))).  [ur(41,a,169,a)].

given #523 (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 #524 (F,wt=9): 5089 -->_s0(true,empty(x)) | -->_s0(x,cons(y,z)) # answer(goal).  [resolve(3046,b,37,b)].

given #525 (F,wt=9): 5090 -->_s0(true,head(x)) | -->_s0(x,cons(false,y)) # answer(goal).  [resolve(3047,b,40,b)].

given #526 (F,wt=9): 5204 -->_s0(true,leq(s(x),y)) | -->_s0(y,0) # answer(goal).  [resolve(3048,b,43,b)].

given #527 (F,wt=8): 6293 -->_s0(true,leq(s(x),sndsplit(0,0))) # answer(goal).  [resolve(5204,b,82,a)].

given #528 (T,wt=8): 775 ->_s0(head(tail(empty(nil))),head(tail(true))).  [ur(40,a,169,a)].

given #529 (T,wt=8): 778 ->_s0(empty(tail(empty(nil))),empty(tail(true))).  [ur(37,a,169,a)].

given #530 (T,wt=8): 782 ->_s0(s(length(empty(nil))),s(length(true))).  [ur(59,a,182,a)].

given #531 (T,wt=8): 787 ->_s0(tail(length(empty(nil))),tail(length(true))).  [ur(54,a,182,a)].

given #532 (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 #533 (F,wt=9): 5205 -->_s0(true,leq(x,0)) | -->_s0(x,s(y)) # answer(goal).  [resolve(3048,b,42,b)].

given #534 (F,wt=8): 6431 -->_s0(true,leq(sndsplit(0,s(x)),0)) # answer(goal).  [resolve(5205,b,82,a)].

given #535 (F,wt=8): 6432 -->_s0(true,leq(length(cons(x,y)),0)) # answer(goal).  [resolve(5205,b,68,a)].

given #536 (F,wt=9): 5206 -->_s0(true,tail(x)) | -->_s0(x,cons(y,false)) # answer(goal).  [resolve(3050,b,54,b)].

given #537 (T,wt=8): 800 ->_s0(length(length(empty(nil))),length(length(true))).  [ur(41,a,182,a)].

given #538 (T,wt=8): 801 ->_s0(head(length(empty(nil))),head(length(true))).  [ur(40,a,182,a)].

given #539 (T,wt=8): 804 ->_s0(empty(length(empty(nil))),empty(length(true))).  [ur(37,a,182,a)].

given #540 (T,wt=8): 808 ->_s0(s(head(empty(nil))),s(head(true))).  [ur(59,a,183,a)].

given #541 (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 #542 (F,wt=9): 5351 -->_s0(true,app(app(nil,nil),app(nil,false))) # answer(goal).  [ur(2781,b,138,a,c,698,a)].

given #543 (F,wt=9): 5352 -->_s0(true,app(app(nil,nil),sndsplit(0,false))) # answer(goal).  [ur(2781,b,138,a,c,641,a)].

given #544 (F,wt=9): 5360 -->_s0(true,app(nil,app(app(nil,nil),false))) # answer(goal).  [resolve(5324,a,3014,b)].

given #545 (F,wt=9): 5362 -->_s0(true,sndsplit(0,app(app(nil,nil),false))) # answer(goal).  [resolve(5324,a,2997,b)].

given #546 (T,wt=8): 813 ->_s0(tail(head(empty(nil))),tail(head(true))).  [ur(54,a,183,a)].

given #547 (T,wt=8): 826 ->_s0(length(head(empty(nil))),length(head(true))).  [ur(41,a,183,a)].

given #548 (T,wt=8): 827 ->_s0(head(head(empty(nil))),head(head(true))).  [ur(40,a,183,a)].

given #549 (T,wt=8): 830 ->_s0(empty(head(empty(nil))),empty(head(true))).  [ur(37,a,183,a)].

given #550 (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 #551 (F,wt=9): 5378 -->_s0(true,app(app(nil,app(nil,nil)),false)) # answer(goal).  [ur(2781,b,138,a,c,5324,a)].

given #552 (F,wt=9): 5505 -->_s0(true,tail(tail(cons(x,cons(y,false))))) # answer(goal).  [resolve(544,a,3050,b)].

given #553 (F,wt=9): 5621 -->_s0(true,head(tail(cons(x,cons(false,y))))) # answer(goal).  [resolve(558,a,3047,b)].

given #554 (F,wt=9): 5659 -->_s0(true,empty(tail(cons(x,cons(y,z))))) # answer(goal).  [resolve(561,a,3046,b)].

given #555 (T,wt=8): 834 ->_s0(s(empty(empty(nil))),s(empty(true))).  [ur(59,a,186,a)].

given #556 (T,wt=8): 839 ->_s0(tail(empty(empty(nil))),tail(empty(true))).  [ur(54,a,186,a)].

given #557 (T,wt=8): 852 ->_s0(length(empty(empty(nil))),length(empty(true))).  [ur(41,a,186,a)].

given #558 (T,wt=8): 853 ->_s0(head(empty(empty(nil))),head(empty(true))).  [ur(40,a,186,a)].

given #559 (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 #560 (F,wt=9): 5919 -->_s0(true,sndsplit(length(nil),empty(cons(x,y)))) # answer(goal).  [ur(2781,b,145,a,c,4574,a)].

given #561 (F,wt=9): 5921 -->_s0(true,sndsplit(length(nil),x)) | -->_s0(x,false) # answer(goal).  [resolve(4634,b,53,b)].

given #562 (F,wt=9): 5922 -->_s0(true,sndsplit(x,false)) | -->_s0(x,length(nil)) # answer(goal).  [resolve(4634,b,52,b)].

given #563 (F,wt=8): 6845 -->_s0(true,sndsplit(length(sndsplit(0,nil)),false)) # answer(goal).  [resolve(5922,b,482,a)].

given #564 (T,wt=8): 856 ->_s0(empty(empty(empty(nil))),empty(empty(true))).  [ur(37,a,186,a)].

given #565 (T,wt=8): 892 ->_s0(s(s(length(nil))),s(s(0))).  [ur(59,a,314,a)].

given #566 (T,wt=8): 897 ->_s0(tail(s(length(nil))),tail(s(0))).  [ur(54,a,314,a)].

given #567 (T,wt=8): 910 ->_s0(length(s(length(nil))),length(s(0))).  [ur(41,a,314,a)].

given #568 (A,wt=10): 153 ->_s0(mapf(x,empty(cons(y,z))),mapf(x,false)).  [ur(45,a,62,a)].

given #569 (F,wt=8): 6846 -->_s0(true,sndsplit(length(mapf(x,nil)),false)) # answer(goal).  [resolve(5922,b,457,a)].

given #570 (F,wt=8): 6849 -->_s0(true,sndsplit(length(fstsplit(0,x)),false)) # answer(goal).  [resolve(5922,b,207,a)].

given #571 (F,wt=8): 6850 -->_s0(true,sndsplit(length(app(nil,nil)),false)) # answer(goal).  [resolve(5922,b,132,a)].

given #572 (F,wt=8): 6852 -->_s0(true,sndsplit(sndsplit(0,length(nil)),false)) # answer(goal).  [resolve(5922,b,82,a)].

given #573 (T,wt=8): 911 ->_s0(head(s(length(nil))),head(s(0))).  [ur(40,a,314,a)].

given #574 (T,wt=8): 914 ->_s0(empty(s(length(nil))),empty(s(0))).  [ur(37,a,314,a)].

given #575 (T,wt=8): 918 ->_s0(s(tail(length(nil))),s(tail(0))).  [ur(59,a,319,a)].

given #576 (T,wt=8): 923 ->_s0(tail(tail(length(nil))),tail(tail(0))).  [ur(54,a,319,a)].

given #577 (A,wt=10): 154 ->_s0(mapf(empty(cons(x,y)),z),mapf(false,z)).  [ur(44,a,62,a)].

given #578 (F,wt=9): 6289 -->_s0(true,empty(fstsplit(s(x),cons(y,z)))) # answer(goal).  [resolve(5089,b,65,a)].

given #579 (F,wt=9): 6290 -->_s0(true,head(fstsplit(s(x),cons(false,y)))) # answer(goal).  [resolve(5090,b,65,a)].

given #580 (F,wt=9): 6291 -->_s0(true,head(cons(x,y))) | -->_s0(x,false) # answer(goal).  [resolve(5090,b,55,b)].

given #581 (F,wt=9): 6292 -->_s0(true,leq(s(x),tail(cons(y,0)))) # answer(goal).  [resolve(5204,b,85,a)].

given #582 (T,wt=8): 936 ->_s0(length(tail(length(nil))),length(tail(0))).  [ur(41,a,319,a)].

given #583 (T,wt=8): 937 ->_s0(head(tail(length(nil))),head(tail(0))).  [ur(40,a,319,a)].

given #584 (T,wt=8): 940 ->_s0(empty(tail(length(nil))),empty(tail(0))).  [ur(37,a,319,a)].

given #585 (T,wt=8): 944 ->_s0(s(length(length(nil))),s(length(0))).  [ur(59,a,332,a)].

given #586 (A,wt=10): 155 ->_s0(leq(x,empty(cons(y,z))),leq(x,false)).  [ur(43,a,62,a)].

given #587 (F,wt=9): 6294 -->_s0(true,leq(s(x),head(cons(0,y)))) # answer(goal).  [resolve(5204,b,67,a)].

given #588 (F,wt=9): 6430 -->_s0(true,leq(tail(cons(x,s(y))),0)) # answer(goal).  [resolve(5205,b,85,a)].

given #589 (F,wt=9): 6433 -->_s0(true,leq(head(cons(s(x),y)),0)) # answer(goal).  [resolve(5205,b,67,a)].

given #590 (F,wt=9): 6434 -->_s0(true,tail(cons(x,y))) | -->_s0(y,false) # answer(goal).  [resolve(5206,b,56,b)].

given #591 (T,wt=8): 949 ->_s0(tail(length(length(nil))),tail(length(0))).  [ur(54,a,332,a)].

given #592 (T,wt=8): 962 ->_s0(length(length(length(nil))),length(length(0))).  [ur(41,a,332,a)].

given #593 (T,wt=8): 963 ->_s0(head(length(length(nil))),head(length(0))).  [ur(40,a,332,a)].

given #594 (T,wt=8): 966 ->_s0(empty(length(length(nil))),empty(length(0))).  [ur(37,a,332,a)].

given #595 (A,wt=10): 156 ->_s0(leq(empty(cons(x,y)),z),leq(false,z)).  [ur(42,a,62,a)].

given #596 (F,wt=9): 6840 -->_s0(true,sndsplit(length(nil),tail(cons(x,false)))) # answer(goal).  [resolve(5921,b,85,a)].

given #597 (F,wt=9): 6841 -->_s0(true,sndsplit(length(nil),leq(s(x),0))) # answer(goal).  [resolve(5921,b,71,a)].

given #598 (F,wt=9): 6842 -->_s0(true,sndsplit(length(nil),head(cons(false,x)))) # answer(goal).  [resolve(5921,b,67,a)].

given #599 (F,wt=9): 6843 -->_s0(true,sndsplit(length(tail(cons(x,nil))),false)) # answer(goal).  [resolve(5922,b,557,a)].

given #600 (T,wt=8): 970 ->_s0(s(head(length(nil))),s(head(0))).  [ur(59,a,333,a)].

given #601 (T,wt=8): 975 ->_s0(tail(head(length(nil))),tail(head(0))).  [ur(54,a,333,a)].

given #602 (T,wt=8): 988 ->_s0(length(head(length(nil))),length(head(0))).  [ur(41,a,333,a)].

given #603 (T,wt=8): 989 ->_s0(head(head(length(nil))),head(head(0))).  [ur(40,a,333,a)].

given #604 (A,wt=10): 159 ->_s0(fstsplit(x,empty(cons(y,z))),fstsplit(x,false)).  [ur(39,a,62,a)].

given #605 (F,wt=9): 6844 -->_s0(true,sndsplit(length(sndsplit(s(x),nil)),false)) # answer(goal).  [resolve(5922,b,532,a)].

given #606 (F,wt=9): 6847 -->_s0(true,sndsplit(length(head(cons(nil,x))),false)) # answer(goal).  [resolve(5922,b,282,a)].

given #607 (F,wt=9): 6848 -->_s0(true,sndsplit(length(fstsplit(s(x),nil)),false)) # answer(goal).  [resolve(5922,b,257,a)].

given #608 (F,wt=9): 6851 -->_s0(true,sndsplit(tail(cons(x,length(nil))),false)) # answer(goal).  [resolve(5922,b,85,a)].

given #609 (T,wt=8): 992 ->_s0(empty(head(length(nil))),empty(head(0))).  [ur(37,a,333,a)].

given #610 (T,wt=8): 1032 ->_s0(s(empty(length(nil))),s(empty(0))).  [ur(59,a,336,a)].

given #611 (T,wt=8): 1037 ->_s0(tail(empty(length(nil))),tail(empty(0))).  [ur(54,a,336,a)].

given #612 (T,wt=8): 1050 ->_s0(length(empty(length(nil))),length(empty(0))).  [ur(41,a,336,a)].

given #613 (A,wt=10): 160 ->_s0(fstsplit(empty(cons(x,y)),z),fstsplit(false,z)).  [ur(38,a,62,a)].

Low Water (keep): wt=22.000, iters=6667

given #614 (F,wt=9): 6853 -->_s0(true,sndsplit(head(cons(length(nil),x)),false)) # answer(goal).  [resolve(5922,b,67,a)].

given #615 (F,wt=9): 6854 -->_s0(true,sndsplit(length(x),false)) | -->_s0(x,nil) # answer(goal).  [resolve(5922,b,41,b)].

given #616 (F,wt=10): 2933 -->_s0(true,empty(sndsplit(0,x))) | -->*_s0(empty(x),false) # answer(goal).  [resolve(2781,b,486,a)].

given #617 (F,wt=10): 2934 -->_s0(true,head(sndsplit(0,x))) | -->*_s0(head(x),false) # answer(goal).  [resolve(2781,b,483,a)].

given #618 (T,wt=8): 1051 ->_s0(head(empty(length(nil))),head(empty(0))).  [ur(40,a,336,a)].

given #619 (T,wt=8): 1054 ->_s0(empty(empty(length(nil))),empty(empty(0))).  [ur(37,a,336,a)].

given #620 (T,wt=8): 1063 ->*_s0(sndsplit(0,tail(cons(x,y))),y).  [ur(87,a,82,a,b,564,a)].

given #621 (T,wt=8): 1065 ->*_s0(app(nil,tail(cons(x,y))),y).  [ur(87,a,61,a,b,564,a)].

given #622 (A,wt=10): 162 ->_s0(app(x,empty(cons(y,z))),app(x,false)).  [ur(36,a,62,a)].

given #623 (F,wt=10): 2935 -->_s0(true,length(sndsplit(0,x))) | -->*_s0(length(x),false) # answer(goal).  [resolve(2781,b,482,a)].

given #624 (F,wt=10): 2936 -->_s0(true,tail(sndsplit(0,x))) | -->*_s0(tail(x),false) # answer(goal).  [resolve(2781,b,469,a)].

given #625 (F,wt=10): 2937 -->_s0(true,s(sndsplit(0,x))) | -->*_s0(s(x),false) # answer(goal).  [resolve(2781,b,464,a)].

given #626 (F,wt=10): 2938 -->_s0(true,empty(mapf(x,nil))) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(2781,b,461,a)].

given #627 (T,wt=8): 1068 ->*_s0(sndsplit(0,sndsplit(s(x),nil)),nil).  [ur(87,a,82,a,b,565,a)].

given #628 (T,wt=8): 1070 ->*_s0(app(nil,sndsplit(s(x),nil)),nil).  [ur(87,a,61,a,b,565,a)].

given #629 (T,wt=8): 1075 ->*_s0(sndsplit(0,leq(s(x),0)),false).  [ur(87,a,82,a,b,571,a)].

given #630 (T,wt=8): 1076 ->*_s0(leq(s(s(x)),s(0)),false).  [ur(87,a,72,a,b,571,a)].

given #631 (A,wt=10): 163 ->_s0(app(empty(cons(x,y)),z),app(false,z)).  [ur(35,a,62,a)].

given #632 (F,wt=10): 2939 -->_s0(true,head(mapf(x,nil))) | -->*_s0(head(nil),false) # answer(goal).  [resolve(2781,b,458,a)].

given #633 (F,wt=10): 2940 -->_s0(true,length(mapf(x,nil))) | -->*_s0(length(nil),false) # answer(goal).  [resolve(2781,b,457,a)].

given #634 (F,wt=10): 2941 -->_s0(true,tail(mapf(x,nil))) | -->*_s0(tail(nil),false) # answer(goal).  [resolve(2781,b,444,a)].

given #635 (F,wt=10): 2942 -->_s0(true,s(mapf(x,nil))) | -->*_s0(s(nil),false) # answer(goal).  [resolve(2781,b,439,a)].

given #636 (T,wt=8): 1078 ->*_s0(app(nil,leq(s(x),0)),false).  [ur(87,a,61,a,b,571,a)].

given #637 (T,wt=8): 1113 ->*_s0(sndsplit(0,head(cons(x,y))),x).  [ur(87,a,82,a,b,575,a)].

given #638 (T,wt=8): 1115 ->*_s0(app(nil,head(cons(x,y))),x).  [ur(87,a,61,a,b,575,a)].

given #639 (T,wt=8): 1117 ->*_s0(sndsplit(0,fstsplit(s(x),nil)),nil).  [ur(87,a,82,a,b,576,a)].

given #640 (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 #641 (F,wt=10): 2943 -->_s0(true,empty(leq(0,x))) | -->*_s0(empty(true),false) # answer(goal).  [resolve(2781,b,361,a)].

given #642 (F,wt=10): 2944 -->_s0(true,head(leq(0,x))) | -->*_s0(head(true),false) # answer(goal).  [resolve(2781,b,358,a)].

given #643 (F,wt=10): 2945 -->_s0(true,length(leq(0,x))) | -->*_s0(length(true),false) # answer(goal).  [resolve(2781,b,357,a)].

given #644 (F,wt=10): 2946 -->_s0(true,tail(leq(0,x))) | -->*_s0(tail(true),false) # answer(goal).  [resolve(2781,b,344,a)].

given #645 (T,wt=8): 1119 ->*_s0(app(nil,fstsplit(s(x),nil)),nil).  [ur(87,a,61,a,b,576,a)].

given #646 (T,wt=8): 1125 ->*_s0(sndsplit(0,empty(cons(x,y))),false).  [ur(87,a,82,a,b,580,a)].

given #647 (T,wt=8): 1127 ->*_s0(app(nil,empty(cons(x,y))),false).  [ur(87,a,61,a,b,580,a)].

given #648 (T,wt=8): 1130 ->*_s0(sndsplit(0,sndsplit(0,length(nil))),0).  [ur(87,a,82,a,b,627,a)].

given #649 (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 #650 (F,wt=10): 2947 -->_s0(true,s(leq(0,x))) | -->*_s0(s(true),false) # answer(goal).  [resolve(2781,b,339,a)].

given #651 (F,wt=10): 2953 -->_s0(true,empty(fstsplit(0,x))) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(2781,b,211,a)].

given #652 (F,wt=10): 2954 -->_s0(true,head(fstsplit(0,x))) | -->*_s0(head(nil),false) # answer(goal).  [resolve(2781,b,208,a)].

given #653 (F,wt=10): 2955 -->_s0(true,length(fstsplit(0,x))) | -->*_s0(length(nil),false) # answer(goal).  [resolve(2781,b,207,a)].

given #654 (T,wt=8): 1132 ->*_s0(app(nil,sndsplit(0,length(nil))),0).  [ur(87,a,61,a,b,627,a)].

given #655 (T,wt=8): 1169 ->*_s0(sndsplit(0,app(nil,length(nil))),0).  [ur(87,a,82,a,b,629,a)].

given #656 (T,wt=8): 1171 ->*_s0(app(nil,app(nil,length(nil))),0).  [ur(87,a,61,a,b,629,a)].

given #657 (T,wt=8): 1176 ->*_s0(sndsplit(0,sndsplit(0,empty(nil))),true).  [ur(87,a,82,a,b,632,a)].

given #658 (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 #659 (F,wt=10): 2956 -->_s0(true,tail(fstsplit(0,x))) | -->*_s0(tail(nil),false) # answer(goal).  [resolve(2781,b,194,a)].

given #660 (F,wt=10): 2957 -->_s0(true,s(fstsplit(0,x))) | -->*_s0(s(nil),false) # answer(goal).  [resolve(2781,b,189,a)].

given #661 (F,wt=10): 2963 -->_s0(true,empty(app(nil,x))) | -->*_s0(empty(x),false) # answer(goal).  [resolve(2781,b,136,a)].

given #662 (F,wt=10): 2964 -->_s0(true,head(app(nil,x))) | -->*_s0(head(x),false) # answer(goal).  [resolve(2781,b,133,a)].

given #663 (T,wt=8): 1178 ->*_s0(app(nil,sndsplit(0,empty(nil))),true).  [ur(87,a,61,a,b,632,a)].

given #664 (T,wt=8): 1182 ->*_s0(sndsplit(0,app(nil,empty(nil))),true).  [ur(87,a,82,a,b,634,a)].

given #665 (T,wt=8): 1184 ->*_s0(app(nil,app(nil,empty(nil))),true).  [ur(87,a,61,a,b,634,a)].

given #666 (T,wt=8): 1186 ->*_s0(sndsplit(0,s(empty(nil))),s(true)).  [ur(87,a,82,a,b,699,a)].

given #667 (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 #668 (F,wt=10): 2965 -->_s0(true,length(app(nil,x))) | -->*_s0(length(x),false) # answer(goal).  [resolve(2781,b,132,a)].

given #669 (F,wt=10): 2966 -->_s0(true,tail(app(nil,x))) | -->*_s0(tail(x),false) # answer(goal).  [resolve(2781,b,119,a)].

given #670 (F,wt=10): 2968 -->_s0(true,s(app(nil,x))) | -->*_s0(s(x),false) # answer(goal).  [resolve(2781,b,114,a)].

given #671 (F,wt=10): 3041 -->_s0(true,x) | -->_s0(x,app(nil,app(nil,false))) # answer(goal).  [resolve(2781,c,698,a)].

given #672 (T,wt=8): 1188 ->*_s0(app(nil,s(empty(nil))),s(true)).  [ur(87,a,61,a,b,699,a)].

given #673 (T,wt=8): 1216 ->*_s0(sndsplit(0,tail(empty(nil))),tail(true)).  [ur(87,a,82,a,b,755,a)].

given #674 (T,wt=8): 1218 ->*_s0(app(nil,tail(empty(nil))),tail(true)).  [ur(87,a,61,a,b,755,a)].

given #675 (T,wt=8): 1220 ->*_s0(sndsplit(0,length(empty(nil))),length(true)).  [ur(87,a,82,a,b,781,a)].

given #676 (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 #677 (F,wt=10): 3042 -->_s0(true,x) | -->_s0(x,sndsplit(0,app(nil,false))) # answer(goal).  [resolve(2781,c,696,a)].

given #678 (F,wt=10): 3043 -->_s0(true,x) | -->_s0(x,app(nil,sndsplit(0,false))) # answer(goal).  [resolve(2781,c,641,a)].

given #679 (F,wt=10): 3044 -->_s0(true,x) | -->_s0(x,sndsplit(0,sndsplit(0,false))) # answer(goal).  [resolve(2781,c,639,a)].

given #680 (F,wt=10): 3060 -->_s0(true,tail(cons(x,app(nil,app(nil,false))))) # answer(goal).  [ur(2781,b,85,a,c,698,a)].

given #681 (T,wt=8): 1222 ->*_s0(app(nil,length(empty(nil))),length(true)).  [ur(87,a,61,a,b,781,a)].

given #682 (T,wt=8): 1224 ->*_s0(sndsplit(0,head(empty(nil))),head(true)).  [ur(87,a,82,a,b,807,a)].

given #683 (T,wt=8): 1226 ->*_s0(app(nil,head(empty(nil))),head(true)).  [ur(87,a,61,a,b,807,a)].

given #684 (T,wt=8): 1228 ->*_s0(sndsplit(0,empty(empty(nil))),empty(true)).  [ur(87,a,82,a,b,833,a)].

given #685 (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)].

Low Water (keep): wt=20.000, iters=6691

given #686 (F,wt=10): 3061 -->_s0(true,tail(cons(x,sndsplit(0,app(nil,false))))) # answer(goal).  [ur(2781,b,85,a,c,696,a)].

given #687 (F,wt=10): 3062 -->_s0(true,tail(cons(x,app(nil,sndsplit(0,false))))) # answer(goal).  [ur(2781,b,85,a,c,641,a)].

given #688 (F,wt=10): 3063 -->_s0(true,tail(cons(x,sndsplit(0,sndsplit(0,false))))) # answer(goal).  [ur(2781,b,85,a,c,639,a)].

given #689 (F,wt=10): 3070 -->_s0(true,sndsplit(s(0),cons(x,app(nil,false)))) # answer(goal).  [ur(2781,b,83,a,c,696,a)].

given #690 (T,wt=8): 1230 ->*_s0(app(nil,empty(empty(nil))),empty(true)).  [ur(87,a,61,a,b,833,a)].

given #691 (T,wt=8): 1260 ->*_s0(sndsplit(0,s(length(nil))),s(0)).  [ur(87,a,82,a,b,891,a)].

given #692 (T,wt=8): 1263 ->*_s0(app(nil,s(length(nil))),s(0)).  [ur(87,a,61,a,b,891,a)].

given #693 (T,wt=8): 1265 ->*_s0(sndsplit(0,tail(length(nil))),tail(0)).  [ur(87,a,82,a,b,917,a)].

given #694 (A,wt=9): 190 ->_s0(f(x,fstsplit(0,y)),f(x,nil)).  [ur(58,a,64,a)].

given #695 (F,wt=10): 3071 -->_s0(true,sndsplit(s(0),cons(x,sndsplit(0,false)))) # answer(goal).  [ur(2781,b,83,a,c,639,a)].

given #696 (F,wt=10): 3082 -->_s0(true,head(cons(app(nil,app(nil,false)),x))) # answer(goal).  [ur(2781,b,67,a,c,698,a)].

given #697 (F,wt=10): 3083 -->_s0(true,head(cons(sndsplit(0,app(nil,false)),x))) # answer(goal).  [ur(2781,b,67,a,c,696,a)].

given #698 (F,wt=10): 3084 -->_s0(true,head(cons(app(nil,sndsplit(0,false)),x))) # answer(goal).  [ur(2781,b,67,a,c,641,a)].

given #699 (T,wt=8): 1267 ->*_s0(app(nil,tail(length(nil))),tail(0)).  [ur(87,a,61,a,b,917,a)].

given #700 (T,wt=8): 1269 ->*_s0(sndsplit(0,length(length(nil))),length(0)).  [ur(87,a,82,a,b,943,a)].

given #701 (T,wt=8): 1271 ->*_s0(app(nil,length(length(nil))),length(0)).  [ur(87,a,61,a,b,943,a)].

given #702 (T,wt=8): 1273 ->*_s0(sndsplit(0,head(length(nil))),head(0)).  [ur(87,a,82,a,b,969,a)].

given #703 (A,wt=9): 191 ->_s0(f(fstsplit(0,x),y),f(nil,y)).  [ur(57,a,64,a)].

given #704 (F,wt=10): 3085 -->_s0(true,head(cons(sndsplit(0,sndsplit(0,false)),x))) # answer(goal).  [ur(2781,b,67,a,c,639,a)].

given #705 (F,wt=10): 3100 -->_s0(true,length(nil)) | -->_s0(0,x) | -->*_s0(x,false) # answer(goal).  [resolve(3008,b,87,c)].

given #706 (F,wt=7): 8318 -->_s0(true,length(nil)) | -->_s0(0,false) # answer(goal).  [resolve(3100,c,86,a)].

given #707 (F,wt=9): 8311 -->_s0(true,length(nil)) | -->_s0(0,app(nil,false)) # answer(goal).  [resolve(3100,c,581,a)].

given #708 (T,wt=8): 1275 ->*_s0(app(nil,head(length(nil))),head(0)).  [ur(87,a,61,a,b,969,a)].

given #709 (T,wt=8): 1304 ->*_s0(sndsplit(0,empty(length(nil))),empty(0)).  [ur(87,a,82,a,b,1031,a)].

given #710 (T,wt=8): 1306 ->*_s0(app(nil,empty(length(nil))),empty(0)).  [ur(87,a,61,a,b,1031,a)].

given #711 (T,wt=8): 1307 ->*_s0(s(app(nil,length(nil))),s(0)).  [ur(87,a,114,a,b,891,a)].

given #712 (A,wt=9): 192 ->_s0(cons(x,fstsplit(0,y)),cons(x,nil)).  [ur(56,a,64,a)].

given #713 (F,wt=9): 8315 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(0,false)) # answer(goal).  [resolve(3100,c,567,a)].

given #714 (F,wt=10): 3568 -->_s0(true,x) | -->_s0(x,sndsplit(app(nil,0),false)) # answer(goal).  [resolve(3536,a,2781,c)].

given #715 (F,wt=10): 3584 -->_s0(true,tail(cons(x,sndsplit(app(nil,0),false)))) # answer(goal).  [ur(2781,b,85,a,c,3536,a)].

given #716 (F,wt=10): 3585 -->_s0(true,sndsplit(s(app(nil,0)),cons(x,false))) # answer(goal).  [ur(2781,b,83,a,c,3536,a)].

given #717 (T,wt=8): 1308 ->*_s0(s(app(nil,empty(nil))),s(true)).  [ur(87,a,114,a,b,699,a)].

given #718 (T,wt=8): 1335 ->*_s0(tail(app(nil,length(nil))),tail(0)).  [ur(87,a,119,a,b,917,a)].

given #719 (T,wt=8): 1336 ->*_s0(tail(app(nil,empty(nil))),tail(true)).  [ur(87,a,119,a,b,755,a)].

given #720 (T,wt=8): 1337 ->*_s0(tail(app(nil,cons(x,y))),y).  [ur(87,a,119,a,b,564,a)].

given #721 (A,wt=9): 193 ->_s0(cons(fstsplit(0,x),y),cons(nil,y)).  [ur(55,a,64,a)].

given #722 (F,wt=10): 3586 -->_s0(true,head(cons(sndsplit(app(nil,0),false),x))) # answer(goal).  [ur(2781,b,67,a,c,3536,a)].

given #723 (F,wt=10): 4786 -->_s0(true,x) | -->_s0(x,leq(s(y),length(nil))) # answer(goal).  [resolve(4756,a,2781,c)].

given #724 (F,wt=10): 4798 -->_s0(true,tail(cons(x,leq(s(y),length(nil))))) # answer(goal).  [ur(2781,b,85,a,c,4756,a)].

given #725 (F,wt=10): 4800 -->_s0(true,head(cons(leq(s(x),length(nil)),y))) # answer(goal).  [ur(2781,b,67,a,c,4756,a)].

given #726 (T,wt=8): 1364 ->*_s0(length(app(nil,length(nil))),length(0)).  [ur(87,a,132,a,b,943,a)].

given #727 (T,wt=8): 1365 ->*_s0(length(app(nil,empty(nil))),length(true)).  [ur(87,a,132,a,b,781,a)].

given #728 (T,wt=8): 1419 ->*_s0(length(app(nil,app(nil,nil))),0).  [ur(87,a,132,a,b,1366,a)].

given #729 (T,wt=8): 1421 ->*_s0(sndsplit(0,length(app(nil,nil))),0).  [ur(87,a,82,a,b,1366,a)].

given #730 (A,wt=9): 195 ->_s0(sndsplit(x,fstsplit(0,y)),sndsplit(x,nil)).  [ur(53,a,64,a)].

given #731 (F,wt=10): 5361 -->_s0(true,head(cons(app(app(nil,nil),false),x))) # answer(goal).  [resolve(5324,a,3010,b)].

given #732 (F,wt=10): 5363 -->_s0(true,tail(cons(x,app(app(nil,nil),false)))) # answer(goal).  [resolve(5324,a,2994,b)].

given #733 (F,wt=10): 5364 -->_s0(true,x) | -->_s0(x,app(app(nil,nil),false)) # answer(goal).  [resolve(5324,a,2781,c)].

given #734 (F,wt=10): 5750 -->_s0(true,app(nil,tail(cons(x,sndsplit(0,false))))) # answer(goal).  [resolve(637,a,3014,b)].

given #735 (T,wt=8): 1423 ->*_s0(app(nil,length(app(nil,nil))),0).  [ur(87,a,61,a,b,1366,a)].

given #736 (T,wt=8): 1424 ->*_s0(head(app(nil,length(nil))),head(0)).  [ur(87,a,133,a,b,969,a)].

given #737 (T,wt=8): 1425 ->*_s0(head(app(nil,empty(nil))),head(true)).  [ur(87,a,133,a,b,807,a)].

given #738 (T,wt=8): 1426 ->*_s0(head(app(nil,cons(x,y))),x).  [ur(87,a,133,a,b,575,a)].

given #739 (A,wt=9): 196 ->_s0(sndsplit(fstsplit(0,x),y),sndsplit(nil,y)).  [ur(52,a,64,a)].

given #740 (F,wt=10): 5752 -->_s0(true,sndsplit(0,tail(cons(x,sndsplit(0,false))))) # answer(goal).  [resolve(637,a,2997,b)].

given #741 (F,wt=10): 5771 -->_s0(true,tail(sndsplit(0,cons(x,sndsplit(0,false))))) # answer(goal).  [ur(2781,b,469,a,c,637,a)].

given #742 (F,wt=10): 5773 -->_s0(true,tail(app(nil,cons(x,sndsplit(0,false))))) # answer(goal).  [ur(2781,b,119,a,c,637,a)].

given #743 (F,wt=10): 5774 -->_s0(true,app(nil,sndsplit(s(0),cons(x,false)))) # answer(goal).  [resolve(638,a,3014,b)].

given #744 (T,wt=8): 1453 ->*_s0(empty(app(nil,length(nil))),empty(0)).  [ur(87,a,136,a,b,1031,a)].

given #745 (T,wt=8): 1454 ->*_s0(empty(app(nil,empty(nil))),empty(true)).  [ur(87,a,136,a,b,833,a)].

given #746 (T,wt=8): 1455 ->*_s0(empty(app(nil,cons(x,y))),false).  [ur(87,a,136,a,b,580,a)].

given #747 (T,wt=8): 1485 ->*_s0(empty(app(nil,app(nil,nil))),true).  [ur(87,a,136,a,b,1456,a)].

given #748 (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 #749 (F,wt=10): 5776 -->_s0(true,sndsplit(0,sndsplit(s(0),cons(x,false)))) # answer(goal).  [resolve(638,a,2997,b)].

given #750 (F,wt=10): 5794 -->_s0(true,sndsplit(app(nil,s(0)),cons(x,false))) # answer(goal).  [ur(2781,b,121,a,c,638,a)].

given #751 (F,wt=10): 5795 -->_s0(true,sndsplit(s(0),app(nil,cons(x,false)))) # answer(goal).  [ur(2781,b,120,a,c,638,a)].

given #752 (F,wt=10): 5797 -->_s0(true,app(nil,head(cons(sndsplit(0,false),x)))) # answer(goal).  [resolve(640,a,3014,b)].

given #753 (T,wt=8): 1487 ->*_s0(sndsplit(0,empty(app(nil,nil))),true).  [ur(87,a,82,a,b,1456,a)].

given #754 (T,wt=8): 1489 ->*_s0(app(nil,empty(app(nil,nil))),true).  [ur(87,a,61,a,b,1456,a)].

given #755 (T,wt=8): 1688 ->*_s0(length(app(nil,fstsplit(0,x))),0).  [ur(87,a,132,a,b,1661,a)].

given #756 (T,wt=8): 1690 ->*_s0(sndsplit(0,length(fstsplit(0,x))),0).  [ur(87,a,82,a,b,1661,a)].

given #757 (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 #758 (F,wt=10): 5799 -->_s0(true,sndsplit(0,head(cons(sndsplit(0,false),x)))) # answer(goal).  [resolve(640,a,2997,b)].

given #759 (F,wt=10): 5819 -->_s0(true,head(sndsplit(0,cons(sndsplit(0,false),x)))) # answer(goal).  [ur(2781,b,483,a,c,640,a)].

given #760 (F,wt=10): 5821 -->_s0(true,head(app(nil,cons(sndsplit(0,false),x)))) # answer(goal).  [ur(2781,b,133,a,c,640,a)].

given #761 (F,wt=10): 5822 -->_s0(true,head(app(cons(sndsplit(0,false),x),y))) # answer(goal).  [ur(2781,b,108,a,c,640,a)].

given #762 (T,wt=8): 1692 ->*_s0(app(nil,length(fstsplit(0,x))),0).  [ur(87,a,61,a,b,1661,a)].

given #763 (T,wt=8): 1779 ->*_s0(empty(app(nil,fstsplit(0,x))),true).  [ur(87,a,136,a,b,1750,a)].

given #764 (T,wt=8): 1781 ->*_s0(sndsplit(0,empty(fstsplit(0,x))),true).  [ur(87,a,82,a,b,1750,a)].

given #765 (T,wt=8): 1783 ->*_s0(app(nil,empty(fstsplit(0,x))),true).  [ur(87,a,61,a,b,1750,a)].

given #766 (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 #767 (F,wt=10): 5920 -->_s0(true,sndsplit(app(nil,0),empty(cons(x,y)))) # answer(goal).  [ur(2781,b,145,a,c,3536,a)].

given #768 (F,wt=10): 5940 -->_s0(true,app(nil,tail(cons(x,app(nil,false))))) # answer(goal).  [resolve(695,a,3014,b)].

given #769 (F,wt=10): 5942 -->_s0(true,sndsplit(0,tail(cons(x,app(nil,false))))) # answer(goal).  [resolve(695,a,2997,b)].

given #770 (F,wt=10): 5962 -->_s0(true,tail(sndsplit(0,cons(x,app(nil,false))))) # answer(goal).  [ur(2781,b,469,a,c,695,a)].

given #771 (T,wt=8): 2073 ->*_s0(length(app(nil,mapf(x,nil))),0).  [ur(87,a,132,a,b,2046,a)].

given #772 (T,wt=8): 2075 ->*_s0(sndsplit(0,length(mapf(x,nil))),0).  [ur(87,a,82,a,b,2046,a)].

given #773 (T,wt=8): 2077 ->*_s0(app(nil,length(mapf(x,nil))),0).  [ur(87,a,61,a,b,2046,a)].

given #774 (T,wt=8): 2177 ->*_s0(empty(app(nil,mapf(x,nil))),true).  [ur(87,a,136,a,b,2147,a)].

given #775 (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 #776 (F,wt=10): 5964 -->_s0(true,tail(app(nil,cons(x,app(nil,false))))) # answer(goal).  [ur(2781,b,119,a,c,695,a)].

given #777 (F,wt=10): 5966 -->_s0(true,app(nil,head(cons(app(nil,false),x)))) # answer(goal).  [resolve(697,a,3014,b)].

given #778 (F,wt=10): 5968 -->_s0(true,sndsplit(0,head(cons(app(nil,false),x)))) # answer(goal).  [resolve(697,a,2997,b)].

given #779 (F,wt=10): 5988 -->_s0(true,head(sndsplit(0,cons(app(nil,false),x)))) # answer(goal).  [ur(2781,b,483,a,c,697,a)].

given #780 (T,wt=8): 2179 ->*_s0(sndsplit(0,empty(mapf(x,nil))),true).  [ur(87,a,82,a,b,2147,a)].

given #781 (T,wt=8): 2181 ->*_s0(app(nil,empty(mapf(x,nil))),true).  [ur(87,a,61,a,b,2147,a)].

given #782 (T,wt=8): 2183 ->*_s0(s(sndsplit(0,length(nil))),s(0)).  [ur(87,a,464,a,b,891,a)].

given #783 (T,wt=8): 2184 ->*_s0(s(sndsplit(0,empty(nil))),s(true)).  [ur(87,a,464,a,b,699,a)].

given #784 (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 #785 (F,wt=10): 5990 -->_s0(true,head(app(nil,cons(app(nil,false),x)))) # answer(goal).  [ur(2781,b,133,a,c,697,a)].

given #786 (F,wt=10): 5991 -->_s0(true,head(app(cons(app(nil,false),x),y))) # answer(goal).  [ur(2781,b,108,a,c,697,a)].

given #787 (F,wt=10): 7716 -->_s0(true,app(nil,sndsplit(0,tail(cons(x,false))))) # answer(goal).  [resolve(1063,a,3014,b)].

given #788 (F,wt=10): 7718 -->_s0(true,sndsplit(0,sndsplit(0,tail(cons(x,false))))) # answer(goal).  [resolve(1063,a,2997,b)].

given #789 (T,wt=8): 2243 ->*_s0(tail(sndsplit(0,length(nil))),tail(0)).  [ur(87,a,469,a,b,917,a)].

given #790 (T,wt=8): 2244 ->*_s0(tail(sndsplit(0,empty(nil))),tail(true)).  [ur(87,a,469,a,b,755,a)].

given #791 (T,wt=8): 2245 ->*_s0(tail(sndsplit(0,cons(x,y))),y).  [ur(87,a,469,a,b,564,a)].

given #792 (T,wt=8): 2273 ->*_s0(length(sndsplit(0,mapf(x,nil))),0).  [ur(87,a,482,a,b,2046,a)].

given #793 (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 #794 (F,wt=10): 7736 -->_s0(true,sndsplit(app(nil,0),tail(cons(x,false)))) # answer(goal).  [ur(2781,b,121,a,c,1063,a)].

given #795 (F,wt=10): 7737 -->_s0(true,sndsplit(0,app(nil,tail(cons(x,false))))) # answer(goal).  [ur(2781,b,120,a,c,1063,a)].

given #796 (F,wt=10): 7739 -->_s0(true,app(nil,app(nil,tail(cons(x,false))))) # answer(goal).  [resolve(1065,a,3014,b)].

given #797 (F,wt=10): 7754 -->_s0(true,app(app(nil,nil),tail(cons(x,false)))) # answer(goal).  [ur(2781,b,138,a,c,1065,a)].

given #798 (T,wt=8): 2274 ->*_s0(length(sndsplit(0,fstsplit(0,x))),0).  [ur(87,a,482,a,b,1661,a)].

given #799 (T,wt=8): 2275 ->*_s0(length(sndsplit(0,app(nil,nil))),0).  [ur(87,a,482,a,b,1366,a)].

given #800 (T,wt=8): 2276 ->*_s0(length(sndsplit(0,length(nil))),length(0)).  [ur(87,a,482,a,b,943,a)].

given #801 (T,wt=8): 2277 ->*_s0(length(sndsplit(0,empty(nil))),length(true)).  [ur(87,a,482,a,b,781,a)].

given #802 (A,wt=9): 203 ->_s0(mapf(x,fstsplit(0,y)),mapf(x,nil)).  [ur(45,a,64,a)].

given #803 (F,wt=10): 7777 -->_s0(true,app(app(nil,nil),empty(cons(x,y)))) # answer(goal).  [ur(2781,b,162,a,c,5324,a)].

given #804 (F,wt=10): 7794 -->_s0(true,app(nil,sndsplit(0,leq(s(x),0)))) # answer(goal).  [resolve(1075,a,3014,b)].

given #805 (F,wt=10): 7796 -->_s0(true,sndsplit(0,sndsplit(0,leq(s(x),0)))) # answer(goal).  [resolve(1075,a,2997,b)].

given #806 (F,wt=10): 7811 -->_s0(true,sndsplit(app(nil,0),leq(s(x),0))) # answer(goal).  [ur(2781,b,121,a,c,1075,a)].

given #807 (T,wt=7): 8867 ->*_s0(mapf(x,fstsplit(0,y)),nil).  [ur(87,a,203,a,b,568,a)].

given #808 (T,wt=8): 2305 ->*_s0(length(sndsplit(0,sndsplit(0,nil))),0).  [ur(87,a,482,a,b,2278,a)].

given #809 (T,wt=8): 2306 ->*_s0(length(app(nil,sndsplit(0,nil))),0).  [ur(87,a,132,a,b,2278,a)].

given #810 (T,wt=8): 2308 ->*_s0(sndsplit(0,length(sndsplit(0,nil))),0).  [ur(87,a,82,a,b,2278,a)].

given #811 (A,wt=9): 204 ->_s0(mapf(fstsplit(0,x),y),mapf(nil,y)).  [ur(44,a,64,a)].

given #812 (F,wt=10): 7812 -->_s0(true,sndsplit(0,app(nil,leq(s(x),0)))) # answer(goal).  [ur(2781,b,120,a,c,1075,a)].

given #813 (F,wt=10): 7814 -->_s0(true,app(nil,leq(s(s(x)),s(0)))) # answer(goal).  [resolve(1076,a,3014,b)].

given #814 (F,wt=10): 7816 -->_s0(true,sndsplit(0,leq(s(s(x)),s(0)))) # answer(goal).  [resolve(1076,a,2997,b)].

given #815 (F,wt=10): 7830 -->_s0(true,leq(app(nil,s(s(x))),s(0))) # answer(goal).  [ur(2781,b,131,a,c,1076,a)].

given #816 (T,wt=8): 2310 ->*_s0(app(nil,length(sndsplit(0,nil))),0).  [ur(87,a,61,a,b,2278,a)].

given #817 (T,wt=8): 2312 ->*_s0(head(sndsplit(0,length(nil))),head(0)).  [ur(87,a,483,a,b,969,a)].

given #818 (T,wt=8): 2313 ->*_s0(head(sndsplit(0,empty(nil))),head(true)).  [ur(87,a,483,a,b,807,a)].

given #819 (T,wt=8): 2314 ->*_s0(head(sndsplit(0,cons(x,y))),x).  [ur(87,a,483,a,b,575,a)].

given #820 (A,wt=9): 205 ->_s0(leq(x,fstsplit(0,y)),leq(x,nil)).  [ur(43,a,64,a)].

given #821 (F,wt=10): 7831 -->_s0(true,leq(s(s(x)),app(nil,s(0)))) # answer(goal).  [ur(2781,b,130,a,c,1076,a)].

given #822 (F,wt=10): 7832 -->_s0(true,leq(s(s(s(x))),s(s(0)))) # answer(goal).  [ur(2781,b,72,a,c,1076,a)].

given #823 (F,wt=10): 7858 -->_s0(true,app(nil,app(nil,leq(s(x),0)))) # answer(goal).  [resolve(1078,a,3014,b)].

given #824 (F,wt=10): 7870 -->_s0(true,app(app(nil,nil),leq(s(x),0))) # answer(goal).  [ur(2781,b,138,a,c,1078,a)].

given #825 (T,wt=8): 2384 ->*_s0(empty(sndsplit(0,mapf(x,nil))),true).  [ur(87,a,486,a,b,2147,a)].

given #826 (T,wt=8): 2385 ->*_s0(empty(sndsplit(0,fstsplit(0,x))),true).  [ur(87,a,486,a,b,1750,a)].

given #827 (T,wt=8): 2386 ->*_s0(empty(sndsplit(0,app(nil,nil))),true).  [ur(87,a,486,a,b,1456,a)].

given #828 (T,wt=8): 2387 ->*_s0(empty(sndsplit(0,length(nil))),empty(0)).  [ur(87,a,486,a,b,1031,a)].

given #829 (A,wt=9): 206 ->_s0(leq(fstsplit(0,x),y),leq(nil,y)).  [ur(42,a,64,a)].

given #830 (F,wt=10): 7871 -->_s0(true,app(nil,sndsplit(0,head(cons(false,x))))) # answer(goal).  [resolve(1113,a,3014,b)].

given #831 (F,wt=10): 7873 -->_s0(true,sndsplit(0,sndsplit(0,head(cons(false,x))))) # answer(goal).  [resolve(1113,a,2997,b)].

given #832 (F,wt=10): 7891 -->_s0(true,sndsplit(app(nil,0),head(cons(false,x)))) # answer(goal).  [ur(2781,b,121,a,c,1113,a)].

given #833 (F,wt=10): 7892 -->_s0(true,sndsplit(0,app(nil,head(cons(false,x))))) # answer(goal).  [ur(2781,b,120,a,c,1113,a)].

given #834 (T,wt=8): 2388 ->*_s0(empty(sndsplit(0,empty(nil))),empty(true)).  [ur(87,a,486,a,b,833,a)].

given #835 (T,wt=8): 2389 ->*_s0(empty(sndsplit(0,cons(x,y))),false).  [ur(87,a,486,a,b,580,a)].

given #836 (T,wt=8): 2420 ->*_s0(empty(sndsplit(0,sndsplit(0,nil))),true).  [ur(87,a,486,a,b,2390,a)].

given #837 (T,wt=8): 2421 ->*_s0(empty(app(nil,sndsplit(0,nil))),true).  [ur(87,a,136,a,b,2390,a)].

given #838 (A,wt=9): 209 ->_s0(fstsplit(x,fstsplit(0,y)),fstsplit(x,nil)).  [ur(39,a,64,a)].

given #839 (F,wt=10): 7894 -->_s0(true,app(nil,app(nil,head(cons(false,x))))) # answer(goal).  [resolve(1115,a,3014,b)].

given #840 (F,wt=10): 7909 -->_s0(true,app(app(nil,nil),head(cons(false,x)))) # answer(goal).  [ur(2781,b,138,a,c,1115,a)].

given #841 (F,wt=10): 7947 -->_s0(true,app(nil,sndsplit(0,empty(cons(x,y))))) # answer(goal).  [resolve(1125,a,3014,b)].

given #842 (F,wt=10): 7949 -->_s0(true,sndsplit(0,sndsplit(0,empty(cons(x,y))))) # answer(goal).  [resolve(1125,a,2997,b)].

given #843 (T,wt=8): 2423 ->*_s0(sndsplit(0,empty(sndsplit(0,nil))),true).  [ur(87,a,82,a,b,2390,a)].

given #844 (T,wt=8): 2425 ->*_s0(app(nil,empty(sndsplit(0,nil))),true).  [ur(87,a,61,a,b,2390,a)].

given #845 (T,wt=8): 2538 ->*_s0(head(app(cons(x,y),z)),x).  [ur(87,a,108,a,b,575,a)].

given #846 (T,wt=8): 2754 ->*_s0(empty(app(cons(x,y),z)),false).  [ur(87,a,111,a,b,580,a)].

given #847 (A,wt=9): 210 ->_s0(fstsplit(fstsplit(0,x),y),fstsplit(nil,y)).  [ur(38,a,64,a)].

given #848 (F,wt=10): 7962 -->_s0(true,sndsplit(0,app(nil,empty(cons(x,y))))) # answer(goal).  [ur(2781,b,120,a,c,1125,a)].

given #849 (F,wt=10): 7964 -->_s0(true,app(nil,app(nil,empty(cons(x,y))))) # answer(goal).  [resolve(1127,a,3014,b)].

given #850 (F,wt=10): 8115 -->_s0(true,app(nil,x)) | -->_s0(x,app(nil,false)) # answer(goal).  [resolve(3041,b,36,b)].

given #851 (F,wt=10): 8116 -->_s0(true,app(x,app(nil,false))) | -->_s0(x,nil) # answer(goal).  [resolve(3041,b,35,b)].

given #852 (T,wt=8): 3230 ->*_s0(s(empty(cons(x,y))),s(false)).  [ur(87,a,139,a,b,86,a)].

given #853 (T,wt=8): 3284 ->*_s0(tail(empty(cons(x,y))),tail(false)).  [ur(87,a,144,a,b,86,a)].

given #854 (T,wt=8): 3311 ->*_s0(length(empty(cons(x,y))),length(false)).  [ur(87,a,157,a,b,86,a)].

given #855 (T,wt=8): 3338 ->*_s0(head(empty(cons(x,y))),head(false)).  [ur(87,a,158,a,b,86,a)].

given #856 (A,wt=9): 212 ->_s0(app(x,fstsplit(0,y)),app(x,nil)).  [ur(36,a,64,a)].

given #857 (F,wt=9): 9235 -->_s0(true,app(sndsplit(0,nil),app(nil,false))) # answer(goal).  [resolve(8116,b,82,a)].

given #858 (F,wt=9): 9236 -->_s0(true,app(mapf(x,nil),app(nil,false))) # answer(goal).  [resolve(8116,b,74,a)].

given #859 (F,wt=9): 9239 -->_s0(true,app(fstsplit(0,x),app(nil,false))) # answer(goal).  [resolve(8116,b,64,a)].

given #860 (F,wt=10): 8162 -->_s0(true,sndsplit(0,x)) | -->_s0(x,app(nil,false)) # answer(goal).  [resolve(3042,b,53,b)].

given #861 (T,wt=8): 3365 ->*_s0(empty(empty(cons(x,y))),empty(false)).  [ur(87,a,161,a,b,86,a)].

given #862 (T,wt=8): 3392 ->*_s0(sndsplit(s(x),app(nil,nil)),nil).  [ur(87,a,120,a,b,565,a)].

given #863 (T,wt=8): 3420 ->*_s0(f(x,empty(nil)),f(x,true)).  [ur(87,a,165,a,b,86,a)].

given #864 (T,wt=8): 3447 ->*_s0(f(empty(nil),x),f(true,x)).  [ur(87,a,166,a,b,86,a)].

given #865 (A,wt=9): 213 ->_s0(app(fstsplit(0,x),y),app(nil,y)).  [ur(35,a,64,a)].

given #866 (F,wt=9): 9331 -->_s0(true,sndsplit(0,app(fstsplit(0,x),false))) # answer(goal).  [resolve(213,a,8162,b)].

given #867 (F,wt=9): 9332 -->_s0(true,app(nil,app(fstsplit(0,x),false))) # answer(goal).  [resolve(213,a,8115,b)].

given #868 (F,wt=9): 9333 -->_s0(true,app(fstsplit(0,x),sndsplit(0,false))) # answer(goal).  [resolve(213,a,3043,b)].

given #869 (F,wt=10): 8163 -->_s0(true,sndsplit(x,app(nil,false))) | -->_s0(x,0) # answer(goal).  [resolve(3042,b,52,b)].

given #870 (T,wt=7): 9370 ->*_s0(app(fstsplit(0,x),y),y).  [ur(87,a,213,a,b,581,a)].

given #871 (T,wt=8): 3474 ->*_s0(cons(x,empty(nil)),cons(x,true)).  [ur(87,a,167,a,b,86,a)].

given #872 (T,wt=8): 3501 ->*_s0(cons(empty(nil),x),cons(true,x)).  [ur(87,a,168,a,b,86,a)].

given #873 (T,wt=8): 3534 ->*_s0(sndsplit(app(nil,0),empty(nil)),true).  [ur(87,a,121,a,b,632,a)].

given #874 (A,wt=14): 214 ->_s0(s(fstsplit(s(x),cons(y,z))),s(cons(y,fstsplit(x,z)))).  [ur(59,a,65,a)].

given #875 (F,wt=9): 9396 -->_s0(true,sndsplit(sndsplit(0,0),app(nil,false))) # answer(goal).  [resolve(8163,b,82,a)].

given #876 (F,wt=9): 9415 -->_s0(true,app(app(nil,fstsplit(0,x)),false)) # answer(goal).  [ur(2781,b,138,a,c,9370,a)].

given #877 (F,wt=10): 8164 -->_s0(true,app(nil,x)) | -->_s0(x,sndsplit(0,false)) # answer(goal).  [resolve(3043,b,36,b)].

given #878 (F,wt=10): 8165 -->_s0(true,app(x,sndsplit(0,false))) | -->_s0(x,nil) # answer(goal).  [resolve(3043,b,35,b)].

given #879 (T,wt=8): 3535 ->*_s0(sndsplit(app(nil,0),length(nil)),0).  [ur(87,a,121,a,b,627,a)].

given #880 (T,wt=8): 3537 ->*_s0(sndsplit(app(nil,s(x)),nil),nil).  [ur(87,a,121,a,b,565,a)].

given #881 (T,wt=8): 3588 ->*_s0(sndsplit(x,empty(nil)),sndsplit(x,true)).  [ur(87,a,170,a,b,86,a)].

given #882 (T,wt=8): 3615 ->*_s0(sndsplit(empty(nil),x),sndsplit(true,x)).  [ur(87,a,171,a,b,86,a)].

given #883 (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 #884 (F,wt=9): 9473 -->_s0(true,app(sndsplit(0,nil),sndsplit(0,false))) # answer(goal).  [resolve(8165,b,82,a)].

given #885 (F,wt=9): 9474 -->_s0(true,app(mapf(x,nil),sndsplit(0,false))) # answer(goal).  [resolve(8165,b,74,a)].

given #886 (F,wt=10): 8166 -->_s0(true,sndsplit(0,x)) | -->_s0(x,sndsplit(0,false)) # answer(goal).  [resolve(3044,b,53,b)].

given #887 (F,wt=10): 8167 -->_s0(true,sndsplit(x,sndsplit(0,false))) | -->_s0(x,0) # answer(goal).  [resolve(3044,b,52,b)].

given #888 (T,wt=8): 3642 ->*_s0(mapf(x,empty(nil)),mapf(x,true)).  [ur(87,a,178,a,b,86,a)].

given #889 (T,wt=8): 3696 ->*_s0(mapf(empty(nil),x),mapf(true,x)).  [ur(87,a,179,a,b,86,a)].

given #890 (T,wt=8): 3723 ->*_s0(leq(x,empty(nil)),leq(x,true)).  [ur(87,a,180,a,b,86,a)].

given #891 (T,wt=8): 3751 ->*_s0(leq(empty(nil),x),leq(true,x)).  [ur(87,a,181,a,b,86,a)].

given #892 (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 #893 (F,wt=9): 9524 -->_s0(true,sndsplit(sndsplit(0,0),sndsplit(0,false))) # answer(goal).  [resolve(8167,b,82,a)].

given #894 (F,wt=10): 8291 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(length(nil),false)) # answer(goal).  [resolve(3100,c,4574,a)].

given #895 (F,wt=10): 8312 -->_s0(true,length(nil)) | -->_s0(0,empty(cons(x,y))) # answer(goal).  [resolve(3100,c,580,a)].

given #896 (F,wt=10): 8313 -->_s0(true,length(nil)) | -->_s0(0,head(cons(false,x))) # answer(goal).  [resolve(3100,c,575,a)].

given #897 (T,wt=8): 3778 ->*_s0(fstsplit(x,empty(nil)),fstsplit(x,true)).  [ur(87,a,184,a,b,86,a)].

given #898 (T,wt=8): 3832 ->*_s0(fstsplit(empty(nil),x),fstsplit(true,x)).  [ur(87,a,185,a,b,86,a)].

given #899 (T,wt=8): 3859 ->*_s0(app(x,empty(nil)),app(x,true)).  [ur(87,a,187,a,b,86,a)].

given #900 (T,wt=8): 3886 ->*_s0(app(empty(nil),x),app(true,x)).  [ur(87,a,188,a,b,86,a)].

given #901 (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 #902 (F,wt=10): 8314 -->_s0(true,length(nil)) | -->_s0(0,leq(s(x),0)) # answer(goal).  [resolve(3100,c,571,a)].

given #903 (F,wt=10): 8316 -->_s0(true,length(nil)) | -->_s0(0,tail(cons(x,false))) # answer(goal).  [resolve(3100,c,564,a)].

given #904 (F,wt=10): 8364 -->_s0(true,sndsplit(app(nil,0),x)) | -->_s0(x,false) # answer(goal).  [resolve(3568,b,53,b)].

given #905 (F,wt=10): 8365 -->_s0(true,sndsplit(x,false)) | -->_s0(x,app(nil,0)) # answer(goal).  [resolve(3568,b,52,b)].

given #906 (T,wt=8): 3913 ->*_s0(s(fstsplit(s(x),nil)),s(nil)).  [ur(87,a,239,a,b,86,a)].

given #907 (T,wt=8): 3975 ->*_s0(tail(fstsplit(s(x),nil)),tail(nil)).  [ur(87,a,244,a,b,86,a)].

given #908 (T,wt=8): 4003 ->*_s0(length(fstsplit(s(x),nil)),length(nil)).  [ur(87,a,257,a,b,86,a)].

given #909 (T,wt=8): 4036 ->*_s0(head(fstsplit(s(x),nil)),head(nil)).  [ur(87,a,258,a,b,86,a)].

given #910 (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 #911 (F,wt=9): 9628 -->_s0(true,sndsplit(app(fstsplit(0,x),0),false)) # answer(goal).  [resolve(8365,b,213,a)].

given #912 (F,wt=9): 9629 -->_s0(true,sndsplit(app(app(nil,nil),0),false)) # answer(goal).  [resolve(8365,b,138,a)].

given #913 (F,wt=9): 9631 -->_s0(true,sndsplit(sndsplit(0,app(nil,0)),false)) # answer(goal).  [resolve(8365,b,82,a)].

given #914 (F,wt=10): 8391 -->_s0(true,app(nil,tail(app(nil,cons(x,false))))) # answer(goal).  [resolve(1337,a,3014,b)].

given #915 (T,wt=8): 4095 ->*_s0(empty(fstsplit(s(x),nil)),empty(nil)).  [ur(87,a,261,a,b,86,a)].

given #916 (T,wt=8): 4138 ->*_s0(s(head(cons(x,y))),s(x)).  [ur(87,a,264,a,b,86,a)].

given #917 (T,wt=8): 4175 ->*_s0(tail(head(cons(x,y))),tail(x)).  [ur(87,a,269,a,b,86,a)].

given #918 (T,wt=8): 4244 ->*_s0(length(head(cons(x,y))),length(x)).  [ur(87,a,282,a,b,86,a)].

given #919 (A,wt=14): 219 ->_s0(tail(fstsplit(s(x),cons(y,z))),tail(cons(y,fstsplit(x,z)))).  [ur(54,a,65,a)].

given #920 (F,wt=10): 8393 -->_s0(true,sndsplit(0,tail(app(nil,cons(x,false))))) # answer(goal).  [resolve(1337,a,2997,b)].

given #921 (F,wt=10): 8395 -->_s0(true,tail(app(nil,app(nil,cons(x,false))))) # answer(goal).  [resolve(1337,a,2966,b)].

given #922 (F,wt=10): 8396 -->_s0(true,tail(sndsplit(0,app(nil,cons(x,false))))) # answer(goal).  [resolve(1337,a,2936,b)].

given #923 (F,wt=10): 8436 -->_s0(true,leq(s(x),y)) | -->_s0(y,length(nil)) # answer(goal).  [resolve(4786,b,43,b)].

given #924 (T,wt=8): 4288 ->*_s0(head(head(cons(x,y))),head(x)).  [ur(87,a,283,a,b,86,a)].

given #925 (T,wt=8): 4330 ->*_s0(empty(head(cons(x,y))),empty(x)).  [ur(87,a,286,a,b,86,a)].

given #926 (T,wt=8): 4395 ->*_s0(f(x,length(nil)),f(x,0)).  [ur(87,a,315,a,b,86,a)].

given #927 (T,wt=8): 4422 ->*_s0(f(length(nil),x),f(0,x)).  [ur(87,a,316,a,b,86,a)].

given #928 (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)].

Low Water (keep): wt=18.000, iters=6667

given #929 (F,wt=9): 9732 -->_s0(true,leq(s(x),length(sndsplit(0,nil)))) # answer(goal).  [resolve(8436,b,482,a)].

given #930 (F,wt=9): 9733 -->_s0(true,leq(s(x),length(mapf(y,nil)))) # answer(goal).  [resolve(8436,b,457,a)].

given #931 (F,wt=9): 9736 -->_s0(true,leq(s(x),length(fstsplit(0,y)))) # answer(goal).  [resolve(8436,b,207,a)].

given #932 (F,wt=9): 9737 -->_s0(true,leq(s(x),length(app(nil,nil)))) # answer(goal).  [resolve(8436,b,132,a)].

given #933 (T,wt=8): 4449 ->*_s0(cons(x,length(nil)),cons(x,0)).  [ur(87,a,317,a,b,86,a)].

given #934 (T,wt=8): 4513 ->*_s0(cons(length(nil),x),cons(0,x)).  [ur(87,a,318,a,b,86,a)].

given #935 (T,wt=8): 4540 ->*_s0(sndsplit(x,length(nil)),sndsplit(x,0)).  [ur(87,a,320,a,b,86,a)].

given #936 (T,wt=8): 4567 ->*_s0(sndsplit(length(nil),app(nil,x)),x).  [ur(87,a,321,a,b,696,a)].

given #937 (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 #938 (F,wt=9): 9739 -->_s0(true,leq(s(x),sndsplit(0,length(nil)))) # answer(goal).  [resolve(8436,b,82,a)].

given #939 (F,wt=10): 8437 -->_s0(true,leq(x,length(nil))) | -->_s0(x,s(y)) # answer(goal).  [resolve(4786,b,42,b)].

given #940 (F,wt=9): 9848 -->_s0(true,leq(sndsplit(0,s(x)),length(nil))) # answer(goal).  [resolve(8437,b,82,a)].

given #941 (F,wt=9): 9849 -->_s0(true,leq(length(cons(x,y)),length(nil))) # answer(goal).  [resolve(8437,b,68,a)].

given #942 (T,wt=8): 4568 ->*_s0(sndsplit(length(nil),fstsplit(0,x)),nil).  [ur(87,a,321,a,b,689,a)].

given #943 (T,wt=8): 4569 ->*_s0(sndsplit(length(nil),leq(0,x)),true).  [ur(87,a,321,a,b,684,a)].

given #944 (T,wt=8): 4570 ->*_s0(sndsplit(length(nil),mapf(x,nil)),nil).  [ur(87,a,321,a,b,643,a)].

given #945 (T,wt=8): 4571 ->*_s0(sndsplit(length(nil),sndsplit(0,x)),x).  [ur(87,a,321,a,b,639,a)].

given #946 (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 #947 (F,wt=10): 8492 -->_s0(true,app(app(nil,nil),x)) | -->_s0(x,false) # answer(goal).  [resolve(5364,b,36,b)].

given #948 (F,wt=10): 8493 -->_s0(true,app(x,false)) | -->_s0(x,app(nil,nil)) # answer(goal).  [resolve(5364,b,35,b)].

given #949 (F,wt=9): 9899 -->_s0(true,app(app(fstsplit(0,x),nil),false)) # answer(goal).  [resolve(8493,b,213,a)].

given #950 (F,wt=9): 9900 -->_s0(true,app(app(app(nil,nil),nil),false)) # answer(goal).  [resolve(8493,b,138,a)].

given #951 (T,wt=8): 4575 ->*_s0(sndsplit(length(nil),x),sndsplit(0,x)).  [ur(87,a,321,a,b,86,a)].

given #952 (T,wt=8): 4642 ->*_s0(sndsplit(app(nil,length(nil)),x),x).  [ur(87,a,121,a,b,4574,a)].

given #953 (T,wt=8): 4646 ->*_s0(sndsplit(0,sndsplit(length(nil),x)),x).  [ur(87,a,82,a,b,4574,a)].

given #954 (T,wt=8): 4648 ->*_s0(app(nil,sndsplit(length(nil),x)),x).  [ur(87,a,61,a,b,4574,a)].

given #955 (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 #956 (F,wt=9): 9902 -->_s0(true,app(sndsplit(0,app(nil,nil)),false)) # answer(goal).  [resolve(8493,b,82,a)].

given #957 (F,wt=9): 9963 -->_s0(true,sndsplit(length(nil),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,321,a,c,4646,a)].

given #958 (F,wt=10): 8515 -->_s0(true,app(nil,head(app(nil,cons(false,x))))) # answer(goal).  [resolve(1426,a,3014,b)].

given #959 (F,wt=10): 8517 -->_s0(true,sndsplit(0,head(app(nil,cons(false,x))))) # answer(goal).  [resolve(1426,a,2997,b)].

given #960 (T,wt=8): 4671 ->*_s0(mapf(x,length(nil)),mapf(x,0)).  [ur(87,a,328,a,b,86,a)].

given #961 (T,wt=8): 4699 ->*_s0(leq(s(x),app(nil,0)),false).  [ur(87,a,130,a,b,571,a)].

given #962 (T,wt=8): 4728 ->*_s0(mapf(length(nil),x),mapf(0,x)).  [ur(87,a,329,a,b,86,a)].

given #963 (T,wt=8): 4757 ->*_s0(leq(x,length(nil)),leq(x,0)).  [ur(87,a,330,a,b,86,a)].

given #964 (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 #965 (F,wt=10): 8519 -->_s0(true,head(app(nil,app(nil,cons(false,x))))) # answer(goal).  [resolve(1426,a,2964,b)].

given #966 (F,wt=10): 8520 -->_s0(true,head(sndsplit(0,app(nil,cons(false,x))))) # answer(goal).  [resolve(1426,a,2934,b)].

given #967 (F,wt=10): 8577 -->_s0(true,app(nil,empty(app(nil,cons(x,y))))) # answer(goal).  [resolve(1455,a,3014,b)].

given #968 (F,wt=10): 8579 -->_s0(true,sndsplit(0,empty(app(nil,cons(x,y))))) # answer(goal).  [resolve(1455,a,2997,b)].

given #969 (T,wt=8): 4804 ->*_s0(leq(length(nil),x),leq(0,x)).  [ur(87,a,331,a,b,86,a)].

given #970 (T,wt=8): 4835 ->*_s0(leq(app(nil,s(x)),0),false).  [ur(87,a,131,a,b,571,a)].

given #971 (T,wt=8): 4869 ->*_s0(leq(app(nil,length(nil)),x),true).  [ur(87,a,131,a,b,4803,a)].

given #972 (T,wt=8): 4871 ->*_s0(sndsplit(0,leq(length(nil),x)),true).  [ur(87,a,82,a,b,4803,a)].

given #973 (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)].

given #974 (F,wt=10): 8581 -->_s0(true,empty(app(nil,app(nil,cons(x,y))))) # answer(goal).  [resolve(1455,a,2963,b)].

given #975 (F,wt=10): 8582 -->_s0(true,empty(sndsplit(0,app(nil,cons(x,y))))) # answer(goal).  [resolve(1455,a,2933,b)].

given #976 (F,wt=10): 8795 -->_s0(true,app(nil,tail(sndsplit(0,cons(x,false))))) # answer(goal).  [resolve(2245,a,3014,b)].

given #977 (F,wt=10): 8797 -->_s0(true,sndsplit(0,tail(sndsplit(0,cons(x,false))))) # answer(goal).  [resolve(2245,a,2997,b)].

given #978 (T,wt=8): 4872 ->*_s0(leq(s(length(nil)),s(x)),true).  [ur(87,a,72,a,b,4803,a)].

given #979 (T,wt=8): 4874 ->*_s0(app(nil,leq(length(nil),x)),true).  [ur(87,a,61,a,b,4803,a)].

given #980 (T,wt=8): 4886 ->*_s0(fstsplit(x,length(nil)),fstsplit(x,0)).  [ur(87,a,334,a,b,86,a)].

given #981 (T,wt=8): 4914 ->*_s0(fstsplit(length(nil),x),fstsplit(0,x)).  [ur(87,a,335,a,b,86,a)].

given #982 (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 #983 (F,wt=10): 8799 -->_s0(true,tail(app(nil,sndsplit(0,cons(x,false))))) # answer(goal).  [resolve(2245,a,2966,b)].

given #984 (F,wt=10): 8800 -->_s0(true,tail(sndsplit(0,sndsplit(0,cons(x,false))))) # answer(goal).  [resolve(2245,a,2936,b)].

given #985 (F,wt=10): 8959 -->_s0(true,app(nil,head(sndsplit(0,cons(false,x))))) # answer(goal).  [resolve(2314,a,3014,b)].

given #986 (F,wt=10): 8961 -->_s0(true,sndsplit(0,head(sndsplit(0,cons(false,x))))) # answer(goal).  [resolve(2314,a,2997,b)].

given #987 (T,wt=8): 4941 ->*_s0(fstsplit(s(x),app(nil,nil)),nil).  [ur(87,a,134,a,b,576,a)].

given #988 (T,wt=8): 4973 ->*_s0(sndsplit(0,fstsplit(length(nil),x)),nil).  [ur(87,a,82,a,b,4913,a)].

given #989 (T,wt=8): 4975 ->*_s0(app(nil,fstsplit(length(nil),x)),nil).  [ur(87,a,61,a,b,4913,a)].

given #990 (T,wt=8): 4977 ->*_s0(app(x,length(nil)),app(x,0)).  [ur(87,a,337,a,b,86,a)].

given #991 (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 #992 (F,wt=10): 8963 -->_s0(true,head(app(nil,sndsplit(0,cons(false,x))))) # answer(goal).  [resolve(2314,a,2964,b)].

given #993 (F,wt=10): 8964 -->_s0(true,head(sndsplit(0,sndsplit(0,cons(false,x))))) # answer(goal).  [resolve(2314,a,2934,b)].

given #994 (F,wt=10): 9076 -->_s0(true,app(nil,empty(sndsplit(0,cons(x,y))))) # answer(goal).  [resolve(2389,a,3014,b)].

given #995 (F,wt=10): 9078 -->_s0(true,sndsplit(0,empty(sndsplit(0,cons(x,y))))) # answer(goal).  [resolve(2389,a,2997,b)].

given #996 (T,wt=8): 5004 ->*_s0(app(length(nil),x),app(0,x)).  [ur(87,a,338,a,b,86,a)].

given #997 (T,wt=8): 5031 ->*_s0(s(leq(s(x),0)),s(false)).  [ur(87,a,364,a,b,86,a)].

given #998 (T,wt=8): 5058 ->*_s0(fstsplit(app(nil,length(nil)),x),nil).  [ur(87,a,135,a,b,4913,a)].

given #999 (T,wt=8): 5060 ->*_s0(fstsplit(app(nil,s(x)),nil),nil).  [ur(87,a,135,a,b,576,a)].

given #1000 (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)].

Low Water (keep): wt=17.000, iters=6733

given #1001 (F,wt=10): 9080 -->_s0(true,empty(app(nil,sndsplit(0,cons(x,y))))) # answer(goal).  [resolve(2389,a,2963,b)].

given #1002 (F,wt=10): 9081 -->_s0(true,empty(sndsplit(0,sndsplit(0,cons(x,y))))) # answer(goal).  [resolve(2389,a,2933,b)].

given #1003 (F,wt=10): 9162 -->_s0(true,app(nil,head(app(cons(false,x),y)))) # answer(goal).  [resolve(2538,a,3014,b)].

given #1004 (F,wt=10): 9164 -->_s0(true,sndsplit(0,head(app(cons(false,x),y)))) # answer(goal).  [resolve(2538,a,2997,b)].

given #1005 (T,wt=8): 5097 ->*_s0(tail(leq(s(x),0)),tail(false)).  [ur(87,a,369,a,b,86,a)].

given #1006 (T,wt=8): 5124 ->*_s0(length(leq(s(x),0)),length(false)).  [ur(87,a,382,a,b,86,a)].

given #1007 (T,wt=8): 5151 ->*_s0(head(leq(s(x),0)),head(false)).  [ur(87,a,383,a,b,86,a)].

given #1008 (T,wt=8): 5208 ->*_s0(empty(leq(s(x),0)),empty(false)).  [ur(87,a,386,a,b,86,a)].

given #1009 (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 #1010 (F,wt=10): 9166 -->_s0(true,head(app(nil,app(cons(false,x),y)))) # answer(goal).  [resolve(2538,a,2964,b)].

given #1011 (F,wt=10): 9167 -->_s0(true,head(sndsplit(0,app(cons(false,x),y)))) # answer(goal).  [resolve(2538,a,2934,b)].

given #1012 (F,wt=10): 9187 -->_s0(true,app(nil,empty(app(cons(x,y),z)))) # answer(goal).  [resolve(2754,a,3014,b)].

given #1013 (F,wt=10): 9189 -->_s0(true,sndsplit(0,empty(app(cons(x,y),z)))) # answer(goal).  [resolve(2754,a,2997,b)].

given #1014 (T,wt=8): 5235 ->*_s0(s(sndsplit(s(x),nil)),s(nil)).  [ur(87,a,514,a,b,86,a)].

given #1015 (T,wt=8): 5262 ->*_s0(tail(sndsplit(s(x),nil)),tail(nil)).  [ur(87,a,519,a,b,86,a)].

given #1016 (T,wt=8): 5290 ->*_s0(length(sndsplit(s(x),nil)),length(nil)).  [ur(87,a,532,a,b,86,a)].

given #1017 (T,wt=8): 5322 ->*_s0(app(app(nil,nil),empty(nil)),true).  [ur(87,a,138,a,b,634,a)].

given #1018 (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 #1019 (F,wt=10): 9191 -->_s0(true,empty(app(nil,app(cons(x,y),z)))) # answer(goal).  [resolve(2754,a,2963,b)].

given #1020 (F,wt=10): 9192 -->_s0(true,empty(sndsplit(0,app(cons(x,y),z)))) # answer(goal).  [resolve(2754,a,2933,b)].

given #1021 (F,wt=10): 9231 -->_s0(true,app(nil,app(nil,x))) | -->_s0(x,false) # answer(goal).  [resolve(8115,b,36,b)].

given #1022 (F,wt=10): 9232 -->_s0(true,app(nil,app(x,false))) | -->_s0(x,nil) # answer(goal).  [resolve(8115,b,35,b)].

given #1023 (T,wt=8): 5323 ->*_s0(app(app(nil,nil),length(nil)),0).  [ur(87,a,138,a,b,629,a)].

given #1024 (T,wt=8): 5380 ->*_s0(head(sndsplit(s(x),nil)),head(nil)).  [ur(87,a,533,a,b,86,a)].

given #1025 (T,wt=8): 5408 ->*_s0(empty(sndsplit(s(x),nil)),empty(nil)).  [ur(87,a,536,a,b,86,a)].

given #1026 (T,wt=8): 5479 ->*_s0(s(tail(cons(x,y))),s(y)).  [ur(87,a,539,a,b,86,a)].

given #1027 (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 #1028 (F,wt=9): 10256 -->_s0(true,app(nil,app(sndsplit(0,nil),false))) # answer(goal).  [resolve(9232,b,82,a)].

given #1029 (F,wt=9): 10257 -->_s0(true,app(nil,app(mapf(x,nil),false))) # answer(goal).  [resolve(9232,b,74,a)].

given #1030 (F,wt=10): 9233 -->_s0(true,app(tail(cons(x,nil)),app(nil,false))) # answer(goal).  [resolve(8116,b,85,a)].

given #1031 (F,wt=10): 9234 -->_s0(true,app(sndsplit(s(x),nil),app(nil,false))) # answer(goal).  [resolve(8116,b,84,a)].

given #1032 (T,wt=8): 5517 ->*_s0(tail(tail(cons(x,y))),tail(y)).  [ur(87,a,544,a,b,86,a)].

given #1033 (T,wt=8): 5560 ->*_s0(length(tail(cons(x,y))),length(y)).  [ur(87,a,557,a,b,86,a)].

given #1034 (T,wt=8): 5633 ->*_s0(head(tail(cons(x,y))),head(y)).  [ur(87,a,558,a,b,86,a)].

given #1035 (T,wt=8): 5677 ->*_s0(empty(tail(cons(x,y))),empty(y)).  [ur(87,a,561,a,b,86,a)].

given #1036 (A,wt=14): 232 ->_s0(length(fstsplit(s(x),cons(y,z))),length(cons(y,fstsplit(x,z)))).  [ur(41,a,65,a)].

given #1037 (F,wt=10): 9237 -->_s0(true,app(head(cons(nil,x)),app(nil,false))) # answer(goal).  [resolve(8116,b,67,a)].

given #1038 (F,wt=10): 9238 -->_s0(true,app(fstsplit(s(x),nil),app(nil,false))) # answer(goal).  [resolve(8116,b,66,a)].

given #1039 (F,wt=10): 9293 -->_s0(true,sndsplit(0,app(nil,x))) | -->_s0(x,false) # answer(goal).  [resolve(8162,b,36,b)].

given #1040 (F,wt=10): 9294 -->_s0(true,sndsplit(0,app(x,false))) | -->_s0(x,nil) # answer(goal).  [resolve(8162,b,35,b)].

given #1041 (T,wt=8): 5956 ->*_s0(tail(app(cons(x,nil),y)),y).  [ur(87,a,94,a,b,695,a)].

given #1042 (T,wt=8): 6020 ->*_s0(s(s(empty(nil))),s(s(true))).  [ur(87,a,700,a,b,86,a)].

given #1043 (T,wt=8): 6047 ->*_s0(tail(s(empty(nil))),tail(s(true))).  [ur(87,a,705,a,b,86,a)].

given #1044 (T,wt=8): 6074 ->*_s0(length(s(empty(nil))),length(s(true))).  [ur(87,a,718,a,b,86,a)].

given #1045 (A,wt=14): 233 ->_s0(head(fstsplit(s(x),cons(y,z))),head(cons(y,fstsplit(x,z)))).  [ur(40,a,65,a)].

Low Water (keep): wt=16.000, iters=6669

given #1046 (F,wt=9): 10334 -->_s0(true,sndsplit(0,app(sndsplit(0,nil),false))) # answer(goal).  [resolve(9294,b,82,a)].

given #1047 (F,wt=9): 10335 -->_s0(true,sndsplit(0,app(mapf(x,nil),false))) # answer(goal).  [resolve(9294,b,74,a)].

given #1048 (F,wt=10): 9391 -->_s0(true,app(fstsplit(0,x),empty(cons(y,z)))) # answer(goal).  [ur(2781,b,213,a,c,1127,a)].

given #1049 (F,wt=10): 9392 -->_s0(true,app(fstsplit(0,x),head(cons(false,y)))) # answer(goal).  [ur(2781,b,213,a,c,1115,a)].

given #1050 (T,wt=8): 6101 ->*_s0(head(s(empty(nil))),head(s(true))).  [ur(87,a,719,a,b,86,a)].

given #1051 (T,wt=8): 6155 ->*_s0(empty(s(empty(nil))),empty(s(true))).  [ur(87,a,722,a,b,86,a)].

given #1052 (T,wt=8): 6182 ->*_s0(s(tail(empty(nil))),s(tail(true))).  [ur(87,a,756,a,b,86,a)].

given #1053 (T,wt=8): 6209 ->*_s0(tail(tail(empty(nil))),tail(tail(true))).  [ur(87,a,761,a,b,86,a)].

given #1054 (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 #1055 (F,wt=10): 9393 -->_s0(true,app(fstsplit(0,x),leq(s(y),0))) # answer(goal).  [ur(2781,b,213,a,c,1078,a)].

given #1056 (F,wt=10): 9394 -->_s0(true,app(fstsplit(0,x),tail(cons(y,false)))) # answer(goal).  [ur(2781,b,213,a,c,1065,a)].

given #1057 (F,wt=10): 9395 -->_s0(true,sndsplit(tail(cons(x,0)),app(nil,false))) # answer(goal).  [resolve(8163,b,85,a)].

given #1058 (F,wt=10): 9397 -->_s0(true,sndsplit(head(cons(0,x)),app(nil,false))) # answer(goal).  [resolve(8163,b,67,a)].

given #1059 (T,wt=8): 6236 ->*_s0(length(tail(empty(nil))),length(tail(true))).  [ur(87,a,774,a,b,86,a)].

given #1060 (T,wt=8): 6296 ->*_s0(head(tail(empty(nil))),head(tail(true))).  [ur(87,a,775,a,b,86,a)].

given #1061 (T,wt=8): 6323 ->*_s0(empty(tail(empty(nil))),empty(tail(true))).  [ur(87,a,778,a,b,86,a)].

given #1062 (T,wt=8): 6350 ->*_s0(s(length(empty(nil))),s(length(true))).  [ur(87,a,782,a,b,86,a)].

given #1063 (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 #1064 (F,wt=10): 9399 -->_s0(true,head(cons(app(fstsplit(0,x),false),y))) # answer(goal).  [resolve(9370,a,3010,b)].

given #1065 (F,wt=10): 9400 -->_s0(true,tail(cons(x,app(fstsplit(0,y),false)))) # answer(goal).  [resolve(9370,a,2994,b)].

given #1066 (F,wt=10): 9401 -->_s0(true,x) | -->_s0(x,app(fstsplit(0,y),false)) # answer(goal).  [resolve(9370,a,2781,c)].

given #1067 (F,wt=10): 9469 -->_s0(true,app(nil,sndsplit(0,x))) | -->_s0(x,false) # answer(goal).  [resolve(8164,b,53,b)].

given #1068 (T,wt=8): 6377 ->*_s0(tail(length(empty(nil))),tail(length(true))).  [ur(87,a,787,a,b,86,a)].

given #1069 (T,wt=8): 6436 ->*_s0(length(length(empty(nil))),length(length(true))).  [ur(87,a,800,a,b,86,a)].

given #1070 (T,wt=8): 6463 ->*_s0(head(length(empty(nil))),head(length(true))).  [ur(87,a,801,a,b,86,a)].

given #1071 (T,wt=8): 6490 ->*_s0(empty(length(empty(nil))),empty(length(true))).  [ur(87,a,804,a,b,86,a)].

given #1072 (A,wt=14): 236 ->_s0(empty(fstsplit(s(x),cons(y,z))),empty(cons(y,fstsplit(x,z)))).  [ur(37,a,65,a)].

given #1073 (F,wt=10): 9470 -->_s0(true,app(nil,sndsplit(x,false))) | -->_s0(x,0) # answer(goal).  [resolve(8164,b,52,b)].

given #1074 (F,wt=9): 10503 -->_s0(true,app(nil,sndsplit(sndsplit(0,0),false))) # answer(goal).  [resolve(9470,b,82,a)].

given #1075 (F,wt=10): 9471 -->_s0(true,app(tail(cons(x,nil)),sndsplit(0,false))) # answer(goal).  [resolve(8165,b,85,a)].

given #1076 (F,wt=10): 9472 -->_s0(true,app(sndsplit(s(x),nil),sndsplit(0,false))) # answer(goal).  [resolve(8165,b,84,a)].

given #1077 (T,wt=8): 6517 ->*_s0(s(head(empty(nil))),s(head(true))).  [ur(87,a,808,a,b,86,a)].

given #1078 (T,wt=8): 6571 ->*_s0(tail(head(empty(nil))),tail(head(true))).  [ur(87,a,813,a,b,86,a)].

given #1079 (T,wt=8): 6598 ->*_s0(length(head(empty(nil))),length(head(true))).  [ur(87,a,826,a,b,86,a)].

given #1080 (T,wt=8): 6625 ->*_s0(head(head(empty(nil))),head(head(true))).  [ur(87,a,827,a,b,86,a)].

given #1081 (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)].

Low Water (keep): wt=14.000, iters=6673

given #1082 (F,wt=10): 9475 -->_s0(true,app(head(cons(nil,x)),sndsplit(0,false))) # answer(goal).  [resolve(8165,b,67,a)].

given #1083 (F,wt=10): 9476 -->_s0(true,app(fstsplit(s(x),nil),sndsplit(0,false))) # answer(goal).  [resolve(8165,b,66,a)].

given #1084 (F,wt=10): 9521 -->_s0(true,sndsplit(0,sndsplit(0,x))) | -->_s0(x,false) # answer(goal).  [resolve(8166,b,53,b)].

given #1085 (F,wt=10): 9522 -->_s0(true,sndsplit(0,sndsplit(x,false))) | -->_s0(x,0) # answer(goal).  [resolve(8166,b,52,b)].

given #1086 (T,wt=8): 6652 ->*_s0(empty(head(empty(nil))),empty(head(true))).  [ur(87,a,830,a,b,86,a)].

given #1087 (T,wt=8): 6706 ->*_s0(s(empty(empty(nil))),s(empty(true))).  [ur(87,a,834,a,b,86,a)].

given #1088 (T,wt=8): 6733 ->*_s0(tail(empty(empty(nil))),tail(empty(true))).  [ur(87,a,839,a,b,86,a)].

given #1089 (T,wt=8): 6760 ->*_s0(length(empty(empty(nil))),length(empty(true))).  [ur(87,a,852,a,b,86,a)].

given #1090 (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 #1091 (F,wt=9): 10539 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,0),false))) # answer(goal).  [resolve(9522,b,82,a)].

given #1092 (F,wt=10): 9523 -->_s0(true,sndsplit(tail(cons(x,0)),sndsplit(0,false))) # answer(goal).  [resolve(8167,b,85,a)].

given #1093 (F,wt=10): 9525 -->_s0(true,sndsplit(head(cons(0,x)),sndsplit(0,false))) # answer(goal).  [resolve(8167,b,67,a)].

given #1094 (F,wt=10): 9630 -->_s0(true,sndsplit(tail(cons(x,app(nil,0))),false)) # answer(goal).  [resolve(8365,b,85,a)].

given #1095 (T,wt=8): 6787 ->*_s0(head(empty(empty(nil))),head(empty(true))).  [ur(87,a,853,a,b,86,a)].

given #1096 (T,wt=8): 6856 ->*_s0(empty(empty(empty(nil))),empty(empty(true))).  [ur(87,a,856,a,b,86,a)].

given #1097 (T,wt=8): 6883 ->*_s0(s(s(length(nil))),s(s(0))).  [ur(87,a,892,a,b,86,a)].

given #1098 (T,wt=8): 6910 ->*_s0(tail(s(length(nil))),tail(s(0))).  [ur(87,a,897,a,b,86,a)].

given #1099 (A,wt=10): 240 ->_s0(f(x,fstsplit(s(y),nil)),f(x,nil)).  [ur(58,a,66,a)].

given #1100 (F,wt=10): 9632 -->_s0(true,sndsplit(head(cons(app(nil,0),x)),false)) # answer(goal).  [resolve(8365,b,67,a)].

given #1101 (F,wt=10): 9633 -->_s0(true,sndsplit(app(nil,x),false)) | -->_s0(x,0) # answer(goal).  [resolve(8365,b,36,b)].

given #1102 (F,wt=9): 10616 -->_s0(true,sndsplit(app(nil,sndsplit(0,0)),false)) # answer(goal).  [resolve(9633,b,82,a)].

given #1103 (F,wt=10): 9634 -->_s0(true,sndsplit(app(x,0),false)) | -->_s0(x,nil) # answer(goal).  [resolve(8365,b,35,b)].

given #1104 (T,wt=8): 6937 ->*_s0(length(s(length(nil))),length(s(0))).  [ur(87,a,910,a,b,86,a)].

given #1105 (T,wt=8): 6991 ->*_s0(head(s(length(nil))),head(s(0))).  [ur(87,a,911,a,b,86,a)].

given #1106 (T,wt=8): 7018 ->*_s0(empty(s(length(nil))),empty(s(0))).  [ur(87,a,914,a,b,86,a)].

given #1107 (T,wt=8): 7045 ->*_s0(s(tail(length(nil))),s(tail(0))).  [ur(87,a,918,a,b,86,a)].

given #1108 (A,wt=10): 241 ->_s0(f(fstsplit(s(x),nil),y),f(nil,y)).  [ur(57,a,66,a)].

given #1109 (F,wt=9): 10620 -->_s0(true,sndsplit(app(sndsplit(0,nil),0),false)) # answer(goal).  [resolve(9634,b,82,a)].

given #1110 (F,wt=9): 10621 -->_s0(true,sndsplit(app(mapf(x,nil),0),false)) # answer(goal).  [resolve(9634,b,74,a)].

given #1111 (F,wt=10): 9730 -->_s0(true,leq(s(x),length(tail(cons(y,nil))))) # answer(goal).  [resolve(8436,b,557,a)].

given #1112 (F,wt=10): 9731 -->_s0(true,leq(s(x),length(sndsplit(s(y),nil)))) # answer(goal).  [resolve(8436,b,532,a)].

given #1113 (T,wt=8): 7072 ->*_s0(tail(tail(length(nil))),tail(tail(0))).  [ur(87,a,923,a,b,86,a)].

given #1114 (T,wt=8): 7126 ->*_s0(length(tail(length(nil))),length(tail(0))).  [ur(87,a,936,a,b,86,a)].

given #1115 (T,wt=8): 7153 ->*_s0(head(tail(length(nil))),head(tail(0))).  [ur(87,a,937,a,b,86,a)].

given #1116 (T,wt=8): 7180 ->*_s0(empty(tail(length(nil))),empty(tail(0))).  [ur(87,a,940,a,b,86,a)].

given #1117 (A,wt=10): 242 ->_s0(cons(x,fstsplit(s(y),nil)),cons(x,nil)).  [ur(56,a,66,a)].

given #1118 (F,wt=10): 9734 -->_s0(true,leq(s(x),length(head(cons(nil,y))))) # answer(goal).  [resolve(8436,b,282,a)].

given #1119 (F,wt=10): 9735 -->_s0(true,leq(s(x),length(fstsplit(s(y),nil)))) # answer(goal).  [resolve(8436,b,257,a)].

given #1120 (F,wt=10): 9738 -->_s0(true,leq(s(x),tail(cons(y,length(nil))))) # answer(goal).  [resolve(8436,b,85,a)].

given #1121 (F,wt=10): 9740 -->_s0(true,leq(s(x),head(cons(length(nil),y)))) # answer(goal).  [resolve(8436,b,67,a)].

given #1122 (T,wt=8): 7207 ->*_s0(s(length(length(nil))),s(length(0))).  [ur(87,a,944,a,b,86,a)].

given #1123 (T,wt=8): 7261 ->*_s0(tail(length(length(nil))),tail(length(0))).  [ur(87,a,949,a,b,86,a)].

given #1124 (T,wt=8): 7288 ->*_s0(length(length(length(nil))),length(length(0))).  [ur(87,a,962,a,b,86,a)].

given #1125 (T,wt=8): 7315 ->*_s0(head(length(length(nil))),head(length(0))).  [ur(87,a,963,a,b,86,a)].

given #1126 (A,wt=10): 243 ->_s0(cons(fstsplit(s(x),nil),y),cons(nil,y)).  [ur(55,a,66,a)].

given #1127 (F,wt=10): 9741 -->_s0(true,leq(s(x),length(y))) | -->_s0(y,nil) # answer(goal).  [resolve(8436,b,41,b)].

given #1128 (F,wt=10): 9821 -->_s0(true,app(nil,sndsplit(length(nil),app(nil,false)))) # answer(goal).  [resolve(4567,a,3014,b)].

given #1129 (F,wt=10): 9823 -->_s0(true,sndsplit(0,sndsplit(length(nil),app(nil,false)))) # answer(goal).  [resolve(4567,a,2997,b)].

given #1130 (F,wt=10): 9840 -->_s0(true,sndsplit(app(nil,length(nil)),app(nil,false))) # answer(goal).  [ur(2781,b,121,a,c,4567,a)].

given #1131 (T,wt=8): 7342 ->*_s0(empty(length(length(nil))),empty(length(0))).  [ur(87,a,966,a,b,86,a)].

given #1132 (T,wt=8): 7397 ->*_s0(s(head(length(nil))),s(head(0))).  [ur(87,a,970,a,b,86,a)].

given #1133 (T,wt=8): 7424 ->*_s0(tail(head(length(nil))),tail(head(0))).  [ur(87,a,975,a,b,86,a)].

given #1134 (T,wt=8): 7451 ->*_s0(length(head(length(nil))),length(head(0))).  [ur(87,a,988,a,b,86,a)].

given #1135 (A,wt=10): 245 ->_s0(sndsplit(x,fstsplit(s(y),nil)),sndsplit(x,nil)).  [ur(53,a,66,a)].

given #1136 (F,wt=10): 9841 -->_s0(true,sndsplit(length(nil),app(nil,app(nil,false)))) # answer(goal).  [ur(2781,b,120,a,c,4567,a)].

given #1137 (F,wt=10): 9847 -->_s0(true,leq(tail(cons(x,s(y))),length(nil))) # answer(goal).  [resolve(8437,b,85,a)].

given #1138 (F,wt=10): 9850 -->_s0(true,leq(head(cons(s(x),y)),length(nil))) # answer(goal).  [resolve(8437,b,67,a)].

given #1139 (F,wt=10): 9876 -->_s0(true,app(nil,sndsplit(length(nil),sndsplit(0,false)))) # answer(goal).  [resolve(4571,a,3014,b)].

given #1140 (T,wt=8): 7478 ->*_s0(head(head(length(nil))),head(head(0))).  [ur(87,a,989,a,b,86,a)].

given #1141 (T,wt=8): 7532 ->*_s0(empty(head(length(nil))),empty(head(0))).  [ur(87,a,992,a,b,86,a)].

given #1142 (T,wt=8): 7559 ->*_s0(s(empty(length(nil))),s(empty(0))).  [ur(87,a,1032,a,b,86,a)].

given #1143 (T,wt=8): 7586 ->*_s0(tail(empty(length(nil))),tail(empty(0))).  [ur(87,a,1037,a,b,86,a)].

given #1144 (A,wt=10): 246 ->_s0(sndsplit(fstsplit(s(x),nil),y),sndsplit(nil,y)).  [ur(52,a,66,a)].

given #1145 (F,wt=10): 9878 -->_s0(true,sndsplit(0,sndsplit(length(nil),sndsplit(0,false)))) # answer(goal).  [resolve(4571,a,2997,b)].

given #1146 (F,wt=10): 9895 -->_s0(true,sndsplit(app(nil,length(nil)),sndsplit(0,false))) # answer(goal).  [ur(2781,b,121,a,c,4571,a)].

given #1147 (F,wt=10): 9896 -->_s0(true,sndsplit(length(nil),app(nil,sndsplit(0,false)))) # answer(goal).  [ur(2781,b,120,a,c,4571,a)].

given #1148 (F,wt=10): 9901 -->_s0(true,app(tail(cons(x,app(nil,nil))),false)) # answer(goal).  [resolve(8493,b,85,a)].

given #1149 (T,wt=8): 7613 ->*_s0(length(empty(length(nil))),length(empty(0))).  [ur(87,a,1050,a,b,86,a)].

given #1150 (T,wt=8): 7663 ->*_s0(head(empty(length(nil))),head(empty(0))).  [ur(87,a,1051,a,b,86,a)].

given #1151 (T,wt=8): 7690 ->*_s0(empty(empty(length(nil))),empty(empty(0))).  [ur(87,a,1054,a,b,86,a)].

given #1152 (T,wt=8): 8471 ->*_s0(sndsplit(s(x),fstsplit(0,y)),nil).  [ur(87,a,195,a,b,565,a)].

given #1153 (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 #1154 (F,wt=10): 9903 -->_s0(true,app(head(cons(app(nil,nil),x)),false)) # answer(goal).  [resolve(8493,b,67,a)].

given #1155 (F,wt=10): 9904 -->_s0(true,app(app(nil,x),false)) | -->_s0(x,nil) # answer(goal).  [resolve(8493,b,36,b)].

given #1156 (F,wt=9): 10866 -->_s0(true,app(app(nil,sndsplit(0,nil)),false)) # answer(goal).  [resolve(9904,b,82,a)].

given #1157 (F,wt=9): 10867 -->_s0(true,app(app(nil,mapf(x,nil)),false)) # answer(goal).  [resolve(9904,b,74,a)].

given #1158 (T,wt=8): 9122 ->*_s0(fstsplit(s(x),fstsplit(0,y)),nil).  [ur(87,a,209,a,b,576,a)].

given #1159 (T,wt=8): 9368 ->*_s0(app(fstsplit(0,x),empty(nil)),true).  [ur(87,a,213,a,b,634,a)].

given #1160 (T,wt=8): 9369 ->*_s0(app(fstsplit(0,x),length(nil)),0).  [ur(87,a,213,a,b,629,a)].

given #1161 (T,wt=9): 340 ->_s0(f(x,leq(0,y)),f(x,true)).  [ur(58,a,70,a)].

Low Water (keep): wt=13.000, iters=6743

given #1162 (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 #1163 (F,wt=10): 9905 -->_s0(true,app(app(x,nil),false)) | -->_s0(x,nil) # answer(goal).  [resolve(8493,b,35,b)].

given #1164 (F,wt=9): 10900 -->_s0(true,app(app(sndsplit(0,nil),nil),false)) # answer(goal).  [resolve(9905,b,82,a)].

given #1165 (F,wt=9): 10901 -->_s0(true,app(app(mapf(x,nil),nil),false)) # answer(goal).  [resolve(9905,b,74,a)].

given #1166 (F,wt=10): 9918 -->_s0(true,app(nil,sndsplit(app(nil,length(nil)),false))) # answer(goal).  [resolve(4642,a,3014,b)].

given #1167 (T,wt=9): 341 ->_s0(f(leq(0,x),y),f(true,y)).  [ur(57,a,70,a)].

given #1168 (T,wt=9): 342 ->_s0(cons(x,leq(0,y)),cons(x,true)).  [ur(56,a,70,a)].

given #1169 (T,wt=9): 343 ->_s0(cons(leq(0,x),y),cons(true,y)).  [ur(55,a,70,a)].

given #1170 (T,wt=9): 345 ->_s0(sndsplit(x,leq(0,y)),sndsplit(x,true)).  [ur(53,a,70,a)].

given #1171 (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 #1172 (F,wt=10): 9920 -->_s0(true,sndsplit(0,sndsplit(app(nil,length(nil)),false))) # answer(goal).  [resolve(4642,a,2997,b)].

given #1173 (F,wt=10): 9940 -->_s0(true,sndsplit(app(nil,app(nil,length(nil))),false)) # answer(goal).  [ur(2781,b,121,a,c,4642,a)].

given #1174 (F,wt=10): 9943 -->_s0(true,app(nil,sndsplit(0,sndsplit(length(nil),false)))) # answer(goal).  [resolve(4646,a,3014,b)].

given #1175 (F,wt=10): 9945 -->_s0(true,sndsplit(0,sndsplit(0,sndsplit(length(nil),false)))) # answer(goal).  [resolve(4646,a,2997,b)].

given #1176 (T,wt=9): 346 ->_s0(sndsplit(leq(0,x),y),sndsplit(true,y)).  [ur(52,a,70,a)].

given #1177 (T,wt=9): 353 ->_s0(mapf(x,leq(0,y)),mapf(x,true)).  [ur(45,a,70,a)].

given #1178 (T,wt=9): 354 ->_s0(mapf(leq(0,x),y),mapf(true,y)).  [ur(44,a,70,a)].

given #1179 (T,wt=9): 355 ->_s0(leq(x,leq(0,y)),leq(x,true)).  [ur(43,a,70,a)].

given #1180 (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 #1181 (F,wt=10): 9964 -->_s0(true,sndsplit(app(nil,0),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,121,a,c,4646,a)].

given #1182 (F,wt=10): 9965 -->_s0(true,sndsplit(0,app(nil,sndsplit(length(nil),false)))) # answer(goal).  [ur(2781,b,120,a,c,4646,a)].

given #1183 (F,wt=10): 9968 -->_s0(true,app(nil,app(nil,sndsplit(length(nil),false)))) # answer(goal).  [resolve(4648,a,3014,b)].

given #1184 (F,wt=10): 9984 -->_s0(true,app(fstsplit(0,x),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,213,a,c,4648,a)].

given #1185 (T,wt=9): 356 ->_s0(leq(leq(0,x),y),leq(true,y)).  [ur(42,a,70,a)].

given #1186 (T,wt=9): 359 ->_s0(fstsplit(x,leq(0,y)),fstsplit(x,true)).  [ur(39,a,70,a)].

given #1187 (T,wt=9): 360 ->_s0(fstsplit(leq(0,x),y),fstsplit(true,y)).  [ur(38,a,70,a)].

given #1188 (T,wt=9): 362 ->_s0(app(x,leq(0,y)),app(x,true)).  [ur(36,a,70,a)].

given #1189 (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 #1190 (F,wt=10): 9985 -->_s0(true,app(app(nil,nil),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,138,a,c,4648,a)].

given #1191 (F,wt=10): 9998 -->_s0(true,app(nil,leq(s(x),app(nil,0)))) # answer(goal).  [resolve(4699,a,3014,b)].

given #1192 (F,wt=10): 10000 -->_s0(true,sndsplit(0,leq(s(x),app(nil,0)))) # answer(goal).  [resolve(4699,a,2997,b)].

given #1193 (F,wt=10): 10014 -->_s0(true,leq(app(nil,s(x)),app(nil,0))) # answer(goal).  [ur(2781,b,131,a,c,4699,a)].

given #1194 (T,wt=9): 363 ->_s0(app(leq(0,x),y),app(true,y)).  [ur(35,a,70,a)].

given #1195 (T,wt=9): 440 ->_s0(f(x,mapf(y,nil)),f(x,nil)).  [ur(58,a,74,a)].

given #1196 (T,wt=9): 441 ->_s0(f(mapf(x,nil),y),f(nil,y)).  [ur(57,a,74,a)].

given #1197 (T,wt=9): 442 ->_s0(cons(x,mapf(y,nil)),cons(x,nil)).  [ur(56,a,74,a)].

given #1198 (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 #1199 (F,wt=10): 10015 -->_s0(true,leq(s(x),app(nil,app(nil,0)))) # answer(goal).  [ur(2781,b,130,a,c,4699,a)].

given #1200 (F,wt=10): 10016 -->_s0(true,leq(s(s(x)),s(app(nil,0)))) # answer(goal).  [ur(2781,b,72,a,c,4699,a)].

given #1201 (F,wt=10): 10049 -->_s0(true,app(nil,leq(app(nil,s(x)),0))) # answer(goal).  [resolve(4835,a,3014,b)].

given #1202 (F,wt=10): 10051 -->_s0(true,sndsplit(0,leq(app(nil,s(x)),0))) # answer(goal).  [resolve(4835,a,2997,b)].

given #1203 (T,wt=9): 443 ->_s0(cons(mapf(x,nil),y),cons(nil,y)).  [ur(55,a,74,a)].

given #1204 (T,wt=9): 445 ->_s0(sndsplit(x,mapf(y,nil)),sndsplit(x,nil)).  [ur(53,a,74,a)].

given #1205 (T,wt=8): 11066 ->*_s0(sndsplit(s(x),mapf(y,nil)),nil).  [ur(87,a,445,a,b,565,a)].

given #1206 (T,wt=9): 446 ->_s0(sndsplit(mapf(x,nil),y),sndsplit(nil,y)).  [ur(52,a,74,a)].

given #1207 (A,wt=10): 253 ->_s0(mapf(x,fstsplit(s(y),nil)),mapf(x,nil)).  [ur(45,a,66,a)].

given #1208 (F,wt=10): 10064 -->_s0(true,leq(app(nil,app(nil,s(x))),0)) # answer(goal).  [ur(2781,b,131,a,c,4835,a)].

given #1209 (F,wt=10): 10065 -->_s0(true,leq(s(app(nil,s(x))),s(0))) # answer(goal).  [ur(2781,b,72,a,c,4835,a)].

given #1210 (F,wt=10): 10254 -->_s0(true,app(nil,app(tail(cons(x,nil)),false))) # answer(goal).  [resolve(9232,b,85,a)].

given #1211 (F,wt=10): 10255 -->_s0(true,app(nil,app(sndsplit(s(x),nil),false))) # answer(goal).  [resolve(9232,b,84,a)].

given #1212 (T,wt=8): 11091 ->*_s0(mapf(x,fstsplit(s(y),nil)),nil).  [ur(87,a,253,a,b,568,a)].

given #1213 (T,wt=9): 453 ->_s0(mapf(x,mapf(y,nil)),mapf(x,nil)).  [ur(45,a,74,a)].

given #1214 (T,wt=7): 11106 ->*_s0(mapf(x,mapf(y,nil)),nil).  [ur(87,a,453,a,b,568,a)].

given #1215 (T,wt=9): 454 ->_s0(mapf(mapf(x,nil),y),mapf(nil,y)).  [ur(44,a,74,a)].

given #1216 (A,wt=10): 254 ->_s0(mapf(fstsplit(s(x),nil),y),mapf(nil,y)).  [ur(44,a,66,a)].

given #1217 (F,wt=10): 10258 -->_s0(true,app(nil,app(head(cons(nil,x)),false))) # answer(goal).  [resolve(9232,b,67,a)].

given #1218 (F,wt=10): 10259 -->_s0(true,app(nil,app(fstsplit(s(x),nil),false))) # answer(goal).  [resolve(9232,b,66,a)].

given #1219 (F,wt=10): 10332 -->_s0(true,sndsplit(0,app(tail(cons(x,nil)),false))) # answer(goal).  [resolve(9294,b,85,a)].

given #1220 (F,wt=10): 10333 -->_s0(true,sndsplit(0,app(sndsplit(s(x),nil),false))) # answer(goal).  [resolve(9294,b,84,a)].

given #1221 (T,wt=9): 455 ->_s0(leq(x,mapf(y,nil)),leq(x,nil)).  [ur(43,a,74,a)].

given #1222 (T,wt=9): 456 ->_s0(leq(mapf(x,nil),y),leq(nil,y)).  [ur(42,a,74,a)].

given #1223 (T,wt=9): 459 ->_s0(fstsplit(x,mapf(y,nil)),fstsplit(x,nil)).  [ur(39,a,74,a)].

given #1224 (T,wt=8): 11159 ->*_s0(fstsplit(s(x),mapf(y,nil)),nil).  [ur(87,a,459,a,b,576,a)].

given #1225 (A,wt=10): 255 ->_s0(leq(x,fstsplit(s(y),nil)),leq(x,nil)).  [ur(43,a,66,a)].

given #1226 (F,wt=10): 10336 -->_s0(true,sndsplit(0,app(head(cons(nil,x)),false))) # answer(goal).  [resolve(9294,b,67,a)].

given #1227 (F,wt=10): 10337 -->_s0(true,sndsplit(0,app(fstsplit(s(x),nil),false))) # answer(goal).  [resolve(9294,b,66,a)].

given #1228 (F,wt=10): 10339 -->_s0(true,app(nil,tail(app(cons(x,nil),false)))) # answer(goal).  [resolve(5956,a,3014,b)].

given #1229 (F,wt=10): 10341 -->_s0(true,sndsplit(0,tail(app(cons(x,nil),false)))) # answer(goal).  [resolve(5956,a,2997,b)].

given #1230 (T,wt=9): 460 ->_s0(fstsplit(mapf(x,nil),y),fstsplit(nil,y)).  [ur(38,a,74,a)].

given #1231 (T,wt=9): 462 ->_s0(app(x,mapf(y,nil)),app(x,nil)).  [ur(36,a,74,a)].

given #1232 (T,wt=9): 463 ->_s0(app(mapf(x,nil),y),app(nil,y)).  [ur(35,a,74,a)].

given #1233 (T,wt=7): 11239 ->*_s0(app(mapf(x,nil),y),y).  [ur(87,a,463,a,b,581,a)].

given #1234 (A,wt=10): 256 ->_s0(leq(fstsplit(s(x),nil),y),leq(nil,y)).  [ur(42,a,66,a)].

given #1235 (F,wt=10): 10343 -->_s0(true,tail(app(nil,app(cons(x,nil),false)))) # answer(goal).  [resolve(5956,a,2966,b)].

given #1236 (F,wt=10): 10344 -->_s0(true,tail(sndsplit(0,app(cons(x,nil),false)))) # answer(goal).  [resolve(5956,a,2936,b)].

given #1237 (F,wt=10): 10466 -->_s0(true,app(fstsplit(0,x),y)) | -->_s0(y,false) # answer(goal).  [resolve(9401,b,36,b)].

given #1238 (F,wt=10): 10467 -->_s0(true,app(x,false)) | -->_s0(x,fstsplit(0,y)) # answer(goal).  [resolve(9401,b,35,b)].

given #1239 (T,wt=8): 11237 ->*_s0(app(mapf(x,nil),empty(nil)),true).  [ur(87,a,463,a,b,634,a)].

given #1240 (T,wt=8): 11238 ->*_s0(app(mapf(x,nil),length(nil)),0).  [ur(87,a,463,a,b,629,a)].

given #1241 (T,wt=9): 465 ->_s0(f(x,sndsplit(0,y)),f(x,y)).  [ur(58,a,82,a)].

given #1242 (T,wt=9): 466 ->_s0(f(sndsplit(0,x),y),f(x,y)).  [ur(57,a,82,a)].

given #1243 (A,wt=10): 259 ->_s0(fstsplit(x,fstsplit(s(y),nil)),fstsplit(x,nil)).  [ur(39,a,66,a)].

given #1244 (F,wt=8): 11277 -->_s0(true,app(fstsplit(length(nil),x),false)) # answer(goal).  [resolve(10467,b,335,a)].

given #1245 (F,wt=9): 11278 -->_s0(true,app(fstsplit(app(nil,0),x),false)) # answer(goal).  [resolve(10467,b,135,a)].

given #1246 (F,wt=9): 11280 -->_s0(true,app(sndsplit(0,fstsplit(0,x)),false)) # answer(goal).  [resolve(10467,b,82,a)].

given #1247 (F,wt=10): 10502 -->_s0(true,app(nil,sndsplit(tail(cons(x,0)),false))) # answer(goal).  [resolve(9470,b,85,a)].

given #1248 (T,wt=9): 467 ->_s0(cons(x,sndsplit(0,y)),cons(x,y)).  [ur(56,a,82,a)].

given #1249 (T,wt=9): 468 ->_s0(cons(sndsplit(0,x),y),cons(x,y)).  [ur(55,a,82,a)].

given #1250 (T,wt=9): 470 ->_s0(sndsplit(x,sndsplit(0,y)),sndsplit(x,y)).  [ur(53,a,82,a)].

given #1251 (T,wt=8): 11365 ->*_s0(sndsplit(s(x),sndsplit(0,nil)),nil).  [ur(87,a,470,a,b,565,a)].

given #1252 (A,wt=10): 260 ->_s0(fstsplit(fstsplit(s(x),nil),y),fstsplit(nil,y)).  [ur(38,a,66,a)].

Low Water (keep): wt=12.000, iters=6687

given #1253 (F,wt=10): 10504 -->_s0(true,app(nil,sndsplit(head(cons(0,x)),false))) # answer(goal).  [resolve(9470,b,67,a)].

given #1254 (F,wt=10): 10538 -->_s0(true,sndsplit(0,sndsplit(tail(cons(x,0)),false))) # answer(goal).  [resolve(9522,b,85,a)].

given #1255 (F,wt=10): 10540 -->_s0(true,sndsplit(0,sndsplit(head(cons(0,x)),false))) # answer(goal).  [resolve(9522,b,67,a)].

given #1256 (F,wt=10): 10615 -->_s0(true,sndsplit(app(nil,tail(cons(x,0))),false)) # answer(goal).  [resolve(9633,b,85,a)].

given #1257 (T,wt=9): 471 ->_s0(sndsplit(sndsplit(0,x),y),sndsplit(x,y)).  [ur(52,a,82,a)].

given #1258 (T,wt=7): 11447 ->*_s0(sndsplit(sndsplit(0,0),x),x).  [ur(87,a,471,a,b,567,a)].

given #1259 (T,wt=8): 11395 ->*_s0(sndsplit(sndsplit(0,length(nil)),x),x).  [ur(87,a,471,a,b,4574,a)].

given #1260 (T,wt=8): 11445 ->*_s0(sndsplit(sndsplit(0,0),empty(nil)),true).  [ur(87,a,471,a,b,632,a)].

given #1261 (A,wt=10): 262 ->_s0(app(x,fstsplit(s(y),nil)),app(x,nil)).  [ur(36,a,66,a)].

given #1262 (F,wt=9): 11482 -->_s0(true,sndsplit(sndsplit(0,sndsplit(0,0)),false)) # answer(goal).  [ur(2781,b,471,a,c,11447,a)].

given #1263 (F,wt=10): 10617 -->_s0(true,sndsplit(app(nil,head(cons(0,x))),false)) # answer(goal).  [resolve(9633,b,67,a)].

given #1264 (F,wt=10): 10618 -->_s0(true,sndsplit(app(tail(cons(x,nil)),0),false)) # answer(goal).  [resolve(9634,b,85,a)].

given #1265 (F,wt=10): 10619 -->_s0(true,sndsplit(app(sndsplit(s(x),nil),0),false)) # answer(goal).  [resolve(9634,b,84,a)].

given #1266 (T,wt=8): 11446 ->*_s0(sndsplit(sndsplit(0,0),length(nil)),0).  [ur(87,a,471,a,b,627,a)].

given #1267 (T,wt=8): 11448 ->*_s0(sndsplit(sndsplit(0,s(x)),nil),nil).  [ur(87,a,471,a,b,565,a)].

given #1268 (T,wt=9): 478 ->_s0(mapf(x,sndsplit(0,y)),mapf(x,y)).  [ur(45,a,82,a)].

given #1269 (T,wt=7): 11548 ->*_s0(mapf(x,sndsplit(0,nil)),nil).  [ur(87,a,478,a,b,568,a)].

given #1270 (A,wt=10): 263 ->_s0(app(fstsplit(s(x),nil),y),app(nil,y)).  [ur(35,a,66,a)].

given #1271 (F,wt=10): 10622 -->_s0(true,sndsplit(app(head(cons(nil,x)),0),false)) # answer(goal).  [resolve(9634,b,67,a)].

given #1272 (F,wt=10): 10623 -->_s0(true,sndsplit(app(fstsplit(s(x),nil),0),false)) # answer(goal).  [resolve(9634,b,66,a)].

given #1273 (F,wt=10): 10864 -->_s0(true,app(app(nil,tail(cons(x,nil))),false)) # answer(goal).  [resolve(9904,b,85,a)].

given #1274 (F,wt=10): 10865 -->_s0(true,app(app(nil,sndsplit(s(x),nil)),false)) # answer(goal).  [resolve(9904,b,84,a)].

given #1275 (T,wt=8): 11602 ->*_s0(app(fstsplit(s(x),nil),y),y).  [ur(87,a,263,a,b,581,a)].

given #1276 (T,wt=9): 479 ->_s0(mapf(sndsplit(0,x),y),mapf(x,y)).  [ur(44,a,82,a)].

given #1277 (T,wt=9): 480 ->_s0(leq(x,sndsplit(0,y)),leq(x,y)).  [ur(43,a,82,a)].

given #1278 (T,wt=8): 11647 ->*_s0(leq(s(x),sndsplit(0,0)),false).  [ur(87,a,480,a,b,571,a)].

given #1279 (A,wt=10): 265 ->_s0(f(x,head(cons(y,z))),f(x,y)).  [ur(58,a,67,a)].

given #1280 (F,wt=10): 10868 -->_s0(true,app(app(nil,head(cons(nil,x))),false)) # answer(goal).  [resolve(9904,b,67,a)].

given #1281 (F,wt=10): 10869 -->_s0(true,app(app(nil,fstsplit(s(x),nil)),false)) # answer(goal).  [resolve(9904,b,66,a)].

given #1282 (F,wt=10): 10898 -->_s0(true,app(app(tail(cons(x,nil)),nil),false)) # answer(goal).  [resolve(9905,b,85,a)].

given #1283 (F,wt=10): 10899 -->_s0(true,app(app(sndsplit(s(x),nil),nil),false)) # answer(goal).  [resolve(9905,b,84,a)].

given #1284 (T,wt=9): 481 ->_s0(leq(sndsplit(0,x),y),leq(x,y)).  [ur(42,a,82,a)].

given #1285 (T,wt=7): 11699 ->*_s0(leq(sndsplit(0,0),x),true).  [ur(87,a,481,a,b,572,a)].

given #1286 (T,wt=8): 11691 ->*_s0(leq(sndsplit(0,length(nil)),x),true).  [ur(87,a,481,a,b,4803,a)].

given #1287 (T,wt=8): 11700 ->*_s0(leq(sndsplit(0,s(x)),0),false).  [ur(87,a,481,a,b,571,a)].

given #1288 (A,wt=10): 266 ->_s0(f(head(cons(x,y)),z),f(x,z)).  [ur(57,a,67,a)].

given #1289 (F,wt=10): 10902 -->_s0(true,app(app(head(cons(nil,x)),nil),false)) # answer(goal).  [resolve(9905,b,67,a)].

given #1290 (F,wt=10): 10903 -->_s0(true,app(app(fstsplit(s(x),nil),nil),false)) # answer(goal).  [resolve(9905,b,66,a)].

given #1291 (F,wt=10): 11246 -->_s0(true,app(mapf(x,nil),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,463,a,c,4648,a)].

given #1292 (F,wt=10): 11247 -->_s0(true,app(mapf(x,nil),empty(cons(y,z)))) # answer(goal).  [ur(2781,b,463,a,c,1127,a)].

given #1293 (T,wt=9): 484 ->_s0(fstsplit(x,sndsplit(0,y)),fstsplit(x,y)).  [ur(39,a,82,a)].

given #1294 (T,wt=8): 11768 ->*_s0(fstsplit(s(x),sndsplit(0,nil)),nil).  [ur(87,a,484,a,b,576,a)].

given #1295 (T,wt=9): 485 ->_s0(fstsplit(sndsplit(0,x),y),fstsplit(x,y)).  [ur(38,a,82,a)].

given #1296 (T,wt=7): 11795 ->*_s0(fstsplit(sndsplit(0,0),x),nil).  [ur(87,a,485,a,b,578,a)].

given #1297 (A,wt=10): 267 ->_s0(cons(x,head(cons(y,z))),cons(x,y)).  [ur(56,a,67,a)].

given #1298 (F,wt=9): 11781 -->_s0(true,app(fstsplit(sndsplit(0,0),x),false)) # answer(goal).  [resolve(485,a,10467,b)].

given #1299 (F,wt=10): 11248 -->_s0(true,app(mapf(x,nil),head(cons(false,y)))) # answer(goal).  [ur(2781,b,463,a,c,1115,a)].

given #1300 (F,wt=10): 11249 -->_s0(true,app(mapf(x,nil),leq(s(y),0))) # answer(goal).  [ur(2781,b,463,a,c,1078,a)].

given #1301 (F,wt=10): 11250 -->_s0(true,app(mapf(x,nil),tail(cons(y,false)))) # answer(goal).  [ur(2781,b,463,a,c,1065,a)].

given #1302 (T,wt=8): 11791 ->*_s0(fstsplit(sndsplit(0,length(nil)),x),nil).  [ur(87,a,485,a,b,4913,a)].

given #1303 (T,wt=8): 11796 ->*_s0(fstsplit(sndsplit(0,s(x)),nil),nil).  [ur(87,a,485,a,b,576,a)].

given #1304 (T,wt=9): 487 ->_s0(app(x,sndsplit(0,y)),app(x,y)).  [ur(36,a,82,a)].

given #1305 (T,wt=9): 488 ->_s0(app(sndsplit(0,x),y),app(x,y)).  [ur(35,a,82,a)].

given #1306 (A,wt=10): 268 ->_s0(cons(head(cons(x,y)),z),cons(x,z)).  [ur(55,a,67,a)].

given #1307 (F,wt=9): 11900 -->_s0(true,app(sndsplit(0,mapf(x,nil)),false)) # answer(goal).  [ur(2781,b,488,a,c,11239,a)].

given #1308 (F,wt=10): 11252 -->_s0(true,head(cons(app(mapf(x,nil),false),y))) # answer(goal).  [resolve(11239,a,3010,b)].

given #1309 (F,wt=10): 11253 -->_s0(true,tail(cons(x,app(mapf(y,nil),false)))) # answer(goal).  [resolve(11239,a,2994,b)].

given #1310 (F,wt=10): 11254 -->_s0(true,x) | -->_s0(x,app(mapf(y,nil),false)) # answer(goal).  [resolve(11239,a,2781,c)].

given #1311 (T,wt=7): 11892 ->*_s0(app(sndsplit(0,nil),x),x).  [ur(87,a,488,a,b,581,a)].

given #1312 (T,wt=8): 11890 ->*_s0(app(sndsplit(0,nil),empty(nil)),true).  [ur(87,a,488,a,b,634,a)].

given #1313 (T,wt=8): 11891 ->*_s0(app(sndsplit(0,nil),length(nil)),0).  [ur(87,a,488,a,b,629,a)].

given #1314 (T,wt=9): 570 ->*_s0(leq(s(x),s(y)),leq(x,y)).  [ur(87,a,72,a,b,86,a)].

given #1315 (A,wt=10): 270 ->_s0(sndsplit(x,head(cons(y,z))),sndsplit(x,y)).  [ur(53,a,67,a)].

given #1316 (F,wt=9): 11931 -->_s0(true,app(sndsplit(0,sndsplit(0,nil)),false)) # answer(goal).  [ur(2781,b,488,a,c,11892,a)].

given #1317 (F,wt=10): 11279 -->_s0(true,app(tail(cons(x,fstsplit(0,y))),false)) # answer(goal).  [resolve(10467,b,85,a)].

given #1318 (F,wt=10): 11281 -->_s0(true,app(head(cons(fstsplit(0,x),y)),false)) # answer(goal).  [resolve(10467,b,67,a)].

given #1319 (F,wt=10): 11282 -->_s0(true,app(fstsplit(x,y),false)) | -->_s0(x,0) # answer(goal).  [resolve(10467,b,38,b)].

given #1320 (T,wt=9): 1062 ->*_s0(tail(cons(x,tail(cons(y,z)))),z).  [ur(87,a,85,a,b,564,a)].

given #1321 (T,wt=9): 1064 ->*_s0(head(cons(tail(cons(x,y)),z)),y).  [ur(87,a,67,a,b,564,a)].

given #1322 (T,wt=9): 1066 ->*_s0(tail(cons(x,sndsplit(s(y),nil))),nil).  [ur(87,a,85,a,b,565,a)].

given #1323 (T,wt=9): 1067 ->*_s0(sndsplit(s(s(x)),cons(y,nil)),nil).  [ur(87,a,83,a,b,565,a)].

given #1324 (A,wt=10): 271 ->_s0(sndsplit(head(cons(x,y)),z),sndsplit(x,z)).  [ur(52,a,67,a)].

given #1325 (F,wt=10): 11372 -->_s0(true,sndsplit(length(nil),sndsplit(0,sndsplit(0,false)))) # answer(goal).  [ur(2781,b,470,a,c,4571,a)].

given #1326 (F,wt=10): 11373 -->_s0(true,sndsplit(length(nil),sndsplit(0,app(nil,false)))) # answer(goal).  [ur(2781,b,470,a,c,4567,a)].

given #1327 (F,wt=10): 11374 -->_s0(true,sndsplit(s(0),sndsplit(0,cons(x,false)))) # answer(goal).  [ur(2781,b,470,a,c,638,a)].

given #1328 (F,wt=10): 11455 -->_s0(true,sndsplit(sndsplit(0,0),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,471,a,c,4646,a)].

given #1329 (T,wt=8): 12143 ->*_s0(sndsplit(head(cons(0,x)),y),y).  [ur(87,a,271,a,b,567,a)].

given #1330 (T,wt=9): 1069 ->*_s0(head(cons(sndsplit(s(x),nil),y)),nil).  [ur(87,a,67,a,b,565,a)].

given #1331 (T,wt=9): 1074 ->*_s0(tail(cons(x,leq(s(y),0))),false).  [ur(87,a,85,a,b,571,a)].

given #1332 (T,wt=9): 1077 ->*_s0(head(cons(leq(s(x),0),y)),false).  [ur(87,a,67,a,b,571,a)].

given #1333 (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 #1334 (F,wt=10): 11456 -->_s0(true,sndsplit(sndsplit(0,app(nil,length(nil))),false)) # answer(goal).  [ur(2781,b,471,a,c,4642,a)].

given #1335 (F,wt=10): 11457 -->_s0(true,sndsplit(sndsplit(0,length(nil)),sndsplit(0,false))) # answer(goal).  [ur(2781,b,471,a,c,4571,a)].

given #1336 (F,wt=10): 11458 -->_s0(true,sndsplit(sndsplit(0,length(nil)),app(nil,false))) # answer(goal).  [ur(2781,b,471,a,c,4567,a)].

given #1337 (F,wt=10): 11459 -->_s0(true,sndsplit(sndsplit(0,0),empty(cons(x,y)))) # answer(goal).  [ur(2781,b,471,a,c,1125,a)].

given #1338 (T,wt=9): 1112 ->*_s0(tail(cons(x,head(cons(y,z)))),y).  [ur(87,a,85,a,b,575,a)].

given #1339 (T,wt=9): 1114 ->*_s0(head(cons(head(cons(x,y)),z)),x).  [ur(87,a,67,a,b,575,a)].

given #1340 (T,wt=9): 1116 ->*_s0(tail(cons(x,fstsplit(s(y),nil))),nil).  [ur(87,a,85,a,b,576,a)].

given #1341 (T,wt=9): 1118 ->*_s0(head(cons(fstsplit(s(x),nil),y)),nil).  [ur(87,a,67,a,b,576,a)].

given #1342 (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 #1343 (F,wt=10): 11460 -->_s0(true,sndsplit(sndsplit(0,0),head(cons(false,x)))) # answer(goal).  [ur(2781,b,471,a,c,1113,a)].

given #1344 (F,wt=10): 11461 -->_s0(true,sndsplit(sndsplit(0,0),leq(s(x),0))) # answer(goal).  [ur(2781,b,471,a,c,1075,a)].

given #1345 (F,wt=10): 11462 -->_s0(true,sndsplit(sndsplit(0,0),tail(cons(x,false)))) # answer(goal).  [ur(2781,b,471,a,c,1063,a)].

given #1346 (F,wt=10): 11463 -->_s0(true,sndsplit(sndsplit(0,s(0)),cons(x,false))) # answer(goal).  [ur(2781,b,471,a,c,638,a)].

given #1347 (T,wt=9): 1124 ->*_s0(tail(cons(x,empty(cons(y,z)))),false).  [ur(87,a,85,a,b,580,a)].

given #1348 (T,wt=9): 1126 ->*_s0(head(cons(empty(cons(x,y)),z)),false).  [ur(87,a,67,a,b,580,a)].

given #1349 (T,wt=9): 1128 ->*_s0(tail(cons(x,sndsplit(0,length(nil)))),0).  [ur(87,a,85,a,b,627,a)].

given #1350 (T,wt=9): 1129 ->*_s0(sndsplit(s(0),cons(x,length(nil))),0).  [ur(87,a,83,a,b,627,a)].

given #1351 (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 #1352 (F,wt=10): 11465 -->_s0(true,head(cons(sndsplit(sndsplit(0,0),false),x))) # answer(goal).  [resolve(11447,a,3010,b)].

given #1353 (F,wt=10): 11466 -->_s0(true,tail(cons(x,sndsplit(sndsplit(0,0),false)))) # answer(goal).  [resolve(11447,a,2994,b)].

given #1354 (F,wt=10): 11467 -->_s0(true,x) | -->_s0(x,sndsplit(sndsplit(0,0),false)) # answer(goal).  [resolve(11447,a,2781,c)].

given #1355 (F,wt=10): 11483 -->_s0(true,sndsplit(s(sndsplit(0,0)),cons(x,false))) # answer(goal).  [ur(2781,b,83,a,c,11447,a)].

given #1356 (T,wt=9): 1131 ->*_s0(head(cons(sndsplit(0,length(nil)),x)),0).  [ur(87,a,67,a,b,627,a)].

given #1357 (T,wt=9): 1168 ->*_s0(tail(cons(x,app(nil,length(nil)))),0).  [ur(87,a,85,a,b,629,a)].

given #1358 (T,wt=9): 1170 ->*_s0(head(cons(app(nil,length(nil)),x)),0).  [ur(87,a,67,a,b,629,a)].

given #1359 (T,wt=9): 1174 ->*_s0(tail(cons(x,sndsplit(0,empty(nil)))),true).  [ur(87,a,85,a,b,632,a)].

given #1360 (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 #1361 (F,wt=10): 11485 -->_s0(true,app(nil,sndsplit(sndsplit(0,length(nil)),false))) # answer(goal).  [resolve(11395,a,3014,b)].

given #1362 (F,wt=10): 11487 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,length(nil)),false))) # answer(goal).  [resolve(11395,a,2997,b)].

given #1363 (F,wt=10): 11506 -->_s0(true,sndsplit(sndsplit(0,sndsplit(0,length(nil))),false)) # answer(goal).  [ur(2781,b,471,a,c,11395,a)].

given #1364 (F,wt=10): 11508 -->_s0(true,sndsplit(app(nil,sndsplit(0,length(nil))),false)) # answer(goal).  [ur(2781,b,121,a,c,11395,a)].

given #1365 (T,wt=9): 1175 ->*_s0(sndsplit(s(0),cons(x,empty(nil))),true).  [ur(87,a,83,a,b,632,a)].

given #1366 (T,wt=9): 1177 ->*_s0(head(cons(sndsplit(0,empty(nil)),x)),true).  [ur(87,a,67,a,b,632,a)].

given #1367 (T,wt=9): 1181 ->*_s0(tail(cons(x,app(nil,empty(nil)))),true).  [ur(87,a,85,a,b,634,a)].

given #1368 (T,wt=9): 1183 ->*_s0(head(cons(app(nil,empty(nil)),x)),true).  [ur(87,a,67,a,b,634,a)].

given #1369 (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 #1370 (F,wt=10): 11654 -->_s0(true,leq(app(nil,s(x)),sndsplit(0,0))) # answer(goal).  [ur(2781,b,480,a,c,4835,a)].

given #1371 (F,wt=10): 11655 -->_s0(true,leq(s(x),sndsplit(0,app(nil,0)))) # answer(goal).  [ur(2781,b,480,a,c,4699,a)].

given #1372 (F,wt=10): 11656 -->_s0(true,leq(s(s(x)),sndsplit(0,s(0)))) # answer(goal).  [ur(2781,b,480,a,c,1076,a)].

given #1373 (F,wt=10): 11658 -->_s0(true,app(nil,leq(s(x),sndsplit(0,0)))) # answer(goal).  [resolve(11647,a,3014,b)].

given #1374 (T,wt=9): 1185 ->*_s0(tail(cons(x,s(empty(nil)))),s(true)).  [ur(87,a,85,a,b,699,a)].

given #1375 (T,wt=9): 1187 ->*_s0(head(cons(s(empty(nil)),x)),s(true)).  [ur(87,a,67,a,b,699,a)].

given #1376 (T,wt=9): 1215 ->*_s0(tail(cons(x,tail(empty(nil)))),tail(true)).  [ur(87,a,85,a,b,755,a)].

given #1377 (T,wt=9): 1217 ->*_s0(head(cons(tail(empty(nil)),x)),tail(true)).  [ur(87,a,67,a,b,755,a)].

given #1378 (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 #1379 (F,wt=10): 11660 -->_s0(true,sndsplit(0,leq(s(x),sndsplit(0,0)))) # answer(goal).  [resolve(11647,a,2997,b)].

given #1380 (F,wt=10): 11674 -->_s0(true,leq(s(x),sndsplit(0,sndsplit(0,0)))) # answer(goal).  [ur(2781,b,480,a,c,11647,a)].

given #1381 (F,wt=10): 11675 -->_s0(true,leq(s(x),app(nil,sndsplit(0,0)))) # answer(goal).  [ur(2781,b,130,a,c,11647,a)].

given #1382 (F,wt=10): 11676 -->_s0(true,leq(s(s(x)),s(sndsplit(0,0)))) # answer(goal).  [ur(2781,b,72,a,c,11647,a)].

given #1383 (T,wt=9): 1219 ->*_s0(tail(cons(x,length(empty(nil)))),length(true)).  [ur(87,a,85,a,b,781,a)].

given #1384 (T,wt=9): 1221 ->*_s0(head(cons(length(empty(nil)),x)),length(true)).  [ur(87,a,67,a,b,781,a)].

given #1385 (T,wt=9): 1223 ->*_s0(tail(cons(x,head(empty(nil)))),head(true)).  [ur(87,a,85,a,b,807,a)].

given #1386 (T,wt=9): 1225 ->*_s0(head(cons(head(empty(nil)),x)),head(true)).  [ur(87,a,67,a,b,807,a)].

given #1387 (A,wt=10): 278 ->_s0(mapf(x,head(cons(y,z))),mapf(x,y)).  [ur(45,a,67,a)].

given #1388 (F,wt=10): 11707 -->_s0(true,leq(sndsplit(0,s(x)),sndsplit(0,0))) # answer(goal).  [ur(2781,b,481,a,c,11647,a)].

given #1389 (F,wt=10): 11708 -->_s0(true,leq(sndsplit(0,app(nil,s(x))),0)) # answer(goal).  [ur(2781,b,481,a,c,4835,a)].

given #1390 (F,wt=10): 11709 -->_s0(true,leq(sndsplit(0,s(x)),app(nil,0))) # answer(goal).  [ur(2781,b,481,a,c,4699,a)].

given #1391 (F,wt=10): 11710 -->_s0(true,leq(sndsplit(0,s(s(x))),s(0))) # answer(goal).  [ur(2781,b,481,a,c,1076,a)].

given #1392 (T,wt=8): 12420 ->*_s0(mapf(x,head(cons(nil,y))),nil).  [ur(87,a,278,a,b,568,a)].

given #1393 (T,wt=9): 1227 ->*_s0(tail(cons(x,empty(empty(nil)))),empty(true)).  [ur(87,a,85,a,b,833,a)].

given #1394 (T,wt=9): 1229 ->*_s0(head(cons(empty(empty(nil)),x)),empty(true)).  [ur(87,a,67,a,b,833,a)].

given #1395 (T,wt=9): 1259 ->*_s0(tail(cons(x,s(length(nil)))),s(0)).  [ur(87,a,85,a,b,891,a)].

given #1396 (A,wt=10): 279 ->_s0(mapf(head(cons(x,y)),z),mapf(x,z)).  [ur(44,a,67,a)].

given #1397 (F,wt=10): 11734 -->_s0(true,app(nil,leq(sndsplit(0,s(x)),0))) # answer(goal).  [resolve(11700,a,3014,b)].

given #1398 (F,wt=10): 11736 -->_s0(true,sndsplit(0,leq(sndsplit(0,s(x)),0))) # answer(goal).  [resolve(11700,a,2997,b)].

given #1399 (F,wt=10): 11750 -->_s0(true,leq(sndsplit(0,sndsplit(0,s(x))),0)) # answer(goal).  [ur(2781,b,481,a,c,11700,a)].

given #1400 (F,wt=10): 11751 -->_s0(true,leq(app(nil,sndsplit(0,s(x))),0)) # answer(goal).  [ur(2781,b,131,a,c,11700,a)].

given #1401 (T,wt=9): 1262 ->*_s0(head(cons(s(length(nil)),x)),s(0)).  [ur(87,a,67,a,b,891,a)].

given #1402 (T,wt=9): 1264 ->*_s0(tail(cons(x,tail(length(nil)))),tail(0)).  [ur(87,a,85,a,b,917,a)].

given #1403 (T,wt=9): 1266 ->*_s0(head(cons(tail(length(nil)),x)),tail(0)).  [ur(87,a,67,a,b,917,a)].

given #1404 (T,wt=9): 1268 ->*_s0(tail(cons(x,length(length(nil)))),length(0)).  [ur(87,a,85,a,b,943,a)].

given #1405 (A,wt=10): 280 ->_s0(leq(x,head(cons(y,z))),leq(x,y)).  [ur(43,a,67,a)].

given #1406 (F,wt=10): 11752 -->_s0(true,leq(s(sndsplit(0,s(x))),s(0))) # answer(goal).  [ur(2781,b,72,a,c,11700,a)].

given #1407 (F,wt=10): 11899 -->_s0(true,app(sndsplit(0,fstsplit(s(x),nil)),false)) # answer(goal).  [ur(2781,b,488,a,c,11602,a)].

given #1408 (F,wt=10): 11901 -->_s0(true,app(sndsplit(0,nil),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,488,a,c,4648,a)].

given #1409 (F,wt=10): 11902 -->_s0(true,app(sndsplit(0,nil),empty(cons(x,y)))) # answer(goal).  [ur(2781,b,488,a,c,1127,a)].

given #1410 (T,wt=9): 1270 ->*_s0(head(cons(length(length(nil)),x)),length(0)).  [ur(87,a,67,a,b,943,a)].

given #1411 (T,wt=9): 1272 ->*_s0(tail(cons(x,head(length(nil)))),head(0)).  [ur(87,a,85,a,b,969,a)].

given #1412 (T,wt=9): 1274 ->*_s0(head(cons(head(length(nil)),x)),head(0)).  [ur(87,a,67,a,b,969,a)].

given #1413 (T,wt=9): 1303 ->*_s0(tail(cons(x,empty(length(nil)))),empty(0)).  [ur(87,a,85,a,b,1031,a)].

given #1414 (A,wt=10): 281 ->_s0(leq(head(cons(x,y)),z),leq(x,z)).  [ur(42,a,67,a)].

given #1415 (F,wt=10): 11903 -->_s0(true,app(sndsplit(0,nil),head(cons(false,x)))) # answer(goal).  [ur(2781,b,488,a,c,1115,a)].

given #1416 (F,wt=10): 11904 -->_s0(true,app(sndsplit(0,nil),leq(s(x),0))) # answer(goal).  [ur(2781,b,488,a,c,1078,a)].

given #1417 (F,wt=10): 11905 -->_s0(true,app(sndsplit(0,nil),tail(cons(x,false)))) # answer(goal).  [ur(2781,b,488,a,c,1065,a)].

given #1418 (F,wt=10): 11912 -->_s0(true,app(mapf(x,nil),y)) | -->_s0(y,false) # answer(goal).  [resolve(11254,b,36,b)].

given #1419 (T,wt=8): 12518 ->*_s0(leq(head(cons(0,x)),y),true).  [ur(87,a,281,a,b,572,a)].

given #1420 (T,wt=9): 1305 ->*_s0(head(cons(empty(length(nil)),x)),empty(0)).  [ur(87,a,67,a,b,1031,a)].

given #1421 (T,wt=9): 1310 ->_s0(s(s(app(nil,x))),s(s(x))).  [ur(59,a,114,a)].

given #1422 (T,wt=9): 1315 ->_s0(tail(s(app(nil,x))),tail(s(x))).  [ur(54,a,114,a)].

given #1423 (A,wt=10): 284 ->_s0(fstsplit(x,head(cons(y,z))),fstsplit(x,y)).  [ur(39,a,67,a)].

given #1424 (F,wt=10): 11913 -->_s0(true,app(x,false)) | -->_s0(x,mapf(y,nil)) # answer(goal).  [resolve(11254,b,35,b)].

given #1425 (F,wt=9): 12573 -->_s0(true,app(mapf(x,sndsplit(0,nil)),false)) # answer(goal).  [resolve(11913,b,478,a)].

given #1426 (F,wt=9): 12574 -->_s0(true,app(mapf(x,mapf(y,nil)),false)) # answer(goal).  [resolve(11913,b,453,a)].

given #1427 (F,wt=9): 12577 -->_s0(true,app(mapf(x,fstsplit(0,y)),false)) # answer(goal).  [resolve(11913,b,203,a)].

given #1428 (T,wt=9): 1328 ->_s0(length(s(app(nil,x))),length(s(x))).  [ur(41,a,114,a)].

given #1429 (T,wt=9): 1329 ->_s0(head(s(app(nil,x))),head(s(x))).  [ur(40,a,114,a)].

given #1430 (T,wt=9): 1332 ->_s0(empty(s(app(nil,x))),empty(s(x))).  [ur(37,a,114,a)].

given #1431 (T,wt=9): 1339 ->_s0(s(tail(app(nil,x))),s(tail(x))).  [ur(59,a,119,a)].

given #1432 (A,wt=10): 285 ->_s0(fstsplit(head(cons(x,y)),z),fstsplit(x,z)).  [ur(38,a,67,a)].

given #1433 (F,wt=9): 12578 -->_s0(true,app(mapf(x,app(nil,nil)),false)) # answer(goal).  [resolve(11913,b,128,a)].

given #1434 (F,wt=10): 11915 -->_s0(true,head(cons(app(sndsplit(0,nil),false),x))) # answer(goal).  [resolve(11892,a,3010,b)].

given #1435 (F,wt=10): 11916 -->_s0(true,tail(cons(x,app(sndsplit(0,nil),false)))) # answer(goal).  [resolve(11892,a,2994,b)].

given #1436 (F,wt=10): 11917 -->_s0(true,x) | -->_s0(x,app(sndsplit(0,nil),false)) # answer(goal).  [resolve(11892,a,2781,c)].

given #1437 (T,wt=8): 12635 ->*_s0(fstsplit(head(cons(0,x)),y),nil).  [ur(87,a,285,a,b,578,a)].

given #1438 (T,wt=9): 1344 ->_s0(tail(tail(app(nil,x))),tail(tail(x))).  [ur(54,a,119,a)].

given #1439 (T,wt=9): 1357 ->_s0(length(tail(app(nil,x))),length(tail(x))).  [ur(41,a,119,a)].

given #1440 (T,wt=9): 1358 ->_s0(head(tail(app(nil,x))),head(tail(x))).  [ur(40,a,119,a)].

given #1441 (A,wt=10): 287 ->_s0(app(x,head(cons(y,z))),app(x,y)).  [ur(36,a,67,a)].

given #1442 (F,wt=10): 12022 -->_s0(true,app(fstsplit(tail(cons(x,0)),y),false)) # answer(goal).  [resolve(11282,b,85,a)].

given #1443 (F,wt=10): 12023 -->_s0(true,app(fstsplit(head(cons(0,x)),y),false)) # answer(goal).  [resolve(11282,b,67,a)].

given #1444 (F,wt=10): 12146 -->_s0(true,sndsplit(head(cons(sndsplit(0,0),x)),false)) # answer(goal).  [ur(2781,b,271,a,c,11447,a)].

given #1445 (F,wt=10): 12176 -->_s0(true,sndsplit(sndsplit(0,head(cons(0,x))),false)) # answer(goal).  [ur(2781,b,471,a,c,12143,a)].

given #1446 (T,wt=9): 1361 ->_s0(empty(tail(app(nil,x))),empty(tail(x))).  [ur(37,a,119,a)].

given #1447 (T,wt=9): 1368 ->_s0(s(length(app(nil,x))),s(length(x))).  [ur(59,a,132,a)].

given #1448 (T,wt=8): 12718 ->*_s0(s(length(app(nil,nil))),s(0)).  [ur(87,a,1368,a,b,891,a)].

given #1449 (T,wt=9): 1373 ->_s0(tail(length(app(nil,x))),tail(length(x))).  [ur(54,a,132,a)].

given #1450 (A,wt=10): 288 ->_s0(app(head(cons(x,y)),z),app(x,z)).  [ur(35,a,67,a)].

given #1451 (F,wt=10): 12322 -->_s0(true,sndsplit(sndsplit(0,0),x)) | -->_s0(x,false) # answer(goal).  [resolve(11467,b,53,b)].

given #1452 (F,wt=10): 12323 -->_s0(true,sndsplit(x,false)) | -->_s0(x,sndsplit(0,0)) # answer(goal).  [resolve(11467,b,52,b)].

given #1453 (F,wt=8): 12811 -->_s0(true,sndsplit(sndsplit(length(nil),0),false)) # answer(goal).  [resolve(12323,b,321,a)].

given #1454 (F,wt=9): 12810 -->_s0(true,sndsplit(sndsplit(sndsplit(0,0),0),false)) # answer(goal).  [resolve(12323,b,471,a)].

given #1455 (T,wt=8): 12738 ->*_s0(tail(length(app(nil,nil))),tail(0)).  [ur(87,a,1373,a,b,917,a)].

given #1456 (T,wt=8): 12802 ->*_s0(app(head(cons(nil,x)),y),y).  [ur(87,a,288,a,b,581,a)].

given #1457 (T,wt=9): 1386 ->_s0(length(length(app(nil,x))),length(length(x))).  [ur(41,a,132,a)].

given #1458 (T,wt=8): 12850 ->*_s0(length(length(app(nil,nil))),length(0)).  [ur(87,a,1386,a,b,943,a)].

given #1459 (A,wt=10): 289 ->_s0(s(length(cons(x,y))),s(s(length(y)))).  [ur(59,a,68,a)].

given #1460 (F,wt=9): 12813 -->_s0(true,sndsplit(sndsplit(app(nil,0),0),false)) # answer(goal).  [resolve(12323,b,121,a)].

given #1461 (F,wt=10): 12575 -->_s0(true,app(mapf(x,head(cons(nil,y))),false)) # answer(goal).  [resolve(11913,b,278,a)].

given #1462 (F,wt=10): 12576 -->_s0(true,app(mapf(x,fstsplit(s(y),nil)),false)) # answer(goal).  [resolve(11913,b,253,a)].

given #1463 (F,wt=10): 12579 -->_s0(true,app(tail(cons(x,mapf(y,nil))),false)) # answer(goal).  [resolve(11913,b,85,a)].

given #1464 (T,wt=9): 1387 ->_s0(head(length(app(nil,x))),head(length(x))).  [ur(40,a,132,a)].

given #1465 (T,wt=8): 12872 ->*_s0(head(length(app(nil,nil))),head(0)).  [ur(87,a,1387,a,b,969,a)].

given #1466 (T,wt=9): 1390 ->_s0(empty(length(app(nil,x))),empty(length(x))).  [ur(37,a,132,a)].

given #1467 (T,wt=8): 12891 ->*_s0(empty(length(app(nil,nil))),empty(0)).  [ur(87,a,1390,a,b,1031,a)].

given #1468 (A,wt=12): 290 ->_s0(f(x,length(cons(y,z))),f(x,s(length(z)))).  [ur(58,a,68,a)].

given #1469 (F,wt=10): 12580 -->_s0(true,app(head(cons(mapf(x,nil),y)),false)) # answer(goal).  [resolve(11913,b,67,a)].

given #1470 (F,wt=10): 12581 -->_s0(true,app(mapf(x,y),false)) | -->_s0(y,nil) # answer(goal).  [resolve(11913,b,45,b)].

given #1471 (F,wt=10): 12638 -->_s0(true,app(sndsplit(0,nil),x)) | -->_s0(x,false) # answer(goal).  [resolve(11917,b,36,b)].

given #1472 (F,wt=10): 12639 -->_s0(true,app(x,false)) | -->_s0(x,sndsplit(0,nil)) # answer(goal).  [resolve(11917,b,35,b)].

given #1473 (T,wt=9): 1420 ->*_s0(tail(cons(x,length(app(nil,nil)))),0).  [ur(87,a,85,a,b,1366,a)].

given #1474 (T,wt=9): 1422 ->*_s0(head(cons(length(app(nil,nil)),x)),0).  [ur(87,a,67,a,b,1366,a)].

given #1475 (T,wt=9): 1428 ->_s0(s(head(app(nil,x))),s(head(x))).  [ur(59,a,133,a)].

given #1476 (T,wt=9): 1433 ->_s0(tail(head(app(nil,x))),tail(head(x))).  [ur(54,a,133,a)].

given #1477 (A,wt=12): 291 ->_s0(f(length(cons(x,y)),z),f(s(length(y)),z)).  [ur(57,a,68,a)].

given #1478 (F,wt=8): 12911 -->_s0(true,app(sndsplit(length(nil),nil),false)) # answer(goal).  [resolve(12639,b,321,a)].

given #1479 (F,wt=9): 12910 -->_s0(true,app(sndsplit(sndsplit(0,0),nil),false)) # answer(goal).  [resolve(12639,b,471,a)].

given #1480 (F,wt=9): 12913 -->_s0(true,app(sndsplit(app(nil,0),nil),false)) # answer(goal).  [resolve(12639,b,121,a)].

given #1481 (F,wt=10): 12745 -->_s0(true,app(head(cons(sndsplit(0,nil),x)),false)) # answer(goal).  [resolve(288,a,11917,b)].

given #1482 (T,wt=9): 1446 ->_s0(length(head(app(nil,x))),length(head(x))).  [ur(41,a,133,a)].

given #1483 (T,wt=9): 1447 ->_s0(head(head(app(nil,x))),head(head(x))).  [ur(40,a,133,a)].

given #1484 (T,wt=9): 1450 ->_s0(empty(head(app(nil,x))),empty(head(x))).  [ur(37,a,133,a)].

given #1485 (T,wt=9): 1458 ->_s0(s(empty(app(nil,x))),s(empty(x))).  [ur(59,a,136,a)].

given #1486 (A,wt=12): 292 ->_s0(cons(x,length(cons(y,z))),cons(x,s(length(z)))).  [ur(56,a,68,a)].

given #1487 (F,wt=10): 12812 -->_s0(true,sndsplit(sndsplit(head(cons(0,x)),0),false)) # answer(goal).  [resolve(12323,b,271,a)].

given #1488 (F,wt=10): 12814 -->_s0(true,sndsplit(tail(cons(x,sndsplit(0,0))),false)) # answer(goal).  [resolve(12323,b,85,a)].

given #1489 (F,wt=10): 12815 -->_s0(true,sndsplit(sndsplit(s(0),cons(x,0)),false)) # answer(goal).  [resolve(12323,b,83,a)].

given #1490 (F,wt=10): 12816 -->_s0(true,sndsplit(sndsplit(0,x),false)) | -->_s0(x,0) # answer(goal).  [resolve(12323,b,53,b)].

given #1491 (T,wt=8): 12982 ->*_s0(s(empty(app(nil,nil))),s(true)).  [ur(87,a,1458,a,b,699,a)].

given #1492 (T,wt=9): 1463 ->_s0(tail(empty(app(nil,x))),tail(empty(x))).  [ur(54,a,136,a)].

given #1493 (T,wt=8): 13004 ->*_s0(tail(empty(app(nil,nil))),tail(true)).  [ur(87,a,1463,a,b,755,a)].

given #1494 (T,wt=9): 1476 ->_s0(length(empty(app(nil,x))),length(empty(x))).  [ur(41,a,136,a)].

given #1495 (A,wt=12): 293 ->_s0(cons(length(cons(x,y)),z),cons(s(length(y)),z)).  [ur(55,a,68,a)].

given #1496 (F,wt=10): 12817 -->_s0(true,sndsplit(sndsplit(x,0),false)) | -->_s0(x,0) # answer(goal).  [resolve(12323,b,52,b)].

given #1497 (F,wt=10): 12845 -->_s0(true,app(sndsplit(0,head(cons(nil,x))),false)) # answer(goal).  [ur(2781,b,488,a,c,12802,a)].

given #1498 (F,wt=10): 12908 -->_s0(true,app(mapf(x,tail(cons(y,nil))),false)) # answer(goal).  [resolve(12581,b,85,a)].

given #1499 (F,wt=10): 12909 -->_s0(true,app(mapf(x,sndsplit(s(y),nil)),false)) # answer(goal).  [resolve(12581,b,84,a)].

given #1500 (T,wt=8): 13024 ->*_s0(length(empty(app(nil,nil))),length(true)).  [ur(87,a,1476,a,b,781,a)].

given #1501 (T,wt=9): 1477 ->_s0(head(empty(app(nil,x))),head(empty(x))).  [ur(40,a,136,a)].

given #1502 (T,wt=8): 13046 ->*_s0(head(empty(app(nil,nil))),head(true)).  [ur(87,a,1477,a,b,807,a)].

given #1503 (T,wt=9): 1480 ->_s0(empty(empty(app(nil,x))),empty(empty(x))).  [ur(37,a,136,a)].

given #1504 (A,wt=10): 294 ->_s0(tail(length(cons(x,y))),tail(s(length(y)))).  [ur(54,a,68,a)].

given #1505 (F,wt=10): 12912 -->_s0(true,app(sndsplit(head(cons(0,x)),nil),false)) # answer(goal).  [resolve(12639,b,271,a)].

given #1506 (F,wt=10): 12914 -->_s0(true,app(tail(cons(x,sndsplit(0,nil))),false)) # answer(goal).  [resolve(12639,b,85,a)].

given #1507 (F,wt=10): 12915 -->_s0(true,app(sndsplit(s(0),cons(x,nil)),false)) # answer(goal).  [resolve(12639,b,83,a)].

given #1508 (F,wt=10): 12916 -->_s0(true,app(sndsplit(0,x),false)) | -->_s0(x,nil) # answer(goal).  [resolve(12639,b,53,b)].

given #1509 (T,wt=8): 13066 ->*_s0(empty(empty(app(nil,nil))),empty(true)).  [ur(87,a,1480,a,b,833,a)].

given #1510 (T,wt=9): 1486 ->*_s0(tail(cons(x,empty(app(nil,nil)))),true).  [ur(87,a,85,a,b,1456,a)].

given #1511 (T,wt=9): 1488 ->*_s0(head(cons(empty(app(nil,nil)),x)),true).  [ur(87,a,67,a,b,1456,a)].

given #1512 (T,wt=9): 1608 ->_s0(s(s(fstsplit(0,x))),s(s(nil))).  [ur(59,a,189,a)].

given #1513 (A,wt=12): 295 ->_s0(sndsplit(x,length(cons(y,z))),sndsplit(x,s(length(z)))).  [ur(53,a,68,a)].

given #1514 (F,wt=10): 12917 -->_s0(true,app(sndsplit(x,nil),false)) | -->_s0(x,0) # answer(goal).  [resolve(12639,b,52,b)].

given #1515 (F,wt=10): 12990 -->_s0(true,sndsplit(sndsplit(0,tail(cons(x,0))),false)) # answer(goal).  [resolve(12816,b,85,a)].

given #1516 (F,wt=10): 13032 -->_s0(true,sndsplit(sndsplit(tail(cons(x,0)),0),false)) # answer(goal).  [resolve(12817,b,85,a)].

given #1517 (F,wt=10): 13076 -->_s0(true,app(sndsplit(0,tail(cons(x,nil))),false)) # answer(goal).  [resolve(12916,b,85,a)].

given #1518 (T,wt=9): 1613 ->_s0(tail(s(fstsplit(0,x))),tail(s(nil))).  [ur(54,a,189,a)].

given #1519 (T,wt=9): 1626 ->_s0(length(s(fstsplit(0,x))),length(s(nil))).  [ur(41,a,189,a)].

given #1520 (T,wt=9): 1627 ->_s0(head(s(fstsplit(0,x))),head(s(nil))).  [ur(40,a,189,a)].

given #1521 (T,wt=9): 1630 ->_s0(empty(s(fstsplit(0,x))),empty(s(nil))).  [ur(37,a,189,a)].

given #1522 (A,wt=12): 296 ->_s0(sndsplit(length(cons(x,y)),z),sndsplit(s(length(y)),z)).  [ur(52,a,68,a)].

given #1523 (F,wt=10): 13077 -->_s0(true,app(sndsplit(0,sndsplit(s(x),nil)),false)) # answer(goal).  [resolve(12916,b,84,a)].

given #1524 (F,wt=10): 13109 -->_s0(true,app(sndsplit(tail(cons(x,0)),nil),false)) # answer(goal).  [resolve(12917,b,85,a)].

given #1525 (F,wt=11): 3009 -->_s0(true,length(cons(x,y))) | -->*_s0(s(length(y)),false) # answer(goal).  [resolve(2781,b,68,a)].

given #1526 (F,wt=11): 3016 -->_s0(true,s(x)) | -->*_s0(s(y),false) | -->_s0(x,y) # answer(goal).  [resolve(2781,b,59,b)].

given #1527 (T,wt=8): 13143 ->*_s0(sndsplit(length(cons(x,y)),nil),nil).  [ur(87,a,296,a,b,565,a)].

given #1528 (T,wt=9): 1635 ->_s0(s(tail(fstsplit(0,x))),s(tail(nil))).  [ur(59,a,194,a)].

given #1529 (T,wt=9): 1640 ->_s0(tail(tail(fstsplit(0,x))),tail(tail(nil))).  [ur(54,a,194,a)].

given #1530 (T,wt=9): 1653 ->_s0(length(tail(fstsplit(0,x))),length(tail(nil))).  [ur(41,a,194,a)].

given #1531 (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 #1532 (F,wt=11): 3021 -->_s0(true,tail(x)) | -->*_s0(tail(y),false) | -->_s0(x,y) # answer(goal).  [resolve(2781,b,54,b)].

given #1533 (F,wt=9): 13997 -->_s0(true,tail(sndsplit(length(nil),cons(x,false)))) # answer(goal).  [ur(3021,b,2245,a,c,321,a)].

given #1534 (F,wt=10): 13989 -->_s0(true,tail(app(sndsplit(0,cons(x,nil)),false))) # answer(goal).  [ur(3021,b,5956,a,c,488,a)].

given #1535 (F,wt=10): 13990 -->_s0(true,tail(app(cons(x,nil),sndsplit(0,false)))) # answer(goal).  [ur(3021,b,5956,a,c,487,a)].

given #1536 (T,wt=9): 1654 ->_s0(head(tail(fstsplit(0,x))),head(tail(nil))).  [ur(40,a,194,a)].

given #1537 (T,wt=9): 1657 ->_s0(empty(tail(fstsplit(0,x))),empty(tail(nil))).  [ur(37,a,194,a)].

given #1538 (T,wt=9): 1663 ->_s0(s(length(fstsplit(0,x))),s(length(nil))).  [ur(59,a,207,a)].

given #1539 (T,wt=8): 14029 ->*_s0(s(length(fstsplit(0,x))),s(0)).  [ur(87,a,1663,a,b,891,a)].

given #1540 (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 #1541 (F,wt=10): 13994 -->_s0(true,tail(app(app(nil,cons(x,nil)),false))) # answer(goal).  [ur(3021,b,5956,a,c,138,a)].

given #1542 (F,wt=10): 13995 -->_s0(true,tail(app(cons(x,nil),app(nil,false)))) # answer(goal).  [ur(3021,b,5956,a,c,137,a)].

given #1543 (F,wt=10): 13996 -->_s0(true,tail(sndsplit(sndsplit(0,0),cons(x,false)))) # answer(goal).  [ur(3021,b,2245,a,c,471,a)].

given #1544 (F,wt=10): 14000 -->_s0(true,tail(sndsplit(app(nil,0),cons(x,false)))) # answer(goal).  [ur(3021,b,2245,a,c,121,a)].

given #1545 (T,wt=9): 1668 ->_s0(tail(length(fstsplit(0,x))),tail(length(nil))).  [ur(54,a,207,a)].

given #1546 (T,wt=8): 14051 ->*_s0(tail(length(fstsplit(0,x))),tail(0)).  [ur(87,a,1668,a,b,917,a)].

given #1547 (T,wt=9): 1681 ->_s0(length(length(fstsplit(0,x))),length(length(nil))).  [ur(41,a,207,a)].

given #1548 (T,wt=8): 14070 ->*_s0(length(length(fstsplit(0,x))),length(0)).  [ur(87,a,1681,a,b,943,a)].

given #1549 (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 #1550 (F,wt=10): 14002 -->_s0(true,tail(app(sndsplit(0,nil),cons(x,false)))) # answer(goal).  [ur(3021,b,1337,a,c,488,a)].

given #1551 (F,wt=10): 14003 -->_s0(true,tail(app(mapf(x,nil),cons(y,false)))) # answer(goal).  [ur(3021,b,1337,a,c,463,a)].

given #1552 (F,wt=10): 14007 -->_s0(true,tail(app(fstsplit(0,x),cons(y,false)))) # answer(goal).  [ur(3021,b,1337,a,c,213,a)].

given #1553 (F,wt=10): 14008 -->_s0(true,tail(app(app(nil,nil),cons(x,false)))) # answer(goal).  [ur(3021,b,1337,a,c,138,a)].

given #1554 (T,wt=9): 1682 ->_s0(head(length(fstsplit(0,x))),head(length(nil))).  [ur(40,a,207,a)].

given #1555 (T,wt=8): 14092 ->*_s0(head(length(fstsplit(0,x))),head(0)).  [ur(87,a,1682,a,b,969,a)].

given #1556 (T,wt=9): 1685 ->_s0(empty(length(fstsplit(0,x))),empty(length(nil))).  [ur(37,a,207,a)].

given #1557 (T,wt=8): 14111 ->*_s0(empty(length(fstsplit(0,x))),empty(0)).  [ur(87,a,1685,a,b,1031,a)].

given #1558 (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 #1559 (F,wt=11): 3034 -->_s0(true,length(x)) | -->*_s0(length(y),false) | -->_s0(x,y) # answer(goal).  [resolve(2781,b,41,b)].

given #1560 (F,wt=11): 3035 -->_s0(true,head(x)) | -->*_s0(head(y),false) | -->_s0(x,y) # answer(goal).  [resolve(2781,b,40,b)].

given #1561 (F,wt=9): 14968 -->_s0(true,head(sndsplit(length(nil),cons(false,x)))) # answer(goal).  [ur(3035,b,2314,a,c,321,a)].

given #1562 (F,wt=10): 14962 -->_s0(true,head(app(sndsplit(0,cons(false,x)),y))) # answer(goal).  [ur(3035,b,2538,a,c,488,a)].

given #1563 (T,wt=9): 1689 ->*_s0(tail(cons(x,length(fstsplit(0,y)))),0).  [ur(87,a,85,a,b,1661,a)].

given #1564 (T,wt=9): 1691 ->*_s0(head(cons(length(fstsplit(0,x)),y)),0).  [ur(87,a,67,a,b,1661,a)].

given #1565 (T,wt=9): 1724 ->_s0(s(head(fstsplit(0,x))),s(head(nil))).  [ur(59,a,208,a)].

given #1566 (T,wt=9): 1729 ->_s0(tail(head(fstsplit(0,x))),tail(head(nil))).  [ur(54,a,208,a)].

given #1567 (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 #1568 (F,wt=10): 14965 -->_s0(true,head(app(app(nil,cons(false,x)),y))) # answer(goal).  [ur(3035,b,2538,a,c,138,a)].

given #1569 (F,wt=10): 14966 -->_s0(true,head(app(app(cons(false,x),y),z))) # answer(goal).  [ur(3035,b,2538,a,c,113,a)].

given #1570 (F,wt=10): 14967 -->_s0(true,head(sndsplit(sndsplit(0,0),cons(false,x)))) # answer(goal).  [ur(3035,b,2314,a,c,471,a)].

given #1571 (F,wt=10): 14972 -->_s0(true,head(sndsplit(app(nil,0),cons(false,x)))) # answer(goal).  [ur(3035,b,2314,a,c,121,a)].

given #1572 (T,wt=9): 1742 ->_s0(length(head(fstsplit(0,x))),length(head(nil))).  [ur(41,a,208,a)].

given #1573 (T,wt=9): 1743 ->_s0(head(head(fstsplit(0,x))),head(head(nil))).  [ur(40,a,208,a)].

given #1574 (T,wt=9): 1746 ->_s0(empty(head(fstsplit(0,x))),empty(head(nil))).  [ur(37,a,208,a)].

given #1575 (T,wt=9): 1752 ->_s0(s(empty(fstsplit(0,x))),s(empty(nil))).  [ur(59,a,211,a)].

given #1576 (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 #1577 (F,wt=10): 14974 -->_s0(true,head(app(sndsplit(0,nil),cons(false,x)))) # answer(goal).  [ur(3035,b,1426,a,c,488,a)].

given #1578 (F,wt=10): 14975 -->_s0(true,head(app(mapf(x,nil),cons(false,y)))) # answer(goal).  [ur(3035,b,1426,a,c,463,a)].

given #1579 (F,wt=10): 14980 -->_s0(true,head(app(fstsplit(0,x),cons(false,y)))) # answer(goal).  [ur(3035,b,1426,a,c,213,a)].

given #1580 (F,wt=10): 14981 -->_s0(true,head(app(app(nil,nil),cons(false,x)))) # answer(goal).  [ur(3035,b,1426,a,c,138,a)].

given #1581 (T,wt=8): 15049 ->*_s0(s(empty(fstsplit(0,x))),s(true)).  [ur(87,a,1752,a,b,699,a)].

given #1582 (T,wt=9): 1757 ->_s0(tail(empty(fstsplit(0,x))),tail(empty(nil))).  [ur(54,a,211,a)].

given #1583 (T,wt=8): 15074 ->*_s0(tail(empty(fstsplit(0,x))),tail(true)).  [ur(87,a,1757,a,b,755,a)].

given #1584 (T,wt=9): 1770 ->_s0(length(empty(fstsplit(0,x))),length(empty(nil))).  [ur(41,a,211,a)].

given #1585 (A,wt=12): 303 ->_s0(mapf(x,length(cons(y,z))),mapf(x,s(length(z)))).  [ur(45,a,68,a)].

given #1586 (F,wt=11): 3038 -->_s0(true,empty(x)) | -->*_s0(empty(y),false) | -->_s0(x,y) # answer(goal).  [resolve(2781,b,37,b)].

given #1587 (F,wt=9): 15507 -->_s0(true,empty(sndsplit(length(nil),cons(x,y)))) # answer(goal).  [ur(3038,b,2389,a,c,321,a)].

given #1588 (F,wt=10): 15446 -->_s0(true,empty(app(app(cons(x,y),z),u))) # answer(goal).  [resolve(3038,c,113,a),unit_del(b,2754)].

given #1589 (F,wt=10): 15503 -->_s0(true,empty(app(sndsplit(0,cons(x,y)),z))) # answer(goal).  [ur(3038,b,2754,a,c,488,a)].

given #1590 (T,wt=8): 15094 ->*_s0(length(empty(fstsplit(0,x))),length(true)).  [ur(87,a,1770,a,b,781,a)].

given #1591 (T,wt=9): 1771 ->_s0(head(empty(fstsplit(0,x))),head(empty(nil))).  [ur(40,a,211,a)].

given #1592 (T,wt=8): 15535 ->*_s0(head(empty(fstsplit(0,x))),head(true)).  [ur(87,a,1771,a,b,807,a)].

given #1593 (T,wt=9): 1774 ->_s0(empty(empty(fstsplit(0,x))),empty(empty(nil))).  [ur(37,a,211,a)].

given #1594 (A,wt=12): 304 ->_s0(mapf(length(cons(x,y)),z),mapf(s(length(y)),z)).  [ur(44,a,68,a)].

given #1595 (F,wt=10): 15505 -->_s0(true,empty(app(app(nil,cons(x,y)),z))) # answer(goal).  [ur(3038,b,2754,a,c,138,a)].

given #1596 (F,wt=10): 15506 -->_s0(true,empty(sndsplit(sndsplit(0,0),cons(x,y)))) # answer(goal).  [ur(3038,b,2389,a,c,471,a)].

given #1597 (F,wt=10): 15511 -->_s0(true,empty(sndsplit(app(nil,0),cons(x,y)))) # answer(goal).  [ur(3038,b,2389,a,c,121,a)].

given #1598 (F,wt=10): 15513 -->_s0(true,empty(app(sndsplit(0,nil),cons(x,y)))) # answer(goal).  [ur(3038,b,1455,a,c,488,a)].

given #1599 (T,wt=8): 15556 ->*_s0(empty(empty(fstsplit(0,x))),empty(true)).  [ur(87,a,1774,a,b,833,a)].

given #1600 (T,wt=9): 1780 ->*_s0(tail(cons(x,empty(fstsplit(0,y)))),true).  [ur(87,a,85,a,b,1750,a)].

given #1601 (T,wt=9): 1782 ->*_s0(head(cons(empty(fstsplit(0,x)),y)),true).  [ur(87,a,67,a,b,1750,a)].

given #1602 (T,wt=9): 1786 ->_s0(s(s(leq(0,x))),s(s(true))).  [ur(59,a,339,a)].

given #1603 (A,wt=12): 305 ->_s0(leq(x,length(cons(y,z))),leq(x,s(length(z)))).  [ur(43,a,68,a)].

given #1604 (F,wt=10): 15514 -->_s0(true,empty(app(mapf(x,nil),cons(y,z)))) # answer(goal).  [ur(3038,b,1455,a,c,463,a)].

given #1605 (F,wt=10): 15519 -->_s0(true,empty(app(fstsplit(0,x),cons(y,z)))) # answer(goal).  [ur(3038,b,1455,a,c,213,a)].

given #1606 (F,wt=10): 15520 -->_s0(true,empty(app(app(nil,nil),cons(x,y)))) # answer(goal).  [ur(3038,b,1455,a,c,138,a)].

given #1607 (F,wt=11): 3152 -->_s0(true,sndsplit(0,x)) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal).  [resolve(2997,b,87,c)].

given #1608 (T,wt=9): 1791 ->_s0(tail(s(leq(0,x))),tail(s(true))).  [ur(54,a,339,a)].

given #1609 (T,wt=9): 1804 ->_s0(length(s(leq(0,x))),length(s(true))).  [ur(41,a,339,a)].

given #1610 (T,wt=9): 1805 ->_s0(head(s(leq(0,x))),head(s(true))).  [ur(40,a,339,a)].

given #1611 (T,wt=9): 1808 ->_s0(empty(s(leq(0,x))),empty(s(true))).  [ur(37,a,339,a)].

given #1612 (A,wt=12): 306 ->_s0(leq(length(cons(x,y)),z),leq(s(length(y)),z)).  [ur(42,a,68,a)].

given #1613 (F,wt=9): 16033 -->_s0(true,sndsplit(0,length(nil))) | -->*_s0(0,false) # answer(goal).  [resolve(3152,b,69,a)].

given #1614 (F,wt=10): 16022 -->_s0(true,sndsplit(0,sndsplit(0,x))) | -->*_s0(x,false) # answer(goal).  [resolve(3152,b,82,a)].

given #1615 (F,wt=10): 16030 -->_s0(true,sndsplit(0,mapf(x,nil))) | -->*_s0(nil,false) # answer(goal).  [resolve(3152,b,74,a)].

given #1616 (F,wt=10): 16038 -->_s0(true,sndsplit(0,fstsplit(0,x))) | -->*_s0(nil,false) # answer(goal).  [resolve(3152,b,64,a)].

given #1617 (T,wt=8): 16693 ->*_s0(leq(length(cons(x,y)),0),false).  [ur(87,a,306,a,b,571,a)].

given #1618 (T,wt=9): 1849 ->_s0(s(tail(leq(0,x))),s(tail(true))).  [ur(59,a,344,a)].

given #1619 (T,wt=9): 1854 ->_s0(tail(tail(leq(0,x))),tail(tail(true))).  [ur(54,a,344,a)].

given #1620 (T,wt=9): 1867 ->_s0(length(tail(leq(0,x))),length(tail(true))).  [ur(41,a,344,a)].

given #1621 (A,wt=10): 307 ->_s0(length(length(cons(x,y))),length(s(length(y)))).  [ur(41,a,68,a)].

given #1622 (F,wt=10): 16039 -->_s0(true,sndsplit(0,app(nil,x))) | -->*_s0(x,false) # answer(goal).  [resolve(3152,b,61,a)].

given #1623 (F,wt=10): 16697 -->_s0(true,sndsplit(0,leq(length(cons(x,y)),0))) # answer(goal).  [ur(3152,b,306,a,c,571,a)].

given #1624 (F,wt=10): 16698 -->_s0(true,leq(length(cons(x,y)),sndsplit(0,0))) # answer(goal).  [ur(2781,b,306,a,c,11647,a)].

given #1625 (F,wt=10): 16699 -->_s0(true,leq(length(cons(x,y)),app(nil,0))) # answer(goal).  [ur(2781,b,306,a,c,4699,a)].

given #1626 (T,wt=9): 1868 ->_s0(head(tail(leq(0,x))),head(tail(true))).  [ur(40,a,344,a)].

given #1627 (T,wt=9): 1871 ->_s0(empty(tail(leq(0,x))),empty(tail(true))).  [ur(37,a,344,a)].

given #1628 (T,wt=9): 1876 ->_s0(s(length(leq(0,x))),s(length(true))).  [ur(59,a,357,a)].

given #1629 (T,wt=9): 1881 ->_s0(tail(length(leq(0,x))),tail(length(true))).  [ur(54,a,357,a)].

given #1630 (A,wt=10): 308 ->_s0(head(length(cons(x,y))),head(s(length(y)))).  [ur(40,a,68,a)].

given #1631 (F,wt=10): 16707 -->_s0(true,app(nil,leq(length(cons(x,y)),0))) # answer(goal).  [resolve(16693,a,3014,b)].

given #1632 (F,wt=10): 16732 -->_s0(true,leq(sndsplit(0,length(cons(x,y))),0)) # answer(goal).  [ur(2781,b,481,a,c,16693,a)].

given #1633 (F,wt=10): 16735 -->_s0(true,leq(app(nil,length(cons(x,y))),0)) # answer(goal).  [ur(2781,b,131,a,c,16693,a)].

given #1634 (F,wt=10): 16736 -->_s0(true,leq(s(length(cons(x,y))),s(0))) # answer(goal).  [ur(2781,b,72,a,c,16693,a)].

given #1635 (T,wt=9): 1894 ->_s0(length(length(leq(0,x))),length(length(true))).  [ur(41,a,357,a)].

given #1636 (T,wt=9): 1895 ->_s0(head(length(leq(0,x))),head(length(true))).  [ur(40,a,357,a)].

given #1637 (T,wt=9): 1898 ->_s0(empty(length(leq(0,x))),empty(length(true))).  [ur(37,a,357,a)].

given #1638 (T,wt=9): 1903 ->_s0(s(head(leq(0,x))),s(head(true))).  [ur(59,a,358,a)].

given #1639 (A,wt=12): 309 ->_s0(fstsplit(x,length(cons(y,z))),fstsplit(x,s(length(z)))).  [ur(39,a,68,a)].

given #1640 (F,wt=11): 3153 -->_s0(true,mapf(x,nil)) | -->_s0(nil,y) | -->*_s0(y,false) # answer(goal).  [resolve(3005,b,87,c)].

given #1641 (F,wt=8): 16957 -->_s0(true,mapf(x,nil)) | -->_s0(nil,false) # answer(goal).  [resolve(3153,c,86,a)].

given #1642 (F,wt=10): 16950 -->_s0(true,mapf(x,nil)) | -->_s0(nil,app(nil,false)) # answer(goal).  [resolve(3153,c,581,a)].

given #1643 (F,wt=10): 16954 -->_s0(true,mapf(x,nil)) | -->_s0(nil,sndsplit(0,false)) # answer(goal).  [resolve(3153,c,567,a)].

given #1644 (T,wt=9): 1908 ->_s0(tail(head(leq(0,x))),tail(head(true))).  [ur(54,a,358,a)].

given #1645 (T,wt=9): 1921 ->_s0(length(head(leq(0,x))),length(head(true))).  [ur(41,a,358,a)].

given #1646 (T,wt=9): 1922 ->_s0(head(head(leq(0,x))),head(head(true))).  [ur(40,a,358,a)].

given #1647 (T,wt=9): 1925 ->_s0(empty(head(leq(0,x))),empty(head(true))).  [ur(37,a,358,a)].

given #1648 (A,wt=12): 310 ->_s0(fstsplit(length(cons(x,y)),z),fstsplit(s(length(y)),z)).  [ur(38,a,68,a)].

given #1649 (F,wt=11): 3154 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,y) | -->*_s0(y,false) # answer(goal).  [resolve(3013,b,87,c)].

given #1650 (F,wt=8): 17082 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,false) # answer(goal).  [resolve(3154,c,86,a)].

given #1651 (F,wt=10): 17075 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,app(nil,false)) # answer(goal).  [resolve(3154,c,581,a)].

given #1652 (F,wt=10): 17079 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,sndsplit(0,false)) # answer(goal).  [resolve(3154,c,567,a)].

given #1653 (T,wt=8): 17017 ->*_s0(fstsplit(length(cons(x,y)),nil),nil).  [ur(87,a,310,a,b,576,a)].

given #1654 (T,wt=9): 1930 ->_s0(s(empty(leq(0,x))),s(empty(true))).  [ur(59,a,361,a)].

given #1655 (T,wt=9): 1935 ->_s0(tail(empty(leq(0,x))),tail(empty(true))).  [ur(54,a,361,a)].

given #1656 (T,wt=9): 1948 ->_s0(length(empty(leq(0,x))),length(empty(true))).  [ur(41,a,361,a)].

given #1657 (A,wt=10): 311 ->_s0(empty(length(cons(x,y))),empty(s(length(y)))).  [ur(37,a,68,a)].

given #1658 (F,wt=11): 3155 -->_s0(true,app(nil,x)) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal).  [resolve(3014,b,87,c)].

given #1659 (F,wt=9): 17586 -->_s0(true,app(nil,length(nil))) | -->*_s0(0,false) # answer(goal).  [resolve(3155,b,69,a)].

given #1660 (F,wt=10): 17575 -->_s0(true,app(nil,sndsplit(0,x))) | -->*_s0(x,false) # answer(goal).  [resolve(3155,b,82,a)].

given #1661 (F,wt=10): 17583 -->_s0(true,app(nil,mapf(x,nil))) | -->*_s0(nil,false) # answer(goal).  [resolve(3155,b,74,a)].

given #1662 (T,wt=9): 1949 ->_s0(head(empty(leq(0,x))),head(empty(true))).  [ur(40,a,361,a)].

given #1663 (T,wt=9): 1952 ->_s0(empty(empty(leq(0,x))),empty(empty(true))).  [ur(37,a,361,a)].

given #1664 (T,wt=9): 1993 ->_s0(s(s(mapf(x,nil))),s(s(nil))).  [ur(59,a,439,a)].

given #1665 (T,wt=9): 1998 ->_s0(tail(s(mapf(x,nil))),tail(s(nil))).  [ur(54,a,439,a)].

given #1666 (A,wt=12): 312 ->_s0(app(x,length(cons(y,z))),app(x,s(length(z)))).  [ur(36,a,68,a)].

given #1667 (F,wt=10): 17591 -->_s0(true,app(nil,fstsplit(0,x))) | -->*_s0(nil,false) # answer(goal).  [resolve(3155,b,64,a)].

given #1668 (F,wt=10): 17592 -->_s0(true,app(nil,app(nil,x))) | -->*_s0(x,false) # answer(goal).  [resolve(3155,b,61,a)].

given #1669 (F,wt=11): 3229 -->_s0(true,s(empty(cons(x,y)))) | -->*_s0(s(false),false) # answer(goal).  [resolve(139,a,2781,b)].

given #1670 (F,wt=11): 3283 -->_s0(true,tail(empty(cons(x,y)))) | -->*_s0(tail(false),false) # answer(goal).  [resolve(144,a,2781,b)].

given #1671 (T,wt=9): 2011 ->_s0(length(s(mapf(x,nil))),length(s(nil))).  [ur(41,a,439,a)].

given #1672 (T,wt=9): 2012 ->_s0(head(s(mapf(x,nil))),head(s(nil))).  [ur(40,a,439,a)].

given #1673 (T,wt=9): 2015 ->_s0(empty(s(mapf(x,nil))),empty(s(nil))).  [ur(37,a,439,a)].

given #1674 (T,wt=9): 2020 ->_s0(s(tail(mapf(x,nil))),s(tail(nil))).  [ur(59,a,444,a)].

given #1675 (A,wt=12): 313 ->_s0(app(length(cons(x,y)),z),app(s(length(y)),z)).  [ur(35,a,68,a)].

given #1676 (F,wt=11): 3310 -->_s0(true,length(empty(cons(x,y)))) | -->*_s0(length(false),false) # answer(goal).  [resolve(157,a,2781,b)].

given #1677 (F,wt=11): 3337 -->_s0(true,head(empty(cons(x,y)))) | -->*_s0(head(false),false) # answer(goal).  [resolve(158,a,2781,b)].

given #1678 (F,wt=11): 3364 -->_s0(true,empty(empty(cons(x,y)))) | -->*_s0(empty(false),false) # answer(goal).  [resolve(161,a,2781,b)].

given #1679 (F,wt=11): 3419 -->_s0(true,f(x,empty(nil))) | -->*_s0(f(x,true),false) # answer(goal).  [resolve(165,a,2781,b)].

given #1680 (T,wt=9): 2025 ->_s0(tail(tail(mapf(x,nil))),tail(tail(nil))).  [ur(54,a,444,a)].

given #1681 (T,wt=9): 2038 ->_s0(length(tail(mapf(x,nil))),length(tail(nil))).  [ur(41,a,444,a)].

given #1682 (T,wt=9): 2039 ->_s0(head(tail(mapf(x,nil))),head(tail(nil))).  [ur(40,a,444,a)].

given #1683 (T,wt=9): 2042 ->_s0(empty(tail(mapf(x,nil))),empty(tail(nil))).  [ur(37,a,444,a)].

given #1684 (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 #1685 (F,wt=11): 3446 -->_s0(true,f(empty(nil),x)) | -->*_s0(f(true,x),false) # answer(goal).  [resolve(166,a,2781,b)].

given #1686 (F,wt=11): 3473 -->_s0(true,cons(x,empty(nil))) | -->*_s0(cons(x,true),false) # answer(goal).  [resolve(167,a,2781,b)].

given #1687 (F,wt=11): 3500 -->_s0(true,cons(empty(nil),x)) | -->*_s0(cons(true,x),false) # answer(goal).  [resolve(168,a,2781,b)].

given #1688 (F,wt=11): 3587 -->_s0(true,sndsplit(x,empty(nil))) | -->*_s0(sndsplit(x,true),false) # answer(goal).  [resolve(170,a,2781,b)].

given #1689 (T,wt=9): 2048 ->_s0(s(length(mapf(x,nil))),s(length(nil))).  [ur(59,a,457,a)].

given #1690 (T,wt=8): 18401 ->*_s0(s(length(mapf(x,nil))),s(0)).  [ur(87,a,2048,a,b,891,a)].

given #1691 (T,wt=9): 2053 ->_s0(tail(length(mapf(x,nil))),tail(length(nil))).  [ur(54,a,457,a)].

given #1692 (T,wt=8): 18425 ->*_s0(tail(length(mapf(x,nil))),tail(0)).  [ur(87,a,2053,a,b,917,a)].

given #1693 (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 #1694 (F,wt=11): 3614 -->_s0(true,sndsplit(empty(nil),x)) | -->*_s0(sndsplit(true,x),false) # answer(goal).  [resolve(171,a,2781,b)].

given #1695 (F,wt=11): 3641 -->_s0(true,mapf(x,empty(nil))) | -->*_s0(mapf(x,true),false) # answer(goal).  [resolve(178,a,2781,b)].

given #1696 (F,wt=11): 3695 -->_s0(true,mapf(empty(nil),x)) | -->*_s0(mapf(true,x),false) # answer(goal).  [resolve(179,a,2781,b)].

given #1697 (F,wt=11): 3722 -->_s0(true,leq(x,empty(nil))) | -->*_s0(leq(x,true),false) # answer(goal).  [resolve(180,a,2781,b)].

given #1698 (T,wt=9): 2066 ->_s0(length(length(mapf(x,nil))),length(length(nil))).  [ur(41,a,457,a)].

given #1699 (T,wt=8): 18460 ->*_s0(length(length(mapf(x,nil))),length(0)).  [ur(87,a,2066,a,b,943,a)].

given #1700 (T,wt=9): 2067 ->_s0(head(length(mapf(x,nil))),head(length(nil))).  [ur(40,a,457,a)].

given #1701 (T,wt=8): 18483 ->*_s0(head(length(mapf(x,nil))),head(0)).  [ur(87,a,2067,a,b,969,a)].

given #1702 (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 #1703 (F,wt=11): 3749 -->_s0(true,leq(empty(nil),x)) | -->*_s0(leq(true,x),false) # answer(goal).  [resolve(181,a,2781,b)].

given #1704 (F,wt=11): 3777 -->_s0(true,fstsplit(x,empty(nil))) | -->*_s0(fstsplit(x,true),false) # answer(goal).  [resolve(184,a,2781,b)].

given #1705 (F,wt=11): 3831 -->_s0(true,fstsplit(empty(nil),x)) | -->*_s0(fstsplit(true,x),false) # answer(goal).  [resolve(185,a,2781,b)].

given #1706 (F,wt=11): 3858 -->_s0(true,app(x,empty(nil))) | -->*_s0(app(x,true),false) # answer(goal).  [resolve(187,a,2781,b)].

given #1707 (T,wt=9): 2070 ->_s0(empty(length(mapf(x,nil))),empty(length(nil))).  [ur(37,a,457,a)].

Low Water (keep): wt=11.000, iters=6666

given #1708 (T,wt=8): 18518 ->*_s0(empty(length(mapf(x,nil))),empty(0)).  [ur(87,a,2070,a,b,1031,a)].

given #1709 (T,wt=9): 2074 ->*_s0(tail(cons(x,length(mapf(y,nil)))),0).  [ur(87,a,85,a,b,2046,a)].

given #1710 (T,wt=9): 2076 ->*_s0(head(cons(length(mapf(x,nil)),y)),0).  [ur(87,a,67,a,b,2046,a)].

given #1711 (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 #1712 (F,wt=11): 3885 -->_s0(true,app(empty(nil),x)) | -->*_s0(app(true,x),false) # answer(goal).  [resolve(188,a,2781,b)].

given #1713 (F,wt=11): 3912 -->_s0(true,s(fstsplit(s(x),nil))) | -->*_s0(s(nil),false) # answer(goal).  [resolve(239,a,2781,b)].

given #1714 (F,wt=11): 3974 -->_s0(true,tail(fstsplit(s(x),nil))) | -->*_s0(tail(nil),false) # answer(goal).  [resolve(244,a,2781,b)].

given #1715 (F,wt=11): 4001 -->_s0(true,length(fstsplit(s(x),nil))) | -->*_s0(length(nil),false) # answer(goal).  [resolve(257,a,2781,b)].

given #1716 (T,wt=9): 2122 ->_s0(s(head(mapf(x,nil))),s(head(nil))).  [ur(59,a,458,a)].

given #1717 (T,wt=9): 2127 ->_s0(tail(head(mapf(x,nil))),tail(head(nil))).  [ur(54,a,458,a)].

given #1718 (T,wt=9): 2140 ->_s0(length(head(mapf(x,nil))),length(head(nil))).  [ur(41,a,458,a)].

given #1719 (T,wt=9): 2141 ->_s0(head(head(mapf(x,nil))),head(head(nil))).  [ur(40,a,458,a)].

given #1720 (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 #1721 (F,wt=11): 4035 -->_s0(true,head(fstsplit(s(x),nil))) | -->*_s0(head(nil),false) # answer(goal).  [resolve(258,a,2781,b)].

given #1722 (F,wt=11): 4093 -->_s0(true,empty(fstsplit(s(x),nil))) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(261,a,2781,b)].

given #1723 (F,wt=11): 4130 -->_s0(true,s(head(cons(x,y)))) | -->*_s0(s(x),false) # answer(goal).  [resolve(264,a,2781,b)].

given #1724 (F,wt=11): 4164 -->_s0(true,tail(head(cons(x,y)))) | -->*_s0(tail(x),false) # answer(goal).  [resolve(269,a,2781,b)].

given #1725 (T,wt=9): 2144 ->_s0(empty(head(mapf(x,nil))),empty(head(nil))).  [ur(37,a,458,a)].

given #1726 (T,wt=9): 2149 ->_s0(s(empty(mapf(x,nil))),s(empty(nil))).  [ur(59,a,461,a)].

given #1727 (T,wt=8): 18596 ->*_s0(s(empty(mapf(x,nil))),s(true)).  [ur(87,a,2149,a,b,699,a)].

given #1728 (T,wt=9): 2154 ->_s0(tail(empty(mapf(x,nil))),tail(empty(nil))).  [ur(54,a,461,a)].

given #1729 (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 #1730 (F,wt=11): 4229 -->_s0(true,length(head(cons(x,y)))) | -->*_s0(length(x),false) # answer(goal).  [resolve(282,a,2781,b)].

given #1731 (F,wt=11): 4277 -->_s0(true,head(head(cons(x,y)))) | -->*_s0(head(x),false) # answer(goal).  [resolve(283,a,2781,b)].

given #1732 (F,wt=11): 4315 -->_s0(true,empty(head(cons(x,y)))) | -->*_s0(empty(x),false) # answer(goal).  [resolve(286,a,2781,b)].

given #1733 (F,wt=11): 4394 -->_s0(true,f(x,length(nil))) | -->*_s0(f(x,0),false) # answer(goal).  [resolve(315,a,2781,b)].

given #1734 (T,wt=8): 18610 ->*_s0(tail(empty(mapf(x,nil))),tail(true)).  [ur(87,a,2154,a,b,755,a)].

given #1735 (T,wt=9): 2167 ->_s0(length(empty(mapf(x,nil))),length(empty(nil))).  [ur(41,a,461,a)].

given #1736 (T,wt=8): 18636 ->*_s0(length(empty(mapf(x,nil))),length(true)).  [ur(87,a,2167,a,b,781,a)].

given #1737 (T,wt=9): 2168 ->_s0(head(empty(mapf(x,nil))),head(empty(nil))).  [ur(40,a,461,a)].

given #1738 (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 #1739 (F,wt=11): 4421 -->_s0(true,f(length(nil),x)) | -->*_s0(f(0,x),false) # answer(goal).  [resolve(316,a,2781,b)].

given #1740 (F,wt=11): 4448 -->_s0(true,cons(x,length(nil))) | -->*_s0(cons(x,0),false) # answer(goal).  [resolve(317,a,2781,b)].

given #1741 (F,wt=11): 4512 -->_s0(true,cons(length(nil),x)) | -->*_s0(cons(0,x),false) # answer(goal).  [resolve(318,a,2781,b)].

given #1742 (F,wt=11): 4539 -->_s0(true,sndsplit(x,length(nil))) | -->*_s0(sndsplit(x,0),false) # answer(goal).  [resolve(320,a,2781,b)].

given #1743 (T,wt=8): 18650 ->*_s0(head(empty(mapf(x,nil))),head(true)).  [ur(87,a,2168,a,b,807,a)].

given #1744 (T,wt=9): 2171 ->_s0(empty(empty(mapf(x,nil))),empty(empty(nil))).  [ur(37,a,461,a)].

given #1745 (T,wt=8): 18676 ->*_s0(empty(empty(mapf(x,nil))),empty(true)).  [ur(87,a,2171,a,b,833,a)].

given #1746 (T,wt=9): 2178 ->*_s0(tail(cons(x,empty(mapf(y,nil)))),true).  [ur(87,a,85,a,b,2147,a)].

given #1747 (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 #1748 (F,wt=11): 4566 -->_s0(true,sndsplit(length(nil),x)) | -->*_s0(sndsplit(0,x),false) # answer(goal).  [resolve(321,a,2781,b)].

given #1749 (F,wt=11): 4670 -->_s0(true,mapf(x,length(nil))) | -->*_s0(mapf(x,0),false) # answer(goal).  [resolve(328,a,2781,b)].

given #1750 (F,wt=11): 4727 -->_s0(true,mapf(length(nil),x)) | -->*_s0(mapf(0,x),false) # answer(goal).  [resolve(329,a,2781,b)].

given #1751 (F,wt=11): 4754 -->_s0(true,leq(x,length(nil))) | -->*_s0(leq(x,0),false) # answer(goal).  [resolve(330,a,2781,b)].

given #1752 (T,wt=9): 2180 ->*_s0(head(cons(empty(mapf(x,nil)),y)),true).  [ur(87,a,67,a,b,2147,a)].

given #1753 (T,wt=9): 2186 ->_s0(s(s(sndsplit(0,x))),s(s(x))).  [ur(59,a,464,a)].

given #1754 (T,wt=9): 2191 ->_s0(tail(s(sndsplit(0,x))),tail(s(x))).  [ur(54,a,464,a)].

given #1755 (T,wt=9): 2204 ->_s0(length(s(sndsplit(0,x))),length(s(x))).  [ur(41,a,464,a)].

given #1756 (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 #1757 (F,wt=11): 4801 -->_s0(true,leq(length(nil),x)) | -->*_s0(leq(0,x),false) # answer(goal).  [resolve(331,a,2781,b)].

given #1758 (F,wt=11): 4885 -->_s0(true,fstsplit(x,length(nil))) | -->*_s0(fstsplit(x,0),false) # answer(goal).  [resolve(334,a,2781,b)].

given #1759 (F,wt=11): 4912 -->_s0(true,fstsplit(length(nil),x)) | -->*_s0(fstsplit(0,x),false) # answer(goal).  [resolve(335,a,2781,b)].

given #1760 (F,wt=11): 4976 -->_s0(true,app(x,length(nil))) | -->*_s0(app(x,0),false) # answer(goal).  [resolve(337,a,2781,b)].

given #1761 (T,wt=9): 2205 ->_s0(head(s(sndsplit(0,x))),head(s(x))).  [ur(40,a,464,a)].

given #1762 (T,wt=9): 2208 ->_s0(empty(s(sndsplit(0,x))),empty(s(x))).  [ur(37,a,464,a)].

given #1763 (T,wt=9): 2247 ->_s0(s(tail(sndsplit(0,x))),s(tail(x))).  [ur(59,a,469,a)].

given #1764 (T,wt=9): 2252 ->_s0(tail(tail(sndsplit(0,x))),tail(tail(x))).  [ur(54,a,469,a)].

given #1765 (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 #1766 (F,wt=11): 5003 -->_s0(true,app(length(nil),x)) | -->*_s0(app(0,x),false) # answer(goal).  [resolve(338,a,2781,b)].

given #1767 (F,wt=11): 5030 -->_s0(true,s(leq(s(x),0))) | -->*_s0(s(false),false) # answer(goal).  [resolve(364,a,2781,b)].

given #1768 (F,wt=11): 5096 -->_s0(true,tail(leq(s(x),0))) | -->*_s0(tail(false),false) # answer(goal).  [resolve(369,a,2781,b)].

given #1769 (F,wt=11): 5123 -->_s0(true,length(leq(s(x),0))) | -->*_s0(length(false),false) # answer(goal).  [resolve(382,a,2781,b)].

given #1770 (T,wt=9): 2265 ->_s0(length(tail(sndsplit(0,x))),length(tail(x))).  [ur(41,a,469,a)].

given #1771 (T,wt=9): 2266 ->_s0(head(tail(sndsplit(0,x))),head(tail(x))).  [ur(40,a,469,a)].

given #1772 (T,wt=9): 2269 ->_s0(empty(tail(sndsplit(0,x))),empty(tail(x))).  [ur(37,a,469,a)].

given #1773 (T,wt=9): 2280 ->_s0(s(length(sndsplit(0,x))),s(length(x))).  [ur(59,a,482,a)].

given #1774 (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 #1775 (F,wt=11): 5150 -->_s0(true,head(leq(s(x),0))) | -->*_s0(head(false),false) # answer(goal).  [resolve(383,a,2781,b)].

given #1776 (F,wt=11): 5207 -->_s0(true,empty(leq(s(x),0))) | -->*_s0(empty(false),false) # answer(goal).  [resolve(386,a,2781,b)].

given #1777 (F,wt=11): 5234 -->_s0(true,s(sndsplit(s(x),nil))) | -->*_s0(s(nil),false) # answer(goal).  [resolve(514,a,2781,b)].

given #1778 (F,wt=11): 5261 -->_s0(true,tail(sndsplit(s(x),nil))) | -->*_s0(tail(nil),false) # answer(goal).  [resolve(519,a,2781,b)].

given #1779 (T,wt=8): 18842 ->*_s0(s(length(sndsplit(0,nil))),s(0)).  [ur(87,a,2280,a,b,891,a)].

given #1780 (T,wt=9): 2285 ->_s0(tail(length(sndsplit(0,x))),tail(length(x))).  [ur(54,a,482,a)].

given #1781 (T,wt=8): 18875 ->*_s0(tail(length(sndsplit(0,nil))),tail(0)).  [ur(87,a,2285,a,b,917,a)].

given #1782 (T,wt=9): 2298 ->_s0(length(length(sndsplit(0,x))),length(length(x))).  [ur(41,a,482,a)].

given #1783 (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 #1784 (F,wt=11): 5288 -->_s0(true,length(sndsplit(s(x),nil))) | -->*_s0(length(nil),false) # answer(goal).  [resolve(532,a,2781,b)].

given #1785 (F,wt=11): 5379 -->_s0(true,head(sndsplit(s(x),nil))) | -->*_s0(head(nil),false) # answer(goal).  [resolve(533,a,2781,b)].

given #1786 (F,wt=11): 5406 -->_s0(true,empty(sndsplit(s(x),nil))) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(536,a,2781,b)].

given #1787 (F,wt=11): 5471 -->_s0(true,s(tail(cons(x,y)))) | -->*_s0(s(y),false) # answer(goal).  [resolve(539,a,2781,b)].

given #1788 (T,wt=8): 18895 ->*_s0(length(length(sndsplit(0,nil))),length(0)).  [ur(87,a,2298,a,b,943,a)].

given #1789 (T,wt=9): 2299 ->_s0(head(length(sndsplit(0,x))),head(length(x))).  [ur(40,a,482,a)].

given #1790 (T,wt=8): 18927 ->*_s0(head(length(sndsplit(0,nil))),head(0)).  [ur(87,a,2299,a,b,969,a)].

given #1791 (T,wt=9): 2302 ->_s0(empty(length(sndsplit(0,x))),empty(length(x))).  [ur(37,a,482,a)].

given #1792 (A,wt=10): 365 ->_s0(f(x,leq(s(y),0)),f(x,false)).  [ur(58,a,71,a)].

given #1793 (F,wt=11): 5506 -->_s0(true,tail(tail(cons(x,y)))) | -->*_s0(tail(y),false) # answer(goal).  [resolve(544,a,2781,b)].

given #1794 (F,wt=11): 5543 -->_s0(true,length(tail(cons(x,y)))) | -->*_s0(length(y),false) # answer(goal).  [resolve(557,a,2781,b)].

given #1795 (F,wt=11): 5622 -->_s0(true,head(tail(cons(x,y)))) | -->*_s0(head(y),false) # answer(goal).  [resolve(558,a,2781,b)].

given #1796 (F,wt=11): 5660 -->_s0(true,empty(tail(cons(x,y)))) | -->*_s0(empty(y),false) # answer(goal).  [resolve(561,a,2781,b)].

given #1797 (T,wt=8): 18947 ->*_s0(empty(length(sndsplit(0,nil))),empty(0)).  [ur(87,a,2302,a,b,1031,a)].

given #1798 (T,wt=9): 2307 ->*_s0(tail(cons(x,length(sndsplit(0,nil)))),0).  [ur(87,a,85,a,b,2278,a)].

given #1799 (T,wt=9): 2309 ->*_s0(head(cons(length(sndsplit(0,nil)),x)),0).  [ur(87,a,67,a,b,2278,a)].

given #1800 (T,wt=9): 2316 ->_s0(s(head(sndsplit(0,x))),s(head(x))).  [ur(59,a,483,a)].

given #1801 (A,wt=10): 366 ->_s0(f(leq(s(x),0),y),f(false,y)).  [ur(57,a,71,a)].

given #1802 (F,wt=11): 5751 -->_s0(true,head(cons(tail(cons(x,sndsplit(0,false))),y))) # answer(goal).  [resolve(637,a,3010,b)].

given #1803 (F,wt=11): 5753 -->_s0(true,tail(cons(x,tail(cons(y,sndsplit(0,false)))))) # answer(goal).  [resolve(637,a,2994,b)].

given #1804 (F,wt=11): 5754 -->_s0(true,x) | -->_s0(x,tail(cons(y,sndsplit(0,false)))) # answer(goal).  [resolve(637,a,2781,c)].

given #1805 (F,wt=11): 5770 -->_s0(true,tail(tail(cons(x,cons(y,sndsplit(0,false)))))) # answer(goal).  [ur(2781,b,544,a,c,637,a)].

given #1806 (T,wt=9): 2321 ->_s0(tail(head(sndsplit(0,x))),tail(head(x))).  [ur(54,a,483,a)].

given #1807 (T,wt=9): 2334 ->_s0(length(head(sndsplit(0,x))),length(head(x))).  [ur(41,a,483,a)].

given #1808 (T,wt=9): 2335 ->_s0(head(head(sndsplit(0,x))),head(head(x))).  [ur(40,a,483,a)].

given #1809 (T,wt=9): 2338 ->_s0(empty(head(sndsplit(0,x))),empty(head(x))).  [ur(37,a,483,a)].

given #1810 (A,wt=10): 367 ->_s0(cons(x,leq(s(y),0)),cons(x,false)).  [ur(56,a,71,a)].

given #1811 (F,wt=11): 5772 -->_s0(true,tail(head(cons(cons(x,sndsplit(0,false)),y)))) # answer(goal).  [ur(2781,b,269,a,c,637,a)].

given #1812 (F,wt=11): 5775 -->_s0(true,head(cons(sndsplit(s(0),cons(x,false)),y))) # answer(goal).  [resolve(638,a,3010,b)].

given #1813 (F,wt=11): 5777 -->_s0(true,tail(cons(x,sndsplit(s(0),cons(y,false))))) # answer(goal).  [resolve(638,a,2994,b)].

given #1814 (F,wt=11): 5778 -->_s0(true,x) | -->_s0(x,sndsplit(s(0),cons(y,false))) # answer(goal).  [resolve(638,a,2781,c)].

given #1815 (T,wt=9): 2392 ->_s0(s(empty(sndsplit(0,x))),s(empty(x))).  [ur(59,a,486,a)].

given #1816 (T,wt=8): 19056 ->*_s0(s(empty(sndsplit(0,nil))),s(true)).  [ur(87,a,2392,a,b,699,a)].

given #1817 (T,wt=9): 2397 ->_s0(tail(empty(sndsplit(0,x))),tail(empty(x))).  [ur(54,a,486,a)].

given #1818 (T,wt=8): 19077 ->*_s0(tail(empty(sndsplit(0,nil))),tail(true)).  [ur(87,a,2397,a,b,755,a)].

given #1819 (A,wt=10): 368 ->_s0(cons(leq(s(x),0),y),cons(false,y)).  [ur(55,a,71,a)].

given #1820 (F,wt=11): 5796 -->_s0(true,sndsplit(s(s(0)),cons(x,cons(y,false)))) # answer(goal).  [ur(2781,b,83,a,c,638,a)].

given #1821 (F,wt=11): 5798 -->_s0(true,head(cons(head(cons(sndsplit(0,false),x)),y))) # answer(goal).  [resolve(640,a,3010,b)].

given #1822 (F,wt=11): 5800 -->_s0(true,tail(cons(x,head(cons(sndsplit(0,false),y))))) # answer(goal).  [resolve(640,a,2994,b)].

given #1823 (F,wt=11): 5801 -->_s0(true,x) | -->_s0(x,head(cons(sndsplit(0,false),y))) # answer(goal).  [resolve(640,a,2781,c)].

given #1824 (T,wt=9): 2410 ->_s0(length(empty(sndsplit(0,x))),length(empty(x))).  [ur(41,a,486,a)].

given #1825 (T,wt=8): 19105 ->*_s0(length(empty(sndsplit(0,nil))),length(true)).  [ur(87,a,2410,a,b,781,a)].

given #1826 (T,wt=9): 2411 ->_s0(head(empty(sndsplit(0,x))),head(empty(x))).  [ur(40,a,486,a)].

given #1827 (T,wt=8): 19126 ->*_s0(head(empty(sndsplit(0,nil))),head(true)).  [ur(87,a,2411,a,b,807,a)].

given #1828 (A,wt=10): 370 ->_s0(sndsplit(x,leq(s(y),0)),sndsplit(x,false)).  [ur(53,a,71,a)].

given #1829 (F,wt=11): 5818 -->_s0(true,head(tail(cons(x,cons(sndsplit(0,false),y))))) # answer(goal).  [ur(2781,b,558,a,c,640,a)].

given #1830 (F,wt=11): 5820 -->_s0(true,head(head(cons(cons(sndsplit(0,false),x),y)))) # answer(goal).  [ur(2781,b,283,a,c,640,a)].

given #1831 (F,wt=11): 5941 -->_s0(true,head(cons(tail(cons(x,app(nil,false))),y))) # answer(goal).  [resolve(695,a,3010,b)].

given #1832 (F,wt=11): 5943 -->_s0(true,tail(cons(x,tail(cons(y,app(nil,false)))))) # answer(goal).  [resolve(695,a,2994,b)].

given #1833 (T,wt=9): 2414 ->_s0(empty(empty(sndsplit(0,x))),empty(empty(x))).  [ur(37,a,486,a)].

given #1834 (T,wt=8): 19162 ->*_s0(empty(empty(sndsplit(0,nil))),empty(true)).  [ur(87,a,2414,a,b,833,a)].

given #1835 (T,wt=9): 2422 ->*_s0(tail(cons(x,empty(sndsplit(0,nil)))),true).  [ur(87,a,85,a,b,2390,a)].

given #1836 (T,wt=9): 2424 ->*_s0(head(cons(empty(sndsplit(0,nil)),x)),true).  [ur(87,a,67,a,b,2390,a)].

given #1837 (A,wt=10): 371 ->_s0(sndsplit(leq(s(x),0),y),sndsplit(false,y)).  [ur(52,a,71,a)].

given #1838 (F,wt=11): 5944 -->_s0(true,x) | -->_s0(x,tail(cons(y,app(nil,false)))) # answer(goal).  [resolve(695,a,2781,c)].

given #1839 (F,wt=11): 5961 -->_s0(true,tail(tail(cons(x,cons(y,app(nil,false)))))) # answer(goal).  [ur(2781,b,544,a,c,695,a)].

given #1840 (F,wt=11): 5963 -->_s0(true,tail(head(cons(cons(x,app(nil,false)),y)))) # answer(goal).  [ur(2781,b,269,a,c,695,a)].

given #1841 (F,wt=11): 5967 -->_s0(true,head(cons(head(cons(app(nil,false),x)),y))) # answer(goal).  [resolve(697,a,3010,b)].

given #1842 (T,wt=9): 2426 ->*_s0(tail(sndsplit(0,cons(x,length(nil)))),0).  [ur(87,a,469,a,b,626,a)].

given #1843 (T,wt=9): 2427 ->*_s0(tail(app(nil,cons(x,length(nil)))),0).  [ur(87,a,119,a,b,626,a)].

given #1844 (T,wt=9): 2429 ->*_s0(sndsplit(0,tail(cons(x,length(nil)))),0).  [ur(87,a,82,a,b,626,a)].

given #1845 (T,wt=9): 2431 ->*_s0(app(nil,tail(cons(x,length(nil)))),0).  [ur(87,a,61,a,b,626,a)].

given #1846 (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 #1847 (F,wt=11): 5969 -->_s0(true,tail(cons(x,head(cons(app(nil,false),y))))) # answer(goal).  [resolve(697,a,2994,b)].

given #1848 (F,wt=11): 5970 -->_s0(true,x) | -->_s0(x,head(cons(app(nil,false),y))) # answer(goal).  [resolve(697,a,2781,c)].

given #1849 (F,wt=11): 5987 -->_s0(true,head(tail(cons(x,cons(app(nil,false),y))))) # answer(goal).  [ur(2781,b,558,a,c,697,a)].

given #1850 (F,wt=11): 5989 -->_s0(true,head(head(cons(cons(app(nil,false),x),y)))) # answer(goal).  [ur(2781,b,283,a,c,697,a)].

given #1851 (T,wt=9): 2432 ->*_s0(head(sndsplit(0,cons(length(nil),x))),0).  [ur(87,a,483,a,b,628,a)].

given #1852 (T,wt=9): 2433 ->*_s0(head(app(nil,cons(length(nil),x))),0).  [ur(87,a,133,a,b,628,a)].

given #1853 (T,wt=9): 2435 ->*_s0(sndsplit(0,head(cons(length(nil),x))),0).  [ur(87,a,82,a,b,628,a)].

given #1854 (T,wt=9): 2437 ->*_s0(app(nil,head(cons(length(nil),x))),0).  [ur(87,a,61,a,b,628,a)].

given #1855 (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 #1856 (F,wt=11): 6019 -->_s0(true,s(s(empty(nil)))) | -->*_s0(s(s(true)),false) # answer(goal).  [resolve(700,a,2781,b)].

given #1857 (F,wt=11): 6046 -->_s0(true,tail(s(empty(nil)))) | -->*_s0(tail(s(true)),false) # answer(goal).  [resolve(705,a,2781,b)].

given #1858 (F,wt=11): 6073 -->_s0(true,length(s(empty(nil)))) | -->*_s0(length(s(true)),false) # answer(goal).  [resolve(718,a,2781,b)].

given #1859 (F,wt=11): 6100 -->_s0(true,head(s(empty(nil)))) | -->*_s0(head(s(true)),false) # answer(goal).  [resolve(719,a,2781,b)].

given #1860 (T,wt=9): 2488 ->*_s0(tail(sndsplit(0,cons(x,empty(nil)))),true).  [ur(87,a,469,a,b,631,a)].

given #1861 (T,wt=9): 2489 ->*_s0(tail(app(nil,cons(x,empty(nil)))),true).  [ur(87,a,119,a,b,631,a)].

given #1862 (T,wt=9): 2491 ->*_s0(sndsplit(0,tail(cons(x,empty(nil)))),true).  [ur(87,a,82,a,b,631,a)].

given #1863 (T,wt=9): 2493 ->*_s0(app(nil,tail(cons(x,empty(nil)))),true).  [ur(87,a,61,a,b,631,a)].

given #1864 (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 #1865 (F,wt=11): 6154 -->_s0(true,empty(s(empty(nil)))) | -->*_s0(empty(s(true)),false) # answer(goal).  [resolve(722,a,2781,b)].

given #1866 (F,wt=11): 6181 -->_s0(true,s(tail(empty(nil)))) | -->*_s0(s(tail(true)),false) # answer(goal).  [resolve(756,a,2781,b)].

given #1867 (F,wt=11): 6208 -->_s0(true,tail(tail(empty(nil)))) | -->*_s0(tail(tail(true)),false) # answer(goal).  [resolve(761,a,2781,b)].

given #1868 (F,wt=11): 6235 -->_s0(true,length(tail(empty(nil)))) | -->*_s0(length(tail(true)),false) # answer(goal).  [resolve(774,a,2781,b)].

given #1869 (T,wt=9): 2498 ->*_s0(head(sndsplit(0,cons(empty(nil),x))),true).  [ur(87,a,483,a,b,633,a)].

given #1870 (T,wt=9): 2499 ->*_s0(head(app(nil,cons(empty(nil),x))),true).  [ur(87,a,133,a,b,633,a)].

given #1871 (T,wt=9): 2501 ->*_s0(sndsplit(0,head(cons(empty(nil),x))),true).  [ur(87,a,82,a,b,633,a)].

given #1872 (T,wt=9): 2503 ->*_s0(app(nil,head(cons(empty(nil),x))),true).  [ur(87,a,61,a,b,633,a)].

given #1873 (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 #1874 (F,wt=11): 6295 -->_s0(true,head(tail(empty(nil)))) | -->*_s0(head(tail(true)),false) # answer(goal).  [resolve(775,a,2781,b)].

given #1875 (F,wt=11): 6322 -->_s0(true,empty(tail(empty(nil)))) | -->*_s0(empty(tail(true)),false) # answer(goal).  [resolve(778,a,2781,b)].

given #1876 (F,wt=11): 6349 -->_s0(true,s(length(empty(nil)))) | -->*_s0(s(length(true)),false) # answer(goal).  [resolve(782,a,2781,b)].

given #1877 (F,wt=11): 6376 -->_s0(true,tail(length(empty(nil)))) | -->*_s0(tail(length(true)),false) # answer(goal).  [resolve(787,a,2781,b)].

given #1878 (T,wt=9): 2517 ->*_s0(sndsplit(0,sndsplit(0,sndsplit(0,x))),x).  [ur(87,a,82,a,b,639,a)].

given #1879 (T,wt=9): 2519 ->*_s0(app(nil,sndsplit(0,sndsplit(0,x))),x).  [ur(87,a,61,a,b,639,a)].

given #1880 (T,wt=9): 2532 ->*_s0(sndsplit(0,app(nil,sndsplit(0,x))),x).  [ur(87,a,82,a,b,641,a)].

given #1881 (T,wt=9): 2534 ->*_s0(app(nil,app(nil,sndsplit(0,x))),x).  [ur(87,a,61,a,b,641,a)].

given #1882 (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 #1883 (F,wt=11): 6435 -->_s0(true,length(length(empty(nil)))) | -->*_s0(length(length(true)),false) # answer(goal).  [resolve(800,a,2781,b)].

given #1884 (F,wt=11): 6462 -->_s0(true,head(length(empty(nil)))) | -->*_s0(head(length(true)),false) # answer(goal).  [resolve(801,a,2781,b)].

given #1885 (F,wt=11): 6489 -->_s0(true,empty(length(empty(nil)))) | -->*_s0(empty(length(true)),false) # answer(goal).  [resolve(804,a,2781,b)].

given #1886 (F,wt=11): 6516 -->_s0(true,s(head(empty(nil)))) | -->*_s0(s(head(true)),false) # answer(goal).  [resolve(808,a,2781,b)].

given #1887 (T,wt=9): 2536 ->*_s0(head(app(cons(empty(nil),x),y)),true).  [ur(87,a,108,a,b,633,a)].

given #1888 (T,wt=9): 2537 ->*_s0(head(app(cons(length(nil),x),y)),0).  [ur(87,a,108,a,b,628,a)].

given #1889 (T,wt=9): 2580 ->*_s0(sndsplit(0,sndsplit(0,mapf(x,nil))),nil).  [ur(87,a,82,a,b,643,a)].

given #1890 (T,wt=9): 2582 ->*_s0(app(nil,sndsplit(0,mapf(x,nil))),nil).  [ur(87,a,61,a,b,643,a)].

given #1891 (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 #1892 (F,wt=11): 6570 -->_s0(true,tail(head(empty(nil)))) | -->*_s0(tail(head(true)),false) # answer(goal).  [resolve(813,a,2781,b)].

given #1893 (F,wt=11): 6597 -->_s0(true,length(head(empty(nil)))) | -->*_s0(length(head(true)),false) # answer(goal).  [resolve(826,a,2781,b)].

given #1894 (F,wt=11): 6624 -->_s0(true,head(head(empty(nil)))) | -->*_s0(head(head(true)),false) # answer(goal).  [resolve(827,a,2781,b)].

given #1895 (F,wt=11): 6651 -->_s0(true,empty(head(empty(nil)))) | -->*_s0(empty(head(true)),false) # answer(goal).  [resolve(830,a,2781,b)].

given #1896 (T,wt=9): 2584 ->*_s0(sndsplit(0,app(nil,mapf(x,nil))),nil).  [ur(87,a,82,a,b,645,a)].

given #1897 (T,wt=9): 2586 ->*_s0(app(nil,app(nil,mapf(x,nil))),nil).  [ur(87,a,61,a,b,645,a)].

given #1898 (T,wt=9): 2593 ->*_s0(sndsplit(0,sndsplit(0,leq(0,x))),true).  [ur(87,a,82,a,b,684,a)].

given #1899 (T,wt=9): 2595 ->*_s0(app(nil,sndsplit(0,leq(0,x))),true).  [ur(87,a,61,a,b,684,a)].

given #1900 (A,wt=10): 378 ->_s0(mapf(x,leq(s(y),0)),mapf(x,false)).  [ur(45,a,71,a)].

given #1901 (F,wt=11): 6705 -->_s0(true,s(empty(empty(nil)))) | -->*_s0(s(empty(true)),false) # answer(goal).  [resolve(834,a,2781,b)].

given #1902 (F,wt=11): 6732 -->_s0(true,tail(empty(empty(nil)))) | -->*_s0(tail(empty(true)),false) # answer(goal).  [resolve(839,a,2781,b)].

given #1903 (F,wt=11): 6759 -->_s0(true,length(empty(empty(nil)))) | -->*_s0(length(empty(true)),false) # answer(goal).  [resolve(852,a,2781,b)].

given #1904 (F,wt=11): 6786 -->_s0(true,head(empty(empty(nil)))) | -->*_s0(head(empty(true)),false) # answer(goal).  [resolve(853,a,2781,b)].

given #1905 (T,wt=9): 2601 ->*_s0(sndsplit(0,leq(s(0),s(x))),true).  [ur(87,a,82,a,b,685,a)].

given #1906 (T,wt=9): 2602 ->*_s0(leq(s(s(0)),s(s(x))),true).  [ur(87,a,72,a,b,685,a)].

given #1907 (T,wt=9): 2604 ->*_s0(app(nil,leq(s(0),s(x))),true).  [ur(87,a,61,a,b,685,a)].

given #1908 (T,wt=9): 2648 ->*_s0(sndsplit(0,app(nil,leq(0,x))),true).  [ur(87,a,82,a,b,687,a)].

given #1909 (A,wt=10): 379 ->_s0(mapf(leq(s(x),0),y),mapf(false,y)).  [ur(44,a,71,a)].

given #1910 (F,wt=11): 6855 -->_s0(true,empty(empty(empty(nil)))) | -->*_s0(empty(empty(true)),false) # answer(goal).  [resolve(856,a,2781,b)].

given #1911 (F,wt=11): 6882 -->_s0(true,s(s(length(nil)))) | -->*_s0(s(s(0)),false) # answer(goal).  [resolve(892,a,2781,b)].

given #1912 (F,wt=11): 6909 -->_s0(true,tail(s(length(nil)))) | -->*_s0(tail(s(0)),false) # answer(goal).  [resolve(897,a,2781,b)].

given #1913 (F,wt=11): 6936 -->_s0(true,length(s(length(nil)))) | -->*_s0(length(s(0)),false) # answer(goal).  [resolve(910,a,2781,b)].

given #1914 (T,wt=9): 2650 ->*_s0(app(nil,app(nil,leq(0,x))),true).  [ur(87,a,61,a,b,687,a)].

given #1915 (T,wt=9): 2653 ->*_s0(sndsplit(0,sndsplit(0,fstsplit(0,x))),nil).  [ur(87,a,82,a,b,689,a)].

given #1916 (T,wt=9): 2655 ->*_s0(app(nil,sndsplit(0,fstsplit(0,x))),nil).  [ur(87,a,61,a,b,689,a)].

given #1917 (T,wt=9): 2657 ->*_s0(sndsplit(0,app(nil,fstsplit(0,x))),nil).  [ur(87,a,82,a,b,691,a)].

given #1918 (A,wt=10): 380 ->_s0(leq(x,leq(s(y),0)),leq(x,false)).  [ur(43,a,71,a)].

given #1919 (F,wt=11): 6990 -->_s0(true,head(s(length(nil)))) | -->*_s0(head(s(0)),false) # answer(goal).  [resolve(911,a,2781,b)].

given #1920 (F,wt=11): 7017 -->_s0(true,empty(s(length(nil)))) | -->*_s0(empty(s(0)),false) # answer(goal).  [resolve(914,a,2781,b)].

given #1921 (F,wt=11): 7044 -->_s0(true,s(tail(length(nil)))) | -->*_s0(s(tail(0)),false) # answer(goal).  [resolve(918,a,2781,b)].

given #1922 (F,wt=11): 7071 -->_s0(true,tail(tail(length(nil)))) | -->*_s0(tail(tail(0)),false) # answer(goal).  [resolve(923,a,2781,b)].

given #1923 (T,wt=9): 2659 ->*_s0(app(nil,app(nil,fstsplit(0,x))),nil).  [ur(87,a,61,a,b,691,a)].

given #1924 (T,wt=9): 2674 ->*_s0(sndsplit(0,sndsplit(0,app(nil,x))),x).  [ur(87,a,82,a,b,696,a)].

given #1925 (T,wt=9): 2676 ->*_s0(app(nil,sndsplit(0,app(nil,x))),x).  [ur(87,a,61,a,b,696,a)].

given #1926 (T,wt=9): 2731 ->*_s0(sndsplit(0,app(nil,app(nil,x))),x).  [ur(87,a,82,a,b,698,a)].

given #1927 (A,wt=10): 381 ->_s0(leq(leq(s(x),0),y),leq(false,y)).  [ur(42,a,71,a)].

given #1928 (F,wt=11): 7125 -->_s0(true,length(tail(length(nil)))) | -->*_s0(length(tail(0)),false) # answer(goal).  [resolve(936,a,2781,b)].

given #1929 (F,wt=11): 7152 -->_s0(true,head(tail(length(nil)))) | -->*_s0(head(tail(0)),false) # answer(goal).  [resolve(937,a,2781,b)].

given #1930 (F,wt=11): 7179 -->_s0(true,empty(tail(length(nil)))) | -->*_s0(empty(tail(0)),false) # answer(goal).  [resolve(940,a,2781,b)].

given #1931 (F,wt=11): 7206 -->_s0(true,s(length(length(nil)))) | -->*_s0(s(length(0)),false) # answer(goal).  [resolve(944,a,2781,b)].

given #1932 (T,wt=9): 2733 ->*_s0(app(nil,app(nil,app(nil,x))),x).  [ur(87,a,61,a,b,698,a)].

given #1933 (T,wt=9): 2735 ->*_s0(length(sndsplit(0,cons(x,nil))),s(0)).  [ur(87,a,482,a,b,1261,a)].

given #1934 (T,wt=9): 2736 ->*_s0(length(app(nil,cons(x,nil))),s(0)).  [ur(87,a,132,a,b,1261,a)].

given #1935 (T,wt=9): 2738 ->*_s0(sndsplit(0,length(cons(x,nil))),s(0)).  [ur(87,a,82,a,b,1261,a)].

given #1936 (A,wt=10): 384 ->_s0(fstsplit(x,leq(s(y),0)),fstsplit(x,false)).  [ur(39,a,71,a)].

given #1937 (F,wt=11): 7260 -->_s0(true,tail(length(length(nil)))) | -->*_s0(tail(length(0)),false) # answer(goal).  [resolve(949,a,2781,b)].

given #1938 (F,wt=11): 7287 -->_s0(true,length(length(length(nil)))) | -->*_s0(length(length(0)),false) # answer(goal).  [resolve(962,a,2781,b)].

given #1939 (F,wt=11): 7314 -->_s0(true,head(length(length(nil)))) | -->*_s0(head(length(0)),false) # answer(goal).  [resolve(963,a,2781,b)].

given #1940 (F,wt=11): 7341 -->_s0(true,empty(length(length(nil)))) | -->*_s0(empty(length(0)),false) # answer(goal).  [resolve(966,a,2781,b)].

given #1941 (T,wt=9): 2740 ->*_s0(app(nil,length(cons(x,nil))),s(0)).  [ur(87,a,61,a,b,1261,a)].

given #1942 (T,wt=9): 2741 ->*_s0(s(sndsplit(0,app(nil,x))),s(x)).  [ur(87,a,464,a,b,1309,a)].

given #1943 (T,wt=9): 2742 ->*_s0(s(app(nil,app(nil,x))),s(x)).  [ur(87,a,114,a,b,1309,a)].

given #1944 (T,wt=9): 2744 ->*_s0(sndsplit(0,s(app(nil,x))),s(x)).  [ur(87,a,82,a,b,1309,a)].

given #1945 (A,wt=10): 385 ->_s0(fstsplit(leq(s(x),0),y),fstsplit(false,y)).  [ur(38,a,71,a)].

given #1946 (F,wt=11): 7396 -->_s0(true,s(head(length(nil)))) | -->*_s0(s(head(0)),false) # answer(goal).  [resolve(970,a,2781,b)].

given #1947 (F,wt=11): 7423 -->_s0(true,tail(head(length(nil)))) | -->*_s0(tail(head(0)),false) # answer(goal).  [resolve(975,a,2781,b)].

given #1948 (F,wt=11): 7450 -->_s0(true,length(head(length(nil)))) | -->*_s0(length(head(0)),false) # answer(goal).  [resolve(988,a,2781,b)].

given #1949 (F,wt=11): 7477 -->_s0(true,head(head(length(nil)))) | -->*_s0(head(head(0)),false) # answer(goal).  [resolve(989,a,2781,b)].

given #1950 (T,wt=9): 2746 ->*_s0(app(nil,s(app(nil,x))),s(x)).  [ur(87,a,61,a,b,1309,a)].

given #1951 (T,wt=9): 2747 ->*_s0(tail(sndsplit(0,app(nil,x))),tail(x)).  [ur(87,a,469,a,b,1338,a)].

given #1952 (T,wt=9): 2748 ->*_s0(tail(app(nil,app(nil,x))),tail(x)).  [ur(87,a,119,a,b,1338,a)].

given #1953 (T,wt=9): 2750 ->*_s0(sndsplit(0,tail(app(nil,x))),tail(x)).  [ur(87,a,82,a,b,1338,a)].

given #1954 (A,wt=10): 387 ->_s0(app(x,leq(s(y),0)),app(x,false)).  [ur(36,a,71,a)].

given #1955 (F,wt=11): 7531 -->_s0(true,empty(head(length(nil)))) | -->*_s0(empty(head(0)),false) # answer(goal).  [resolve(992,a,2781,b)].

given #1956 (F,wt=11): 7558 -->_s0(true,s(empty(length(nil)))) | -->*_s0(s(empty(0)),false) # answer(goal).  [resolve(1032,a,2781,b)].

given #1957 (F,wt=11): 7585 -->_s0(true,tail(empty(length(nil)))) | -->*_s0(tail(empty(0)),false) # answer(goal).  [resolve(1037,a,2781,b)].

given #1958 (F,wt=11): 7612 -->_s0(true,length(empty(length(nil)))) | -->*_s0(length(empty(0)),false) # answer(goal).  [resolve(1050,a,2781,b)].

given #1959 (T,wt=9): 2752 ->*_s0(app(nil,tail(app(nil,x))),tail(x)).  [ur(87,a,61,a,b,1338,a)].

given #1960 (T,wt=9): 2782 ->*_s0(length(sndsplit(0,app(nil,x))),length(x)).  [ur(87,a,482,a,b,1367,a)].

given #1961 (T,wt=9): 2783 ->*_s0(length(app(nil,app(nil,x))),length(x)).  [ur(87,a,132,a,b,1367,a)].

given #1962 (T,wt=9): 2785 ->*_s0(sndsplit(0,length(app(nil,x))),length(x)).  [ur(87,a,82,a,b,1367,a)].

given #1963 (A,wt=10): 388 ->_s0(app(leq(s(x),0),y),app(false,y)).  [ur(35,a,71,a)].

given #1964 (F,wt=11): 7662 -->_s0(true,head(empty(length(nil)))) | -->*_s0(head(empty(0)),false) # answer(goal).  [resolve(1051,a,2781,b)].

given #1965 (F,wt=11): 7689 -->_s0(true,empty(empty(length(nil)))) | -->*_s0(empty(empty(0)),false) # answer(goal).  [resolve(1054,a,2781,b)].

given #1966 (F,wt=11): 7717 -->_s0(true,head(cons(sndsplit(0,tail(cons(x,false))),y))) # answer(goal).  [resolve(1063,a,3010,b)].

given #1967 (F,wt=11): 7719 -->_s0(true,tail(cons(x,sndsplit(0,tail(cons(y,false)))))) # answer(goal).  [resolve(1063,a,2994,b)].

given #1968 (T,wt=9): 2787 ->*_s0(app(nil,length(app(nil,x))),length(x)).  [ur(87,a,61,a,b,1367,a)].

given #1969 (T,wt=9): 2788 ->*_s0(head(sndsplit(0,app(nil,x))),head(x)).  [ur(87,a,483,a,b,1427,a)].

given #1970 (T,wt=9): 2789 ->*_s0(head(app(nil,app(nil,x))),head(x)).  [ur(87,a,133,a,b,1427,a)].

given #1971 (T,wt=9): 2791 ->*_s0(sndsplit(0,head(app(nil,x))),head(x)).  [ur(87,a,82,a,b,1427,a)].

given #1972 (A,wt=11): 389 ->_s0(s(leq(s(x),s(y))),s(leq(x,y))).  [ur(59,a,72,a)].

given #1973 (F,wt=11): 7720 -->_s0(true,x) | -->_s0(x,sndsplit(0,tail(cons(y,false)))) # answer(goal).  [resolve(1063,a,2781,c)].

given #1974 (F,wt=11): 7738 -->_s0(true,sndsplit(s(0),cons(x,tail(cons(y,false))))) # answer(goal).  [ur(2781,b,83,a,c,1063,a)].

given #1975 (F,wt=11): 7740 -->_s0(true,head(cons(app(nil,tail(cons(x,false))),y))) # answer(goal).  [resolve(1065,a,3010,b)].

given #1976 (F,wt=11): 7741 -->_s0(true,tail(cons(x,app(nil,tail(cons(y,false)))))) # answer(goal).  [resolve(1065,a,2994,b)].

given #1977 (T,wt=9): 2793 ->*_s0(app(nil,head(app(nil,x))),head(x)).  [ur(87,a,61,a,b,1427,a)].

given #1978 (T,wt=9): 2794 ->*_s0(empty(sndsplit(0,app(nil,x))),empty(x)).  [ur(87,a,486,a,b,1457,a)].

given #1979 (T,wt=9): 2795 ->*_s0(empty(app(nil,app(nil,x))),empty(x)).  [ur(87,a,136,a,b,1457,a)].

given #1980 (T,wt=9): 2797 ->*_s0(sndsplit(0,empty(app(nil,x))),empty(x)).  [ur(87,a,82,a,b,1457,a)].

given #1981 (A,wt=13): 390 ->_s0(f(x,leq(s(y),s(z))),f(x,leq(y,z))).  [ur(58,a,72,a)].

given #1982 (F,wt=11): 7742 -->_s0(true,x) | -->_s0(x,app(nil,tail(cons(y,false)))) # answer(goal).  [resolve(1065,a,2781,c)].

given #1983 (F,wt=11): 7795 -->_s0(true,head(cons(sndsplit(0,leq(s(x),0)),y))) # answer(goal).  [resolve(1075,a,3010,b)].

given #1984 (F,wt=11): 7797 -->_s0(true,tail(cons(x,sndsplit(0,leq(s(y),0))))) # answer(goal).  [resolve(1075,a,2994,b)].

given #1985 (F,wt=11): 7798 -->_s0(true,x) | -->_s0(x,sndsplit(0,leq(s(y),0))) # answer(goal).  [resolve(1075,a,2781,c)].

given #1986 (T,wt=9): 2799 ->*_s0(app(nil,empty(app(nil,x))),empty(x)).  [ur(87,a,61,a,b,1457,a)].

given #1987 (T,wt=9): 2800 ->*_s0(s(sndsplit(0,fstsplit(0,x))),s(nil)).  [ur(87,a,464,a,b,1607,a)].

given #1988 (T,wt=9): 2801 ->*_s0(s(app(nil,fstsplit(0,x))),s(nil)).  [ur(87,a,114,a,b,1607,a)].

given #1989 (T,wt=9): 2803 ->*_s0(sndsplit(0,s(fstsplit(0,x))),s(nil)).  [ur(87,a,82,a,b,1607,a)].

given #1990 (A,wt=13): 391 ->_s0(f(leq(s(x),s(y)),z),f(leq(x,y),z)).  [ur(57,a,72,a)].

given #1991 (F,wt=11): 7813 -->_s0(true,sndsplit(s(0),cons(x,leq(s(y),0)))) # answer(goal).  [ur(2781,b,83,a,c,1075,a)].

given #1992 (F,wt=11): 7815 -->_s0(true,head(cons(leq(s(s(x)),s(0)),y))) # answer(goal).  [resolve(1076,a,3010,b)].

given #1993 (F,wt=11): 7817 -->_s0(true,tail(cons(x,leq(s(s(y)),s(0))))) # answer(goal).  [resolve(1076,a,2994,b)].

given #1994 (F,wt=11): 7818 -->_s0(true,x) | -->_s0(x,leq(s(s(y)),s(0))) # answer(goal).  [resolve(1076,a,2781,c)].

given #1995 (T,wt=9): 2805 ->*_s0(app(nil,s(fstsplit(0,x))),s(nil)).  [ur(87,a,61,a,b,1607,a)].

given #1996 (T,wt=9): 2833 ->*_s0(tail(sndsplit(0,fstsplit(0,x))),tail(nil)).  [ur(87,a,469,a,b,1634,a)].

given #1997 (T,wt=9): 2834 ->*_s0(tail(app(nil,fstsplit(0,x))),tail(nil)).  [ur(87,a,119,a,b,1634,a)].

given #1998 (T,wt=9): 2836 ->*_s0(sndsplit(0,tail(fstsplit(0,x))),tail(nil)).  [ur(87,a,82,a,b,1634,a)].

given #1999 (A,wt=13): 392 ->_s0(cons(x,leq(s(y),s(z))),cons(x,leq(y,z))).  [ur(56,a,72,a)].

given #2000 (F,wt=11): 7859 -->_s0(true,head(cons(app(nil,leq(s(x),0)),y))) # answer(goal).  [resolve(1078,a,3010,b)].

given #2001 (F,wt=11): 7860 -->_s0(true,tail(cons(x,app(nil,leq(s(y),0))))) # answer(goal).  [resolve(1078,a,2994,b)].

given #2002 (F,wt=11): 7861 -->_s0(true,x) | -->_s0(x,app(nil,leq(s(y),0))) # answer(goal).  [resolve(1078,a,2781,c)].

given #2003 (F,wt=11): 7872 -->_s0(true,head(cons(sndsplit(0,head(cons(false,x))),y))) # answer(goal).  [resolve(1113,a,3010,b)].

given #2004 (T,wt=9): 2838 ->*_s0(app(nil,tail(fstsplit(0,x))),tail(nil)).  [ur(87,a,61,a,b,1634,a)].

given #2005 (T,wt=9): 2839 ->*_s0(length(sndsplit(0,fstsplit(0,x))),length(nil)).  [ur(87,a,482,a,b,1662,a)].

given #2006 (T,wt=9): 2840 ->*_s0(length(app(nil,fstsplit(0,x))),length(nil)).  [ur(87,a,132,a,b,1662,a)].

given #2007 (T,wt=9): 2842 ->*_s0(sndsplit(0,length(fstsplit(0,x))),length(nil)).  [ur(87,a,82,a,b,1662,a)].

given #2008 (A,wt=13): 393 ->_s0(cons(leq(s(x),s(y)),z),cons(leq(x,y),z)).  [ur(55,a,72,a)].

given #2009 (F,wt=11): 7874 -->_s0(true,tail(cons(x,sndsplit(0,head(cons(false,y)))))) # answer(goal).  [resolve(1113,a,2994,b)].

given #2010 (F,wt=11): 7875 -->_s0(true,x) | -->_s0(x,sndsplit(0,head(cons(false,y)))) # answer(goal).  [resolve(1113,a,2781,c)].

given #2011 (F,wt=11): 7893 -->_s0(true,sndsplit(s(0),cons(x,head(cons(false,y))))) # answer(goal).  [ur(2781,b,83,a,c,1113,a)].

given #2012 (F,wt=11): 7895 -->_s0(true,head(cons(app(nil,head(cons(false,x))),y))) # answer(goal).  [resolve(1115,a,3010,b)].

given #2013 (T,wt=9): 2844 ->*_s0(app(nil,length(fstsplit(0,x))),length(nil)).  [ur(87,a,61,a,b,1662,a)].

given #2014 (T,wt=9): 2845 ->*_s0(head(sndsplit(0,fstsplit(0,x))),head(nil)).  [ur(87,a,483,a,b,1723,a)].

given #2015 (T,wt=9): 2846 ->*_s0(head(app(nil,fstsplit(0,x))),head(nil)).  [ur(87,a,133,a,b,1723,a)].

given #2016 (T,wt=9): 2848 ->*_s0(sndsplit(0,head(fstsplit(0,x))),head(nil)).  [ur(87,a,82,a,b,1723,a)].

given #2017 (A,wt=11): 394 ->_s0(tail(leq(s(x),s(y))),tail(leq(x,y))).  [ur(54,a,72,a)].

given #2018 (F,wt=11): 7896 -->_s0(true,tail(cons(x,app(nil,head(cons(false,y)))))) # answer(goal).  [resolve(1115,a,2994,b)].

given #2019 (F,wt=11): 7897 -->_s0(true,x) | -->_s0(x,app(nil,head(cons(false,y)))) # answer(goal).  [resolve(1115,a,2781,c)].

given #2020 (F,wt=11): 7948 -->_s0(true,head(cons(sndsplit(0,empty(cons(x,y))),z))) # answer(goal).  [resolve(1125,a,3010,b)].

given #2021 (F,wt=11): 7950 -->_s0(true,tail(cons(x,sndsplit(0,empty(cons(y,z)))))) # answer(goal).  [resolve(1125,a,2994,b)].

given #2022 (T,wt=9): 2850 ->*_s0(app(nil,head(fstsplit(0,x))),head(nil)).  [ur(87,a,61,a,b,1723,a)].

given #2023 (T,wt=9): 2851 ->*_s0(empty(sndsplit(0,fstsplit(0,x))),empty(nil)).  [ur(87,a,486,a,b,1751,a)].

given #2024 (T,wt=9): 2852 ->*_s0(empty(app(nil,fstsplit(0,x))),empty(nil)).  [ur(87,a,136,a,b,1751,a)].

given #2025 (T,wt=9): 2854 ->*_s0(sndsplit(0,empty(fstsplit(0,x))),empty(nil)).  [ur(87,a,82,a,b,1751,a)].

given #2026 (A,wt=13): 395 ->_s0(sndsplit(x,leq(s(y),s(z))),sndsplit(x,leq(y,z))).  [ur(53,a,72,a)].

given #2027 (F,wt=11): 7951 -->_s0(true,x) | -->_s0(x,sndsplit(0,empty(cons(y,z)))) # answer(goal).  [resolve(1125,a,2781,c)].

given #2028 (F,wt=11): 7963 -->_s0(true,sndsplit(s(0),cons(x,empty(cons(y,z))))) # answer(goal).  [ur(2781,b,83,a,c,1125,a)].

given #2029 (F,wt=11): 7965 -->_s0(true,head(cons(app(nil,empty(cons(x,y))),z))) # answer(goal).  [resolve(1127,a,3010,b)].

given #2030 (F,wt=11): 7966 -->_s0(true,tail(cons(x,app(nil,empty(cons(y,z)))))) # answer(goal).  [resolve(1127,a,2994,b)].

given #2031 (T,wt=9): 2856 ->*_s0(app(nil,empty(fstsplit(0,x))),empty(nil)).  [ur(87,a,61,a,b,1751,a)].

given #2032 (T,wt=9): 2883 ->*_s0(s(sndsplit(0,leq(0,x))),s(true)).  [ur(87,a,464,a,b,1785,a)].

given #2033 (T,wt=9): 2884 ->*_s0(s(app(nil,leq(0,x))),s(true)).  [ur(87,a,114,a,b,1785,a)].

given #2034 (T,wt=9): 2886 ->*_s0(sndsplit(0,s(leq(0,x))),s(true)).  [ur(87,a,82,a,b,1785,a)].

given #2035 (A,wt=13): 396 ->_s0(sndsplit(leq(s(x),s(y)),z),sndsplit(leq(x,y),z)).  [ur(52,a,72,a)].

given #2036 (F,wt=11): 7967 -->_s0(true,x) | -->_s0(x,app(nil,empty(cons(y,z)))) # answer(goal).  [resolve(1127,a,2781,c)].

given #2037 (F,wt=11): 8289 -->_s0(true,length(nil)) | -->_s0(0,app(app(nil,nil),false)) # answer(goal).  [resolve(3100,c,5324,a)].

given #2038 (F,wt=11): 8290 -->_s0(true,length(nil)) | -->_s0(0,leq(s(x),length(nil))) # answer(goal).  [resolve(3100,c,4756,a)].

given #2039 (F,wt=11): 8292 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(app(nil,0),false)) # answer(goal).  [resolve(3100,c,3536,a)].

given #2040 (T,wt=9): 2888 ->*_s0(app(nil,s(leq(0,x))),s(true)).  [ur(87,a,61,a,b,1785,a)].

given #2041 (T,wt=9): 2889 ->*_s0(tail(sndsplit(0,leq(0,x))),tail(true)).  [ur(87,a,469,a,b,1848,a)].

given #2042 (T,wt=9): 2890 ->*_s0(tail(app(nil,leq(0,x))),tail(true)).  [ur(87,a,119,a,b,1848,a)].

given #2043 (T,wt=9): 2892 ->*_s0(sndsplit(0,tail(leq(0,x))),tail(true)).  [ur(87,a,82,a,b,1848,a)].

given #2044 (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 #2045 (F,wt=11): 8302 -->_s0(true,length(nil)) | -->_s0(0,app(nil,app(nil,false))) # answer(goal).  [resolve(3100,c,698,a)].

given #2046 (F,wt=11): 8304 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(0,app(nil,false))) # answer(goal).  [resolve(3100,c,696,a)].

given #2047 (F,wt=11): 8306 -->_s0(true,length(nil)) | -->_s0(0,app(nil,sndsplit(0,false))) # answer(goal).  [resolve(3100,c,641,a)].

given #2048 (F,wt=11): 8308 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(0,sndsplit(0,false))) # answer(goal).  [resolve(3100,c,639,a)].

given #2049 (T,wt=9): 2894 ->*_s0(app(nil,tail(leq(0,x))),tail(true)).  [ur(87,a,61,a,b,1848,a)].

given #2050 (T,wt=9): 2895 ->*_s0(length(sndsplit(0,leq(0,x))),length(true)).  [ur(87,a,482,a,b,1875,a)].

given #2051 (T,wt=9): 2896 ->*_s0(length(app(nil,leq(0,x))),length(true)).  [ur(87,a,132,a,b,1875,a)].

given #2052 (T,wt=9): 2898 ->*_s0(sndsplit(0,length(leq(0,x))),length(true)).  [ur(87,a,82,a,b,1875,a)].

given #2053 (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 #2054 (F,wt=11): 8392 -->_s0(true,head(cons(tail(app(nil,cons(x,false))),y))) # answer(goal).  [resolve(1337,a,3010,b)].

given #2055 (F,wt=11): 8394 -->_s0(true,tail(cons(x,tail(app(nil,cons(y,false)))))) # answer(goal).  [resolve(1337,a,2994,b)].

given #2056 (F,wt=11): 8397 -->_s0(true,x) | -->_s0(x,tail(app(nil,cons(y,false)))) # answer(goal).  [resolve(1337,a,2781,c)].

given #2057 (F,wt=11): 8413 -->_s0(true,tail(tail(cons(x,app(nil,cons(y,false)))))) # answer(goal).  [ur(2781,b,544,a,c,1337,a)].

given #2058 (T,wt=9): 2900 ->*_s0(app(nil,length(leq(0,x))),length(true)).  [ur(87,a,61,a,b,1875,a)].

given #2059 (T,wt=9): 2901 ->*_s0(head(sndsplit(0,leq(0,x))),head(true)).  [ur(87,a,483,a,b,1902,a)].

given #2060 (T,wt=9): 2902 ->*_s0(head(app(nil,leq(0,x))),head(true)).  [ur(87,a,133,a,b,1902,a)].

given #2061 (T,wt=9): 2904 ->*_s0(sndsplit(0,head(leq(0,x))),head(true)).  [ur(87,a,82,a,b,1902,a)].

given #2062 (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 #2063 (F,wt=11): 8414 -->_s0(true,tail(head(cons(app(nil,cons(x,false)),y)))) # answer(goal).  [ur(2781,b,269,a,c,1337,a)].

given #2064 (F,wt=11): 8516 -->_s0(true,head(cons(head(app(nil,cons(false,x))),y))) # answer(goal).  [resolve(1426,a,3010,b)].

given #2065 (F,wt=11): 8518 -->_s0(true,tail(cons(x,head(app(nil,cons(false,y)))))) # answer(goal).  [resolve(1426,a,2994,b)].

given #2066 (F,wt=11): 8521 -->_s0(true,x) | -->_s0(x,head(app(nil,cons(false,y)))) # answer(goal).  [resolve(1426,a,2781,c)].

given #2067 (T,wt=9): 2906 ->*_s0(app(nil,head(leq(0,x))),head(true)).  [ur(87,a,61,a,b,1902,a)].

given #2068 (T,wt=9): 2907 ->*_s0(f(x,app(nil,y)),f(x,y)).  [ur(87,a,115,a,b,86,a)].

given #2069 (T,wt=9): 3101 ->*_s0(empty(sndsplit(0,leq(0,x))),empty(true)).  [ur(87,a,486,a,b,1929,a)].

given #2070 (T,wt=9): 3102 ->*_s0(empty(app(nil,leq(0,x))),empty(true)).  [ur(87,a,136,a,b,1929,a)].

given #2071 (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 #2072 (F,wt=11): 8537 -->_s0(true,head(tail(cons(x,app(nil,cons(false,y)))))) # answer(goal).  [ur(2781,b,558,a,c,1426,a)].

given #2073 (F,wt=11): 8538 -->_s0(true,head(head(cons(app(nil,cons(false,x)),y)))) # answer(goal).  [ur(2781,b,283,a,c,1426,a)].

given #2074 (F,wt=11): 8578 -->_s0(true,head(cons(empty(app(nil,cons(x,y))),z))) # answer(goal).  [resolve(1455,a,3010,b)].

given #2075 (F,wt=11): 8580 -->_s0(true,tail(cons(x,empty(app(nil,cons(y,z)))))) # answer(goal).  [resolve(1455,a,2994,b)].

given #2076 (T,wt=9): 3104 ->*_s0(sndsplit(0,empty(leq(0,x))),empty(true)).  [ur(87,a,82,a,b,1929,a)].

given #2077 (T,wt=9): 3106 ->*_s0(app(nil,empty(leq(0,x))),empty(true)).  [ur(87,a,61,a,b,1929,a)].

given #2078 (T,wt=9): 3107 ->*_s0(s(sndsplit(0,mapf(x,nil))),s(nil)).  [ur(87,a,464,a,b,1992,a)].

given #2079 (T,wt=9): 3108 ->*_s0(s(app(nil,mapf(x,nil))),s(nil)).  [ur(87,a,114,a,b,1992,a)].

given #2080 (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 #2081 (F,wt=11): 8583 -->_s0(true,x) | -->_s0(x,empty(app(nil,cons(y,z)))) # answer(goal).  [resolve(1455,a,2781,c)].

given #2082 (F,wt=11): 8598 -->_s0(true,empty(tail(cons(x,app(nil,cons(y,z)))))) # answer(goal).  [ur(2781,b,561,a,c,1455,a)].

given #2083 (F,wt=11): 8599 -->_s0(true,empty(head(cons(app(nil,cons(x,y)),z)))) # answer(goal).  [ur(2781,b,286,a,c,1455,a)].

given #2084 (F,wt=11): 8796 -->_s0(true,head(cons(tail(sndsplit(0,cons(x,false))),y))) # answer(goal).  [resolve(2245,a,3010,b)].

given #2085 (T,wt=9): 3110 ->*_s0(sndsplit(0,s(mapf(x,nil))),s(nil)).  [ur(87,a,82,a,b,1992,a)].

given #2086 (T,wt=9): 3112 ->*_s0(app(nil,s(mapf(x,nil))),s(nil)).  [ur(87,a,61,a,b,1992,a)].

given #2087 (T,wt=9): 3113 ->*_s0(tail(sndsplit(0,mapf(x,nil))),tail(nil)).  [ur(87,a,469,a,b,2019,a)].

given #2088 (T,wt=9): 3114 ->*_s0(tail(app(nil,mapf(x,nil))),tail(nil)).  [ur(87,a,119,a,b,2019,a)].

given #2089 (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 #2090 (F,wt=11): 8798 -->_s0(true,tail(cons(x,tail(sndsplit(0,cons(y,false)))))) # answer(goal).  [resolve(2245,a,2994,b)].

given #2091 (F,wt=11): 8801 -->_s0(true,x) | -->_s0(x,tail(sndsplit(0,cons(y,false)))) # answer(goal).  [resolve(2245,a,2781,c)].

given #2092 (F,wt=11): 8817 -->_s0(true,tail(tail(cons(x,sndsplit(0,cons(y,false)))))) # answer(goal).  [ur(2781,b,544,a,c,2245,a)].

given #2093 (F,wt=11): 8818 -->_s0(true,tail(head(cons(sndsplit(0,cons(x,false)),y)))) # answer(goal).  [ur(2781,b,269,a,c,2245,a)].

given #2094 (T,wt=9): 3116 ->*_s0(sndsplit(0,tail(mapf(x,nil))),tail(nil)).  [ur(87,a,82,a,b,2019,a)].

given #2095 (T,wt=9): 3118 ->*_s0(app(nil,tail(mapf(x,nil))),tail(nil)).  [ur(87,a,61,a,b,2019,a)].

given #2096 (T,wt=9): 3119 ->*_s0(length(sndsplit(0,mapf(x,nil))),length(nil)).  [ur(87,a,482,a,b,2047,a)].

given #2097 (T,wt=9): 3120 ->*_s0(length(app(nil,mapf(x,nil))),length(nil)).  [ur(87,a,132,a,b,2047,a)].

given #2098 (A,wt=13): 403 ->_s0(mapf(x,leq(s(y),s(z))),mapf(x,leq(y,z))).  [ur(45,a,72,a)].

given #2099 (F,wt=11): 8960 -->_s0(true,head(cons(head(sndsplit(0,cons(false,x))),y))) # answer(goal).  [resolve(2314,a,3010,b)].

given #2100 (F,wt=11): 8962 -->_s0(true,tail(cons(x,head(sndsplit(0,cons(false,y)))))) # answer(goal).  [resolve(2314,a,2994,b)].

given #2101 (F,wt=11): 8965 -->_s0(true,x) | -->_s0(x,head(sndsplit(0,cons(false,y)))) # answer(goal).  [resolve(2314,a,2781,c)].

given #2102 (F,wt=11): 8981 -->_s0(true,head(tail(cons(x,sndsplit(0,cons(false,y)))))) # answer(goal).  [ur(2781,b,558,a,c,2314,a)].

given #2103 (T,wt=9): 3122 ->*_s0(sndsplit(0,length(mapf(x,nil))),length(nil)).  [ur(87,a,82,a,b,2047,a)].

given #2104 (T,wt=9): 3124 ->*_s0(app(nil,length(mapf(x,nil))),length(nil)).  [ur(87,a,61,a,b,2047,a)].

given #2105 (T,wt=9): 3126 ->*_s0(f(app(nil,x),y),f(x,y)).  [ur(87,a,116,a,b,86,a)].

given #2106 (T,wt=9): 3156 ->*_s0(head(sndsplit(0,mapf(x,nil))),head(nil)).  [ur(87,a,483,a,b,2121,a)].

given #2107 (A,wt=13): 404 ->_s0(mapf(leq(s(x),s(y)),z),mapf(leq(x,y),z)).  [ur(44,a,72,a)].

given #2108 (F,wt=11): 8982 -->_s0(true,head(head(cons(sndsplit(0,cons(false,x)),y)))) # answer(goal).  [ur(2781,b,283,a,c,2314,a)].

given #2109 (F,wt=11): 9077 -->_s0(true,head(cons(empty(sndsplit(0,cons(x,y))),z))) # answer(goal).  [resolve(2389,a,3010,b)].

given #2110 (F,wt=11): 9079 -->_s0(true,tail(cons(x,empty(sndsplit(0,cons(y,z)))))) # answer(goal).  [resolve(2389,a,2994,b)].

given #2111 (F,wt=11): 9082 -->_s0(true,x) | -->_s0(x,empty(sndsplit(0,cons(y,z)))) # answer(goal).  [resolve(2389,a,2781,c)].

given #2112 (T,wt=9): 3157 ->*_s0(head(app(nil,mapf(x,nil))),head(nil)).  [ur(87,a,133,a,b,2121,a)].

given #2113 (T,wt=9): 3159 ->*_s0(sndsplit(0,head(mapf(x,nil))),head(nil)).  [ur(87,a,82,a,b,2121,a)].

given #2114 (T,wt=9): 3161 ->*_s0(app(nil,head(mapf(x,nil))),head(nil)).  [ur(87,a,61,a,b,2121,a)].

given #2115 (T,wt=9): 3162 ->*_s0(empty(sndsplit(0,mapf(x,nil))),empty(nil)).  [ur(87,a,486,a,b,2148,a)].

given #2116 (A,wt=13): 405 ->_s0(leq(x,leq(s(y),s(z))),leq(x,leq(y,z))).  [ur(43,a,72,a)].

given #2117 (F,wt=11): 9097 -->_s0(true,empty(tail(cons(x,sndsplit(0,cons(y,z)))))) # answer(goal).  [ur(2781,b,561,a,c,2389,a)].

given #2118 (F,wt=11): 9098 -->_s0(true,empty(head(cons(sndsplit(0,cons(x,y)),z)))) # answer(goal).  [ur(2781,b,286,a,c,2389,a)].

given #2119 (F,wt=11): 9163 -->_s0(true,head(cons(head(app(cons(false,x),y)),z))) # answer(goal).  [resolve(2538,a,3010,b)].

given #2120 (F,wt=11): 9165 -->_s0(true,tail(cons(x,head(app(cons(false,y),z))))) # answer(goal).  [resolve(2538,a,2994,b)].

given #2121 (T,wt=9): 3163 ->*_s0(empty(app(nil,mapf(x,nil))),empty(nil)).  [ur(87,a,136,a,b,2148,a)].

given #2122 (T,wt=9): 3165 ->*_s0(sndsplit(0,empty(mapf(x,nil))),empty(nil)).  [ur(87,a,82,a,b,2148,a)].

given #2123 (T,wt=9): 3167 ->*_s0(app(nil,empty(mapf(x,nil))),empty(nil)).  [ur(87,a,61,a,b,2148,a)].

given #2124 (T,wt=9): 3168 ->*_s0(s(sndsplit(0,sndsplit(0,x))),s(x)).  [ur(87,a,464,a,b,2185,a)].

given #2125 (A,wt=13): 406 ->_s0(leq(leq(s(x),s(y)),z),leq(leq(x,y),z)).  [ur(42,a,72,a)].

given #2126 (F,wt=11): 9168 -->_s0(true,x) | -->_s0(x,head(app(cons(false,y),z))) # answer(goal).  [resolve(2538,a,2781,c)].

given #2127 (F,wt=11): 9184 -->_s0(true,head(tail(cons(x,app(cons(false,y),z))))) # answer(goal).  [ur(2781,b,558,a,c,2538,a)].

given #2128 (F,wt=11): 9185 -->_s0(true,head(head(cons(app(cons(false,x),y),z)))) # answer(goal).  [ur(2781,b,283,a,c,2538,a)].

given #2129 (F,wt=11): 9188 -->_s0(true,head(cons(empty(app(cons(x,y),z)),u))) # answer(goal).  [resolve(2754,a,3010,b)].

given #2130 (T,wt=9): 3169 ->*_s0(s(app(nil,sndsplit(0,x))),s(x)).  [ur(87,a,114,a,b,2185,a)].

given #2131 (T,wt=9): 3171 ->*_s0(sndsplit(0,s(sndsplit(0,x))),s(x)).  [ur(87,a,82,a,b,2185,a)].

given #2132 (T,wt=9): 3173 ->*_s0(app(nil,s(sndsplit(0,x))),s(x)).  [ur(87,a,61,a,b,2185,a)].

given #2133 (T,wt=9): 3174 ->*_s0(tail(sndsplit(0,sndsplit(0,x))),tail(x)).  [ur(87,a,469,a,b,2246,a)].

given #2134 (A,wt=11): 407 ->_s0(length(leq(s(x),s(y))),length(leq(x,y))).  [ur(41,a,72,a)].

given #2135 (F,wt=11): 9190 -->_s0(true,tail(cons(x,empty(app(cons(y,z),u))))) # answer(goal).  [resolve(2754,a,2994,b)].

given #2136 (F,wt=11): 9193 -->_s0(true,x) | -->_s0(x,empty(app(cons(y,z),u))) # answer(goal).  [resolve(2754,a,2781,c)].

given #2137 (F,wt=11): 9208 -->_s0(true,empty(tail(cons(x,app(cons(y,z),u))))) # answer(goal).  [ur(2781,b,561,a,c,2754,a)].

given #2138 (F,wt=11): 9209 -->_s0(true,empty(head(cons(app(cons(x,y),z),u)))) # answer(goal).  [ur(2781,b,286,a,c,2754,a)].

given #2139 (T,wt=9): 3175 ->*_s0(tail(app(nil,sndsplit(0,x))),tail(x)).  [ur(87,a,119,a,b,2246,a)].

given #2140 (T,wt=9): 3177 ->*_s0(sndsplit(0,tail(sndsplit(0,x))),tail(x)).  [ur(87,a,82,a,b,2246,a)].

given #2141 (T,wt=9): 3179 ->*_s0(app(nil,tail(sndsplit(0,x))),tail(x)).  [ur(87,a,61,a,b,2246,a)].

given #2142 (T,wt=9): 3181 ->*_s0(cons(x,app(nil,y)),cons(x,y)).  [ur(87,a,117,a,b,86,a)].

given #2143 (A,wt=11): 408 ->_s0(head(leq(s(x),s(y))),head(leq(x,y))).  [ur(40,a,72,a)].

given #2144 (F,wt=11): 9398 -->_s0(true,length(nil)) | -->_s0(0,app(fstsplit(0,x),false)) # answer(goal).  [resolve(9370,a,3100,c)].

given #2145 (F,wt=11): 9822 -->_s0(true,head(cons(sndsplit(length(nil),app(nil,false)),x))) # answer(goal).  [resolve(4567,a,3010,b)].

given #2146 (F,wt=11): 9824 -->_s0(true,tail(cons(x,sndsplit(length(nil),app(nil,false))))) # answer(goal).  [resolve(4567,a,2994,b)].

given #2147 (F,wt=11): 9825 -->_s0(true,x) | -->_s0(x,sndsplit(length(nil),app(nil,false))) # answer(goal).  [resolve(4567,a,2781,c)].

given #2148 (T,wt=9): 3211 ->*_s0(length(sndsplit(0,sndsplit(0,x))),length(x)).  [ur(87,a,482,a,b,2279,a)].

given #2149 (T,wt=9): 3212 ->*_s0(length(app(nil,sndsplit(0,x))),length(x)).  [ur(87,a,132,a,b,2279,a)].

given #2150 (T,wt=9): 3214 ->*_s0(sndsplit(0,length(sndsplit(0,x))),length(x)).  [ur(87,a,82,a,b,2279,a)].

given #2151 (T,wt=9): 3216 ->*_s0(app(nil,length(sndsplit(0,x))),length(x)).  [ur(87,a,61,a,b,2279,a)].

given #2152 (A,wt=13): 409 ->_s0(fstsplit(x,leq(s(y),s(z))),fstsplit(x,leq(y,z))).  [ur(39,a,72,a)].

given #2153 (F,wt=11): 9842 -->_s0(true,sndsplit(s(length(nil)),cons(x,app(nil,false)))) # answer(goal).  [ur(2781,b,83,a,c,4567,a)].

given #2154 (F,wt=11): 9877 -->_s0(true,head(cons(sndsplit(length(nil),sndsplit(0,false)),x))) # answer(goal).  [resolve(4571,a,3010,b)].

given #2155 (F,wt=11): 9879 -->_s0(true,tail(cons(x,sndsplit(length(nil),sndsplit(0,false))))) # answer(goal).  [resolve(4571,a,2994,b)].

given #2156 (F,wt=11): 9880 -->_s0(true,x) | -->_s0(x,sndsplit(length(nil),sndsplit(0,false))) # answer(goal).  [resolve(4571,a,2781,c)].

given #2157 (T,wt=9): 3217 ->*_s0(head(sndsplit(0,sndsplit(0,x))),head(x)).  [ur(87,a,483,a,b,2315,a)].

given #2158 (T,wt=9): 3218 ->*_s0(head(app(nil,sndsplit(0,x))),head(x)).  [ur(87,a,133,a,b,2315,a)].

given #2159 (T,wt=9): 3220 ->*_s0(sndsplit(0,head(sndsplit(0,x))),head(x)).  [ur(87,a,82,a,b,2315,a)].

given #2160 (T,wt=9): 3222 ->*_s0(app(nil,head(sndsplit(0,x))),head(x)).  [ur(87,a,61,a,b,2315,a)].

given #2161 (A,wt=13): 410 ->_s0(fstsplit(leq(s(x),s(y)),z),fstsplit(leq(x,y),z)).  [ur(38,a,72,a)].

given #2162 (F,wt=11): 9897 -->_s0(true,sndsplit(s(length(nil)),cons(x,sndsplit(0,false)))) # answer(goal).  [ur(2781,b,83,a,c,4571,a)].

given #2163 (F,wt=11): 9919 -->_s0(true,head(cons(sndsplit(app(nil,length(nil)),false),x))) # answer(goal).  [resolve(4642,a,3010,b)].

given #2164 (F,wt=11): 9921 -->_s0(true,tail(cons(x,sndsplit(app(nil,length(nil)),false)))) # answer(goal).  [resolve(4642,a,2994,b)].

given #2165 (F,wt=11): 9922 -->_s0(true,x) | -->_s0(x,sndsplit(app(nil,length(nil)),false)) # answer(goal).  [resolve(4642,a,2781,c)].

given #2166 (T,wt=9): 3223 ->*_s0(empty(sndsplit(0,sndsplit(0,x))),empty(x)).  [ur(87,a,486,a,b,2391,a)].

given #2167 (T,wt=9): 3224 ->*_s0(empty(app(nil,sndsplit(0,x))),empty(x)).  [ur(87,a,136,a,b,2391,a)].

given #2168 (T,wt=9): 3226 ->*_s0(sndsplit(0,empty(sndsplit(0,x))),empty(x)).  [ur(87,a,82,a,b,2391,a)].

given #2169 (T,wt=9): 3228 ->*_s0(app(nil,empty(sndsplit(0,x))),empty(x)).  [ur(87,a,61,a,b,2391,a)].

given #2170 (A,wt=11): 411 ->_s0(empty(leq(s(x),s(y))),empty(leq(x,y))).  [ur(37,a,72,a)].

given #2171 (F,wt=11): 9939 -->_s0(true,sndsplit(app(nil,length(nil)),empty(cons(x,y)))) # answer(goal).  [ur(2781,b,145,a,c,4642,a)].

given #2172 (F,wt=11): 9941 -->_s0(true,sndsplit(s(app(nil,length(nil))),cons(x,false))) # answer(goal).  [ur(2781,b,83,a,c,4642,a)].

given #2173 (F,wt=11): 9944 -->_s0(true,head(cons(sndsplit(0,sndsplit(length(nil),false)),x))) # answer(goal).  [resolve(4646,a,3010,b)].

given #2174 (F,wt=11): 9946 -->_s0(true,tail(cons(x,sndsplit(0,sndsplit(length(nil),false))))) # answer(goal).  [resolve(4646,a,2994,b)].

given #2175 (T,wt=9): 3257 ->*_s0(cons(app(nil,x),y),cons(x,y)).  [ur(87,a,118,a,b,86,a)].

given #2176 (T,wt=9): 3393 ->*_s0(sndsplit(x,app(nil,y)),sndsplit(x,y)).  [ur(87,a,120,a,b,86,a)].

given #2177 (T,wt=9): 3529 ->*_s0(sndsplit(app(nil,0),app(nil,x)),x).  [ur(87,a,121,a,b,696,a)].

given #2178 (T,wt=9): 3530 ->*_s0(sndsplit(app(nil,0),fstsplit(0,x)),nil).  [ur(87,a,121,a,b,689,a)].

given #2179 (A,wt=13): 412 ->_s0(app(x,leq(s(y),s(z))),app(x,leq(y,z))).  [ur(36,a,72,a)].

given #2180 (F,wt=11): 9947 -->_s0(true,x) | -->_s0(x,sndsplit(0,sndsplit(length(nil),false))) # answer(goal).  [resolve(4646,a,2781,c)].

given #2181 (F,wt=11): 9966 -->_s0(true,sndsplit(s(0),cons(x,sndsplit(length(nil),false)))) # answer(goal).  [ur(2781,b,83,a,c,4646,a)].

given #2182 (F,wt=11): 9969 -->_s0(true,head(cons(app(nil,sndsplit(length(nil),false)),x))) # answer(goal).  [resolve(4648,a,3010,b)].

given #2183 (F,wt=11): 9970 -->_s0(true,tail(cons(x,app(nil,sndsplit(length(nil),false))))) # answer(goal).  [resolve(4648,a,2994,b)].

given #2184 (T,wt=9): 3531 ->*_s0(sndsplit(app(nil,0),leq(0,x)),true).  [ur(87,a,121,a,b,684,a)].

given #2185 (T,wt=9): 3532 ->*_s0(sndsplit(app(nil,0),mapf(x,nil)),nil).  [ur(87,a,121,a,b,643,a)].

given #2186 (T,wt=9): 3533 ->*_s0(sndsplit(app(nil,0),sndsplit(0,x)),x).  [ur(87,a,121,a,b,639,a)].

given #2187 (T,wt=9): 3538 ->*_s0(sndsplit(app(nil,x),y),sndsplit(x,y)).  [ur(87,a,121,a,b,86,a)].

given #2188 (A,wt=13): 413 ->_s0(app(leq(s(x),s(y)),z),app(leq(x,y),z)).  [ur(35,a,72,a)].

given #2189 (F,wt=11): 9971 -->_s0(true,x) | -->_s0(x,app(nil,sndsplit(length(nil),false))) # answer(goal).  [resolve(4648,a,2781,c)].

given #2190 (F,wt=11): 9999 -->_s0(true,head(cons(leq(s(x),app(nil,0)),y))) # answer(goal).  [resolve(4699,a,3010,b)].

given #2191 (F,wt=11): 10001 -->_s0(true,tail(cons(x,leq(s(y),app(nil,0))))) # answer(goal).  [resolve(4699,a,2994,b)].

given #2192 (F,wt=11): 10002 -->_s0(true,x) | -->_s0(x,leq(s(y),app(nil,0))) # answer(goal).  [resolve(4699,a,2781,c)].

given #2193 (T,wt=9): 3576 ->*_s0(sndsplit(app(nil,app(nil,0)),x),x).  [ur(87,a,121,a,b,3536,a)].

given #2194 (T,wt=9): 3580 ->*_s0(sndsplit(0,sndsplit(app(nil,0),x)),x).  [ur(87,a,82,a,b,3536,a)].

given #2195 (T,wt=9): 3582 ->*_s0(app(nil,sndsplit(app(nil,0),x)),x).  [ur(87,a,61,a,b,3536,a)].

given #2196 (T,wt=9): 4029 ->*_s0(length(sndsplit(0,fstsplit(s(x),nil))),0).  [ur(87,a,482,a,b,4002,a)].

given #2197 (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 #2198 (F,wt=10): 19974 -->_s0(true,sndsplit(length(nil),sndsplit(app(nil,0),false))) # answer(goal).  [resolve(3580,a,4566,b)].

given #2199 (F,wt=11): 10050 -->_s0(true,head(cons(leq(app(nil,s(x)),0),y))) # answer(goal).  [resolve(4835,a,3010,b)].

given #2200 (F,wt=11): 10052 -->_s0(true,tail(cons(x,leq(app(nil,s(y)),0)))) # answer(goal).  [resolve(4835,a,2994,b)].

given #2201 (F,wt=11): 10053 -->_s0(true,x) | -->_s0(x,leq(app(nil,s(y)),0)) # answer(goal).  [resolve(4835,a,2781,c)].

given #2202 (T,wt=9): 4030 ->*_s0(length(app(nil,fstsplit(s(x),nil))),0).  [ur(87,a,132,a,b,4002,a)].

given #2203 (T,wt=9): 4032 ->*_s0(sndsplit(0,length(fstsplit(s(x),nil))),0).  [ur(87,a,82,a,b,4002,a)].

given #2204 (T,wt=9): 4034 ->*_s0(app(nil,length(fstsplit(s(x),nil))),0).  [ur(87,a,61,a,b,4002,a)].

given #2205 (T,wt=9): 4124 ->*_s0(empty(sndsplit(0,fstsplit(s(x),nil))),true).  [ur(87,a,486,a,b,4094,a)].

given #2206 (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 #2207 (F,wt=11): 10340 -->_s0(true,head(cons(tail(app(cons(x,nil),false)),y))) # answer(goal).  [resolve(5956,a,3010,b)].

given #2208 (F,wt=11): 10342 -->_s0(true,tail(cons(x,tail(app(cons(y,nil),false))))) # answer(goal).  [resolve(5956,a,2994,b)].

given #2209 (F,wt=11): 10345 -->_s0(true,x) | -->_s0(x,tail(app(cons(y,nil),false))) # answer(goal).  [resolve(5956,a,2781,c)].

given #2210 (F,wt=11): 10361 -->_s0(true,tail(tail(cons(x,app(cons(y,nil),false))))) # answer(goal).  [ur(2781,b,544,a,c,5956,a)].

given #2211 (T,wt=9): 4125 ->*_s0(empty(app(nil,fstsplit(s(x),nil))),true).  [ur(87,a,136,a,b,4094,a)].

given #2212 (T,wt=9): 4127 ->*_s0(sndsplit(0,empty(fstsplit(s(x),nil))),true).  [ur(87,a,82,a,b,4094,a)].

given #2213 (T,wt=9): 4129 ->*_s0(app(nil,empty(fstsplit(s(x),nil))),true).  [ur(87,a,61,a,b,4094,a)].

given #2214 (T,wt=9): 4136 ->*_s0(s(head(cons(length(nil),x))),s(0)).  [ur(87,a,264,a,b,891,a)].

given #2215 (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 #2216 (F,wt=11): 10362 -->_s0(true,tail(head(cons(app(cons(x,nil),false),y)))) # answer(goal).  [ur(2781,b,269,a,c,5956,a)].

given #2217 (F,wt=11): 10397 -->_s0(true,head(fstsplit(s(x),cons(app(nil,false),y)))) # answer(goal).  [ur(2781,b,233,a,c,697,a)].

given #2218 (F,wt=11): 10398 -->_s0(true,head(fstsplit(s(x),cons(sndsplit(0,false),y)))) # answer(goal).  [ur(2781,b,233,a,c,640,a)].

given #2219 (F,wt=11): 11251 -->_s0(true,length(nil)) | -->_s0(0,app(mapf(x,nil),false)) # answer(goal).  [resolve(11239,a,3100,c)].

given #2220 (T,wt=9): 4137 ->*_s0(s(head(cons(empty(nil),x))),s(true)).  [ur(87,a,264,a,b,699,a)].

given #2221 (T,wt=9): 4170 ->*_s0(tail(head(cons(length(nil),x))),tail(0)).  [ur(87,a,269,a,b,917,a)].

given #2222 (T,wt=9): 4171 ->*_s0(tail(head(cons(empty(nil),x))),tail(true)).  [ur(87,a,269,a,b,755,a)].

given #2223 (T,wt=9): 4174 ->*_s0(tail(head(cons(cons(x,y),z))),y).  [ur(87,a,269,a,b,564,a)].

given #2224 (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 #2225 (F,wt=11): 11464 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(sndsplit(0,0),false)) # answer(goal).  [resolve(11447,a,3100,c)].

given #2226 (F,wt=11): 11486 -->_s0(true,head(cons(sndsplit(sndsplit(0,length(nil)),false),x))) # answer(goal).  [resolve(11395,a,3010,b)].

given #2227 (F,wt=11): 11488 -->_s0(true,tail(cons(x,sndsplit(sndsplit(0,length(nil)),false)))) # answer(goal).  [resolve(11395,a,2994,b)].

given #2228 (F,wt=11): 11489 -->_s0(true,x) | -->_s0(x,sndsplit(sndsplit(0,length(nil)),false)) # answer(goal).  [resolve(11395,a,2781,c)].

given #2229 (T,wt=9): 4232 ->*_s0(length(head(cons(sndsplit(0,nil),x))),0).  [ur(87,a,282,a,b,2278,a)].

given #2230 (T,wt=9): 4234 ->*_s0(length(head(cons(mapf(x,nil),y))),0).  [ur(87,a,282,a,b,2046,a)].

given #2231 (T,wt=9): 4237 ->*_s0(length(head(cons(fstsplit(0,x),y))),0).  [ur(87,a,282,a,b,1661,a)].

given #2232 (T,wt=9): 4239 ->*_s0(length(head(cons(app(nil,nil),x))),0).  [ur(87,a,282,a,b,1366,a)].

given #2233 (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 #2234 (F,wt=11): 11507 -->_s0(true,sndsplit(sndsplit(0,length(nil)),empty(cons(x,y)))) # answer(goal).  [ur(2781,b,145,a,c,11395,a)].

given #2235 (F,wt=11): 11509 -->_s0(true,sndsplit(s(sndsplit(0,length(nil))),cons(x,false))) # answer(goal).  [ur(2781,b,83,a,c,11395,a)].

given #2236 (F,wt=11): 11604 -->_s0(true,app(fstsplit(s(x),nil),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,263,a,c,4648,a)].

given #2237 (F,wt=11): 11605 -->_s0(true,app(fstsplit(s(x),nil),empty(cons(y,z)))) # answer(goal).  [ur(2781,b,263,a,c,1127,a)].

given #2238 (T,wt=9): 4241 ->*_s0(length(head(cons(length(nil),x))),length(0)).  [ur(87,a,282,a,b,943,a)].

given #2239 (T,wt=9): 4242 ->*_s0(length(head(cons(empty(nil),x))),length(true)).  [ur(87,a,282,a,b,781,a)].

given #2240 (T,wt=9): 4270 ->*_s0(length(sndsplit(0,head(cons(nil,x)))),0).  [ur(87,a,482,a,b,4243,a)].

given #2241 (T,wt=9): 4272 ->*_s0(length(app(nil,head(cons(nil,x)))),0).  [ur(87,a,132,a,b,4243,a)].

given #2242 (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 #2243 (F,wt=11): 11606 -->_s0(true,app(fstsplit(s(x),nil),head(cons(false,y)))) # answer(goal).  [ur(2781,b,263,a,c,1115,a)].

given #2244 (F,wt=11): 11607 -->_s0(true,app(fstsplit(s(x),nil),leq(s(y),0))) # answer(goal).  [ur(2781,b,263,a,c,1078,a)].

given #2245 (F,wt=11): 11608 -->_s0(true,app(fstsplit(s(x),nil),tail(cons(y,false)))) # answer(goal).  [ur(2781,b,263,a,c,1065,a)].

given #2246 (F,wt=11): 11610 -->_s0(true,head(cons(app(fstsplit(s(x),nil),false),y))) # answer(goal).  [resolve(11602,a,3010,b)].

given #2247 (T,wt=9): 4274 ->*_s0(sndsplit(0,length(head(cons(nil,x)))),0).  [ur(87,a,82,a,b,4243,a)].

given #2248 (T,wt=9): 4276 ->*_s0(app(nil,length(head(cons(nil,x)))),0).  [ur(87,a,61,a,b,4243,a)].

given #2249 (T,wt=9): 4283 ->*_s0(head(head(cons(length(nil),x))),head(0)).  [ur(87,a,283,a,b,969,a)].

given #2250 (T,wt=9): 4284 ->*_s0(head(head(cons(empty(nil),x))),head(true)).  [ur(87,a,283,a,b,807,a)].

given #2251 (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 #2252 (F,wt=11): 11611 -->_s0(true,tail(cons(x,app(fstsplit(s(y),nil),false)))) # answer(goal).  [resolve(11602,a,2994,b)].

given #2253 (F,wt=11): 11612 -->_s0(true,x) | -->_s0(x,app(fstsplit(s(y),nil),false)) # answer(goal).  [resolve(11602,a,2781,c)].

given #2254 (F,wt=11): 11659 -->_s0(true,head(cons(leq(s(x),sndsplit(0,0)),y))) # answer(goal).  [resolve(11647,a,3010,b)].

given #2255 (F,wt=11): 11661 -->_s0(true,tail(cons(x,leq(s(y),sndsplit(0,0))))) # answer(goal).  [resolve(11647,a,2994,b)].

given #2256 (T,wt=9): 4287 ->*_s0(head(head(cons(cons(x,y),z))),x).  [ur(87,a,283,a,b,575,a)].

given #2257 (T,wt=9): 4318 ->*_s0(empty(head(cons(sndsplit(0,nil),x))),true).  [ur(87,a,286,a,b,2390,a)].

given #2258 (T,wt=9): 4320 ->*_s0(empty(head(cons(mapf(x,nil),y))),true).  [ur(87,a,286,a,b,2147,a)].

given #2259 (T,wt=9): 4323 ->*_s0(empty(head(cons(fstsplit(0,x),y))),true).  [ur(87,a,286,a,b,1750,a)].

given #2260 (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 #2261 (F,wt=11): 11662 -->_s0(true,x) | -->_s0(x,leq(s(y),sndsplit(0,0))) # answer(goal).  [resolve(11647,a,2781,c)].

given #2262 (F,wt=11): 11735 -->_s0(true,head(cons(leq(sndsplit(0,s(x)),0),y))) # answer(goal).  [resolve(11700,a,3010,b)].

given #2263 (F,wt=11): 11737 -->_s0(true,tail(cons(x,leq(sndsplit(0,s(y)),0)))) # answer(goal).  [resolve(11700,a,2994,b)].

given #2264 (F,wt=11): 11738 -->_s0(true,x) | -->_s0(x,leq(sndsplit(0,s(y)),0)) # answer(goal).  [resolve(11700,a,2781,c)].

given #2265 (T,wt=9): 4325 ->*_s0(empty(head(cons(app(nil,nil),x))),true).  [ur(87,a,286,a,b,1456,a)].

given #2266 (T,wt=9): 4326 ->*_s0(empty(head(cons(length(nil),x))),empty(0)).  [ur(87,a,286,a,b,1031,a)].

given #2267 (T,wt=9): 4327 ->*_s0(empty(head(cons(empty(nil),x))),empty(true)).  [ur(87,a,286,a,b,833,a)].

given #2268 (T,wt=9): 4328 ->*_s0(empty(head(cons(cons(x,y),z))),false).  [ur(87,a,286,a,b,580,a)].

given #2269 (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 #2270 (F,wt=11): 11914 -->_s0(true,length(nil)) | -->_s0(0,app(sndsplit(0,nil),false)) # answer(goal).  [resolve(11892,a,3100,c)].

given #2271 (F,wt=11): 12012 -->_s0(true,sndsplit(sndsplit(0,length(nil)),head(cons(false,x)))) # answer(goal).  [ur(2781,b,270,a,c,11395,a)].

given #2272 (F,wt=11): 12013 -->_s0(true,sndsplit(0,head(cons(sndsplit(length(nil),false),x)))) # answer(goal).  [ur(2781,b,270,a,c,4646,a)].

given #2273 (F,wt=11): 12014 -->_s0(true,sndsplit(app(nil,length(nil)),head(cons(false,x)))) # answer(goal).  [ur(2781,b,270,a,c,4642,a)].

given #2274 (T,wt=9): 4387 ->*_s0(empty(sndsplit(0,head(cons(nil,x)))),true).  [ur(87,a,486,a,b,4329,a)].

given #2275 (T,wt=9): 4389 ->*_s0(empty(app(nil,head(cons(nil,x)))),true).  [ur(87,a,136,a,b,4329,a)].

given #2276 (T,wt=9): 4391 ->*_s0(sndsplit(0,empty(head(cons(nil,x)))),true).  [ur(87,a,82,a,b,4329,a)].

given #2277 (T,wt=9): 4393 ->*_s0(app(nil,empty(head(cons(nil,x)))),true).  [ur(87,a,61,a,b,4329,a)].

given #2278 (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 #2279 (F,wt=11): 12015 -->_s0(true,sndsplit(length(nil),head(cons(sndsplit(0,false),x)))) # answer(goal).  [ur(2781,b,270,a,c,4571,a)].

given #2280 (F,wt=11): 12016 -->_s0(true,sndsplit(length(nil),head(cons(app(nil,false),x)))) # answer(goal).  [ur(2781,b,270,a,c,4567,a)].

given #2281 (F,wt=11): 12017 -->_s0(true,sndsplit(0,head(cons(empty(cons(x,y)),z)))) # answer(goal).  [ur(2781,b,270,a,c,1125,a)].

given #2282 (F,wt=11): 12018 -->_s0(true,sndsplit(0,head(cons(head(cons(false,x)),y)))) # answer(goal).  [ur(2781,b,270,a,c,1113,a)].

given #2283 (T,wt=9): 4477 ->*_s0(mapf(x,app(nil,y)),mapf(x,y)).  [ur(87,a,128,a,b,86,a)].

given #2284 (T,wt=9): 4507 ->*_s0(mapf(x,app(nil,app(nil,nil))),nil).  [ur(87,a,128,a,b,4476,a)].

given #2285 (T,wt=9): 4509 ->*_s0(sndsplit(0,mapf(x,app(nil,nil))),nil).  [ur(87,a,82,a,b,4476,a)].

given #2286 (T,wt=9): 4511 ->*_s0(app(nil,mapf(x,app(nil,nil))),nil).  [ur(87,a,61,a,b,4476,a)].

given #2287 (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 #2288 (F,wt=11): 12019 -->_s0(true,sndsplit(0,head(cons(leq(s(x),0),y)))) # answer(goal).  [ur(2781,b,270,a,c,1075,a)].

given #2289 (F,wt=11): 12020 -->_s0(true,sndsplit(0,head(cons(tail(cons(x,false)),y)))) # answer(goal).  [ur(2781,b,270,a,c,1063,a)].

given #2290 (F,wt=11): 12021 -->_s0(true,sndsplit(s(0),head(cons(cons(x,false),y)))) # answer(goal).  [ur(2781,b,270,a,c,638,a)].

given #2291 (F,wt=11): 12025 -->_s0(true,app(nil,tail(cons(x,tail(cons(y,false)))))) # answer(goal).  [resolve(1062,a,3014,b)].

given #2292 (T,wt=9): 4604 ->*_s0(mapf(app(nil,x),y),mapf(x,y)).  [ur(87,a,129,a,b,86,a)].

given #2293 (T,wt=9): 4644 ->*_s0(tail(cons(x,sndsplit(length(nil),y))),y).  [ur(87,a,85,a,b,4574,a)].

given #2294 (T,wt=9): 4645 ->*_s0(sndsplit(s(length(nil)),cons(x,y)),y).  [ur(87,a,83,a,b,4574,a)].

given #2295 (T,wt=9): 4647 ->*_s0(head(cons(sndsplit(length(nil),x),y)),x).  [ur(87,a,67,a,b,4574,a)].

given #2296 (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 #2297 (F,wt=10): 20265 -->_s0(true,sndsplit(length(cons(x,nil)),cons(y,false))) # answer(goal).  [ur(2781,b,296,a,c,4645,a)].

given #2298 (F,wt=11): 12027 -->_s0(true,sndsplit(0,tail(cons(x,tail(cons(y,false)))))) # answer(goal).  [resolve(1062,a,2997,b)].

given #2299 (F,wt=11): 12029 -->_s0(true,tail(app(nil,cons(x,tail(cons(y,false)))))) # answer(goal).  [resolve(1062,a,2966,b)].

given #2300 (F,wt=11): 12030 -->_s0(true,tail(sndsplit(0,cons(x,tail(cons(y,false)))))) # answer(goal).  [resolve(1062,a,2936,b)].

given #2301 (T,wt=9): 4656 ->*_s0(sndsplit(app(nil,length(nil)),empty(nil)),true).  [ur(87,a,121,a,b,4572,a)].

given #2302 (T,wt=9): 4657 ->*_s0(sndsplit(length(nil),app(nil,empty(nil))),true).  [ur(87,a,120,a,b,4572,a)].

given #2303 (T,wt=9): 4660 ->*_s0(sndsplit(0,sndsplit(length(nil),empty(nil))),true).  [ur(87,a,82,a,b,4572,a)].

given #2304 (T,wt=9): 4662 ->*_s0(app(nil,sndsplit(length(nil),empty(nil))),true).  [ur(87,a,61,a,b,4572,a)].

given #2305 (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 #2306 (F,wt=11): 12046 -->_s0(true,app(nil,head(cons(tail(cons(x,false)),y)))) # answer(goal).  [resolve(1064,a,3014,b)].

given #2307 (F,wt=11): 12049 -->_s0(true,head(app(nil,cons(tail(cons(x,false)),y)))) # answer(goal).  [resolve(1064,a,2964,b)].

given #2308 (F,wt=11): 12050 -->_s0(true,head(sndsplit(0,cons(tail(cons(x,false)),y)))) # answer(goal).  [resolve(1064,a,2934,b)].

given #2309 (F,wt=11): 12066 -->_s0(true,head(app(cons(tail(cons(x,false)),y),z))) # answer(goal).  [ur(2781,b,108,a,c,1064,a)].

given #2310 (T,wt=9): 4663 ->*_s0(sndsplit(app(nil,length(nil)),length(nil)),0).  [ur(87,a,121,a,b,4573,a)].

given #2311 (T,wt=9): 4664 ->*_s0(sndsplit(length(nil),app(nil,length(nil))),0).  [ur(87,a,120,a,b,4573,a)].

given #2312 (T,wt=9): 4667 ->*_s0(sndsplit(0,sndsplit(length(nil),length(nil))),0).  [ur(87,a,82,a,b,4573,a)].

given #2313 (T,wt=9): 4669 ->*_s0(app(nil,sndsplit(length(nil),length(nil))),0).  [ur(87,a,61,a,b,4573,a)].

given #2314 (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 #2315 (F,wt=11): 12147 -->_s0(true,sndsplit(head(cons(sndsplit(0,length(nil)),x)),false)) # answer(goal).  [ur(2781,b,271,a,c,11395,a)].

given #2316 (F,wt=11): 12148 -->_s0(true,sndsplit(head(cons(0,x)),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,271,a,c,4646,a)].

given #2317 (F,wt=11): 12149 -->_s0(true,sndsplit(head(cons(app(nil,length(nil)),x)),false)) # answer(goal).  [ur(2781,b,271,a,c,4642,a)].

given #2318 (F,wt=11): 12150 -->_s0(true,sndsplit(head(cons(length(nil),x)),sndsplit(0,false))) # answer(goal).  [ur(2781,b,271,a,c,4571,a)].

given #2319 (T,wt=9): 4698 ->*_s0(leq(s(0),app(nil,s(x))),true).  [ur(87,a,130,a,b,685,a)].

given #2320 (T,wt=9): 4700 ->*_s0(leq(x,app(nil,y)),leq(x,y)).  [ur(87,a,130,a,b,86,a)].

given #2321 (T,wt=9): 4791 ->*_s0(leq(s(x),app(nil,length(nil))),false).  [ur(87,a,130,a,b,4756,a)].

given #2322 (T,wt=9): 4793 ->*_s0(sndsplit(0,leq(s(x),length(nil))),false).  [ur(87,a,82,a,b,4756,a)].

given #2323 (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 #2324 (F,wt=10): 20349 -->_s0(true,sndsplit(length(nil),leq(s(x),length(nil)))) # answer(goal).  [resolve(4793,a,4566,b)].

given #2325 (F,wt=11): 12151 -->_s0(true,sndsplit(head(cons(length(nil),x)),app(nil,false))) # answer(goal).  [ur(2781,b,271,a,c,4567,a)].

given #2326 (F,wt=11): 12152 -->_s0(true,sndsplit(head(cons(0,x)),empty(cons(y,z)))) # answer(goal).  [ur(2781,b,271,a,c,1125,a)].

given #2327 (F,wt=11): 12153 -->_s0(true,sndsplit(head(cons(0,x)),head(cons(false,y)))) # answer(goal).  [ur(2781,b,271,a,c,1113,a)].

given #2328 (T,wt=9): 4794 ->*_s0(leq(s(s(x)),s(length(nil))),false).  [ur(87,a,72,a,b,4756,a)].

given #2329 (T,wt=9): 4796 ->*_s0(app(nil,leq(s(x),length(nil))),false).  [ur(87,a,61,a,b,4756,a)].

given #2330 (T,wt=9): 4832 ->*_s0(leq(app(nil,s(x)),length(nil)),false).  [ur(87,a,131,a,b,4756,a)].

given #2331 (T,wt=9): 4833 ->*_s0(leq(app(nil,s(0)),s(x)),true).  [ur(87,a,131,a,b,685,a)].

given #2332 (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 #2333 (F,wt=10): 20418 -->_s0(true,leq(s(s(x)),length(cons(y,nil)))) # answer(goal).  [ur(2781,b,305,a,c,4794,a)].

given #2334 (F,wt=11): 12154 -->_s0(true,sndsplit(head(cons(0,x)),leq(s(y),0))) # answer(goal).  [ur(2781,b,271,a,c,1075,a)].

given #2335 (F,wt=11): 12155 -->_s0(true,sndsplit(head(cons(0,x)),tail(cons(y,false)))) # answer(goal).  [ur(2781,b,271,a,c,1063,a)].

given #2336 (F,wt=11): 12156 -->_s0(true,sndsplit(head(cons(s(0),x)),cons(y,false))) # answer(goal).  [ur(2781,b,271,a,c,638,a)].

given #2337 (T,wt=9): 4836 ->*_s0(leq(app(nil,x),y),leq(x,y)).  [ur(87,a,131,a,b,86,a)].

given #2338 (T,wt=9): 4870 ->*_s0(tail(cons(x,leq(length(nil),y))),true).  [ur(87,a,85,a,b,4803,a)].

given #2339 (T,wt=9): 4873 ->*_s0(head(cons(leq(length(nil),x),y)),true).  [ur(87,a,67,a,b,4803,a)].

given #2340 (T,wt=9): 4879 ->*_s0(leq(app(nil,app(nil,0)),x),true).  [ur(87,a,131,a,b,4834,a)].

given #2341 (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)].

given #2342 (F,wt=11): 12158 -->_s0(true,head(cons(sndsplit(head(cons(0,x)),false),y))) # answer(goal).  [resolve(12143,a,3010,b)].

given #2343 (F,wt=11): 12159 -->_s0(true,tail(cons(x,sndsplit(head(cons(0,y)),false)))) # answer(goal).  [resolve(12143,a,2994,b)].

given #2344 (F,wt=11): 12160 -->_s0(true,x) | -->_s0(x,sndsplit(head(cons(0,y)),false)) # answer(goal).  [resolve(12143,a,2781,c)].

given #2345 (F,wt=11): 12177 -->_s0(true,sndsplit(head(cons(head(cons(0,x)),y)),false)) # answer(goal).  [ur(2781,b,271,a,c,12143,a)].

given #2346 (T,wt=9): 4881 ->*_s0(sndsplit(0,leq(app(nil,0),x)),true).  [ur(87,a,82,a,b,4834,a)].

given #2347 (T,wt=9): 4882 ->*_s0(leq(s(app(nil,0)),s(x)),true).  [ur(87,a,72,a,b,4834,a)].

given #2348 (T,wt=9): 4884 ->*_s0(app(nil,leq(app(nil,0),x)),true).  [ur(87,a,61,a,b,4834,a)].

given #2349 (T,wt=9): 4942 ->*_s0(fstsplit(x,app(nil,y)),fstsplit(x,y)).  [ur(87,a,134,a,b,86,a)].

given #2350 (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 #2351 (F,wt=11): 12178 -->_s0(true,sndsplit(s(head(cons(0,x))),cons(y,false))) # answer(goal).  [ur(2781,b,83,a,c,12143,a)].

given #2352 (F,wt=11): 12184 -->_s0(true,app(nil,tail(cons(x,leq(s(y),0))))) # answer(goal).  [resolve(1074,a,3014,b)].

given #2353 (F,wt=11): 12186 -->_s0(true,sndsplit(0,tail(cons(x,leq(s(y),0))))) # answer(goal).  [resolve(1074,a,2997,b)].

given #2354 (F,wt=11): 12188 -->_s0(true,tail(app(nil,cons(x,leq(s(y),0))))) # answer(goal).  [resolve(1074,a,2966,b)].

given #2355 (T,wt=9): 4972 ->*_s0(tail(cons(x,fstsplit(length(nil),y))),nil).  [ur(87,a,85,a,b,4913,a)].

given #2356 (T,wt=9): 4974 ->*_s0(head(cons(fstsplit(length(nil),x),y)),nil).  [ur(87,a,67,a,b,4913,a)].

given #2357 (T,wt=9): 5061 ->*_s0(fstsplit(app(nil,x),y),fstsplit(x,y)).  [ur(87,a,135,a,b,86,a)].

given #2358 (T,wt=9): 5091 ->*_s0(fstsplit(app(nil,app(nil,0)),x),nil).  [ur(87,a,135,a,b,5059,a)].

given #2359 (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 #2360 (F,wt=11): 12189 -->_s0(true,tail(sndsplit(0,cons(x,leq(s(y),0))))) # answer(goal).  [resolve(1074,a,2936,b)].

given #2361 (F,wt=11): 12202 -->_s0(true,app(nil,head(cons(leq(s(x),0),y)))) # answer(goal).  [resolve(1077,a,3014,b)].

given #2362 (F,wt=11): 12205 -->_s0(true,head(app(nil,cons(leq(s(x),0),y)))) # answer(goal).  [resolve(1077,a,2964,b)].

given #2363 (F,wt=11): 12206 -->_s0(true,head(sndsplit(0,cons(leq(s(x),0),y)))) # answer(goal).  [resolve(1077,a,2934,b)].

given #2364 (T,wt=9): 5093 ->*_s0(sndsplit(0,fstsplit(app(nil,0),x)),nil).  [ur(87,a,82,a,b,5059,a)].

given #2365 (T,wt=9): 5095 ->*_s0(app(nil,fstsplit(app(nil,0),x)),nil).  [ur(87,a,61,a,b,5059,a)].

given #2366 (T,wt=9): 5178 ->*_s0(app(x,app(nil,y)),app(x,y)).  [ur(87,a,137,a,b,86,a)].

given #2367 (T,wt=9): 5317 ->*_s0(app(app(nil,nil),app(nil,x)),x).  [ur(87,a,138,a,b,698,a)].

given #2368 (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 #2369 (F,wt=11): 12219 -->_s0(true,head(app(cons(leq(s(x),0),y),z))) # answer(goal).  [ur(2781,b,108,a,c,1077,a)].

given #2370 (F,wt=11): 12222 -->_s0(true,app(nil,tail(cons(x,head(cons(false,y)))))) # answer(goal).  [resolve(1112,a,3014,b)].

given #2371 (F,wt=11): 12224 -->_s0(true,sndsplit(0,tail(cons(x,head(cons(false,y)))))) # answer(goal).  [resolve(1112,a,2997,b)].

given #2372 (F,wt=11): 12226 -->_s0(true,tail(app(nil,cons(x,head(cons(false,y)))))) # answer(goal).  [resolve(1112,a,2966,b)].

given #2373 (T,wt=9): 5318 ->*_s0(app(app(nil,nil),fstsplit(0,x)),nil).  [ur(87,a,138,a,b,691,a)].

given #2374 (T,wt=9): 5319 ->*_s0(app(app(nil,nil),leq(0,x)),true).  [ur(87,a,138,a,b,687,a)].

given #2375 (T,wt=9): 5320 ->*_s0(app(app(nil,nil),mapf(x,nil)),nil).  [ur(87,a,138,a,b,645,a)].

given #2376 (T,wt=9): 5321 ->*_s0(app(app(nil,nil),sndsplit(0,x)),x).  [ur(87,a,138,a,b,641,a)].

given #2377 (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 #2378 (F,wt=11): 12227 -->_s0(true,tail(sndsplit(0,cons(x,head(cons(false,y)))))) # answer(goal).  [resolve(1112,a,2936,b)].

given #2379 (F,wt=11): 12243 -->_s0(true,app(nil,head(cons(head(cons(false,x)),y)))) # answer(goal).  [resolve(1114,a,3014,b)].

given #2380 (F,wt=11): 12246 -->_s0(true,head(app(nil,cons(head(cons(false,x)),y)))) # answer(goal).  [resolve(1114,a,2964,b)].

given #2381 (F,wt=11): 12247 -->_s0(true,head(sndsplit(0,cons(head(cons(false,x)),y)))) # answer(goal).  [resolve(1114,a,2934,b)].

given #2382 (T,wt=9): 5325 ->*_s0(app(app(nil,x),y),app(x,y)).  [ur(87,a,138,a,b,86,a)].

given #2383 (T,wt=9): 5353 ->*_s0(length(sndsplit(0,sndsplit(s(x),nil))),0).  [ur(87,a,482,a,b,5289,a)].

given #2384 (T,wt=9): 5355 ->*_s0(length(app(nil,sndsplit(s(x),nil))),0).  [ur(87,a,132,a,b,5289,a)].

given #2385 (T,wt=9): 5357 ->*_s0(sndsplit(0,length(sndsplit(s(x),nil))),0).  [ur(87,a,82,a,b,5289,a)].

given #2386 (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 #2387 (F,wt=11): 12263 -->_s0(true,head(app(cons(head(cons(false,x)),y),z))) # answer(goal).  [ur(2781,b,108,a,c,1114,a)].

given #2388 (F,wt=11): 12275 -->_s0(true,app(nil,tail(cons(x,empty(cons(y,z)))))) # answer(goal).  [resolve(1124,a,3014,b)].

given #2389 (F,wt=11): 12277 -->_s0(true,sndsplit(0,tail(cons(x,empty(cons(y,z)))))) # answer(goal).  [resolve(1124,a,2997,b)].

given #2390 (F,wt=11): 12279 -->_s0(true,tail(app(nil,cons(x,empty(cons(y,z)))))) # answer(goal).  [resolve(1124,a,2966,b)].

given #2391 (T,wt=9): 5359 ->*_s0(app(nil,length(sndsplit(s(x),nil))),0).  [ur(87,a,61,a,b,5289,a)].

given #2392 (T,wt=9): 5372 ->*_s0(app(app(nil,app(nil,nil)),x),x).  [ur(87,a,138,a,b,5324,a)].

given #2393 (T,wt=9): 5375 ->*_s0(sndsplit(0,app(app(nil,nil),x)),x).  [ur(87,a,82,a,b,5324,a)].

given #2394 (T,wt=9): 5377 ->*_s0(app(nil,app(app(nil,nil),x)),x).  [ur(87,a,61,a,b,5324,a)].

given #2395 (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 #2396 (F,wt=10): 20611 -->_s0(true,sndsplit(length(nil),app(app(nil,nil),false))) # answer(goal).  [resolve(5375,a,4566,b)].

given #2397 (F,wt=11): 12280 -->_s0(true,tail(sndsplit(0,cons(x,empty(cons(y,z)))))) # answer(goal).  [resolve(1124,a,2936,b)].

given #2398 (F,wt=11): 12293 -->_s0(true,app(nil,head(cons(empty(cons(x,y)),z)))) # answer(goal).  [resolve(1126,a,3014,b)].

given #2399 (F,wt=11): 12296 -->_s0(true,head(app(nil,cons(empty(cons(x,y)),z)))) # answer(goal).  [resolve(1126,a,2964,b)].

given #2400 (T,wt=9): 5464 ->*_s0(empty(sndsplit(0,sndsplit(s(x),nil))),true).  [ur(87,a,486,a,b,5407,a)].

given #2401 (T,wt=9): 5466 ->*_s0(empty(app(nil,sndsplit(s(x),nil))),true).  [ur(87,a,136,a,b,5407,a)].

given #2402 (T,wt=9): 5468 ->*_s0(sndsplit(0,empty(sndsplit(s(x),nil))),true).  [ur(87,a,82,a,b,5407,a)].

given #2403 (T,wt=9): 5470 ->*_s0(app(nil,empty(sndsplit(s(x),nil))),true).  [ur(87,a,61,a,b,5407,a)].

given #2404 (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 #2405 (F,wt=11): 12297 -->_s0(true,head(sndsplit(0,cons(empty(cons(x,y)),z)))) # answer(goal).  [resolve(1126,a,2934,b)].

given #2406 (F,wt=11): 12310 -->_s0(true,head(app(cons(empty(cons(x,y)),z),u))) # answer(goal).  [ur(2781,b,108,a,c,1126,a)].

given #2407 (F,wt=11): 12478 -->_s0(true,leq(sndsplit(0,s(x)),head(cons(0,y)))) # answer(goal).  [ur(2781,b,280,a,c,11700,a)].

given #2408 (F,wt=11): 12479 -->_s0(true,leq(s(x),head(cons(sndsplit(0,0),y)))) # answer(goal).  [ur(2781,b,280,a,c,11647,a)].

given #2409 (T,wt=9): 5477 ->*_s0(s(tail(cons(x,length(nil)))),s(0)).  [ur(87,a,539,a,b,891,a)].

given #2410 (T,wt=9): 5478 ->*_s0(s(tail(cons(x,empty(nil)))),s(true)).  [ur(87,a,539,a,b,699,a)].

given #2411 (T,wt=9): 5512 ->*_s0(tail(tail(cons(x,length(nil)))),tail(0)).  [ur(87,a,544,a,b,917,a)].

given #2412 (T,wt=9): 5513 ->*_s0(tail(tail(cons(x,empty(nil)))),tail(true)).  [ur(87,a,544,a,b,755,a)].

given #2413 (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 #2414 (F,wt=11): 12480 -->_s0(true,leq(app(nil,s(x)),head(cons(0,y)))) # answer(goal).  [ur(2781,b,280,a,c,4835,a)].

given #2415 (F,wt=11): 12481 -->_s0(true,leq(s(x),head(cons(app(nil,0),y)))) # answer(goal).  [ur(2781,b,280,a,c,4699,a)].

given #2416 (F,wt=11): 12482 -->_s0(true,leq(s(s(x)),head(cons(s(0),y)))) # answer(goal).  [ur(2781,b,280,a,c,1076,a)].

given #2417 (F,wt=11): 12521 -->_s0(true,leq(head(cons(sndsplit(0,s(x)),y)),0)) # answer(goal).  [ur(2781,b,281,a,c,11700,a)].

given #2418 (T,wt=9): 5516 ->*_s0(tail(tail(cons(x,cons(y,z)))),z).  [ur(87,a,544,a,b,564,a)].

given #2419 (T,wt=9): 5548 ->*_s0(length(tail(cons(x,sndsplit(0,nil)))),0).  [ur(87,a,557,a,b,2278,a)].

given #2420 (T,wt=9): 5550 ->*_s0(length(tail(cons(x,mapf(y,nil)))),0).  [ur(87,a,557,a,b,2046,a)].

given #2421 (T,wt=9): 5553 ->*_s0(length(tail(cons(x,fstsplit(0,y)))),0).  [ur(87,a,557,a,b,1661,a)].

given #2422 (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 #2423 (F,wt=11): 12522 -->_s0(true,leq(head(cons(s(x),y)),sndsplit(0,0))) # answer(goal).  [ur(2781,b,281,a,c,11647,a)].

given #2424 (F,wt=11): 12523 -->_s0(true,leq(head(cons(app(nil,s(x)),y)),0)) # answer(goal).  [ur(2781,b,281,a,c,4835,a)].

given #2425 (F,wt=11): 12524 -->_s0(true,leq(head(cons(s(x),y)),app(nil,0))) # answer(goal).  [ur(2781,b,281,a,c,4699,a)].

given #2426 (F,wt=11): 12525 -->_s0(true,leq(head(cons(s(s(x)),y)),s(0))) # answer(goal).  [ur(2781,b,281,a,c,1076,a)].

given #2427 (T,wt=9): 5555 ->*_s0(length(tail(cons(x,app(nil,nil)))),0).  [ur(87,a,557,a,b,1366,a)].

given #2428 (T,wt=9): 5557 ->*_s0(length(tail(cons(x,length(nil)))),length(0)).  [ur(87,a,557,a,b,943,a)].

given #2429 (T,wt=9): 5558 ->*_s0(length(tail(cons(x,empty(nil)))),length(true)).  [ur(87,a,557,a,b,781,a)].

given #2430 (T,wt=9): 5614 ->*_s0(length(sndsplit(0,tail(cons(x,nil)))),0).  [ur(87,a,482,a,b,5559,a)].

given #2431 (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 #2432 (F,wt=11): 12703 -->_s0(true,app(nil,head(cons(sndsplit(length(nil),false),x)))) # answer(goal).  [ur(2781,b,287,a,c,4648,a)].

given #2433 (F,wt=11): 12804 -->_s0(true,app(head(cons(fstsplit(s(x),nil),y)),false)) # answer(goal).  [ur(2781,b,288,a,c,11602,a)].

given #2434 (F,wt=11): 12805 -->_s0(true,app(head(cons(nil,x)),sndsplit(length(nil),false))) # answer(goal).  [ur(2781,b,288,a,c,4648,a)].

given #2435 (F,wt=11): 12806 -->_s0(true,app(head(cons(nil,x)),empty(cons(y,z)))) # answer(goal).  [ur(2781,b,288,a,c,1127,a)].

given #2436 (T,wt=9): 5616 ->*_s0(length(app(nil,tail(cons(x,nil)))),0).  [ur(87,a,132,a,b,5559,a)].

given #2437 (T,wt=9): 5618 ->*_s0(sndsplit(0,length(tail(cons(x,nil)))),0).  [ur(87,a,82,a,b,5559,a)].

given #2438 (T,wt=9): 5620 ->*_s0(app(nil,length(tail(cons(x,nil)))),0).  [ur(87,a,61,a,b,5559,a)].

given #2439 (T,wt=9): 5628 ->*_s0(head(tail(cons(x,length(nil)))),head(0)).  [ur(87,a,558,a,b,969,a)].

given #2440 (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 #2441 (F,wt=11): 12807 -->_s0(true,app(head(cons(nil,x)),head(cons(false,y)))) # answer(goal).  [ur(2781,b,288,a,c,1115,a)].

given #2442 (F,wt=11): 12808 -->_s0(true,app(head(cons(nil,x)),leq(s(y),0))) # answer(goal).  [ur(2781,b,288,a,c,1078,a)].

given #2443 (F,wt=11): 12809 -->_s0(true,app(head(cons(nil,x)),tail(cons(y,false)))) # answer(goal).  [ur(2781,b,288,a,c,1065,a)].

given #2444 (F,wt=11): 12828 -->_s0(true,head(cons(app(head(cons(nil,x)),false),y))) # answer(goal).  [resolve(12802,a,3010,b)].

given #2445 (T,wt=9): 5629 ->*_s0(head(tail(cons(x,empty(nil)))),head(true)).  [ur(87,a,558,a,b,807,a)].

given #2446 (T,wt=9): 5632 ->*_s0(head(tail(cons(x,cons(y,z)))),y).  [ur(87,a,558,a,b,575,a)].

given #2447 (T,wt=9): 5665 ->*_s0(empty(tail(cons(x,sndsplit(0,nil)))),true).  [ur(87,a,561,a,b,2390,a)].

given #2448 (T,wt=9): 5667 ->*_s0(empty(tail(cons(x,mapf(y,nil)))),true).  [ur(87,a,561,a,b,2147,a)].

given #2449 (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 #2450 (F,wt=11): 12829 -->_s0(true,tail(cons(x,app(head(cons(nil,y)),false)))) # answer(goal).  [resolve(12802,a,2994,b)].

given #2451 (F,wt=11): 12830 -->_s0(true,x) | -->_s0(x,app(head(cons(nil,y)),false)) # answer(goal).  [resolve(12802,a,2781,c)].

given #2452 (F,wt=11): 12846 -->_s0(true,app(head(cons(head(cons(nil,x)),y)),false)) # answer(goal).  [ur(2781,b,288,a,c,12802,a)].

given #2453 (F,wt=11): 13579 -->_s0(true,tail(x)) | -->_s0(x,app(cons(y,nil),false)) # answer(goal).  [resolve(3021,b,5956,a)].

given #2454 (T,wt=9): 5670 ->*_s0(empty(tail(cons(x,fstsplit(0,y)))),true).  [ur(87,a,561,a,b,1750,a)].

given #2455 (T,wt=9): 5672 ->*_s0(empty(tail(cons(x,app(nil,nil)))),true).  [ur(87,a,561,a,b,1456,a)].

given #2456 (T,wt=9): 5673 ->*_s0(empty(tail(cons(x,length(nil)))),empty(0)).  [ur(87,a,561,a,b,1031,a)].

given #2457 (T,wt=9): 5674 ->*_s0(empty(tail(cons(x,empty(nil)))),empty(true)).  [ur(87,a,561,a,b,833,a)].

given #2458 (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 #2459 (F,wt=11): 13580 -->_s0(true,tail(x)) | -->_s0(x,sndsplit(0,cons(y,false))) # answer(goal).  [resolve(3021,b,2245,a)].

given #2460 (F,wt=11): 13581 -->_s0(true,tail(x)) | -->_s0(x,app(nil,cons(y,false))) # answer(goal).  [resolve(3021,b,1337,a)].

given #2461 (F,wt=11): 13586 -->_s0(true,tail(x)) | -->_s0(x,cons(y,app(nil,false))) # answer(goal).  [resolve(3021,b,695,a)].

given #2462 (F,wt=11): 13587 -->_s0(true,tail(x)) | -->_s0(x,cons(y,sndsplit(0,false))) # answer(goal).  [resolve(3021,b,637,a)].

given #2463 (T,wt=9): 5675 ->*_s0(empty(tail(cons(x,cons(y,z)))),false).  [ur(87,a,561,a,b,580,a)].

given #2464 (T,wt=9): 5707 ->*_s0(empty(sndsplit(0,tail(cons(x,nil)))),true).  [ur(87,a,486,a,b,5676,a)].

given #2465 (T,wt=9): 5709 ->*_s0(empty(app(nil,tail(cons(x,nil)))),true).  [ur(87,a,136,a,b,5676,a)].

given #2466 (T,wt=9): 5711 ->*_s0(sndsplit(0,empty(tail(cons(x,nil)))),true).  [ur(87,a,82,a,b,5676,a)].

given #2467 (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 #2468 (F,wt=11): 13991 -->_s0(true,tail(app(head(cons(cons(x,nil),y)),false))) # answer(goal).  [ur(3021,b,5956,a,c,288,a)].

given #2469 (F,wt=11): 13992 -->_s0(true,tail(app(cons(x,nil),head(cons(false,y))))) # answer(goal).  [ur(3021,b,5956,a,c,287,a)].

given #2470 (F,wt=11): 13993 -->_s0(true,tail(app(cons(x,nil),empty(cons(y,z))))) # answer(goal).  [ur(3021,b,5956,a,c,162,a)].

given #2471 (F,wt=11): 13998 -->_s0(true,tail(sndsplit(head(cons(0,x)),cons(y,false)))) # answer(goal).  [ur(3021,b,2245,a,c,271,a)].

given #2472 (T,wt=9): 5713 ->*_s0(app(nil,empty(tail(cons(x,nil)))),true).  [ur(87,a,61,a,b,5676,a)].

given #2473 (T,wt=9): 5891 ->*_s0(sndsplit(length(nil),empty(cons(x,y))),false).  [ur(87,a,145,a,b,4574,a)].

given #2474 (T,wt=9): 7728 ->*_s0(sndsplit(length(nil),tail(cons(x,y))),y).  [ur(87,a,321,a,b,1063,a)].

given #2475 (T,wt=9): 7782 ->*_s0(sndsplit(length(nil),sndsplit(s(x),nil)),nil).  [ur(87,a,321,a,b,1068,a)].

given #2476 (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 #2477 (F,wt=11): 13999 -->_s0(true,tail(sndsplit(0,head(cons(cons(x,false),y))))) # answer(goal).  [ur(3021,b,2245,a,c,270,a)].

given #2478 (F,wt=11): 14001 -->_s0(true,tail(sndsplit(s(0),cons(x,cons(y,false))))) # answer(goal).  [ur(3021,b,2245,a,c,83,a)].

given #2479 (F,wt=11): 14004 -->_s0(true,tail(app(head(cons(nil,x)),cons(y,false)))) # answer(goal).  [ur(3021,b,1337,a,c,288,a)].

given #2480 (F,wt=11): 14005 -->_s0(true,tail(app(nil,head(cons(cons(x,false),y))))) # answer(goal).  [ur(3021,b,1337,a,c,287,a)].

given #2481 (T,wt=9): 7803 ->*_s0(sndsplit(length(nil),leq(s(x),0)),false).  [ur(87,a,321,a,b,1075,a)].

given #2482 (T,wt=9): 7883 ->*_s0(sndsplit(length(nil),head(cons(x,y))),x).  [ur(87,a,321,a,b,1113,a)].

given #2483 (T,wt=9): 7910 ->*_s0(sndsplit(length(nil),fstsplit(s(x),nil)),nil).  [ur(87,a,321,a,b,1117,a)].

given #2484 (T,wt=9): 7975 ->*_s0(sndsplit(length(nil),sndsplit(0,length(nil))),0).  [ur(87,a,321,a,b,1130,a)].

given #2485 (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 #2486 (F,wt=11): 14006 -->_s0(true,tail(app(fstsplit(s(x),nil),cons(y,false)))) # answer(goal).  [ur(3021,b,1337,a,c,263,a)].

given #2487 (F,wt=11): 14542 -->_s0(true,head(x)) | -->_s0(x,app(cons(false,y),z)) # answer(goal).  [resolve(3035,b,2538,a)].

given #2488 (F,wt=11): 14543 -->_s0(true,head(x)) | -->_s0(x,sndsplit(0,cons(false,y))) # answer(goal).  [resolve(3035,b,2314,a)].

given #2489 (F,wt=11): 14544 -->_s0(true,head(x)) | -->_s0(x,app(nil,cons(false,y))) # answer(goal).  [resolve(3035,b,1426,a)].

given #2490 (T,wt=9): 8026 ->*_s0(sndsplit(length(nil),sndsplit(0,empty(nil))),true).  [ur(87,a,321,a,b,1176,a)].

given #2491 (T,wt=9): 8083 ->*_s0(sndsplit(length(nil),s(empty(nil))),s(true)).  [ur(87,a,321,a,b,1186,a)].

given #2492 (T,wt=9): 8121 ->*_s0(sndsplit(length(nil),tail(empty(nil))),tail(true)).  [ur(87,a,321,a,b,1216,a)].

given #2493 (T,wt=9): 8133 ->*_s0(sndsplit(length(nil),length(empty(nil))),length(true)).  [ur(87,a,321,a,b,1220,a)].

given #2494 (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 #2495 (F,wt=11): 14549 -->_s0(true,head(x)) | -->_s0(x,cons(app(nil,false),y)) # answer(goal).  [resolve(3035,b,697,a)].

given #2496 (F,wt=11): 14550 -->_s0(true,head(x)) | -->_s0(x,cons(sndsplit(0,false),y)) # answer(goal).  [resolve(3035,b,640,a)].

given #2497 (F,wt=11): 14963 -->_s0(true,head(app(head(cons(cons(false,x),y)),z))) # answer(goal).  [ur(3035,b,2538,a,c,288,a)].

given #2498 (F,wt=11): 14964 -->_s0(true,head(app(fstsplit(s(x),cons(false,y)),z))) # answer(goal).  [ur(3035,b,2538,a,c,238,a)].

given #2499 (T,wt=9): 8172 ->*_s0(sndsplit(length(nil),head(empty(nil))),head(true)).  [ur(87,a,321,a,b,1224,a)].

given #2500 (T,wt=9): 8184 ->*_s0(sndsplit(length(nil),empty(empty(nil))),empty(true)).  [ur(87,a,321,a,b,1228,a)].

given #2501 (T,wt=9): 8203 ->*_s0(sndsplit(length(nil),s(length(nil))),s(0)).  [ur(87,a,321,a,b,1260,a)].

given #2502 (T,wt=9): 8215 ->*_s0(sndsplit(length(nil),tail(length(nil))),tail(0)).  [ur(87,a,321,a,b,1265,a)].

given #2503 (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 #2504 (F,wt=11): 14969 -->_s0(true,head(sndsplit(head(cons(0,x)),cons(false,y)))) # answer(goal).  [ur(3035,b,2314,a,c,271,a)].

given #2505 (F,wt=11): 14970 -->_s0(true,head(sndsplit(0,head(cons(cons(false,x),y))))) # answer(goal).  [ur(3035,b,2314,a,c,270,a)].

given #2506 (F,wt=11): 14971 -->_s0(true,head(sndsplit(0,fstsplit(s(x),cons(false,y))))) # answer(goal).  [ur(3035,b,2314,a,c,220,a)].

given #2507 (F,wt=11): 14973 -->_s0(true,head(sndsplit(s(0),cons(x,cons(false,y))))) # answer(goal).  [ur(3035,b,2314,a,c,83,a)].

given #2508 (T,wt=9): 8224 ->*_s0(f(x,fstsplit(0,y)),f(x,nil)).  [ur(87,a,190,a,b,86,a)].

given #2509 (T,wt=9): 8248 ->*_s0(sndsplit(length(nil),length(length(nil))),length(0)).  [ur(87,a,321,a,b,1269,a)].

given #2510 (T,wt=9): 8260 ->*_s0(sndsplit(length(nil),head(length(nil))),head(0)).  [ur(87,a,321,a,b,1273,a)].

given #2511 (T,wt=9): 8269 ->*_s0(f(fstsplit(0,x),y),f(nil,y)).  [ur(87,a,191,a,b,86,a)].

given #2512 (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 #2513 (F,wt=11): 14976 -->_s0(true,head(app(head(cons(nil,x)),cons(false,y)))) # answer(goal).  [ur(3035,b,1426,a,c,288,a)].

given #2514 (F,wt=11): 14977 -->_s0(true,head(app(nil,head(cons(cons(false,x),y))))) # answer(goal).  [ur(3035,b,1426,a,c,287,a)].

given #2515 (F,wt=11): 14978 -->_s0(true,head(app(fstsplit(s(x),nil),cons(false,y)))) # answer(goal).  [ur(3035,b,1426,a,c,263,a)].

given #2516 (F,wt=11): 14979 -->_s0(true,head(app(nil,fstsplit(s(x),cons(false,y))))) # answer(goal).  [ur(3035,b,1426,a,c,237,a)].

given #2517 (T,wt=9): 8323 ->*_s0(sndsplit(length(nil),empty(length(nil))),empty(0)).  [ur(87,a,321,a,b,1304,a)].

given #2518 (T,wt=9): 8344 ->*_s0(cons(x,fstsplit(0,y)),cons(x,nil)).  [ur(87,a,192,a,b,86,a)].

given #2519 (T,wt=9): 8416 ->*_s0(cons(fstsplit(0,x),y),cons(nil,y)).  [ur(87,a,193,a,b,86,a)].

given #2520 (T,wt=9): 8462 ->*_s0(sndsplit(length(nil),length(app(nil,nil))),0).  [ur(87,a,321,a,b,1421,a)].

given #2521 (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 #2522 (F,wt=11): 15106 -->_s0(true,empty(x)) | -->_s0(x,app(cons(y,z),u)) # answer(goal).  [resolve(3038,b,2754,a)].

given #2523 (F,wt=11): 15107 -->_s0(true,empty(x)) | -->_s0(x,sndsplit(0,cons(y,z))) # answer(goal).  [resolve(3038,b,2389,a)].

given #2524 (F,wt=11): 15108 -->_s0(true,empty(x)) | -->_s0(x,app(nil,cons(y,z))) # answer(goal).  [resolve(3038,b,1455,a)].

given #2525 (F,wt=11): 15345 -->_s0(true,empty(app(fstsplit(s(x),cons(y,z)),u))) # answer(goal).  [resolve(3038,c,238,a),unit_del(b,2754)].

given #2526 (T,wt=9): 8472 ->*_s0(sndsplit(x,fstsplit(0,y)),sndsplit(x,nil)).  [ur(87,a,195,a,b,86,a)].

given #2527 (T,wt=9): 8540 ->*_s0(sndsplit(fstsplit(0,x),y),sndsplit(nil,y)).  [ur(87,a,196,a,b,86,a)].

given #2528 (T,wt=9): 8621 ->*_s0(sndsplit(length(nil),empty(app(nil,nil))),true).  [ur(87,a,321,a,b,1487,a)].

given #2529 (T,wt=9): 8644 ->*_s0(sndsplit(length(nil),length(fstsplit(0,x))),0).  [ur(87,a,321,a,b,1690,a)].

given #2530 (A,wt=12): 489 ->_s0(s(sndsplit(s(x),cons(y,z))),s(sndsplit(x,z))).  [ur(59,a,83,a)].

given #2531 (F,wt=11): 15504 -->_s0(true,empty(app(head(cons(cons(x,y),z)),u))) # answer(goal).  [ur(3038,b,2754,a,c,288,a)].

given #2532 (F,wt=11): 15508 -->_s0(true,empty(sndsplit(head(cons(0,x)),cons(y,z)))) # answer(goal).  [ur(3038,b,2389,a,c,271,a)].

given #2533 (F,wt=11): 15509 -->_s0(true,empty(sndsplit(0,head(cons(cons(x,y),z))))) # answer(goal).  [ur(3038,b,2389,a,c,270,a)].

given #2534 (F,wt=11): 15510 -->_s0(true,empty(sndsplit(0,fstsplit(s(x),cons(y,z))))) # answer(goal).  [ur(3038,b,2389,a,c,220,a)].

given #2535 (T,wt=9): 8677 ->*_s0(sndsplit(length(nil),empty(fstsplit(0,x))),true).  [ur(87,a,321,a,b,1781,a)].

given #2536 (T,wt=9): 8707 ->*_s0(sndsplit(length(nil),length(mapf(x,nil))),0).  [ur(87,a,321,a,b,2075,a)].

given #2537 (T,wt=9): 8740 ->*_s0(sndsplit(length(nil),empty(mapf(x,nil))),true).  [ur(87,a,321,a,b,2179,a)].

given #2538 (T,wt=9): 8868 ->*_s0(mapf(x,fstsplit(0,y)),mapf(x,nil)).  [ur(87,a,203,a,b,86,a)].

given #2539 (A,wt=14): 490 ->_s0(f(x,sndsplit(s(y),cons(z,u))),f(x,sndsplit(y,u))).  [ur(58,a,83,a)].

given #2540 (F,wt=11): 15512 -->_s0(true,empty(sndsplit(s(0),cons(x,cons(y,z))))) # answer(goal).  [ur(3038,b,2389,a,c,83,a)].

given #2541 (F,wt=11): 15515 -->_s0(true,empty(app(head(cons(nil,x)),cons(y,z)))) # answer(goal).  [ur(3038,b,1455,a,c,288,a)].

given #2542 (F,wt=11): 15516 -->_s0(true,empty(app(nil,head(cons(cons(x,y),z))))) # answer(goal).  [ur(3038,b,1455,a,c,287,a)].

given #2543 (F,wt=11): 15517 -->_s0(true,empty(app(fstsplit(s(x),nil),cons(y,z)))) # answer(goal).  [ur(3038,b,1455,a,c,263,a)].

given #2544 (T,wt=9): 8888 ->*_s0(mapf(x,app(nil,fstsplit(0,y))),nil).  [ur(87,a,128,a,b,8867,a)].

given #2545 (T,wt=9): 8890 ->*_s0(sndsplit(0,mapf(x,fstsplit(0,y))),nil).  [ur(87,a,82,a,b,8867,a)].

given #2546 (T,wt=9): 8892 ->*_s0(app(nil,mapf(x,fstsplit(0,y))),nil).  [ur(87,a,61,a,b,8867,a)].

given #2547 (T,wt=9): 8909 ->*_s0(sndsplit(length(nil),length(sndsplit(0,nil))),0).  [ur(87,a,321,a,b,2308,a)].

given #2548 (A,wt=14): 491 ->_s0(f(sndsplit(s(x),cons(y,z)),u),f(sndsplit(x,z),u)).  [ur(57,a,83,a)].

given #2549 (F,wt=11): 15518 -->_s0(true,empty(app(nil,fstsplit(s(x),cons(y,z))))) # answer(goal).  [ur(3038,b,1455,a,c,237,a)].

given #2550 (F,wt=11): 15786 -->_s0(true,sndsplit(0,empty(length(nil)))) | -->*_s0(empty(0),false) # answer(goal).  [resolve(3152,b,336,a)].

given #2551 (F,wt=11): 15789 -->_s0(true,sndsplit(0,head(length(nil)))) | -->*_s0(head(0),false) # answer(goal).  [resolve(3152,b,333,a)].

given #2552 (F,wt=11): 15790 -->_s0(true,sndsplit(0,length(length(nil)))) | -->*_s0(length(0),false) # answer(goal).  [resolve(3152,b,332,a)].

given #2553 (T,wt=9): 8918 ->*_s0(mapf(fstsplit(0,x),y),mapf(nil,y)).  [ur(87,a,204,a,b,86,a)].

given #2554 (T,wt=9): 8984 ->*_s0(leq(x,fstsplit(0,y)),leq(x,nil)).  [ur(87,a,205,a,b,86,a)].

given #2555 (T,wt=9): 9047 ->*_s0(leq(fstsplit(0,x),y),leq(nil,y)).  [ur(87,a,206,a,b,86,a)].

given #2556 (T,wt=9): 9123 ->*_s0(fstsplit(x,fstsplit(0,y)),fstsplit(x,nil)).  [ur(87,a,209,a,b,86,a)].

given #2557 (A,wt=14): 492 ->_s0(cons(x,sndsplit(s(y),cons(z,u))),cons(x,sndsplit(y,u))).  [ur(56,a,83,a)].

given #2558 (F,wt=11): 15797 -->_s0(true,sndsplit(0,tail(length(nil)))) | -->*_s0(tail(0),false) # answer(goal).  [resolve(3152,b,319,a)].

given #2559 (F,wt=11): 15802 -->_s0(true,sndsplit(0,s(length(nil)))) | -->*_s0(s(0),false) # answer(goal).  [resolve(3152,b,314,a)].

given #2560 (F,wt=11): 15872 -->_s0(true,sndsplit(0,empty(fstsplit(s(x),cons(y,z))))) # answer(goal).  [resolve(3152,b,236,a),unit_del(b,580)].

given #2561 (F,wt=11): 15922 -->_s0(true,sndsplit(0,empty(empty(nil)))) | -->*_s0(empty(true),false) # answer(goal).  [resolve(3152,b,186,a)].

given #2562 (T,wt=9): 9146 ->*_s0(sndsplit(length(nil),empty(sndsplit(0,nil))),true).  [ur(87,a,321,a,b,2423,a)].

given #2563 (T,wt=9): 9211 ->*_s0(fstsplit(fstsplit(0,x),y),fstsplit(nil,y)).  [ur(87,a,210,a,b,86,a)].

given #2564 (T,wt=9): 9273 ->*_s0(app(x,fstsplit(0,y)),app(x,nil)).  [ur(87,a,212,a,b,86,a)].

given #2565 (T,wt=9): 9310 ->*_s0(f(length(nil),empty(nil)),f(0,true)).  [ur(87,a,316,a,b,3420,a)].

given #2566 (A,wt=14): 493 ->_s0(cons(sndsplit(s(x),cons(y,z)),u),cons(sndsplit(x,z),u)).  [ur(55,a,83,a)].

given #2567 (F,wt=11): 15925 -->_s0(true,sndsplit(0,head(empty(nil)))) | -->*_s0(head(true),false) # answer(goal).  [resolve(3152,b,183,a)].

given #2568 (F,wt=11): 15926 -->_s0(true,sndsplit(0,length(empty(nil)))) | -->*_s0(length(true),false) # answer(goal).  [resolve(3152,b,182,a)].

given #2569 (F,wt=11): 15939 -->_s0(true,sndsplit(0,tail(empty(nil)))) | -->*_s0(tail(true),false) # answer(goal).  [resolve(3152,b,169,a)].

given #2570 (F,wt=11): 15944 -->_s0(true,sndsplit(0,s(empty(nil)))) | -->*_s0(s(true),false) # answer(goal).  [resolve(3152,b,164,a)].

given #2571 (T,wt=9): 9312 ->*_s0(f(empty(nil),empty(nil)),f(true,true)).  [ur(87,a,166,a,b,3420,a)].

given #2572 (T,wt=9): 9321 ->*_s0(f(empty(nil),length(nil)),f(true,0)).  [ur(87,a,315,a,b,3447,a)].

given #2573 (T,wt=9): 9363 ->*_s0(app(fstsplit(0,x),app(nil,y)),y).  [ur(87,a,213,a,b,698,a)].

given #2574 (T,wt=9): 9364 ->*_s0(app(fstsplit(0,x),fstsplit(0,y)),nil).  [ur(87,a,213,a,b,691,a)].

given #2575 (A,wt=12): 494 ->_s0(tail(sndsplit(s(x),cons(y,z))),tail(sndsplit(x,z))).  [ur(54,a,83,a)].

given #2576 (F,wt=11): 16019 -->_s0(true,sndsplit(0,tail(cons(x,y)))) | -->*_s0(y,false) # answer(goal).  [resolve(3152,b,85,a)].

given #2577 (F,wt=11): 16020 -->_s0(true,sndsplit(0,sndsplit(s(x),nil))) | -->*_s0(nil,false) # answer(goal).  [resolve(3152,b,84,a)].

given #2578 (F,wt=11): 16035 -->_s0(true,sndsplit(0,head(cons(x,y)))) | -->*_s0(x,false) # answer(goal).  [resolve(3152,b,67,a)].

given #2579 (F,wt=11): 16036 -->_s0(true,sndsplit(0,fstsplit(s(x),nil))) | -->*_s0(nil,false) # answer(goal).  [resolve(3152,b,66,a)].

given #2580 (T,wt=9): 9365 ->*_s0(app(fstsplit(0,x),leq(0,y)),true).  [ur(87,a,213,a,b,687,a)].

given #2581 (T,wt=9): 9366 ->*_s0(app(fstsplit(0,x),mapf(y,nil)),nil).  [ur(87,a,213,a,b,645,a)].

given #2582 (T,wt=9): 9367 ->*_s0(app(fstsplit(0,x),sndsplit(0,y)),y).  [ur(87,a,213,a,b,641,a)].

given #2583 (T,wt=9): 9371 ->*_s0(app(fstsplit(0,x),y),app(nil,y)).  [ur(87,a,213,a,b,86,a)].

given #2584 (A,wt=14): 495 ->_s0(sndsplit(x,sndsplit(s(y),cons(z,u))),sndsplit(x,sndsplit(y,u))).  [ur(53,a,83,a)].

given #2585 (F,wt=11): 16084 -->_s0(true,sndsplit(0,x)) | -->_s0(x,sndsplit(length(nil),false)) # answer(goal).  [resolve(3152,c,4574,a)].

given #2586 (F,wt=11): 16122 -->_s0(true,sndsplit(0,x)) | -->_s0(x,empty(cons(y,z))) # answer(goal).  [resolve(3152,c,580,a)].

given #2587 (F,wt=11): 16123 -->_s0(true,sndsplit(0,x)) | -->_s0(x,head(cons(false,y))) # answer(goal).  [resolve(3152,c,575,a)].

given #2588 (F,wt=11): 16124 -->_s0(true,sndsplit(0,x)) | -->_s0(x,leq(s(y),0)) # answer(goal).  [resolve(3152,c,571,a)].

given #2589 (T,wt=9): 9409 ->*_s0(app(app(nil,fstsplit(0,x)),y),y).  [ur(87,a,138,a,b,9370,a)].

given #2590 (T,wt=9): 9412 ->*_s0(sndsplit(0,app(fstsplit(0,x),y)),y).  [ur(87,a,82,a,b,9370,a)].

given #2591 (T,wt=9): 9414 ->*_s0(app(nil,app(fstsplit(0,x),y)),y).  [ur(87,a,61,a,b,9370,a)].

given #2592 (T,wt=9): 9416 ->*_s0(cons(length(nil),empty(nil)),cons(0,true)).  [ur(87,a,318,a,b,3474,a)].

given #2593 (A,wt=14): 496 ->_s0(sndsplit(sndsplit(s(x),cons(y,z)),u),sndsplit(sndsplit(x,z),u)).  [ur(52,a,83,a)].

given #2594 (F,wt=10): 21165 -->_s0(true,sndsplit(length(nil),app(fstsplit(0,x),false))) # answer(goal).  [resolve(9412,a,4566,b)].

given #2595 (F,wt=11): 16125 -->_s0(true,sndsplit(0,x)) | -->_s0(x,tail(cons(y,false))) # answer(goal).  [resolve(3152,c,564,a)].

given #2596 (F,wt=11): 16130 -->_s0(true,sndsplit(0,empty(tail(cons(x,cons(y,z)))))) # answer(goal).  [ur(3152,b,561,a,c,580,a)].

given #2597 (F,wt=11): 16140 -->_s0(true,sndsplit(0,head(tail(cons(x,cons(false,y)))))) # answer(goal).  [ur(3152,b,558,a,c,575,a)].

given #2598 (T,wt=9): 9418 ->*_s0(cons(empty(nil),empty(nil)),cons(true,true)).  [ur(87,a,168,a,b,3474,a)].

given #2599 (T,wt=9): 9427 ->*_s0(cons(empty(nil),length(nil)),cons(true,0)).  [ur(87,a,317,a,b,3501,a)].

given #2600 (T,wt=9): 9490 ->*_s0(sndsplit(length(nil),empty(nil)),sndsplit(0,true)).  [ur(87,a,321,a,b,3588,a)].

given #2601 (T,wt=9): 9492 ->*_s0(sndsplit(empty(nil),empty(nil)),sndsplit(true,true)).  [ur(87,a,171,a,b,3588,a)].

given #2602 (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 #2603 (F,wt=11): 16150 -->_s0(true,sndsplit(0,tail(tail(cons(x,cons(y,false)))))) # answer(goal).  [ur(3152,b,544,a,c,564,a)].

given #2604 (F,wt=11): 16152 -->_s0(true,sndsplit(0,app(sndsplit(0,sndsplit(0,nil)),false))) # answer(goal).  [ur(3152,b,488,a,c,11892,a)].

given #2605 (F,wt=11): 16154 -->_s0(true,sndsplit(0,app(sndsplit(0,mapf(x,nil)),false))) # answer(goal).  [ur(3152,b,488,a,c,11239,a)].

given #2606 (F,wt=11): 16155 -->_s0(true,sndsplit(0,app(sndsplit(0,fstsplit(0,x)),false))) # answer(goal).  [ur(3152,b,488,a,c,9370,a)].

given #2607 (T,wt=9): 9502 ->*_s0(sndsplit(empty(nil),length(nil)),sndsplit(true,0)).  [ur(87,a,320,a,b,3615,a)].

given #2608 (T,wt=9): 9526 ->*_s0(mapf(length(nil),empty(nil)),mapf(0,true)).  [ur(87,a,329,a,b,3642,a)].

given #2609 (T,wt=9): 9528 ->*_s0(mapf(empty(nil),empty(nil)),mapf(true,true)).  [ur(87,a,179,a,b,3642,a)].

given #2610 (T,wt=9): 9537 ->*_s0(mapf(empty(nil),length(nil)),mapf(true,0)).  [ur(87,a,328,a,b,3696,a)].

given #2611 (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 #2612 (F,wt=11): 16156 -->_s0(true,sndsplit(0,app(sndsplit(0,app(nil,nil)),false))) # answer(goal).  [ur(3152,b,488,a,c,5324,a)].

given #2613 (F,wt=11): 16162 -->_s0(true,sndsplit(0,app(sndsplit(0,nil),app(nil,false)))) # answer(goal).  [ur(3152,b,488,a,c,698,a)].

given #2614 (F,wt=11): 16163 -->_s0(true,sndsplit(0,app(sndsplit(0,nil),sndsplit(0,false)))) # answer(goal).  [ur(3152,b,488,a,c,641,a)].

given #2615 (F,wt=11): 16166 -->_s0(true,sndsplit(0,app(mapf(x,nil),sndsplit(0,false)))) # answer(goal).  [ur(3152,b,487,a,c,11239,a)].

given #2616 (T,wt=9): 9547 ->*_s0(leq(length(nil),empty(nil)),leq(0,true)).  [ur(87,a,331,a,b,3723,a)].

given #2617 (T,wt=9): 9549 ->*_s0(leq(empty(nil),empty(nil)),leq(true,true)).  [ur(87,a,181,a,b,3723,a)].

given #2618 (T,wt=9): 9559 ->*_s0(leq(empty(nil),length(nil)),leq(true,0)).  [ur(87,a,330,a,b,3751,a)].

given #2619 (T,wt=9): 9578 ->*_s0(fstsplit(length(nil),empty(nil)),fstsplit(0,true)).  [ur(87,a,335,a,b,3778,a)].

given #2620 (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 #2621 (F,wt=11): 16167 -->_s0(true,sndsplit(0,app(fstsplit(0,x),sndsplit(0,false)))) # answer(goal).  [ur(3152,b,487,a,c,9370,a)].

given #2622 (F,wt=11): 16168 -->_s0(true,sndsplit(0,app(app(nil,nil),sndsplit(0,false)))) # answer(goal).  [ur(3152,b,487,a,c,5324,a)].

given #2623 (F,wt=11): 16174 -->_s0(true,sndsplit(0,app(nil,sndsplit(0,app(nil,false))))) # answer(goal).  [ur(3152,b,487,a,c,698,a)].

given #2624 (F,wt=11): 16175 -->_s0(true,sndsplit(0,app(nil,sndsplit(0,sndsplit(0,false))))) # answer(goal).  [ur(3152,b,487,a,c,641,a)].

given #2625 (T,wt=9): 9580 ->*_s0(fstsplit(empty(nil),empty(nil)),fstsplit(true,true)).  [ur(87,a,185,a,b,3778,a)].

given #2626 (T,wt=9): 9589 ->*_s0(fstsplit(empty(nil),length(nil)),fstsplit(true,0)).  [ur(87,a,334,a,b,3832,a)].

given #2627 (T,wt=9): 9599 ->*_s0(app(length(nil),empty(nil)),app(0,true)).  [ur(87,a,338,a,b,3859,a)].

given #2628 (T,wt=9): 9601 ->*_s0(app(empty(nil),empty(nil)),app(true,true)).  [ur(87,a,188,a,b,3859,a)].

given #2629 (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 #2630 (F,wt=11): 16191 -->_s0(true,sndsplit(0,leq(sndsplit(0,s(x)),length(nil)))) # answer(goal).  [ur(3152,b,481,a,c,4756,a)].

given #2631 (F,wt=11): 16196 -->_s0(true,sndsplit(0,leq(s(x),sndsplit(0,length(nil))))) # answer(goal).  [ur(3152,b,480,a,c,4756,a)].

given #2632 (F,wt=11): 16200 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,sndsplit(0,0)),false))) # answer(goal).  [ur(3152,b,471,a,c,11447,a)].

given #2633 (F,wt=11): 16206 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,app(nil,0)),false))) # answer(goal).  [ur(3152,b,471,a,c,3536,a)].

given #2634 (T,wt=9): 9610 ->*_s0(app(empty(nil),length(nil)),app(true,0)).  [ur(87,a,337,a,b,3886,a)].

given #2635 (T,wt=9): 9708 ->*_s0(tail(fstsplit(s(0),cons(x,y))),nil).  [ur(87,a,219,a,b,688,a)].

given #2636 (T,wt=9): 9758 ->*_s0(f(length(nil),length(nil)),f(0,0)).  [ur(87,a,316,a,b,4395,a)].

given #2637 (T,wt=9): 9786 ->*_s0(cons(length(nil),length(nil)),cons(0,0)).  [ur(87,a,318,a,b,4449,a)].

given #2638 (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 #2639 (F,wt=11): 16211 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,0),app(nil,false)))) # answer(goal).  [ur(3152,b,471,a,c,696,a)].

given #2640 (F,wt=11): 16212 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,0),sndsplit(0,false)))) # answer(goal).  [ur(3152,b,471,a,c,639,a)].

given #2641 (F,wt=11): 16219 -->_s0(true,sndsplit(0,sndsplit(app(nil,0),sndsplit(0,false)))) # answer(goal).  [ur(3152,b,470,a,c,3536,a)].

given #2642 (F,wt=11): 16224 -->_s0(true,sndsplit(0,sndsplit(0,sndsplit(0,app(nil,false))))) # answer(goal).  [ur(3152,b,470,a,c,696,a)].

given #2643 (T,wt=9): 9809 ->*_s0(sndsplit(length(nil),length(nil)),sndsplit(0,0)).  [ur(87,a,321,a,b,4540,a)].

given #2644 (T,wt=9): 9955 ->*_s0(sndsplit(length(nil),sndsplit(length(nil),x)),x).  [ur(87,a,321,a,b,4646,a)].

given #2645 (T,wt=9): 9987 ->*_s0(mapf(length(nil),length(nil)),mapf(0,0)).  [ur(87,a,329,a,b,4671,a)].

given #2646 (T,wt=9): 10026 ->*_s0(leq(length(nil),length(nil)),leq(0,0)).  [ur(87,a,331,a,b,4757,a)].

given #2647 (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 #2648 (F,wt=11): 16225 -->_s0(true,sndsplit(0,sndsplit(0,sndsplit(0,sndsplit(0,false))))) # answer(goal).  [ur(3152,b,470,a,c,639,a)].

given #2649 (F,wt=11): 16241 -->_s0(true,sndsplit(0,app(mapf(x,nil),app(nil,false)))) # answer(goal).  [ur(3152,b,463,a,c,698,a)].

given #2650 (F,wt=11): 16242 -->_s0(true,sndsplit(0,leq(app(nil,s(x)),length(nil)))) # answer(goal).  [ur(3152,b,330,a,c,4835,a)].

given #2651 (F,wt=11): 16243 -->_s0(true,sndsplit(0,sndsplit(length(nil),sndsplit(length(nil),false)))) # answer(goal).  [ur(3152,b,321,a,c,4646,a)].

given #2652 (T,wt=9): 10079 ->*_s0(sndsplit(length(nil),leq(length(nil),x)),true).  [ur(87,a,321,a,b,4871,a)].

given #2653 (T,wt=9): 10106 ->*_s0(fstsplit(length(nil),length(nil)),fstsplit(0,0)).  [ur(87,a,335,a,b,4886,a)].

given #2654 (T,wt=9): 10132 ->*_s0(sndsplit(length(nil),fstsplit(length(nil),x)),nil).  [ur(87,a,321,a,b,4973,a)].

given #2655 (T,wt=9): 10145 ->*_s0(app(length(nil),length(nil)),app(0,0)).  [ur(87,a,338,a,b,4977,a)].

given #2656 (A,wt=14): 503 ->_s0(mapf(x,sndsplit(s(y),cons(z,u))),mapf(x,sndsplit(y,u))).  [ur(45,a,83,a)].

given #2657 (F,wt=11): 16244 -->_s0(true,sndsplit(0,sndsplit(length(nil),empty(cons(x,y))))) # answer(goal).  [ur(3152,b,321,a,c,1125,a)].

given #2658 (F,wt=11): 16245 -->_s0(true,sndsplit(0,sndsplit(length(nil),head(cons(false,x))))) # answer(goal).  [ur(3152,b,321,a,c,1113,a)].

given #2659 (F,wt=11): 16246 -->_s0(true,sndsplit(0,sndsplit(length(nil),leq(s(x),0)))) # answer(goal).  [ur(3152,b,321,a,c,1075,a)].

given #2660 (F,wt=11): 16247 -->_s0(true,sndsplit(0,sndsplit(length(nil),tail(cons(x,false))))) # answer(goal).  [ur(3152,b,321,a,c,1063,a)].

given #2661 (T,wt=9): 10395 ->*_s0(head(fstsplit(s(x),cons(y,z))),y).  [ur(87,a,233,a,b,575,a)].

given #2662 (T,wt=9): 10462 ->*_s0(length(cons(x,empty(nil))),s(length(true))).  [ur(87,a,68,a,b,6350,a)].

given #2663 (T,wt=9): 10500 ->*_s0(empty(fstsplit(s(x),cons(y,z))),false).  [ur(87,a,236,a,b,580,a)].

given #2664 (T,wt=9): 10712 ->*_s0(length(cons(x,length(nil))),s(length(0))).  [ur(87,a,68,a,b,7207,a)].

given #2665 (A,wt=14): 504 ->_s0(mapf(sndsplit(s(x),cons(y,z)),u),mapf(sndsplit(x,z),u)).  [ur(44,a,83,a)].

given #2666 (F,wt=7): 21379 -->*_s0(empty(mapf(two,head(x))),true) # answer(goal).  [ur(583,a,10500,a,c,305,a,d,4882,a)].

given #2667 (F,wt=7): 21588 -->_s0(empty(mapf(two,head(x))),true) # answer(goal).  [ur(87,b,86,a,c,21379,a)].

given #2668 (F,wt=8): 21583 -->_s0(empty(mapf(two,head(x))),empty(nil)) # answer(goal).  [ur(87,b,579,a,c,21379,a)].

given #2669 (F,wt=6): 21589 -->_s0(mapf(two,head(x)),nil) # answer(goal).  [resolve(21583,a,37,b)].

given #2670 (T,wt=9): 10785 ->*_s0(sndsplit(s(x),fstsplit(s(y),nil)),nil).  [ur(87,a,245,a,b,565,a)].

given #2671 (T,wt=9): 10891 ->*_s0(f(x,leq(0,y)),f(x,true)).  [ur(87,a,340,a,b,86,a)].

given #2672 (T,wt=9): 10907 ->*_s0(f(leq(0,x),y),f(true,y)).  [ur(87,a,341,a,b,86,a)].

given #2673 (T,wt=9): 10916 ->*_s0(cons(x,leq(0,y)),cons(x,true)).  [ur(87,a,342,a,b,86,a)].

given #2674 (A,wt=14): 505 ->_s0(leq(x,sndsplit(s(y),cons(z,u))),leq(x,sndsplit(y,u))).  [ur(43,a,83,a)].

given #2675 (F,wt=9): 21582 -->_s0(empty(mapf(two,head(x))),app(nil,true)) # answer(goal).  [ur(87,b,581,a,c,21379,a)].

given #2676 (F,wt=9): 21585 -->_s0(empty(mapf(two,head(x))),leq(0,y)) # answer(goal).  [ur(87,b,572,a,c,21379,a)].

given #2677 (F,wt=9): 21586 -->_s0(empty(mapf(two,head(x))),sndsplit(0,true)) # answer(goal).  [ur(87,b,567,a,c,21379,a)].

given #2678 (F,wt=10): 21359 -->_s0(mapf(two,head(x)),nil) | -->_s0(0,s(y)) # answer(goal).  [resolve(10500,a,1023,b)].

given #2679 (T,wt=9): 10925 ->*_s0(cons(leq(0,x),y),cons(true,y)).  [ur(87,a,343,a,b,86,a)].

given #2680 (T,wt=9): 10934 ->*_s0(sndsplit(x,leq(0,y)),sndsplit(x,true)).  [ur(87,a,345,a,b,86,a)].

given #2681 (T,wt=9): 10944 ->*_s0(sndsplit(leq(0,x),y),sndsplit(true,y)).  [ur(87,a,346,a,b,86,a)].

given #2682 (T,wt=9): 10953 ->*_s0(mapf(x,leq(0,y)),mapf(x,true)).  [ur(87,a,353,a,b,86,a)].

given #2683 (A,wt=14): 506 ->_s0(leq(sndsplit(s(x),cons(y,z)),u),leq(sndsplit(x,z),u)).  [ur(42,a,83,a)].

given #2684 (F,wt=10): 21380 -->_s0(empty(mapf(two,head(x))),y) | -->*_s0(y,true) # answer(goal).  [resolve(21379,a,87,c)].

given #2685 (F,wt=10): 21449 -->_s0(empty(mapf(two,head(x))),leq(length(nil),y)) # answer(goal).  [ur(87,b,4803,a,c,21379,a)].

given #2686 (F,wt=10): 21461 -->_s0(empty(mapf(two,head(x))),sndsplit(length(nil),true)) # answer(goal).  [ur(87,b,4574,a,c,21379,a)].

given #2687 (F,wt=10): 21521 -->_s0(empty(mapf(two,head(x))),empty(sndsplit(0,nil))) # answer(goal).  [ur(87,b,2390,a,c,21379,a)].

given #2688 (T,wt=9): 10962 ->*_s0(mapf(leq(0,x),y),mapf(true,y)).  [ur(87,a,354,a,b,86,a)].

given #2689 (T,wt=9): 10971 ->*_s0(leq(x,leq(0,y)),leq(x,true)).  [ur(87,a,355,a,b,86,a)].

given #2690 (T,wt=9): 10982 ->*_s0(leq(leq(0,x),y),leq(true,y)).  [ur(87,a,356,a,b,86,a)].

given #2691 (T,wt=9): 10991 ->*_s0(fstsplit(x,leq(0,y)),fstsplit(x,true)).  [ur(87,a,359,a,b,86,a)].

given #2692 (A,wt=12): 507 ->_s0(length(sndsplit(s(x),cons(y,z))),length(sndsplit(x,z))).  [ur(41,a,83,a)].

given #2693 (F,wt=8): 21609 -->_s0(mapf(two,head(x)),sndsplit(0,nil)) # answer(goal).  [resolve(21521,a,37,b)].

given #2694 (F,wt=10): 21532 -->_s0(empty(mapf(two,head(x))),empty(mapf(y,nil))) # answer(goal).  [ur(87,b,2147,a,c,21379,a)].

============================== PROOF =================================

% Proof 1 at 0.41 (+ 0.03) seconds: goal.
% Length of proof is 39.
% Level of proof is 8.
% Maximum clause weight is 22.000.
% Given clauses 2694.

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].
11 ->_s0(x2,y) -> ->_s0(mapf(x1,x2),mapf(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(empty(mapf(two,head(x15))),true))) # 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)].
45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence).  [clausify(11)].
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].
65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # 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].
70 ->_s0(leq(0,x),true) # label(replacement).  [assumption].
72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement).  [assumption].
74 ->_s0(mapf(x,nil),nil) # 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(empty(mapf(two,head(z))),true) # 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)].
278 ->_s0(mapf(x,head(cons(y,z))),mapf(x,y)).  [ur(45,a,67,a)].
305 ->_s0(leq(x,length(cons(y,z))),leq(x,s(length(z)))).  [ur(43,a,68,a)].
461 ->_s0(empty(mapf(x,nil)),empty(nil)).  [ur(37,a,74,a)].
572 ->*_s0(leq(0,x),true).  [ur(87,a,70,a,b,86,a)].
579 ->*_s0(empty(nil),true).  [ur(87,a,63,a,b,86,a)].
580 ->*_s0(empty(cons(x,y)),false).  [ur(87,a,62,a,b,86,a)].
583 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(empty(mapf(two,head(z))),true) | -->_s0(leq(x,length(y)),u) | -->*_s0(u,true) # answer(goal).  [resolve(88,a,87,c)].
2147 ->*_s0(empty(mapf(x,nil)),true).  [ur(87,a,461,a,b,579,a)].
4834 ->*_s0(leq(app(nil,0),x),true).  [ur(87,a,131,a,b,572,a)].
4882 ->*_s0(leq(s(app(nil,0)),s(x)),true).  [ur(87,a,72,a,b,4834,a)].
10500 ->*_s0(empty(fstsplit(s(x),cons(y,z))),false).  [ur(87,a,236,a,b,580,a)].
21379 -->*_s0(empty(mapf(two,head(x))),true) # answer(goal).  [ur(583,a,10500,a,c,305,a,d,4882,a)].
21532 -->_s0(empty(mapf(two,head(x))),empty(mapf(y,nil))) # answer(goal).  [ur(87,b,2147,a,c,21379,a)].
21613 -->_s0(mapf(two,head(x)),mapf(y,nil)) # answer(goal).  [resolve(21532,a,37,b)].
21614 $F # answer(goal).  [resolve(21613,a,278,a)].

============================== end of proof ==========================

============================== STATISTICS ============================

Given=2694. Generated=45335. Kept=21579. proofs=1.
Usable=2653. Sos=18708. Demods=0. Limbo=0, Disabled=271. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=8906. Back_subsumed=217.
Sos_limit_deleted=14850. 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=47817. Nonunit_bsub_feature_tests=3676.
Megabytes=43.10.
User_CPU=0.41, System_CPU=0.03, Wall_clock=0.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 3268716 exit (max_proofs) Tue Jul 30 09:06:55 2024


The problem is feasible.