NO

Problem 1: 

Infeasibility Problem:
[(VAR vNonEmpty x n h t m pid st1 in2 st2 in3 st3 vNonEmpty x2 x6 x5)
(STRATEGY CONTEXTSENSITIVE
(app 1 2)
(empty 1)
(fstsplit 1 2)
(head 1)
(length 1)
(leq 1 2)
(mapf 1 2)
(ring 1 2 3 4 5 6)
(sndsplit 1 2)
(tail 1)
(0)
(cons 1 2)
(f 1 2)
(fSNonEmpty)
(false)
(nil)
(s 1)
(three)
(true)
(two)
)
(RULES
app(cons(h,t),x) -> cons(h,app(t,x))
app(nil,x) -> x
empty(cons(h,t)) -> false
empty(nil) -> true
fstsplit(0,x) -> nil
fstsplit(s(n),cons(h,t)) -> cons(h,fstsplit(n,t))
fstsplit(s(n),nil) -> nil
head(cons(h,t)) -> h
length(cons(h,t)) -> s(length(t))
length(nil) -> 0
leq(0,m) -> true
leq(s(n),0) -> false
leq(s(n),s(m)) -> leq(n,m)
mapf(pid,cons(h,t)) -> app(f(pid,h),mapf(pid,t))
mapf(pid,nil) -> nil
ring(st1,in2,st2,in3,st3,m) -> ring(sndsplit(m,st1),cons(fstsplit(m,st1),in2),st2,in3,st3,m) | empty(fstsplit(m,st1)) ->* false
ring(st1,in2,st2,in3,st3,m) -> ring(st1,tail(in2),sndsplit(m,app(mapf(two,head(in2)),st2)),cons(fstsplit(m,app(mapf(two,head(in2)),st2)),in3),st3,m) | leq(m,length(st2)) ->* false, empty(fstsplit(m,app(mapf(two,head(in2)),st2))) ->* false
ring(st1,in2,st2,in3,st3,m) -> ring(st1,tail(in2),st2,in3,st3,m) | empty(mapf(two,head(in2))) ->* true
ring(st1,in2,st2,in3,st3,m) -> ring(st1,in2,sndsplit(m,st2),cons(fstsplit(m,st2),in3),st3,m) | leq(m,length(st2)) ->* true, empty(fstsplit(m,st2)) ->* false
ring(st1,in2,st2,in3,st3,m) -> ring(st1,in2,st2,tail(in3),sndsplit(m,app(mapf(three,head(in3)),st3)),m) | leq(m,length(st3)) ->* false, empty(fstsplit(m,app(mapf(three,head(in3)),st3))) ->* false
ring(st1,in2,st2,in3,st3,m) -> ring(st1,in2,st2,tail(in3),st3,m) | empty(mapf(three,head(in3))) ->* true
ring(st1,in2,st2,in3,st3,m) -> ring(st1,in2,st2,in3,sndsplit(m,st3),m) | leq(m,length(st3)) ->* true, empty(fstsplit(m,st3)) ->* false
sndsplit(0,x) -> x
sndsplit(s(n),cons(h,t)) -> sndsplit(n,t)
sndsplit(s(n),nil) -> nil
tail(cons(h,t)) -> t
)
]

Infeasibility Conditions:
empty(mapf(two,head(x2))) ->* true, leq(x6,length(x5)) ->* true, empty(fstsplit(x6,x5)) ->* false

Problem 1: 

Obtaining a proof using Prover9:

 -> Prover9 Output:
============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 3343811 was started by sandbox on z030.star.cs.uiowa.edu,
Tue Jul 30 09:38:55 2024
The command was "./prover9 -f /tmp/prover93343804-0.in".
============================== end of head ===========================

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

% Reading from file /tmp/prover93343804-0.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(empty(mapf(two,head(x13))),true) & ->*_s0(leq(x14,length(x15)),true) & ->*_s0(empty(fstsplit(x14,x15)),false))) # label(goal).
end_of_list.

============================== end of input ==========================

============================== PROCESS NON-CLAUSAL FORMULAS ==========

% Formulas that are not ordinary clauses:
1 ->_s0(x1,y) -> ->_s0(app(x1,x2),app(y,x2)) # label(congruence) # label(non_clause).  [assumption].
2 ->_s0(x2,y) -> ->_s0(app(x1,x2),app(x1,y)) # label(congruence) # label(non_clause).  [assumption].
3 ->_s0(x1,y) -> ->_s0(empty(x1),empty(y)) # label(congruence) # label(non_clause).  [assumption].
4 ->_s0(x1,y) -> ->_s0(fstsplit(x1,x2),fstsplit(y,x2)) # label(congruence) # label(non_clause).  [assumption].
5 ->_s0(x2,y) -> ->_s0(fstsplit(x1,x2),fstsplit(x1,y)) # label(congruence) # label(non_clause).  [assumption].
6 ->_s0(x1,y) -> ->_s0(head(x1),head(y)) # label(congruence) # label(non_clause).  [assumption].
7 ->_s0(x1,y) -> ->_s0(length(x1),length(y)) # label(congruence) # label(non_clause).  [assumption].
8 ->_s0(x1,y) -> ->_s0(leq(x1,x2),leq(y,x2)) # label(congruence) # label(non_clause).  [assumption].
9 ->_s0(x2,y) -> ->_s0(leq(x1,x2),leq(x1,y)) # label(congruence) # label(non_clause).  [assumption].
10 ->_s0(x1,y) -> ->_s0(mapf(x1,x2),mapf(y,x2)) # label(congruence) # label(non_clause).  [assumption].
11 ->_s0(x2,y) -> ->_s0(mapf(x1,x2),mapf(x1,y)) # label(congruence) # label(non_clause).  [assumption].
12 ->_s0(x1,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(y,x2,x3,x4,x5,x6)) # label(congruence) # label(non_clause).  [assumption].
13 ->_s0(x2,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,y,x3,x4,x5,x6)) # label(congruence) # label(non_clause).  [assumption].
14 ->_s0(x3,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,y,x4,x5,x6)) # label(congruence) # label(non_clause).  [assumption].
15 ->_s0(x4,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,y,x5,x6)) # label(congruence) # label(non_clause).  [assumption].
16 ->_s0(x5,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,x4,y,x6)) # label(congruence) # label(non_clause).  [assumption].
17 ->_s0(x6,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,x4,x5,y)) # label(congruence) # label(non_clause).  [assumption].
18 ->_s0(x1,y) -> ->_s0(sndsplit(x1,x2),sndsplit(y,x2)) # label(congruence) # label(non_clause).  [assumption].
19 ->_s0(x2,y) -> ->_s0(sndsplit(x1,x2),sndsplit(x1,y)) # label(congruence) # label(non_clause).  [assumption].
20 ->_s0(x1,y) -> ->_s0(tail(x1),tail(y)) # label(congruence) # label(non_clause).  [assumption].
21 ->_s0(x1,y) -> ->_s0(cons(x1,x2),cons(y,x2)) # label(congruence) # label(non_clause).  [assumption].
22 ->_s0(x2,y) -> ->_s0(cons(x1,x2),cons(x1,y)) # label(congruence) # label(non_clause).  [assumption].
23 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause).  [assumption].
24 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause).  [assumption].
25 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause).  [assumption].
26 ->*_s0(empty(fstsplit(x5,x7)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(sndsplit(x5,x7),cons(fstsplit(x5,x7),x8),x9,x10,x11,x5)) # label(replacement) # label(non_clause).  [assumption].
27 ->*_s0(leq(x5,length(x9)),false) & ->*_s0(empty(fstsplit(x5,app(mapf(two,head(x8)),x9))),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,tail(x8),sndsplit(x5,app(mapf(two,head(x8)),x9)),cons(fstsplit(x5,app(mapf(two,head(x8)),x9)),x10),x11,x5)) # label(replacement) # label(non_clause).  [assumption].
28 ->*_s0(empty(mapf(two,head(x8))),true) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,tail(x8),x9,x10,x11,x5)) # label(replacement) # label(non_clause).  [assumption].
29 ->*_s0(leq(x5,length(x9)),true) & ->*_s0(empty(fstsplit(x5,x9)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,sndsplit(x5,x9),cons(fstsplit(x5,x9),x10),x11,x5)) # label(replacement) # label(non_clause).  [assumption].
30 ->*_s0(leq(x5,length(x11)),false) & ->*_s0(empty(fstsplit(x5,app(mapf(three,head(x10)),x11))),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,tail(x10),sndsplit(x5,app(mapf(three,head(x10)),x11)),x5)) # label(replacement) # label(non_clause).  [assumption].
31 ->*_s0(empty(mapf(three,head(x10))),true) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,tail(x10),x11,x5)) # label(replacement) # label(non_clause).  [assumption].
32 ->*_s0(leq(x5,length(x11)),true) & ->*_s0(empty(fstsplit(x5,x11)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,x10,sndsplit(x5,x11),x5)) # label(replacement) # label(non_clause).  [assumption].
33 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause).  [assumption].
34 (exists x13 exists x14 exists x15 (->*_s0(empty(mapf(two,head(x13))),true) & ->*_s0(leq(x14,length(x15)),true) & ->*_s0(empty(fstsplit(x14,x15)),false))) # label(goal) # label(non_clause) # label(goal).  [goal].

============================== end of process non-clausal formulas ===

============================== PROCESS INITIAL CLAUSES ===============

% Clauses before input processing:

formulas(usable).
end_of_list.

formulas(sos).
-->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence).  [clausify(1)].
-->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence).  [clausify(2)].
-->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence).  [clausify(3)].
-->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence).  [clausify(4)].
-->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence).  [clausify(5)].
-->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence).  [clausify(6)].
-->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence).  [clausify(7)].
-->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence).  [clausify(8)].
-->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence).  [clausify(9)].
-->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence).  [clausify(10)].
-->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence).  [clausify(11)].
-->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence).  [clausify(12)].
-->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence).  [clausify(13)].
-->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence).  [clausify(14)].
-->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence).  [clausify(15)].
-->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence).  [clausify(16)].
-->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence).  [clausify(17)].
-->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence).  [clausify(18)].
-->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence).  [clausify(19)].
-->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence).  [clausify(20)].
-->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence).  [clausify(21)].
-->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence).  [clausify(22)].
-->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence).  [clausify(23)].
-->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence).  [clausify(24)].
-->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence).  [clausify(25)].
->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement).  [assumption].
->_s0(app(nil,x),x) # label(replacement).  [assumption].
->_s0(empty(cons(x,y)),false) # label(replacement).  [assumption].
->_s0(empty(nil),true) # label(replacement).  [assumption].
->_s0(fstsplit(0,x),nil) # label(replacement).  [assumption].
->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement).  [assumption].
->_s0(fstsplit(s(x),nil),nil) # label(replacement).  [assumption].
->_s0(head(cons(x,y)),x) # label(replacement).  [assumption].
->_s0(length(cons(x,y)),s(length(y))) # label(replacement).  [assumption].
->_s0(length(nil),0) # label(replacement).  [assumption].
->_s0(leq(0,x),true) # label(replacement).  [assumption].
->_s0(leq(s(x),0),false) # label(replacement).  [assumption].
->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement).  [assumption].
->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement).  [assumption].
->_s0(mapf(x,nil),nil) # label(replacement).  [assumption].
-->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement).  [clausify(26)].
-->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement).  [clausify(27)].
-->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement).  [clausify(28)].
-->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement).  [clausify(29)].
-->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement).  [clausify(30)].
-->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement).  [clausify(31)].
-->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement).  [clausify(32)].
->_s0(sndsplit(0,x),x) # label(replacement).  [assumption].
->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement).  [assumption].
->_s0(sndsplit(s(x),nil),nil) # label(replacement).  [assumption].
->_s0(tail(cons(x,y)),y) # label(replacement).  [assumption].
->*_s0(x,x) # label(reflexivity).  [assumption].
-->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity).  [clausify(33)].
-->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(leq(y,length(z)),true) | -->*_s0(empty(fstsplit(y,z)),false) # label(goal).  [deny(34)].
end_of_list.

formulas(demodulators).
end_of_list.

============================== PREDICATE ELIMINATION =================

No predicates eliminated.

============================== end predicate elimination =============

Auto_denials:
  % copying label goal to answer in negative clause

Term ordering decisions:
Predicate symbol precedence:  predicate_order([ ->_s0, ->*_s0 ]).
Function symbol precedence:  function_order([ nil, false, true, 0, two, three, cons, fstsplit, mapf, sndsplit, app, leq, f, empty, s, head, length, tail, ring ]).
After inverse_order:  (no changes).
Unfolding symbols: (none).

Auto_inference settings:
  % set(neg_binary_resolution).  % (HNE depth_diff=-26)
  % clear(ordered_res).  % (HNE depth_diff=-26)
  % set(ur_resolution).  % (HNE depth_diff=-26)
    % set(ur_resolution) -> set(pos_ur_resolution).
    % set(ur_resolution) -> set(neg_ur_resolution).

Auto_process settings:
  % set(unit_deletion).  % (Horn set with negative nonunits)

kept:      35 -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence).  [clausify(1)].
kept:      36 -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence).  [clausify(2)].
kept:      37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence).  [clausify(3)].
kept:      38 -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence).  [clausify(4)].
kept:      39 -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence).  [clausify(5)].
kept:      40 -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence).  [clausify(6)].
kept:      41 -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence).  [clausify(7)].
kept:      42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence).  [clausify(8)].
kept:      43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence).  [clausify(9)].
kept:      44 -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence).  [clausify(10)].
kept:      45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence).  [clausify(11)].
kept:      46 -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence).  [clausify(12)].
kept:      47 -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence).  [clausify(13)].
kept:      48 -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence).  [clausify(14)].
kept:      49 -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence).  [clausify(15)].
kept:      50 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence).  [clausify(16)].
kept:      51 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence).  [clausify(17)].
kept:      52 -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence).  [clausify(18)].
kept:      53 -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence).  [clausify(19)].
kept:      54 -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence).  [clausify(20)].
kept:      55 -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence).  [clausify(21)].
kept:      56 -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence).  [clausify(22)].
kept:      57 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence).  [clausify(23)].
kept:      58 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence).  [clausify(24)].
kept:      59 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence).  [clausify(25)].
kept:      60 ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement).  [assumption].
kept:      61 ->_s0(app(nil,x),x) # label(replacement).  [assumption].
kept:      62 ->_s0(empty(cons(x,y)),false) # label(replacement).  [assumption].
kept:      63 ->_s0(empty(nil),true) # label(replacement).  [assumption].
kept:      64 ->_s0(fstsplit(0,x),nil) # label(replacement).  [assumption].
kept:      65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement).  [assumption].
kept:      66 ->_s0(fstsplit(s(x),nil),nil) # label(replacement).  [assumption].
kept:      67 ->_s0(head(cons(x,y)),x) # label(replacement).  [assumption].
kept:      68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement).  [assumption].
kept:      69 ->_s0(length(nil),0) # label(replacement).  [assumption].
kept:      70 ->_s0(leq(0,x),true) # label(replacement).  [assumption].
kept:      71 ->_s0(leq(s(x),0),false) # label(replacement).  [assumption].
kept:      72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement).  [assumption].
kept:      73 ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement).  [assumption].
kept:      74 ->_s0(mapf(x,nil),nil) # label(replacement).  [assumption].
kept:      75 -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement).  [clausify(26)].
kept:      76 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement).  [clausify(27)].
kept:      77 -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement).  [clausify(28)].
kept:      78 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement).  [clausify(29)].
kept:      79 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement).  [clausify(30)].
kept:      80 -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement).  [clausify(31)].
kept:      81 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement).  [clausify(32)].
kept:      82 ->_s0(sndsplit(0,x),x) # label(replacement).  [assumption].
kept:      83 ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement).  [assumption].
kept:      84 ->_s0(sndsplit(s(x),nil),nil) # label(replacement).  [assumption].
kept:      85 ->_s0(tail(cons(x,y)),y) # label(replacement).  [assumption].
kept:      86 ->*_s0(x,x) # label(reflexivity).  [assumption].
kept:      87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity).  [clausify(33)].
kept:      88 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(leq(y,length(z)),true) | -->*_s0(empty(fstsplit(y,z)),false) # label(goal) # answer(goal).  [deny(34)].

============================== end of process initial clauses ========

============================== CLAUSES FOR SEARCH ====================

% Clauses after input processing:

formulas(usable).
end_of_list.

formulas(sos).
35 -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence).  [clausify(1)].
36 -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence).  [clausify(2)].
37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence).  [clausify(3)].
38 -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence).  [clausify(4)].
39 -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence).  [clausify(5)].
40 -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence).  [clausify(6)].
41 -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence).  [clausify(7)].
42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence).  [clausify(8)].
43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence).  [clausify(9)].
44 -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence).  [clausify(10)].
45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence).  [clausify(11)].
46 -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence).  [clausify(12)].
47 -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence).  [clausify(13)].
48 -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence).  [clausify(14)].
49 -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence).  [clausify(15)].
50 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence).  [clausify(16)].
51 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence).  [clausify(17)].
52 -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence).  [clausify(18)].
53 -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence).  [clausify(19)].
54 -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence).  [clausify(20)].
55 -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence).  [clausify(21)].
56 -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence).  [clausify(22)].
57 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence).  [clausify(23)].
58 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence).  [clausify(24)].
59 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence).  [clausify(25)].
60 ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement).  [assumption].
61 ->_s0(app(nil,x),x) # label(replacement).  [assumption].
62 ->_s0(empty(cons(x,y)),false) # label(replacement).  [assumption].
63 ->_s0(empty(nil),true) # label(replacement).  [assumption].
64 ->_s0(fstsplit(0,x),nil) # label(replacement).  [assumption].
65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement).  [assumption].
66 ->_s0(fstsplit(s(x),nil),nil) # label(replacement).  [assumption].
67 ->_s0(head(cons(x,y)),x) # label(replacement).  [assumption].
68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement).  [assumption].
69 ->_s0(length(nil),0) # label(replacement).  [assumption].
70 ->_s0(leq(0,x),true) # label(replacement).  [assumption].
71 ->_s0(leq(s(x),0),false) # label(replacement).  [assumption].
72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement).  [assumption].
73 ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement).  [assumption].
74 ->_s0(mapf(x,nil),nil) # label(replacement).  [assumption].
75 -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement).  [clausify(26)].
76 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement).  [clausify(27)].
77 -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement).  [clausify(28)].
78 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement).  [clausify(29)].
79 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement).  [clausify(30)].
80 -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement).  [clausify(31)].
81 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement).  [clausify(32)].
82 ->_s0(sndsplit(0,x),x) # label(replacement).  [assumption].
83 ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement).  [assumption].
84 ->_s0(sndsplit(s(x),nil),nil) # label(replacement).  [assumption].
85 ->_s0(tail(cons(x,y)),y) # label(replacement).  [assumption].
86 ->*_s0(x,x) # label(reflexivity).  [assumption].
87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity).  [clausify(33)].
88 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(leq(y,length(z)),true) | -->*_s0(empty(fstsplit(y,z)),false) # label(goal) # answer(goal).  [deny(34)].
end_of_list.

formulas(demodulators).
end_of_list.

============================== end of clauses for search =============

============================== SEARCH ================================

% Starting search at 0.01 seconds.

given #1 (I,wt=10): 35 -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence).  [clausify(1)].

given #2 (I,wt=10): 36 -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence).  [clausify(2)].

given #3 (I,wt=8): 37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence).  [clausify(3)].

given #4 (I,wt=10): 38 -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence).  [clausify(4)].

given #5 (I,wt=10): 39 -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence).  [clausify(5)].

given #6 (I,wt=8): 40 -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence).  [clausify(6)].

given #7 (I,wt=8): 41 -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence).  [clausify(7)].

given #8 (I,wt=10): 42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence).  [clausify(8)].

given #9 (I,wt=10): 43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence).  [clausify(9)].

given #10 (I,wt=10): 44 -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence).  [clausify(10)].

given #11 (I,wt=10): 45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence).  [clausify(11)].

given #12 (I,wt=18): 46 -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence).  [clausify(12)].

given #13 (I,wt=18): 47 -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence).  [clausify(13)].

given #14 (I,wt=18): 48 -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence).  [clausify(14)].

given #15 (I,wt=18): 49 -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence).  [clausify(15)].

given #16 (I,wt=18): 50 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence).  [clausify(16)].

given #17 (I,wt=18): 51 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence).  [clausify(17)].

given #18 (I,wt=10): 52 -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence).  [clausify(18)].

given #19 (I,wt=10): 53 -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence).  [clausify(19)].

given #20 (I,wt=8): 54 -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence).  [clausify(20)].

given #21 (I,wt=10): 55 -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence).  [clausify(21)].

given #22 (I,wt=10): 56 -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence).  [clausify(22)].

given #23 (I,wt=10): 57 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence).  [clausify(23)].

given #24 (I,wt=10): 58 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence).  [clausify(24)].

given #25 (I,wt=8): 59 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence).  [clausify(25)].

given #26 (I,wt=11): 60 ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement).  [assumption].

given #27 (I,wt=5): 61 ->_s0(app(nil,x),x) # label(replacement).  [assumption].

given #28 (I,wt=6): 62 ->_s0(empty(cons(x,y)),false) # label(replacement).  [assumption].

given #29 (I,wt=4): 63 ->_s0(empty(nil),true) # label(replacement).  [assumption].

given #30 (I,wt=5): 64 ->_s0(fstsplit(0,x),nil) # label(replacement).  [assumption].

given #31 (I,wt=12): 65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement).  [assumption].

given #32 (I,wt=6): 66 ->_s0(fstsplit(s(x),nil),nil) # label(replacement).  [assumption].

given #33 (I,wt=6): 67 ->_s0(head(cons(x,y)),x) # label(replacement).  [assumption].

given #34 (I,wt=8): 68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement).  [assumption].

given #35 (I,wt=4): 69 ->_s0(length(nil),0) # label(replacement).  [assumption].

given #36 (I,wt=5): 70 ->_s0(leq(0,x),true) # label(replacement).  [assumption].

given #37 (I,wt=6): 71 ->_s0(leq(s(x),0),false) # label(replacement).  [assumption].

given #38 (I,wt=9): 72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement).  [assumption].

given #39 (I,wt=13): 73 ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement).  [assumption].

given #40 (I,wt=5): 74 ->_s0(mapf(x,nil),nil) # label(replacement).  [assumption].

given #41 (I,wt=27): 75 -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement).  [clausify(26)].

given #42 (I,wt=49): 76 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement).  [clausify(27)].

given #43 (I,wt=23): 77 -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement).  [clausify(28)].

given #44 (I,wt=33): 78 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement).  [clausify(29)].

given #45 (I,wt=40): 79 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement).  [clausify(30)].

given #46 (I,wt=23): 80 -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement).  [clausify(31)].

given #47 (I,wt=29): 81 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement).  [clausify(32)].

given #48 (I,wt=5): 82 ->_s0(sndsplit(0,x),x) # label(replacement).  [assumption].

given #49 (I,wt=10): 83 ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement).  [assumption].

given #50 (I,wt=6): 84 ->_s0(sndsplit(s(x),nil),nil) # label(replacement).  [assumption].

given #51 (I,wt=6): 85 ->_s0(tail(cons(x,y)),y) # label(replacement).  [assumption].

given #52 (I,wt=3): 86 ->*_s0(x,x) # label(reflexivity).  [assumption].

given #53 (I,wt=9): 87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity).  [clausify(33)].

given #54 (I,wt=19): 88 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(leq(y,length(z)),true) | -->*_s0(empty(fstsplit(y,z)),false) # label(goal) # answer(goal).  [deny(34)].

given #55 (A,wt=13): 89 ->_s0(s(app(cons(x,y),z)),s(cons(x,app(y,z)))).  [ur(59,a,60,a)].

given #56 (F,wt=22): 583 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | -->_s0(empty(mapf(two,head(z))),u) | -->*_s0(u,true) # answer(goal).  [resolve(88,a,87,c)].

given #57 (F,wt=19): 616 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | -->_s0(empty(mapf(two,head(z))),true) # answer(goal).  [resolve(583,d,86,a)].

given #58 (F,wt=22): 584 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(empty(fstsplit(y,z)),false) | -->_s0(leq(y,length(z)),u) | -->*_s0(u,true) # answer(goal).  [resolve(88,b,87,c)].

given #59 (F,wt=13): 620 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(empty(fstsplit(0,y)),false) # answer(goal).  [resolve(584,c,70,a),unit_del(c,86)].

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=16): 625 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),z) | -->*_s0(z,true) # answer(goal).  [resolve(620,a,87,c)].

given #66 (F,wt=13): 679 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),true) # answer(goal).  [resolve(625,c,86,a)].

given #67 (F,wt=14): 676 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),empty(nil)) # answer(goal).  [resolve(625,c,579,a)].

given #68 (F,wt=12): 682 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(mapf(two,head(y)),nil) # answer(goal).  [resolve(676,b,37,b)].

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=15): 677 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),sndsplit(0,true)) # answer(goal).  [resolve(625,c,567,a)].

given #75 (F,wt=15): 683 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),z) | -->*_s0(z,false) # answer(goal).  [resolve(682,a,87,c)].

given #76 (F,wt=12): 760 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),false) # answer(goal).  [resolve(683,c,86,a)].

given #77 (F,wt=14): 757 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),app(nil,false)) # answer(goal).  [resolve(683,c,581,a)].

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=14): 758 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),sndsplit(0,false)) # answer(goal).  [resolve(683,c,567,a)].

given #84 (F,wt=15): 684 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),leq(0,z)) # answer(goal).  [resolve(572,a,625,c)].

given #85 (F,wt=15): 696 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(mapf(two,head(y))),app(nil,true)) # answer(goal).  [resolve(581,a,625,c)].

given #86 (F,wt=15): 756 -->_s0(mapf(two,head(x)),nil) | -->*_s0(empty(y),false) | -->_s0(fstsplit(0,z),y) # answer(goal).  [resolve(683,b,37,b)].

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=10): 894 -->_s0(mapf(two,head(x)),nil) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(756,c,64,a)].

given #93 (F,wt=13): 1026 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),y) | -->*_s0(y,false) # answer(goal).  [resolve(894,b,87,c)].

given #94 (F,wt=9): 1027 -->_s0(mapf(two,head(x)),nil) | -->*_s0(true,false) # answer(goal).  [resolve(1026,b,63,a)].

given #95 (F,wt=10): 1032 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),false) # answer(goal).  [resolve(1026,c,86,a)].

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=12): 1029 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),app(nil,false)) # answer(goal).  [resolve(1026,c,581,a)].

given #102 (F,wt=12): 1030 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),sndsplit(0,false)) # answer(goal).  [resolve(1026,c,567,a)].

given #103 (F,wt=12): 1033 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->*_s0(y,false) # answer(goal).  [resolve(1027,b,87,c)].

given #104 (F,wt=9): 1113 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,false) # answer(goal).  [resolve(1033,c,86,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): 628 ->*_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=11): 1108 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,false)) # answer(goal).  [resolve(1033,c,581,a)].

given #111 (F,wt=11): 1110 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,false)) # answer(goal).  [resolve(1033,c,567,a)].

given #112 (F,wt=12): 1109 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(s(y),0)) # answer(goal).  [resolve(1033,c,571,a)].

given #113 (F,wt=12): 1111 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,false))) # answer(goal).  [resolve(1033,c,564,a)].

given #114 (T,wt=6): 630 ->*_s0(app(nil,length(nil)),0).  [ur(87,a,61,a,b,573,a)].

given #115 (T,wt=6): 634 ->*_s0(sndsplit(0,empty(nil)),true).  [ur(87,a,82,a,b,579,a)].

given #116 (T,wt=6): 636 ->*_s0(app(nil,empty(nil)),true).  [ur(87,a,61,a,b,579,a)].

given #117 (T,wt=6): 703 ->*_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): 1114 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(false,y))) # answer(goal).  [resolve(575,a,1033,c)].

given #120 (F,wt=12): 1128 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(cons(y,z))) # answer(goal).  [resolve(580,a,1033,c)].

given #121 (F,wt=13): 1028 -->_s0(mapf(two,head(x)),nil) | -->*_s0(empty(y),false) | -->_s0(nil,y) # answer(goal).  [resolve(1026,b,37,b)].

given #122 (F,wt=11): 1217 -->_s0(mapf(two,head(x)),nil) | -->_s0(nil,cons(y,z)) # answer(goal).  [resolve(1028,b,580,a)].

given #123 (T,wt=6): 761 ->*_s0(tail(empty(nil)),tail(true)).  [ur(87,a,169,a,b,86,a)].

given #124 (T,wt=6): 787 ->*_s0(length(empty(nil)),length(true)).  [ur(87,a,182,a,b,86,a)].

given #125 (T,wt=6): 813 ->*_s0(head(empty(nil)),head(true)).  [ur(87,a,183,a,b,86,a)].

given #126 (T,wt=6): 839 ->*_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): 1060 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),tail(cons(y,false))) # answer(goal).  [resolve(564,a,1026,c)].

given #129 (F,wt=13): 1074 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),leq(s(y),0)) # answer(goal).  [resolve(571,a,1026,c)].

given #130 (F,wt=13): 1115 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),head(cons(false,y))) # answer(goal).  [resolve(575,a,1026,c)].

given #131 (F,wt=13): 1129 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),empty(cons(y,z))) # answer(goal).  [resolve(580,a,1026,c)].

given #132 (T,wt=6): 896 ->*_s0(s(length(nil)),s(0)).  [ur(87,a,314,a,b,86,a)].

given #133 (T,wt=6): 922 ->*_s0(tail(length(nil)),tail(0)).  [ur(87,a,319,a,b,86,a)].

given #134 (T,wt=6): 948 ->*_s0(length(length(nil)),length(0)).  [ur(87,a,332,a,b,86,a)].

given #135 (T,wt=6): 974 ->*_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): 1130 -->_s0(mapf(two,head(x)),nil) | -->_s0(fstsplit(0,y),cons(z,u)) # answer(goal).  [resolve(580,a,756,b)].

given #138 (F,wt=15): 895 -->_s0(mapf(two,head(x)),nil) | -->*_s0(empty(fstsplit(y,z)),false) | -->_s0(0,y) # answer(goal).  [resolve(756,c,38,b)].

given #139 (F,wt=15): 1061 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),tail(cons(z,false))) # answer(goal).  [resolve(564,a,683,c)].

given #140 (F,wt=15): 1075 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),leq(s(z),0)) # answer(goal).  [resolve(571,a,683,c)].

given #141 (T,wt=6): 1034 ->*_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): 1112 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,z) | -->*_s0(z,false) # answer(goal).  [resolve(1033,c,87,c)].

given #147 (F,wt=12): 1499 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,false) # answer(goal).  [resolve(1112,d,86,a)].

given #148 (F,wt=13): 1459 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,length(nil)) | -->*_s0(0,false) # answer(goal).  [resolve(1112,c,69,a)].

given #149 (F,wt=14): 1448 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,y)) | -->*_s0(y,false) # answer(goal).  [resolve(1112,c,82,a)].

given #150 (T,wt=6): 1368 ->*_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): 1547 ->*_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=13): 1501 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,app(nil,false))) # answer(goal).  [resolve(1448,c,581,a)].

given #156 (F,wt=13): 1505 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,sndsplit(0,false))) # answer(goal).  [resolve(1448,c,567,a)].

given #157 (F,wt=14): 1456 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,mapf(y,nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(1112,c,74,a)].

given #158 (F,wt=14): 1464 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,fstsplit(0,y)) | -->*_s0(nil,false) # answer(goal).  [resolve(1112,c,64,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): 1666 ->*_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=14): 1465 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,y)) | -->*_s0(y,false) # answer(goal).  [resolve(1112,c,61,a)].

given #165 (F,wt=13): 1725 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,app(nil,false))) # answer(goal).  [resolve(1465,c,581,a)].

given #166 (F,wt=13): 1729 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,sndsplit(0,false))) # answer(goal).  [resolve(1465,c,567,a)].

given #167 (F,wt=14): 1492 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,app(nil,false)) # answer(goal).  [resolve(1112,d,581,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): 1763 ->*_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=14): 1496 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,sndsplit(0,false)) # answer(goal).  [resolve(1112,d,567,a)].

given #174 (F,wt=14): 1502 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,empty(cons(y,z)))) # answer(goal).  [resolve(1448,c,580,a)].

given #175 (F,wt=14): 1503 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,head(cons(false,y)))) # answer(goal).  [resolve(1448,c,575,a)].

given #176 (F,wt=14): 1504 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,leq(s(y),0))) # answer(goal).  [resolve(1448,c,571,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): 1506 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,tail(cons(y,false)))) # answer(goal).  [resolve(1448,c,564,a)].

given #183 (F,wt=14): 1726 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,empty(cons(y,z)))) # answer(goal).  [resolve(1465,c,580,a)].

given #184 (F,wt=14): 1727 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,head(cons(false,y)))) # answer(goal).  [resolve(1465,c,575,a)].

given #185 (F,wt=14): 1728 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,leq(s(y),0))) # answer(goal).  [resolve(1465,c,571,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): 2047 ->*_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): 1730 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,tail(cons(y,false)))) # answer(goal).  [resolve(1465,c,564,a)].

given #192 (F,wt=14): 1732 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,app(nil,false)))) # answer(goal).  [resolve(1492,c,85,a)].

given #193 (F,wt=14): 1733 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(app(nil,false),y))) # answer(goal).  [resolve(1492,c,67,a)].

given #194 (F,wt=14): 1734 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,y)) | -->_s0(y,false) # answer(goal).  [resolve(1492,c,36,b)].

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): 2133 ->*_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=14): 1735 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(y,false)) | -->_s0(y,nil) # answer(goal).  [resolve(1492,c,35,b)].

given #201 (F,wt=13): 2226 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(sndsplit(0,nil),false)) # answer(goal).  [resolve(1735,c,82,a)].

given #202 (F,wt=13): 2227 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(mapf(y,nil),false)) # answer(goal).  [resolve(1735,c,74,a)].

given #203 (F,wt=13): 2230 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(fstsplit(0,y),false)) # answer(goal).  [resolve(1735,c,64,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): 2268 ->*_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=13): 2231 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(app(nil,nil),false)) # answer(goal).  [resolve(1735,c,61,a)].

given #210 (F,wt=14): 1852 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,sndsplit(0,false)))) # answer(goal).  [resolve(1496,c,85,a)].

given #211 (F,wt=14): 1853 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(s(0),cons(y,false))) # answer(goal).  [resolve(1496,c,83,a)].

given #212 (F,wt=14): 1854 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(sndsplit(0,false),y))) # answer(goal).  [resolve(1496,c,67,a)].

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

given #214 (T,wt=6): 2366 ->*_s0(empty(sndsplit(0,nil)),true).  [ur(87,a,486,a,b,579,a)].

given #215 (T,wt=7): 627 ->*_s0(tail(cons(x,length(nil))),0).  [ur(87,a,85,a,b,573,a)].

given #216 (T,wt=7): 629 ->*_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=14): 1855 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,y)) | -->_s0(y,false) # answer(goal).  [resolve(1496,c,53,b)].

given #219 (F,wt=14): 1856 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(y,false)) | -->_s0(y,0) # answer(goal).  [resolve(1496,c,52,b)].

given #220 (F,wt=12): 2443 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(nil),false)) # answer(goal).  [resolve(1856,c,69,a)].

given #221 (F,wt=13): 2442 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(sndsplit(0,0),false)) # answer(goal).  [resolve(1856,c,82,a)].

given #222 (T,wt=7): 633 ->*_s0(tail(cons(x,empty(nil))),true).  [ur(87,a,85,a,b,579,a)].

given #223 (T,wt=7): 635 ->*_s0(head(cons(empty(nil),x)),true).  [ur(87,a,67,a,b,579,a)].

given #224 (T,wt=7): 641 ->*_s0(sndsplit(0,sndsplit(0,x)),x).  [ur(87,a,82,a,b,567,a)].

given #225 (T,wt=7): 643 ->*_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=13): 2445 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(app(nil,0),false)) # answer(goal).  [resolve(1856,c,61,a)].

given #228 (F,wt=14): 2224 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(tail(cons(y,nil)),false)) # answer(goal).  [resolve(1735,c,85,a)].

given #229 (F,wt=14): 2225 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(sndsplit(s(y),nil),false)) # answer(goal).  [resolve(1735,c,84,a)].

given #230 (F,wt=14): 2228 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(head(cons(nil,y)),false)) # answer(goal).  [resolve(1735,c,67,a)].

given #231 (T,wt=7): 645 ->*_s0(sndsplit(0,mapf(x,nil)),nil).  [ur(87,a,82,a,b,568,a)].

given #232 (T,wt=7): 647 ->*_s0(app(nil,mapf(x,nil)),nil).  [ur(87,a,61,a,b,568,a)].

given #233 (T,wt=7): 688 ->*_s0(sndsplit(0,leq(0,x)),true).  [ur(87,a,82,a,b,572,a)].

given #234 (T,wt=7): 689 ->*_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=14): 2229 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(fstsplit(s(y),nil),false)) # answer(goal).  [resolve(1735,c,66,a)].

given #237 (F,wt=14): 2441 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(tail(cons(y,0)),false)) # answer(goal).  [resolve(1856,c,85,a)].

given #238 (F,wt=14): 2444 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(head(cons(0,y)),false)) # answer(goal).  [resolve(1856,c,67,a)].

given #239 (F,wt=14): 2467 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),sndsplit(0,sndsplit(0,false))) # answer(goal).  [resolve(641,a,1026,c)].

given #240 (T,wt=7): 691 ->*_s0(app(nil,leq(0,x)),true).  [ur(87,a,61,a,b,572,a)].

given #241 (T,wt=7): 693 ->*_s0(sndsplit(0,fstsplit(0,x)),nil).  [ur(87,a,82,a,b,578,a)].

given #242 (T,wt=7): 695 ->*_s0(app(nil,fstsplit(0,x)),nil).  [ur(87,a,61,a,b,578,a)].

given #243 (T,wt=7): 700 ->*_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=14): 2480 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),app(nil,sndsplit(0,false))) # answer(goal).  [resolve(643,a,1026,c)].

given #246 (F,wt=14): 2590 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),sndsplit(0,app(nil,false))) # answer(goal).  [resolve(700,a,1026,c)].

given #247 (F,wt=15): 1116 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),head(cons(false,z))) # answer(goal).  [resolve(575,a,683,c)].

given #248 (F,wt=15): 1131 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),empty(cons(z,u))) # answer(goal).  [resolve(580,a,683,c)].

given #249 (T,wt=7): 702 ->*_s0(app(nil,app(nil,x)),x).  [ur(87,a,61,a,b,581,a)].

given #250 (T,wt=7): 1263 ->*_s0(length(cons(x,nil)),s(0)).  [ur(87,a,68,a,b,896,a)].

given #251 (T,wt=7): 1311 ->*_s0(s(app(nil,x)),s(x)).  [ur(87,a,114,a,b,86,a)].

given #252 (T,wt=7): 1340 ->*_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=14): 2630 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),app(nil,app(nil,false))) # answer(goal).  [resolve(702,a,1026,c)].

given #255 (F,wt=14): 2657 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(app(cons(y,z),u))) # answer(goal).  [resolve(111,a,1112,c),unit_del(c,580)].

given #256 (F,wt=15): 1421 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(length(nil))) | -->*_s0(empty(0),false) # answer(goal).  [resolve(1112,c,336,a)].

given #257 (F,wt=15): 1422 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(length(nil))) | -->*_s0(head(0),false) # answer(goal).  [resolve(1112,c,333,a)].

given #258 (T,wt=7): 1369 ->*_s0(length(app(nil,x)),length(x)).  [ur(87,a,132,a,b,86,a)].

given #259 (T,wt=7): 1517 ->*_s0(head(app(nil,x)),head(x)).  [ur(87,a,133,a,b,86,a)].

given #260 (T,wt=7): 1548 ->*_s0(empty(app(nil,x)),empty(x)).  [ur(87,a,136,a,b,86,a)].

given #261 (T,wt=7): 1612 ->*_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=15): 1423 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,length(length(nil))) | -->*_s0(length(0),false) # answer(goal).  [resolve(1112,c,332,a)].

given #264 (F,wt=15): 1424 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(length(nil))) | -->*_s0(tail(0),false) # answer(goal).  [resolve(1112,c,319,a)].

given #265 (F,wt=15): 1425 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,s(length(nil))) | -->*_s0(s(0),false) # answer(goal).  [resolve(1112,c,314,a)].

given #266 (F,wt=15): 1426 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(empty(nil))) | -->*_s0(empty(true),false) # answer(goal).  [resolve(1112,c,186,a)].

given #267 (T,wt=7): 1639 ->*_s0(tail(fstsplit(0,x)),tail(nil)).  [ur(87,a,194,a,b,86,a)].

given #268 (T,wt=7): 1667 ->*_s0(length(fstsplit(0,x)),length(nil)).  [ur(87,a,207,a,b,86,a)].

given #269 (T,wt=7): 1737 ->*_s0(head(fstsplit(0,x)),head(nil)).  [ur(87,a,208,a,b,86,a)].

given #270 (T,wt=7): 1764 ->*_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=15): 1427 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(empty(nil))) | -->*_s0(head(true),false) # answer(goal).  [resolve(1112,c,183,a)].

given #273 (F,wt=15): 1428 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,length(empty(nil))) | -->*_s0(length(true),false) # answer(goal).  [resolve(1112,c,182,a)].

given #274 (F,wt=15): 1429 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(empty(nil))) | -->*_s0(tail(true),false) # answer(goal).  [resolve(1112,c,169,a)].

given #275 (F,wt=15): 1430 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,s(empty(nil))) | -->*_s0(s(true),false) # answer(goal).  [resolve(1112,c,164,a)].

given #276 (T,wt=7): 1799 ->*_s0(s(leq(0,x)),s(true)).  [ur(87,a,339,a,b,86,a)].

given #277 (T,wt=7): 1858 ->*_s0(tail(leq(0,x)),tail(true)).  [ur(87,a,344,a,b,86,a)].

given #278 (T,wt=7): 1885 ->*_s0(length(leq(0,x)),length(true)).  [ur(87,a,357,a,b,86,a)].

given #279 (T,wt=7): 1912 ->*_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=15): 1445 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,z))) | -->*_s0(z,false) # answer(goal).  [resolve(1112,c,85,a)].

given #282 (F,wt=15): 1446 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(s(y),nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(1112,c,84,a)].

given #283 (F,wt=15): 1461 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(y,z))) | -->*_s0(y,false) # answer(goal).  [resolve(1112,c,67,a)].

given #284 (F,wt=15): 1462 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,fstsplit(s(y),nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(1112,c,66,a)].

given #285 (T,wt=7): 1939 ->*_s0(empty(leq(0,x)),empty(true)).  [ur(87,a,361,a,b,86,a)].

given #286 (T,wt=7): 1993 ->*_s0(s(mapf(x,nil)),s(nil)).  [ur(87,a,439,a,b,86,a)].

given #287 (T,wt=7): 2020 ->*_s0(tail(mapf(x,nil)),tail(nil)).  [ur(87,a,444,a,b,86,a)].

given #288 (T,wt=7): 2048 ->*_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=15): 1493 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,empty(cons(z,u))) # answer(goal).  [resolve(1112,d,580,a)].

given #291 (F,wt=14): 2920 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(sndsplit(0,cons(y,z)))) # answer(goal).  [resolve(1493,c,486,a)].

given #292 (F,wt=14): 2921 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(app(nil,cons(y,z)))) # answer(goal).  [resolve(1493,c,136,a)].

given #293 (F,wt=15): 1494 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,head(cons(false,z))) # answer(goal).  [resolve(1112,d,575,a)].

given #294 (T,wt=7): 2107 ->*_s0(head(mapf(x,nil)),head(nil)).  [ur(87,a,458,a,b,86,a)].

given #295 (T,wt=7): 2134 ->*_s0(empty(mapf(x,nil)),empty(nil)).  [ur(87,a,461,a,b,86,a)].

given #296 (T,wt=7): 2171 ->*_s0(s(sndsplit(0,x)),s(x)).  [ur(87,a,464,a,b,86,a)].

given #297 (T,wt=7): 2236 ->*_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=14): 2923 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(sndsplit(0,cons(false,y)))) # answer(goal).  [resolve(1494,c,483,a)].

given #300 (F,wt=14): 2924 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(app(nil,cons(false,y)))) # answer(goal).  [resolve(1494,c,133,a)].

given #301 (F,wt=14): 2925 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(app(cons(false,y),z))) # answer(goal).  [resolve(1494,c,108,a)].

given #302 (F,wt=15): 1495 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,leq(s(z),0)) # answer(goal).  [resolve(1112,d,571,a)].

given #303 (T,wt=7): 2269 ->*_s0(length(sndsplit(0,x)),length(x)).  [ur(87,a,482,a,b,86,a)].

given #304 (T,wt=7): 2305 ->*_s0(head(sndsplit(0,x)),head(x)).  [ur(87,a,483,a,b,86,a)].

given #305 (T,wt=7): 2367 ->*_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=14): 2978 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(s(s(y)),s(0))) # answer(goal).  [resolve(1495,c,72,a)].

given #309 (F,wt=15): 1497 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,tail(cons(z,false))) # answer(goal).  [resolve(1112,d,564,a)].

given #310 (F,wt=14): 3053 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(sndsplit(0,cons(y,false)))) # answer(goal).  [resolve(1497,c,469,a)].

given #311 (F,wt=14): 3054 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(app(nil,cons(y,false)))) # answer(goal).  [resolve(1497,c,119,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=15): 2464 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,sndsplit(0,sndsplit(0,false)))) # answer(goal).  [resolve(641,a,1465,c)].

given #318 (F,wt=15): 2465 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,sndsplit(0,sndsplit(0,false)))) # answer(goal).  [resolve(641,a,1448,c)].

given #319 (F,wt=15): 2477 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,app(nil,sndsplit(0,false)))) # answer(goal).  [resolve(643,a,1465,c)].

given #320 (F,wt=15): 2478 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,app(nil,sndsplit(0,false)))) # answer(goal).  [resolve(643,a,1448,c)].

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=15): 2587 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,sndsplit(0,app(nil,false)))) # answer(goal).  [resolve(700,a,1465,c)].

given #327 (F,wt=15): 2588 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,sndsplit(0,app(nil,false)))) # answer(goal).  [resolve(700,a,1448,c)].

given #328 (F,wt=15): 2627 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,app(nil,app(nil,false)))) # answer(goal).  [resolve(702,a,1465,c)].

given #329 (F,wt=15): 2628 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,app(nil,app(nil,false)))) # answer(goal).  [resolve(702,a,1448,c)].

given #330 (T,wt=7): 3308 ->*_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=14): 3341 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),sndsplit(app(nil,0),false)) # answer(goal).  [resolve(3308,a,1026,c)].

given #336 (F,wt=15): 2853 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,empty(cons(z,u))))) # answer(goal).  [resolve(1445,c,580,a)].

given #337 (F,wt=15): 2854 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,head(cons(false,z))))) # answer(goal).  [resolve(1445,c,575,a)].

given #338 (F,wt=15): 2855 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,leq(s(z),0)))) # answer(goal).  [resolve(1445,c,571,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=15): 2856 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,tail(cons(z,false))))) # answer(goal).  [resolve(1445,c,564,a)].

given #345 (F,wt=15): 2863 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(empty(cons(y,z)),u))) # answer(goal).  [resolve(1461,c,580,a)].

given #346 (F,wt=15): 2864 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(head(cons(false,y)),z))) # answer(goal).  [resolve(1461,c,575,a)].

given #347 (F,wt=15): 2865 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(leq(s(y),0),z))) # answer(goal).  [resolve(1461,c,571,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=15): 2866 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(tail(cons(y,false)),z))) # answer(goal).  [resolve(1461,c,564,a)].

given #354 (F,wt=15): 2922 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(y)) | -->_s0(y,cons(z,u)) # answer(goal).  [resolve(1493,c,37,b)].

given #355 (F,wt=15): 2926 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(y)) | -->_s0(y,cons(false,z)) # answer(goal).  [resolve(1494,c,40,b)].

given #356 (F,wt=15): 2979 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(s(y),z)) | -->_s0(z,0) # answer(goal).  [resolve(1495,c,43,b)].

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): 3772 ->*_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=13): 3741 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(s(y),length(nil))) # answer(goal).  [resolve(2979,c,69,a)].

given #363 (F,wt=14): 3740 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(s(y),sndsplit(0,0))) # answer(goal).  [resolve(2979,c,82,a)].

given #364 (F,wt=14): 3743 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(s(y),app(nil,0))) # answer(goal).  [resolve(2979,c,61,a)].

given #365 (F,wt=15): 2980 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(y,0)) | -->_s0(y,s(z)) # answer(goal).  [resolve(1495,c,42,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): 3864 ->*_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=14): 3860 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(sndsplit(0,s(y)),0)) # answer(goal).  [resolve(2980,c,82,a)].

given #372 (F,wt=14): 3861 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(length(cons(y,z)),0)) # answer(goal).  [resolve(2980,c,68,a)].

given #373 (F,wt=14): 3863 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(app(nil,s(y)),0)) # answer(goal).  [resolve(2980,c,61,a)].

given #374 (F,wt=15): 3055 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(y)) | -->_s0(y,cons(z,false)) # answer(goal).  [resolve(1497,c,54,b)].

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

given #376 (T,wt=7): 4015 ->*_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=15): 3336 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,sndsplit(app(nil,0),false))) # answer(goal).  [resolve(3308,a,1465,c)].

given #381 (F,wt=15): 3338 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,sndsplit(app(nil,0),false))) # answer(goal).  [resolve(3308,a,1448,c)].

given #382 (F,wt=15): 3732 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(tail(cons(y,cons(z,u))))) # answer(goal).  [resolve(2922,c,85,a)].

given #383 (F,wt=15): 3733 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(head(cons(cons(y,z),u)))) # answer(goal).  [resolve(2922,c,67,a)].

given #384 (T,wt=7): 4100 ->*_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=15): 3734 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,empty(fstsplit(s(y),cons(z,u)))) # answer(goal).  [resolve(2922,c,65,a)].

given #390 (F,wt=15): 3735 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(tail(cons(y,cons(false,z))))) # answer(goal).  [resolve(2926,c,85,a)].

given #391 (F,wt=15): 3736 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(head(cons(cons(false,y),z)))) # answer(goal).  [resolve(2926,c,67,a)].

given #392 (F,wt=15): 3737 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(fstsplit(s(y),cons(false,z)))) # answer(goal).  [resolve(2926,c,65,a)].

given #393 (T,wt=7): 4246 ->*_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=15): 3738 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(y,z))) | -->_s0(y,false) # answer(goal).  [resolve(2926,c,55,b)].

given #399 (F,wt=15): 3739 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(s(y),tail(cons(z,0)))) # answer(goal).  [resolve(2979,c,85,a)].

given #400 (F,wt=15): 3742 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(s(y),head(cons(0,z)))) # answer(goal).  [resolve(2979,c,67,a)].

given #401 (F,wt=15): 3859 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(tail(cons(y,s(z))),0)) # answer(goal).  [resolve(2980,c,85,a)].

given #402 (T,wt=6): 4340 ->*_s0(sndsplit(length(nil),x),x).  [ur(87,a,321,a,b,567,a)].

given #403 (T,wt=7): 4338 ->*_s0(sndsplit(length(nil),empty(nil)),true).  [ur(87,a,321,a,b,634,a)].

given #404 (T,wt=7): 4339 ->*_s0(sndsplit(length(nil),length(nil)),0).  [ur(87,a,321,a,b,628,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=13): 4399 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),sndsplit(length(nil),false)) # answer(goal).  [resolve(4340,a,1026,c)].

given #408 (F,wt=14): 4394 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,sndsplit(length(nil),false))) # answer(goal).  [resolve(4340,a,1465,c)].

given #409 (F,wt=14): 4396 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,sndsplit(length(nil),false))) # answer(goal).  [resolve(4340,a,1448,c)].

given #410 (F,wt=15): 3862 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,leq(head(cons(s(y),z)),0)) # answer(goal).  [resolve(2980,c,67,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): 4513 ->*_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=14): 4545 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),leq(s(y),length(nil))) # answer(goal).  [resolve(4513,a,1026,c)].

given #417 (F,wt=14): 4554 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(empty(fstsplit(length(nil),y)),false) # answer(goal).  [resolve(331,a,584,c),unit_del(c,572)].

given #418 (F,wt=15): 3934 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(head(cons(cons(y,false),z)))) # answer(goal).  [resolve(269,a,1497,c)].

given #419 (F,wt=15): 3999 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(tail(cons(y,cons(z,false))))) # answer(goal).  [resolve(3055,c,85,a)].

given #420 (T,wt=6): 4555 ->*_s0(leq(length(nil),x),true).  [ur(87,a,331,a,b,572,a)].

given #421 (T,wt=7): 4586 ->*_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=14): 4617 -->*_s0(empty(fstsplit(length(nil),x)),false) | -->_s0(empty(mapf(two,head(y))),true) # answer(goal).  [resolve(4555,a,616,a)].

given #426 (F,wt=15): 4000 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,z))) | -->_s0(z,false) # answer(goal).  [resolve(3055,c,56,b)].

given #427 (F,wt=15): 4395 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,head(cons(sndsplit(length(nil),false),y))) # answer(goal).  [resolve(4340,a,1461,c)].

given #428 (F,wt=15): 4397 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,tail(cons(y,sndsplit(length(nil),false)))) # answer(goal).  [resolve(4340,a,1445,c)].

given #429 (T,wt=6): 4666 ->*_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=15): 4398 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,y) | -->_s0(y,sndsplit(length(nil),false)) # answer(goal).  [resolve(4340,a,1112,d)].

given #435 (F,wt=14): 4837 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(app(nil,length(nil)),false)) # answer(goal).  [resolve(4398,c,121,a)].

given #436 (F,wt=14): 4838 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(nil),app(nil,false))) # answer(goal).  [resolve(4398,c,120,a)].

given #437 (F,wt=15): 4400 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(fstsplit(0,y)),sndsplit(length(nil),false)) # answer(goal).  [resolve(4340,a,683,c)].

given #438 (T,wt=7): 4809 ->*_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=15): 4540 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,leq(s(y),length(nil)))) # answer(goal).  [resolve(4513,a,1465,c)].

given #444 (F,wt=15): 4542 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,leq(s(y),length(nil)))) # answer(goal).  [resolve(4513,a,1448,c)].

given #445 (F,wt=15): 4627 -->*_s0(empty(fstsplit(app(nil,0),x)),false) | -->_s0(empty(mapf(two,head(y))),true) # answer(goal).  [resolve(4586,a,616,a)].

given #446 (F,wt=15): 4631 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(empty(fstsplit(app(nil,0),y)),false) # answer(goal).  [resolve(4586,a,88,b)].

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=15): 4839 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(s(length(nil)),cons(y,false))) # answer(goal).  [resolve(4398,c,83,a)].

given #453 (F,wt=15): 4840 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(nil),y)) | -->_s0(y,false) # answer(goal).  [resolve(4398,c,53,b)].

given #454 (F,wt=14): 5102 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(nil),sndsplit(0,false))) # answer(goal).  [resolve(4840,c,82,a)].

given #455 (F,wt=15): 4841 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(y,false)) | -->_s0(y,length(nil)) # answer(goal).  [resolve(4398,c,52,b)].

given #456 (T,wt=7): 5039 ->*_s0(length(sndsplit(s(x),nil)),0).  [ur(87,a,532,a,b,573,a)].

given #457 (T,wt=7): 5074 ->*_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=14): 5107 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(sndsplit(0,nil)),false)) # answer(goal).  [resolve(4841,c,482,a)].

given #462 (F,wt=14): 5108 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(mapf(y,nil)),false)) # answer(goal).  [resolve(4841,c,457,a)].

given #463 (F,wt=14): 5111 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(fstsplit(0,y)),false)) # answer(goal).  [resolve(4841,c,207,a)].

given #464 (F,wt=14): 5112 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(app(nil,nil)),false)) # answer(goal).  [resolve(4841,c,132,a)].

given #465 (T,wt=7): 5167 ->*_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=14): 5114 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(sndsplit(0,length(nil)),false)) # answer(goal).  [resolve(4841,c,82,a)].

given #471 (F,wt=14): 5129 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),app(app(nil,nil),false)) # answer(goal).  [resolve(5074,a,1026,c)].

given #472 (F,wt=15): 5101 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(nil),tail(cons(y,false)))) # answer(goal).  [resolve(4840,c,85,a)].

given #473 (F,wt=15): 5103 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(nil),leq(s(y),0))) # answer(goal).  [resolve(4840,c,71,a)].

given #474 (T,wt=7): 5319 ->*_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): 5434 ->*_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=15): 5104 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(nil),head(cons(false,y)))) # answer(goal).  [resolve(4840,c,67,a)].

given #480 (F,wt=15): 5105 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(nil),empty(cons(y,z)))) # answer(goal).  [resolve(4840,c,62,a)].

given #481 (F,wt=15): 5106 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(sndsplit(s(y),nil)),false)) # answer(goal).  [resolve(4841,c,532,a)].

given #482 (F,wt=15): 5109 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(head(cons(nil,y))),false)) # answer(goal).  [resolve(4841,c,282,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): 639 ->*_s0(tail(cons(x,sndsplit(0,y))),y).  [ur(87,a,85,a,b,567,a)].

given #485 (T,wt=8): 640 ->*_s0(sndsplit(s(0),cons(x,y)),y).  [ur(87,a,83,a,b,567,a)].

given #486 (T,wt=8): 642 ->*_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=15): 5110 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(fstsplit(s(y),nil)),false)) # answer(goal).  [resolve(4841,c,257,a)].

given #489 (F,wt=15): 5113 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(tail(cons(y,length(nil))),false)) # answer(goal).  [resolve(4841,c,85,a)].

given #490 (F,wt=15): 5115 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(head(cons(length(nil),y)),false)) # answer(goal).  [resolve(4841,c,67,a)].

given #491 (F,wt=15): 5116 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(y),false)) | -->_s0(y,nil) # answer(goal).  [resolve(4841,c,41,b)].

given #492 (T,wt=8): 644 ->*_s0(tail(cons(x,mapf(y,nil))),nil).  [ur(87,a,85,a,b,568,a)].

given #493 (T,wt=8): 646 ->*_s0(head(cons(mapf(x,nil),y)),nil).  [ur(87,a,67,a,b,568,a)].

given #494 (T,wt=8): 687 ->*_s0(tail(cons(x,leq(0,y))),true).  [ur(87,a,85,a,b,572,a)].

given #495 (T,wt=8): 690 ->*_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=15): 5124 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,app(nil,app(app(nil,nil),false))) # answer(goal).  [resolve(5074,a,1465,c)].

given #498 (F,wt=15): 5126 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(0,app(app(nil,nil),false))) # answer(goal).  [resolve(5074,a,1448,c)].

given #499 (F,wt=15): 5302 -->_s0(mapf(two,head(x)),nil) | -->_s0(true,sndsplit(length(tail(cons(y,nil))),false)) # answer(goal).  [resolve(557,a,4841,c)].

NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.10 sec).

given #500 (F,wt=15): 5513 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),tail(cons(y,sndsplit(0,false)))) # answer(goal).  [resolve(639,a,1026,c)].

given #501 (T,wt=8): 692 ->*_s0(tail(cons(x,fstsplit(0,y))),nil).  [ur(87,a,85,a,b,578,a)].

given #502 (T,wt=8): 694 ->*_s0(head(cons(fstsplit(0,x),y)),nil).  [ur(87,a,67,a,b,578,a)].

given #503 (T,wt=8): 699 ->*_s0(tail(cons(x,app(nil,y))),y).  [ur(87,a,85,a,b,581,a)].

given #504 (T,wt=8): 701 ->*_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=15): 5531 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),sndsplit(s(0),cons(y,false))) # answer(goal).  [resolve(640,a,1026,c)].

given #507 (F,wt=15): 5549 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),head(cons(sndsplit(0,false),y))) # answer(goal).  [resolve(642,a,1026,c)].

given #508 (F,wt=15): 5681 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),tail(cons(y,app(nil,false)))) # answer(goal).  [resolve(699,a,1026,c)].

given #509 (F,wt=15): 5700 -->_s0(mapf(two,head(x)),nil) | -->_s0(empty(nil),head(cons(app(nil,false),y))) # answer(goal).  [resolve(701,a,1026,c)].

given #510 (T,wt=8): 704 ->_s0(s(s(empty(nil))),s(s(true))).  [ur(59,a,164,a)].

given #511 (T,wt=8): 709 ->_s0(tail(s(empty(nil))),tail(s(true))).  [ur(54,a,164,a)].

given #512 (T,wt=8): 722 ->_s0(length(s(empty(nil))),length(s(true))).  [ur(41,a,164,a)].

given #513 (T,wt=8): 723 ->_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=16): 626 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(fstsplit(0,y)),z) | -->*_s0(z,false) # answer(goal).  [resolve(620,b,87,c)].

given #516 (F,wt=11): 5876 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(626,b,211,a)].

given #517 (F,wt=13): 5898 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(fstsplit(0,y)),false) # answer(goal).  [resolve(626,c,86,a)].

given #518 (F,wt=14): 5899 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),y) | -->*_s0(y,true) # answer(goal).  [resolve(5876,a,87,c)].

given #519 (T,wt=8): 726 ->_s0(empty(s(empty(nil))),empty(s(true))).  [ur(37,a,164,a)].

given #520 (T,wt=8): 762 ->_s0(s(tail(empty(nil))),s(tail(true))).  [ur(59,a,169,a)].

given #521 (T,wt=8): 767 ->_s0(tail(tail(empty(nil))),tail(tail(true))).  [ur(54,a,169,a)].

given #522 (T,wt=8): 780 ->_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=11): 5943 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),true) # answer(goal).  [resolve(5899,c,86,a)].

given #525 (F,wt=12): 5937 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),empty(nil)) # answer(goal).  [resolve(5899,c,579,a)].

given #526 (F,wt=13): 5936 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),app(nil,true)) # answer(goal).  [resolve(5899,c,581,a)].

given #527 (F,wt=13): 5939 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),leq(0,y)) # answer(goal).  [resolve(5899,c,572,a)].

given #528 (T,wt=8): 781 ->_s0(head(tail(empty(nil))),head(tail(true))).  [ur(40,a,169,a)].

given #529 (T,wt=8): 784 ->_s0(empty(tail(empty(nil))),empty(tail(true))).  [ur(37,a,169,a)].

given #530 (T,wt=8): 788 ->_s0(s(length(empty(nil))),s(length(true))).  [ur(59,a,182,a)].

given #531 (T,wt=8): 793 ->_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=13): 5940 -->*_s0(empty(nil),false) | -->_s0(empty(mapf(two,head(x))),sndsplit(0,true)) # answer(goal).  [resolve(5899,c,567,a)].

given #534 (F,wt=14): 5900 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(nil),y) | -->*_s0(y,false) # answer(goal).  [resolve(5876,b,87,c)].

given #535 (F,wt=10): 6219 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(true,false) # answer(goal).  [resolve(5900,b,63,a)].

given #536 (F,wt=11): 6241 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(nil),false) # answer(goal).  [resolve(5900,c,86,a)].

given #537 (T,wt=8): 806 ->_s0(length(length(empty(nil))),length(length(true))).  [ur(41,a,182,a)].

given #538 (T,wt=8): 807 ->_s0(head(length(empty(nil))),head(length(true))).  [ur(40,a,182,a)].

given #539 (T,wt=8): 810 ->_s0(empty(length(empty(nil))),empty(length(true))).  [ur(37,a,182,a)].

given #540 (T,wt=8): 814 ->_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=13): 6234 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(nil),app(nil,false)) # answer(goal).  [resolve(5900,c,581,a)].

given #543 (F,wt=13): 6238 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(empty(nil),sndsplit(0,false)) # answer(goal).  [resolve(5900,c,567,a)].

given #544 (F,wt=13): 6242 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),y) | -->*_s0(y,true) # answer(goal).  [resolve(6219,a,87,c)].

given #545 (F,wt=10): 6423 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),true) # answer(goal).  [resolve(6242,c,86,a)].

given #546 (T,wt=8): 819 ->_s0(tail(head(empty(nil))),tail(head(true))).  [ur(54,a,183,a)].

given #547 (T,wt=8): 832 ->_s0(length(head(empty(nil))),length(head(true))).  [ur(41,a,183,a)].

given #548 (T,wt=8): 833 ->_s0(head(head(empty(nil))),head(head(true))).  [ur(40,a,183,a)].

given #549 (T,wt=8): 836 ->_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=11): 6417 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),empty(nil)) # answer(goal).  [resolve(6242,c,579,a)].

given #552 (F,wt=12): 6416 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),app(nil,true)) # answer(goal).  [resolve(6242,c,581,a)].

given #553 (F,wt=12): 6419 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),leq(0,y)) # answer(goal).  [resolve(6242,c,572,a)].

given #554 (F,wt=12): 6420 -->*_s0(true,false) | -->_s0(empty(mapf(two,head(x))),sndsplit(0,true)) # answer(goal).  [resolve(6242,c,567,a)].

given #555 (T,wt=8): 840 ->_s0(s(empty(empty(nil))),s(empty(true))).  [ur(59,a,186,a)].

given #556 (T,wt=8): 845 ->_s0(tail(empty(empty(nil))),tail(empty(true))).  [ur(54,a,186,a)].

given #557 (T,wt=8): 858 ->_s0(length(empty(empty(nil))),length(empty(true))).  [ur(41,a,186,a)].

given #558 (T,wt=8): 859 ->_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=13): 6243 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(true,y) | -->*_s0(y,false) # answer(goal).  [resolve(6219,b,87,c)].

given #561 (F,wt=10): 6719 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(true,false) # answer(goal).  [resolve(6243,c,86,a)].

given #562 (F,wt=12): 6712 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(true,app(nil,false)) # answer(goal).  [resolve(6243,c,581,a)].

given #563 (F,wt=12): 6716 -->*_s0(empty(mapf(two,head(x))),true) | -->_s0(true,sndsplit(0,false)) # answer(goal).  [resolve(6243,c,567,a)].

given #564 (T,wt=8): 862 ->_s0(empty(empty(empty(nil))),empty(empty(true))).  [ur(37,a,186,a)].

given #565 (T,wt=8): 897 ->_s0(s(s(length(nil))),s(s(0))).  [ur(59,a,314,a)].

given #566 (T,wt=8): 902 ->_s0(tail(s(length(nil))),tail(s(0))).  [ur(54,a,314,a)].

given #567 (T,wt=8): 915 ->_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=13): 6383 -->*_s0(true,false) | -->*_s0(empty(x),true) | -->_s0(mapf(two,head(y)),x) # answer(goal).  [resolve(6242,b,37,b)].

given #570 (F,wt=11): 6863 -->*_s0(true,false) | -->_s0(mapf(two,head(x)),sndsplit(0,nil)) # answer(goal).  [resolve(6383,b,2366,a)].

given #571 (F,wt=11): 6864 -->*_s0(true,false) | -->_s0(mapf(two,head(x)),mapf(y,nil)) # answer(goal).  [resolve(6383,b,2133,a)].

given #572 (F,wt=7): 6872 -->*_s0(true,false) | -->_s0(head(x),nil) # answer(goal).  [resolve(6864,b,45,b)].

given #573 (T,wt=8): 916 ->_s0(head(s(length(nil))),head(s(0))).  [ur(40,a,314,a)].

given #574 (T,wt=8): 919 ->_s0(empty(s(length(nil))),empty(s(0))).  [ur(37,a,314,a)].

given #575 (T,wt=8): 923 ->_s0(s(tail(length(nil))),s(tail(0))).  [ur(59,a,319,a)].

given #576 (T,wt=8): 928 ->_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=3): 6874 -->*_s0(true,false) # answer(goal).  [resolve(6872,b,67,a)].

given #579 (F,wt=3): 7030 -->_s0(true,false) # answer(goal).  [ur(87,b,86,a,c,6874,a)].

given #580 (F,wt=5): 7024 -->_s0(true,app(nil,false)) # answer(goal).  [ur(87,b,581,a,c,6874,a)].

given #581 (F,wt=5): 7028 -->_s0(true,sndsplit(0,false)) # answer(goal).  [ur(87,b,567,a,c,6874,a)].

given #582 (T,wt=8): 941 ->_s0(length(tail(length(nil))),length(tail(0))).  [ur(41,a,319,a)].

given #583 (T,wt=8): 942 ->_s0(head(tail(length(nil))),head(tail(0))).  [ur(40,a,319,a)].

given #584 (T,wt=8): 945 ->_s0(empty(tail(length(nil))),empty(tail(0))).  [ur(37,a,319,a)].

given #585 (T,wt=8): 949 ->_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=6): 7010 -->_s0(true,x) | -->*_s0(x,false) # answer(goal).  [resolve(6874,a,87,c)].

given #588 (F,wt=6): 7013 -->_s0(true,sndsplit(length(nil),false)) # answer(goal).  [ur(87,b,4340,a,c,6874,a)].

given #589 (F,wt=6): 7025 -->_s0(true,empty(cons(x,y))) # answer(goal).  [ur(87,b,580,a,c,6874,a)].

given #590 (F,wt=6): 7026 -->_s0(true,head(cons(false,x))) # answer(goal).  [ur(87,b,575,a,c,6874,a)].

given #591 (T,wt=8): 954 ->_s0(tail(length(length(nil))),tail(length(0))).  [ur(54,a,332,a)].

given #592 (T,wt=8): 967 ->_s0(length(length(length(nil))),length(length(0))).  [ur(41,a,332,a)].

given #593 (T,wt=8): 968 ->_s0(head(length(length(nil))),head(length(0))).  [ur(40,a,332,a)].

given #594 (T,wt=8): 971 ->_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=6): 7027 -->_s0(true,leq(s(x),0)) # answer(goal).  [ur(87,b,571,a,c,6874,a)].

given #597 (F,wt=6): 7029 -->_s0(true,tail(cons(x,false))) # answer(goal).  [ur(87,b,564,a,c,6874,a)].

given #598 (F,wt=7): 7011 -->_s0(true,app(app(nil,nil),false)) # answer(goal).  [ur(87,b,5074,a,c,6874,a)].

given #599 (F,wt=7): 7012 -->_s0(true,leq(s(x),length(nil))) # answer(goal).  [ur(87,b,4513,a,c,6874,a)].

given #600 (T,wt=8): 975 ->_s0(s(head(length(nil))),s(head(0))).  [ur(59,a,333,a)].

given #601 (T,wt=8): 980 ->_s0(tail(head(length(nil))),tail(head(0))).  [ur(54,a,333,a)].

given #602 (T,wt=8): 993 ->_s0(length(head(length(nil))),length(head(0))).  [ur(41,a,333,a)].

given #603 (T,wt=8): 994 ->_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=7): 7014 -->_s0(true,sndsplit(app(nil,0),false)) # answer(goal).  [ur(87,b,3308,a,c,6874,a)].

given #606 (F,wt=7): 7015 -->_s0(true,app(nil,app(nil,false))) # answer(goal).  [ur(87,b,702,a,c,6874,a)].

given #607 (F,wt=7): 7017 -->_s0(true,sndsplit(0,app(nil,false))) # answer(goal).  [ur(87,b,700,a,c,6874,a)].

given #608 (F,wt=7): 7019 -->_s0(true,app(nil,sndsplit(0,false))) # answer(goal).  [ur(87,b,643,a,c,6874,a)].

given #609 (T,wt=8): 997 ->_s0(empty(head(length(nil))),empty(head(0))).  [ur(37,a,333,a)].

given #610 (T,wt=8): 1035 ->_s0(s(empty(length(nil))),s(empty(0))).  [ur(59,a,336,a)].

given #611 (T,wt=8): 1040 ->_s0(tail(empty(length(nil))),tail(empty(0))).  [ur(54,a,336,a)].

given #612 (T,wt=8): 1053 ->_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=7): 7021 -->_s0(true,sndsplit(0,sndsplit(0,false))) # answer(goal).  [ur(87,b,641,a,c,6874,a)].

given #615 (F,wt=8): 7016 -->_s0(true,head(cons(app(nil,false),x))) # answer(goal).  [ur(87,b,701,a,c,6874,a)].

given #616 (F,wt=8): 7018 -->_s0(true,tail(cons(x,app(nil,false)))) # answer(goal).  [ur(87,b,699,a,c,6874,a)].

given #617 (F,wt=8): 7020 -->_s0(true,head(cons(sndsplit(0,false),x))) # answer(goal).  [ur(87,b,642,a,c,6874,a)].

given #618 (T,wt=8): 1054 ->_s0(head(empty(length(nil))),head(empty(0))).  [ur(40,a,336,a)].

given #619 (T,wt=8): 1057 ->_s0(empty(empty(length(nil))),empty(empty(0))).  [ur(37,a,336,a)].

given #620 (T,wt=8): 1066 ->*_s0(sndsplit(0,tail(cons(x,y))),y).  [ur(87,a,82,a,b,564,a)].

given #621 (T,wt=8): 1068 ->*_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=8): 7022 -->_s0(true,sndsplit(s(0),cons(x,false))) # answer(goal).  [ur(87,b,640,a,c,6874,a)].

given #624 (F,wt=8): 7023 -->_s0(true,tail(cons(x,sndsplit(0,false)))) # answer(goal).  [ur(87,b,639,a,c,6874,a)].

given #625 (F,wt=8): 7621 -->_s0(true,sndsplit(0,tail(cons(x,false)))) # answer(goal).  [resolve(1066,a,7010,b)].

given #626 (F,wt=8): 7643 -->_s0(true,app(nil,tail(cons(x,false)))) # answer(goal).  [resolve(1068,a,7010,b)].

given #627 (T,wt=8): 1071 ->*_s0(sndsplit(0,sndsplit(s(x),nil)),nil).  [ur(87,a,82,a,b,565,a)].

given #628 (T,wt=8): 1073 ->*_s0(app(nil,sndsplit(s(x),nil)),nil).  [ur(87,a,61,a,b,565,a)].

given #629 (T,wt=8): 1077 ->*_s0(sndsplit(0,leq(s(x),0)),false).  [ur(87,a,82,a,b,571,a)].

given #630 (T,wt=8): 1078 ->*_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=8): 7695 -->_s0(true,sndsplit(0,leq(s(x),0))) # answer(goal).  [resolve(1077,a,7010,b)].

given #633 (F,wt=8): 7713 -->_s0(true,leq(s(s(x)),s(0))) # answer(goal).  [resolve(1078,a,7010,b)].

given #634 (F,wt=9): 7166 -->_s0(true,x) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal).  [resolve(7010,b,87,c)].

given #635 (F,wt=6): 8030 -->_s0(true,x) | -->_s0(x,false) # answer(goal).  [resolve(7166,c,86,a)].

given #636 (T,wt=8): 1080 ->*_s0(app(nil,leq(s(x),0)),false).  [ur(87,a,61,a,b,571,a)].

given #637 (T,wt=8): 1121 ->*_s0(sndsplit(0,head(cons(x,y))),x).  [ur(87,a,82,a,b,575,a)].

given #638 (T,wt=8): 1123 ->*_s0(app(nil,head(cons(x,y))),x).  [ur(87,a,61,a,b,575,a)].

given #639 (T,wt=8): 1125 ->*_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=7): 7973 -->_s0(true,length(nil)) | -->*_s0(0,false) # answer(goal).  [resolve(7166,b,69,a)].

given #642 (F,wt=8): 7936 -->_s0(true,empty(app(cons(x,y),z))) # answer(goal).  [resolve(7166,b,111,a),unit_del(b,580)].

given #643 (F,wt=8): 7962 -->_s0(true,sndsplit(0,x)) | -->*_s0(x,false) # answer(goal).  [resolve(7166,b,82,a)].

given #644 (F,wt=8): 7970 -->_s0(true,mapf(x,nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(7166,b,74,a)].

given #645 (T,wt=8): 1127 ->*_s0(app(nil,fstsplit(s(x),nil)),nil).  [ur(87,a,61,a,b,576,a)].

given #646 (T,wt=8): 1133 ->*_s0(sndsplit(0,empty(cons(x,y))),false).  [ur(87,a,82,a,b,580,a)].

given #647 (T,wt=8): 1135 ->*_s0(app(nil,empty(cons(x,y))),false).  [ur(87,a,61,a,b,580,a)].

given #648 (T,wt=8): 1138 ->*_s0(sndsplit(0,sndsplit(0,length(nil))),0).  [ur(87,a,82,a,b,628,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=8): 7978 -->_s0(true,fstsplit(0,x)) | -->*_s0(nil,false) # answer(goal).  [resolve(7166,b,64,a)].

given #651 (F,wt=8): 7979 -->_s0(true,app(nil,x)) | -->*_s0(x,false) # answer(goal).  [resolve(7166,b,61,a)].

given #652 (F,wt=8): 8023 -->_s0(true,x) | -->_s0(x,app(nil,false)) # answer(goal).  [resolve(7166,c,581,a)].

given #653 (F,wt=8): 8027 -->_s0(true,x) | -->_s0(x,sndsplit(0,false)) # answer(goal).  [resolve(7166,c,567,a)].

given #654 (T,wt=8): 1140 ->*_s0(app(nil,sndsplit(0,length(nil))),0).  [ur(87,a,61,a,b,628,a)].

given #655 (T,wt=8): 1169 ->*_s0(sndsplit(0,app(nil,length(nil))),0).  [ur(87,a,82,a,b,630,a)].

given #656 (T,wt=8): 1171 ->*_s0(app(nil,app(nil,length(nil))),0).  [ur(87,a,61,a,b,630,a)].

given #657 (T,wt=8): 1177 ->*_s0(sndsplit(0,sndsplit(0,empty(nil))),true).  [ur(87,a,82,a,b,634,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=8): 8038 -->_s0(true,empty(sndsplit(0,cons(x,y)))) # answer(goal).  [ur(7166,b,486,a,c,580,a)].

given #660 (F,wt=8): 8041 -->_s0(true,head(sndsplit(0,cons(false,x)))) # answer(goal).  [ur(7166,b,483,a,c,575,a)].

given #661 (F,wt=8): 8044 -->_s0(true,tail(sndsplit(0,cons(x,false)))) # answer(goal).  [ur(7166,b,469,a,c,564,a)].

given #662 (F,wt=8): 8047 -->_s0(true,sndsplit(length(nil),app(nil,false))) # answer(goal).  [ur(7166,b,321,a,c,700,a)].

given #663 (T,wt=8): 1179 ->*_s0(app(nil,sndsplit(0,empty(nil))),true).  [ur(87,a,61,a,b,634,a)].

given #664 (T,wt=8): 1184 ->*_s0(sndsplit(0,app(nil,empty(nil))),true).  [ur(87,a,82,a,b,636,a)].

given #665 (T,wt=8): 1186 ->*_s0(app(nil,app(nil,empty(nil))),true).  [ur(87,a,61,a,b,636,a)].

given #666 (T,wt=8): 1188 ->*_s0(sndsplit(0,s(empty(nil))),s(true)).  [ur(87,a,82,a,b,703,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=8): 8048 -->_s0(true,sndsplit(length(nil),sndsplit(0,false))) # answer(goal).  [ur(7166,b,321,a,c,641,a)].

given #669 (F,wt=8): 8057 -->_s0(true,app(nil,empty(cons(x,y)))) # answer(goal).  [ur(7166,b,162,a,c,581,a)].

given #670 (F,wt=8): 8060 -->_s0(true,sndsplit(0,empty(cons(x,y)))) # answer(goal).  [ur(7166,b,145,a,c,567,a)].

given #671 (F,wt=8): 8068 -->_s0(true,empty(app(nil,cons(x,y)))) # answer(goal).  [ur(7166,b,136,a,c,580,a)].

given #672 (T,wt=8): 1190 ->*_s0(app(nil,s(empty(nil))),s(true)).  [ur(87,a,61,a,b,703,a)].

given #673 (T,wt=8): 1220 ->*_s0(sndsplit(0,tail(empty(nil))),tail(true)).  [ur(87,a,82,a,b,761,a)].

given #674 (T,wt=8): 1222 ->*_s0(app(nil,tail(empty(nil))),tail(true)).  [ur(87,a,61,a,b,761,a)].

given #675 (T,wt=8): 1224 ->*_s0(sndsplit(0,length(empty(nil))),length(true)).  [ur(87,a,82,a,b,787,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=8): 8071 -->_s0(true,head(app(nil,cons(false,x)))) # answer(goal).  [ur(7166,b,133,a,c,575,a)].

given #678 (F,wt=8): 8074 -->_s0(true,leq(app(nil,s(x)),0)) # answer(goal).  [ur(7166,b,131,a,c,571,a)].

given #679 (F,wt=8): 8077 -->_s0(true,leq(s(x),app(nil,0))) # answer(goal).  [ur(7166,b,130,a,c,571,a)].

given #680 (F,wt=8): 8078 -->_s0(true,sndsplit(app(nil,length(nil)),false)) # answer(goal).  [ur(7166,b,121,a,c,4340,a)].

given #681 (T,wt=8): 1226 ->*_s0(app(nil,length(empty(nil))),length(true)).  [ur(87,a,61,a,b,787,a)].

given #682 (T,wt=8): 1228 ->*_s0(sndsplit(0,head(empty(nil))),head(true)).  [ur(87,a,82,a,b,813,a)].

given #683 (T,wt=8): 1230 ->*_s0(app(nil,head(empty(nil))),head(true)).  [ur(87,a,61,a,b,813,a)].

given #684 (T,wt=8): 1232 ->*_s0(sndsplit(0,empty(empty(nil))),empty(true)).  [ur(87,a,82,a,b,839,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=8): 8092 -->_s0(true,tail(app(nil,cons(x,false)))) # answer(goal).  [ur(7166,b,119,a,c,564,a)].

given #687 (F,wt=8): 8095 -->_s0(true,head(app(cons(false,x),y))) # answer(goal).  [ur(7166,b,108,a,c,575,a)].

given #688 (F,wt=8): 8096 -->_s0(true,tail(app(cons(x,nil),false))) # answer(goal).  [ur(7166,b,94,a,c,699,a)].

given #689 (F,wt=8): 8127 -->_s0(true,sndsplit(0,sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,82,a,c,4340,a)].

given #690 (T,wt=8): 1234 ->*_s0(app(nil,empty(empty(nil))),empty(true)).  [ur(87,a,61,a,b,839,a)].

given #691 (T,wt=8): 1262 ->*_s0(sndsplit(0,s(length(nil))),s(0)).  [ur(87,a,82,a,b,896,a)].

given #692 (T,wt=8): 1265 ->*_s0(app(nil,s(length(nil))),s(0)).  [ur(87,a,61,a,b,896,a)].

given #693 (T,wt=8): 1267 ->*_s0(sndsplit(0,tail(length(nil))),tail(0)).  [ur(87,a,82,a,b,922,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=8): 8139 -->_s0(true,sndsplit(0,head(cons(false,x)))) # answer(goal).  [ur(7166,b,82,a,c,575,a)].

given #696 (F,wt=8): 8165 -->_s0(true,app(nil,sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,61,a,c,4340,a)].

given #697 (F,wt=8): 8177 -->_s0(true,app(nil,head(cons(false,x)))) # answer(goal).  [ur(7166,b,61,a,c,575,a)].

given #698 (F,wt=8): 8178 -->_s0(true,app(nil,leq(s(x),0))) # answer(goal).  [ur(7166,b,61,a,c,571,a)].

given #699 (T,wt=8): 1269 ->*_s0(app(nil,tail(length(nil))),tail(0)).  [ur(87,a,61,a,b,922,a)].

given #700 (T,wt=8): 1271 ->*_s0(sndsplit(0,length(length(nil))),length(0)).  [ur(87,a,82,a,b,948,a)].

given #701 (T,wt=8): 1273 ->*_s0(app(nil,length(length(nil))),length(0)).  [ur(87,a,61,a,b,948,a)].

given #702 (T,wt=8): 1275 ->*_s0(sndsplit(0,head(length(nil))),head(0)).  [ur(87,a,82,a,b,974,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=8): 8345 -->_s0(true,app(nil,x)) | -->_s0(x,false) # answer(goal).  [resolve(8023,b,36,b)].

given #705 (F,wt=8): 8346 -->_s0(true,app(x,false)) | -->_s0(x,nil) # answer(goal).  [resolve(8023,b,35,b)].

given #706 (F,wt=7): 8621 -->_s0(true,app(sndsplit(0,nil),false)) # answer(goal).  [resolve(8346,b,82,a)].

given #707 (F,wt=7): 8622 -->_s0(true,app(mapf(x,nil),false)) # answer(goal).  [resolve(8346,b,74,a)].

given #708 (T,wt=8): 1277 ->*_s0(app(nil,head(length(nil))),head(0)).  [ur(87,a,61,a,b,974,a)].

given #709 (T,wt=8): 1306 ->*_s0(sndsplit(0,empty(length(nil))),empty(0)).  [ur(87,a,82,a,b,1034,a)].

given #710 (T,wt=8): 1308 ->*_s0(app(nil,empty(length(nil))),empty(0)).  [ur(87,a,61,a,b,1034,a)].

given #711 (T,wt=8): 1309 ->*_s0(s(app(nil,length(nil))),s(0)).  [ur(87,a,114,a,b,896,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=7): 8625 -->_s0(true,app(fstsplit(0,x),false)) # answer(goal).  [resolve(8346,b,64,a)].

given #714 (F,wt=8): 8347 -->_s0(true,sndsplit(0,x)) | -->_s0(x,false) # answer(goal).  [resolve(8027,b,53,b)].

given #715 (F,wt=8): 8348 -->_s0(true,sndsplit(x,false)) | -->_s0(x,0) # answer(goal).  [resolve(8027,b,52,b)].

given #716 (F,wt=7): 8672 -->_s0(true,sndsplit(sndsplit(0,0),false)) # answer(goal).  [resolve(8348,b,82,a)].

given #717 (T,wt=8): 1310 ->*_s0(s(app(nil,empty(nil))),s(true)).  [ur(87,a,114,a,b,703,a)].

given #718 (T,wt=8): 1337 ->*_s0(tail(app(nil,length(nil))),tail(0)).  [ur(87,a,119,a,b,922,a)].

given #719 (T,wt=8): 1338 ->*_s0(tail(app(nil,empty(nil))),tail(true)).  [ur(87,a,119,a,b,761,a)].

given #720 (T,wt=8): 1339 ->*_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=8): 8619 -->_s0(true,app(tail(cons(x,nil)),false)) # answer(goal).  [resolve(8346,b,85,a)].

given #723 (F,wt=8): 8620 -->_s0(true,app(sndsplit(s(x),nil),false)) # answer(goal).  [resolve(8346,b,84,a)].

given #724 (F,wt=8): 8623 -->_s0(true,app(head(cons(nil,x)),false)) # answer(goal).  [resolve(8346,b,67,a)].

given #725 (F,wt=8): 8624 -->_s0(true,app(fstsplit(s(x),nil),false)) # answer(goal).  [resolve(8346,b,66,a)].

given #726 (T,wt=8): 1366 ->*_s0(length(app(nil,length(nil))),length(0)).  [ur(87,a,132,a,b,948,a)].

given #727 (T,wt=8): 1367 ->*_s0(length(app(nil,empty(nil))),length(true)).  [ur(87,a,132,a,b,787,a)].

given #728 (T,wt=8): 1508 ->*_s0(length(app(nil,app(nil,nil))),0).  [ur(87,a,132,a,b,1368,a)].

given #729 (T,wt=8): 1510 ->*_s0(sndsplit(0,length(app(nil,nil))),0).  [ur(87,a,82,a,b,1368,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=8): 8671 -->_s0(true,sndsplit(tail(cons(x,0)),false)) # answer(goal).  [resolve(8348,b,85,a)].

given #732 (F,wt=8): 8673 -->_s0(true,sndsplit(head(cons(0,x)),false)) # answer(goal).  [resolve(8348,b,67,a)].

given #733 (F,wt=9): 7833 -->_s0(true,empty(length(nil))) | -->*_s0(empty(0),false) # answer(goal).  [resolve(7166,b,336,a)].

given #734 (F,wt=9): 7836 -->_s0(true,head(length(nil))) | -->*_s0(head(0),false) # answer(goal).  [resolve(7166,b,333,a)].

given #735 (T,wt=8): 1512 ->*_s0(app(nil,length(app(nil,nil))),0).  [ur(87,a,61,a,b,1368,a)].

given #736 (T,wt=8): 1514 ->*_s0(head(app(nil,length(nil))),head(0)).  [ur(87,a,133,a,b,974,a)].

given #737 (T,wt=8): 1515 ->*_s0(head(app(nil,empty(nil))),head(true)).  [ur(87,a,133,a,b,813,a)].

given #738 (T,wt=8): 1516 ->*_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=9): 7837 -->_s0(true,length(length(nil))) | -->*_s0(length(0),false) # answer(goal).  [resolve(7166,b,332,a)].

given #741 (F,wt=9): 7844 -->_s0(true,tail(length(nil))) | -->*_s0(tail(0),false) # answer(goal).  [resolve(7166,b,319,a)].

given #742 (F,wt=9): 7849 -->_s0(true,s(length(nil))) | -->*_s0(s(0),false) # answer(goal).  [resolve(7166,b,314,a)].

given #743 (F,wt=9): 7867 -->_s0(true,empty(empty(nil))) | -->*_s0(empty(true),false) # answer(goal).  [resolve(7166,b,186,a)].

given #744 (T,wt=8): 1544 ->*_s0(empty(app(nil,length(nil))),empty(0)).  [ur(87,a,136,a,b,1034,a)].

given #745 (T,wt=8): 1545 ->*_s0(empty(app(nil,empty(nil))),empty(true)).  [ur(87,a,136,a,b,839,a)].

given #746 (T,wt=8): 1546 ->*_s0(empty(app(nil,cons(x,y))),false).  [ur(87,a,136,a,b,580,a)].

given #747 (T,wt=8): 1577 ->*_s0(empty(app(nil,app(nil,nil))),true).  [ur(87,a,136,a,b,1547,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=9): 7870 -->_s0(true,head(empty(nil))) | -->*_s0(head(true),false) # answer(goal).  [resolve(7166,b,183,a)].

given #750 (F,wt=9): 7871 -->_s0(true,length(empty(nil))) | -->*_s0(length(true),false) # answer(goal).  [resolve(7166,b,182,a)].

given #751 (F,wt=9): 7878 -->_s0(true,tail(empty(nil))) | -->*_s0(tail(true),false) # answer(goal).  [resolve(7166,b,169,a)].

given #752 (F,wt=9): 7883 -->_s0(true,s(empty(nil))) | -->*_s0(s(true),false) # answer(goal).  [resolve(7166,b,164,a)].

given #753 (T,wt=8): 1579 ->*_s0(sndsplit(0,empty(app(nil,nil))),true).  [ur(87,a,82,a,b,1547,a)].

given #754 (T,wt=8): 1581 ->*_s0(app(nil,empty(app(nil,nil))),true).  [ur(87,a,61,a,b,1547,a)].

given #755 (T,wt=8): 1693 ->*_s0(length(app(nil,fstsplit(0,x))),0).  [ur(87,a,132,a,b,1666,a)].

given #756 (T,wt=8): 1695 ->*_s0(sndsplit(0,length(fstsplit(0,x))),0).  [ur(87,a,82,a,b,1666,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=9): 7959 -->_s0(true,tail(cons(x,y))) | -->*_s0(y,false) # answer(goal).  [resolve(7166,b,85,a)].

given #759 (F,wt=9): 7960 -->_s0(true,sndsplit(s(x),nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(7166,b,84,a)].

given #760 (F,wt=9): 7975 -->_s0(true,head(cons(x,y))) | -->*_s0(x,false) # answer(goal).  [resolve(7166,b,67,a)].

given #761 (F,wt=9): 7976 -->_s0(true,fstsplit(s(x),nil)) | -->*_s0(nil,false) # answer(goal).  [resolve(7166,b,66,a)].

given #762 (T,wt=8): 1697 ->*_s0(app(nil,length(fstsplit(0,x))),0).  [ur(87,a,61,a,b,1666,a)].

given #763 (T,wt=8): 1793 ->*_s0(empty(app(nil,fstsplit(0,x))),true).  [ur(87,a,136,a,b,1763,a)].

given #764 (T,wt=8): 1795 ->*_s0(sndsplit(0,empty(fstsplit(0,x))),true).  [ur(87,a,82,a,b,1763,a)].

given #765 (T,wt=8): 1797 ->*_s0(app(nil,empty(fstsplit(0,x))),true).  [ur(87,a,61,a,b,1763,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=9): 8008 -->_s0(true,x) | -->_s0(x,sndsplit(length(nil),false)) # answer(goal).  [resolve(7166,c,4340,a)].

given #768 (F,wt=9): 8024 -->_s0(true,x) | -->_s0(x,empty(cons(y,z))) # answer(goal).  [resolve(7166,c,580,a)].

given #769 (F,wt=9): 8025 -->_s0(true,x) | -->_s0(x,head(cons(false,y))) # answer(goal).  [resolve(7166,c,575,a)].

given #770 (F,wt=9): 8026 -->_s0(true,x) | -->_s0(x,leq(s(y),0)) # answer(goal).  [resolve(7166,c,571,a)].

given #771 (T,wt=8): 2074 ->*_s0(length(app(nil,mapf(x,nil))),0).  [ur(87,a,132,a,b,2047,a)].

given #772 (T,wt=8): 2076 ->*_s0(sndsplit(0,length(mapf(x,nil))),0).  [ur(87,a,82,a,b,2047,a)].

given #773 (T,wt=8): 2078 ->*_s0(app(nil,length(mapf(x,nil))),0).  [ur(87,a,61,a,b,2047,a)].

given #774 (T,wt=8): 2163 ->*_s0(empty(app(nil,mapf(x,nil))),true).  [ur(87,a,136,a,b,2133,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=9): 8028 -->_s0(true,x) | -->_s0(x,tail(cons(y,false))) # answer(goal).  [resolve(7166,c,564,a)].

given #777 (F,wt=9): 8031 -->_s0(true,empty(tail(cons(x,cons(y,z))))) # answer(goal).  [ur(7166,b,561,a,c,580,a)].

given #778 (F,wt=9): 8034 -->_s0(true,head(tail(cons(x,cons(false,y))))) # answer(goal).  [ur(7166,b,558,a,c,575,a)].

given #779 (F,wt=9): 8037 -->_s0(true,tail(tail(cons(x,cons(y,false))))) # answer(goal).  [ur(7166,b,544,a,c,564,a)].

given #780 (T,wt=8): 2165 ->*_s0(sndsplit(0,empty(mapf(x,nil))),true).  [ur(87,a,82,a,b,2133,a)].

given #781 (T,wt=8): 2167 ->*_s0(app(nil,empty(mapf(x,nil))),true).  [ur(87,a,61,a,b,2133,a)].

given #782 (T,wt=8): 2169 ->*_s0(s(sndsplit(0,length(nil))),s(0)).  [ur(87,a,464,a,b,896,a)].

given #783 (T,wt=8): 2170 ->*_s0(s(sndsplit(0,empty(nil))),s(true)).  [ur(87,a,464,a,b,703,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=9): 8045 -->_s0(true,sndsplit(length(nil),leq(s(x),0))) # answer(goal).  [ur(7166,b,321,a,c,1077,a)].

given #786 (F,wt=9): 8046 -->_s0(true,sndsplit(length(nil),tail(cons(x,false)))) # answer(goal).  [ur(7166,b,321,a,c,1066,a)].

given #787 (F,wt=9): 8049 -->_s0(true,empty(head(cons(cons(x,y),z)))) # answer(goal).  [ur(7166,b,286,a,c,580,a)].

given #788 (F,wt=9): 8052 -->_s0(true,head(head(cons(cons(false,x),y)))) # answer(goal).  [ur(7166,b,283,a,c,575,a)].

given #789 (T,wt=8): 2233 ->*_s0(tail(sndsplit(0,length(nil))),tail(0)).  [ur(87,a,469,a,b,922,a)].

given #790 (T,wt=8): 2234 ->*_s0(tail(sndsplit(0,empty(nil))),tail(true)).  [ur(87,a,469,a,b,761,a)].

given #791 (T,wt=8): 2235 ->*_s0(tail(sndsplit(0,cons(x,y))),y).  [ur(87,a,469,a,b,564,a)].

given #792 (T,wt=8): 2263 ->*_s0(length(sndsplit(0,mapf(x,nil))),0).  [ur(87,a,482,a,b,2047,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=9): 8055 -->_s0(true,tail(head(cons(cons(x,false),y)))) # answer(goal).  [ur(7166,b,269,a,c,564,a)].

given #795 (F,wt=9): 8058 -->_s0(true,sndsplit(length(nil),empty(cons(x,y)))) # answer(goal).  [ur(7166,b,145,a,c,4340,a)].

given #796 (F,wt=9): 8061 -->_s0(true,app(app(nil,app(nil,nil)),false)) # answer(goal).  [ur(7166,b,138,a,c,5074,a)].

given #797 (F,wt=9): 8063 -->_s0(true,app(app(nil,nil),app(nil,false))) # answer(goal).  [ur(7166,b,138,a,c,702,a)].

given #798 (T,wt=8): 2264 ->*_s0(length(sndsplit(0,fstsplit(0,x))),0).  [ur(87,a,482,a,b,1666,a)].

given #799 (T,wt=8): 2265 ->*_s0(length(sndsplit(0,app(nil,nil))),0).  [ur(87,a,482,a,b,1368,a)].

given #800 (T,wt=8): 2266 ->*_s0(length(sndsplit(0,length(nil))),length(0)).  [ur(87,a,482,a,b,948,a)].

given #801 (T,wt=8): 2267 ->*_s0(length(sndsplit(0,empty(nil))),length(true)).  [ur(87,a,482,a,b,787,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=9): 8064 -->_s0(true,app(app(nil,nil),sndsplit(0,false))) # answer(goal).  [ur(7166,b,138,a,c,643,a)].

given #804 (F,wt=9): 8066 -->_s0(true,app(nil,app(nil,app(nil,false)))) # answer(goal).  [ur(7166,b,137,a,c,702,a)].

given #805 (F,wt=9): 8067 -->_s0(true,app(nil,app(nil,sndsplit(0,false)))) # answer(goal).  [ur(7166,b,137,a,c,643,a)].

given #806 (F,wt=9): 8072 -->_s0(true,leq(app(nil,s(x)),length(nil))) # answer(goal).  [ur(7166,b,131,a,c,4513,a)].

given #807 (T,wt=7): 9206 ->*_s0(mapf(x,fstsplit(0,y)),nil).  [ur(87,a,203,a,b,568,a)].

given #808 (T,wt=8): 2295 ->*_s0(length(sndsplit(0,sndsplit(0,nil))),0).  [ur(87,a,482,a,b,2268,a)].

given #809 (T,wt=8): 2296 ->*_s0(length(app(nil,sndsplit(0,nil))),0).  [ur(87,a,132,a,b,2268,a)].

given #810 (T,wt=8): 2298 ->*_s0(sndsplit(0,length(sndsplit(0,nil))),0).  [ur(87,a,82,a,b,2268,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=9): 8075 -->_s0(true,leq(s(x),app(nil,length(nil)))) # answer(goal).  [ur(7166,b,130,a,c,4513,a)].

given #813 (F,wt=9): 8079 -->_s0(true,sndsplit(app(nil,app(nil,0)),false)) # answer(goal).  [ur(7166,b,121,a,c,3308,a)].

given #814 (F,wt=9): 8082 -->_s0(true,sndsplit(app(nil,0),app(nil,false))) # answer(goal).  [ur(7166,b,121,a,c,700,a)].

given #815 (F,wt=9): 8083 -->_s0(true,sndsplit(app(nil,0),sndsplit(0,false))) # answer(goal).  [ur(7166,b,121,a,c,641,a)].

given #816 (T,wt=8): 2300 ->*_s0(app(nil,length(sndsplit(0,nil))),0).  [ur(87,a,61,a,b,2268,a)].

given #817 (T,wt=8): 2302 ->*_s0(head(sndsplit(0,length(nil))),head(0)).  [ur(87,a,483,a,b,974,a)].

given #818 (T,wt=8): 2303 ->*_s0(head(sndsplit(0,empty(nil))),head(true)).  [ur(87,a,483,a,b,813,a)].

given #819 (T,wt=8): 2304 ->*_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=9): 8087 -->_s0(true,sndsplit(0,app(nil,app(nil,false)))) # answer(goal).  [ur(7166,b,120,a,c,700,a)].

given #822 (F,wt=9): 8088 -->_s0(true,sndsplit(0,app(nil,sndsplit(0,false)))) # answer(goal).  [ur(7166,b,120,a,c,641,a)].

given #823 (F,wt=9): 8099 -->_s0(true,tail(cons(x,sndsplit(length(nil),false)))) # answer(goal).  [ur(7166,b,85,a,c,4340,a)].

given #824 (F,wt=9): 8114 -->_s0(true,tail(cons(x,empty(cons(y,z))))) # answer(goal).  [ur(7166,b,85,a,c,580,a)].

given #825 (T,wt=8): 2360 ->*_s0(empty(sndsplit(0,mapf(x,nil))),true).  [ur(87,a,486,a,b,2133,a)].

given #826 (T,wt=8): 2361 ->*_s0(empty(sndsplit(0,fstsplit(0,x))),true).  [ur(87,a,486,a,b,1763,a)].

given #827 (T,wt=8): 2362 ->*_s0(empty(sndsplit(0,app(nil,nil))),true).  [ur(87,a,486,a,b,1547,a)].

given #828 (T,wt=8): 2363 ->*_s0(empty(sndsplit(0,length(nil))),empty(0)).  [ur(87,a,486,a,b,1034,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=9): 8115 -->_s0(true,tail(cons(x,head(cons(false,y))))) # answer(goal).  [ur(7166,b,85,a,c,575,a)].

given #831 (F,wt=9): 8116 -->_s0(true,tail(cons(x,leq(s(y),0)))) # answer(goal).  [ur(7166,b,85,a,c,571,a)].

given #832 (F,wt=9): 8117 -->_s0(true,tail(cons(x,tail(cons(y,false))))) # answer(goal).  [ur(7166,b,85,a,c,564,a)].

given #833 (F,wt=9): 8118 -->_s0(true,sndsplit(s(length(nil)),cons(x,false))) # answer(goal).  [ur(7166,b,83,a,c,4340,a)].

given #834 (T,wt=8): 2364 ->*_s0(empty(sndsplit(0,empty(nil))),empty(true)).  [ur(87,a,486,a,b,839,a)].

given #835 (T,wt=8): 2365 ->*_s0(empty(sndsplit(0,cons(x,y))),false).  [ur(87,a,486,a,b,580,a)].

given #836 (T,wt=8): 2396 ->*_s0(empty(sndsplit(0,sndsplit(0,nil))),true).  [ur(87,a,486,a,b,2366,a)].

given #837 (T,wt=8): 2397 ->*_s0(empty(app(nil,sndsplit(0,nil))),true).  [ur(87,a,136,a,b,2366,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=9): 8125 -->_s0(true,sndsplit(0,app(app(nil,nil),false))) # answer(goal).  [ur(7166,b,82,a,c,5074,a)].

given #840 (F,wt=9): 8126 -->_s0(true,sndsplit(0,leq(s(x),length(nil)))) # answer(goal).  [ur(7166,b,82,a,c,4513,a)].

given #841 (F,wt=9): 8128 -->_s0(true,sndsplit(0,sndsplit(app(nil,0),false))) # answer(goal).  [ur(7166,b,82,a,c,3308,a)].

given #842 (F,wt=9): 8133 -->_s0(true,sndsplit(0,sndsplit(0,app(nil,false)))) # answer(goal).  [ur(7166,b,82,a,c,700,a)].

given #843 (T,wt=8): 2399 ->*_s0(sndsplit(0,empty(sndsplit(0,nil))),true).  [ur(87,a,82,a,b,2366,a)].

given #844 (T,wt=8): 2401 ->*_s0(app(nil,empty(sndsplit(0,nil))),true).  [ur(87,a,61,a,b,2366,a)].

given #845 (T,wt=8): 2492 ->*_s0(head(app(cons(x,y),z)),x).  [ur(87,a,108,a,b,575,a)].

given #846 (T,wt=8): 2658 ->*_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=9): 8136 -->_s0(true,sndsplit(0,sndsplit(0,sndsplit(0,false)))) # answer(goal).  [ur(7166,b,82,a,c,641,a)].

given #849 (F,wt=9): 8140 -->_s0(true,leq(s(s(x)),s(length(nil)))) # answer(goal).  [ur(7166,b,72,a,c,4513,a)].

given #850 (F,wt=9): 8144 -->_s0(true,head(cons(sndsplit(length(nil),false),x))) # answer(goal).  [ur(7166,b,67,a,c,4340,a)].

given #851 (F,wt=9): 8159 -->_s0(true,head(cons(empty(cons(x,y)),z))) # answer(goal).  [ur(7166,b,67,a,c,580,a)].

given #852 (T,wt=8): 3000 ->*_s0(s(empty(cons(x,y))),s(false)).  [ur(87,a,139,a,b,86,a)].

given #853 (T,wt=8): 3057 ->*_s0(tail(empty(cons(x,y))),tail(false)).  [ur(87,a,144,a,b,86,a)].

given #854 (T,wt=8): 3084 ->*_s0(length(empty(cons(x,y))),length(false)).  [ur(87,a,157,a,b,86,a)].

given #855 (T,wt=8): 3111 ->*_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): 8160 -->_s0(true,head(cons(head(cons(false,x)),y))) # answer(goal).  [ur(7166,b,67,a,c,575,a)].

given #858 (F,wt=9): 8161 -->_s0(true,head(cons(leq(s(x),0),y))) # answer(goal).  [ur(7166,b,67,a,c,571,a)].

given #859 (F,wt=9): 8162 -->_s0(true,head(cons(tail(cons(x,false)),y))) # answer(goal).  [ur(7166,b,67,a,c,564,a)].

given #860 (F,wt=9): 8163 -->_s0(true,app(nil,app(app(nil,nil),false))) # answer(goal).  [ur(7166,b,61,a,c,5074,a)].

given #861 (T,wt=8): 3138 ->*_s0(empty(empty(cons(x,y))),empty(false)).  [ur(87,a,161,a,b,86,a)].

given #862 (T,wt=8): 3165 ->*_s0(sndsplit(s(x),app(nil,nil)),nil).  [ur(87,a,120,a,b,565,a)].

given #863 (T,wt=8): 3193 ->*_s0(f(x,empty(nil)),f(x,true)).  [ur(87,a,165,a,b,86,a)].

given #864 (T,wt=8): 3220 ->*_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): 8164 -->_s0(true,app(nil,leq(s(x),length(nil)))) # answer(goal).  [ur(7166,b,61,a,c,4513,a)].

given #867 (F,wt=9): 8166 -->_s0(true,app(nil,sndsplit(app(nil,0),false))) # answer(goal).  [ur(7166,b,61,a,c,3308,a)].

given #868 (F,wt=9): 8171 -->_s0(true,app(nil,sndsplit(0,app(nil,false)))) # answer(goal).  [ur(7166,b,61,a,c,700,a)].

given #869 (F,wt=9): 8174 -->_s0(true,app(nil,sndsplit(0,sndsplit(0,false)))) # answer(goal).  [ur(7166,b,61,a,c,641,a)].

given #870 (T,wt=7): 9700 ->*_s0(app(fstsplit(0,x),y),y).  [ur(87,a,213,a,b,581,a)].

given #871 (T,wt=8): 3247 ->*_s0(cons(x,empty(nil)),cons(x,true)).  [ur(87,a,167,a,b,86,a)].

given #872 (T,wt=8): 3274 ->*_s0(cons(empty(nil),x),cons(true,x)).  [ur(87,a,168,a,b,86,a)].

given #873 (T,wt=8): 3306 ->*_s0(sndsplit(app(nil,0),empty(nil)),true).  [ur(87,a,121,a,b,634,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): 8216 -->_s0(true,sndsplit(length(nil),head(cons(false,x)))) # answer(goal).  [ur(7166,b,321,a,c,1121,a)].

given #876 (F,wt=9): 9028 -->_s0(true,sndsplit(length(nil),x)) | -->_s0(x,false) # answer(goal).  [resolve(8008,b,53,b)].

given #877 (F,wt=9): 9029 -->_s0(true,sndsplit(x,false)) | -->_s0(x,length(nil)) # answer(goal).  [resolve(8008,b,52,b)].

given #878 (F,wt=8): 9803 -->_s0(true,sndsplit(length(sndsplit(0,nil)),false)) # answer(goal).  [resolve(9029,b,482,a)].

given #879 (T,wt=8): 3307 ->*_s0(sndsplit(app(nil,0),length(nil)),0).  [ur(87,a,121,a,b,628,a)].

given #880 (T,wt=8): 3309 ->*_s0(sndsplit(app(nil,s(x)),nil),nil).  [ur(87,a,121,a,b,565,a)].

given #881 (T,wt=8): 3354 ->*_s0(sndsplit(x,empty(nil)),sndsplit(x,true)).  [ur(87,a,170,a,b,86,a)].

given #882 (T,wt=8): 3381 ->*_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=8): 9804 -->_s0(true,sndsplit(length(mapf(x,nil)),false)) # answer(goal).  [resolve(9029,b,457,a)].

given #885 (F,wt=8): 9807 -->_s0(true,sndsplit(length(fstsplit(0,x)),false)) # answer(goal).  [resolve(9029,b,207,a)].

given #886 (F,wt=8): 9808 -->_s0(true,sndsplit(length(app(nil,nil)),false)) # answer(goal).  [resolve(9029,b,132,a)].

given #887 (F,wt=8): 9810 -->_s0(true,sndsplit(sndsplit(0,length(nil)),false)) # answer(goal).  [resolve(9029,b,82,a)].

given #888 (T,wt=8): 3408 ->*_s0(mapf(x,empty(nil)),mapf(x,true)).  [ur(87,a,178,a,b,86,a)].

given #889 (T,wt=8): 3462 ->*_s0(mapf(empty(nil),x),mapf(true,x)).  [ur(87,a,179,a,b,86,a)].

given #890 (T,wt=8): 3489 ->*_s0(leq(x,empty(nil)),leq(x,true)).  [ur(87,a,180,a,b,86,a)].

given #891 (T,wt=8): 3517 ->*_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): 9030 -->_s0(true,empty(x)) | -->_s0(x,cons(y,z)) # answer(goal).  [resolve(8024,b,37,b)].

given #894 (F,wt=9): 9031 -->_s0(true,head(x)) | -->_s0(x,cons(false,y)) # answer(goal).  [resolve(8025,b,40,b)].

given #895 (F,wt=9): 9032 -->_s0(true,leq(s(x),y)) | -->_s0(y,0) # answer(goal).  [resolve(8026,b,43,b)].

given #896 (F,wt=8): 9913 -->_s0(true,leq(s(x),sndsplit(0,0))) # answer(goal).  [resolve(9032,b,82,a)].

given #897 (T,wt=8): 3544 ->*_s0(fstsplit(x,empty(nil)),fstsplit(x,true)).  [ur(87,a,184,a,b,86,a)].

given #898 (T,wt=8): 3598 ->*_s0(fstsplit(empty(nil),x),fstsplit(true,x)).  [ur(87,a,185,a,b,86,a)].

given #899 (T,wt=8): 3625 ->*_s0(app(x,empty(nil)),app(x,true)).  [ur(87,a,187,a,b,86,a)].

given #900 (T,wt=8): 3652 ->*_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=9): 9033 -->_s0(true,leq(x,0)) | -->_s0(x,s(y)) # answer(goal).  [resolve(8026,b,42,b)].

given #903 (F,wt=8): 9966 -->_s0(true,leq(sndsplit(0,s(x)),0)) # answer(goal).  [resolve(9033,b,82,a)].

given #904 (F,wt=8): 9967 -->_s0(true,leq(length(cons(x,y)),0)) # answer(goal).  [resolve(9033,b,68,a)].

given #905 (F,wt=9): 9073 -->_s0(true,tail(x)) | -->_s0(x,cons(y,false)) # answer(goal).  [resolve(8028,b,54,b)].

given #906 (T,wt=8): 3679 ->*_s0(s(fstsplit(s(x),nil)),s(nil)).  [ur(87,a,239,a,b,86,a)].

given #907 (T,wt=8): 3745 ->*_s0(tail(fstsplit(s(x),nil)),tail(nil)).  [ur(87,a,244,a,b,86,a)].

given #908 (T,wt=8): 3773 ->*_s0(length(fstsplit(s(x),nil)),length(nil)).  [ur(87,a,257,a,b,86,a)].

given #909 (T,wt=8): 3806 ->*_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): 9725 -->_s0(true,app(fstsplit(0,x),app(nil,false))) # answer(goal).  [ur(7166,b,213,a,c,702,a)].

given #912 (F,wt=9): 9726 -->_s0(true,app(fstsplit(0,x),sndsplit(0,false))) # answer(goal).  [ur(7166,b,213,a,c,643,a)].

given #913 (F,wt=9): 9727 -->_s0(true,app(nil,app(fstsplit(0,x),false))) # answer(goal).  [resolve(9700,a,7979,b)].

given #914 (F,wt=9): 9729 -->_s0(true,sndsplit(0,app(fstsplit(0,x),false))) # answer(goal).  [resolve(9700,a,7962,b)].

given #915 (T,wt=8): 3865 ->*_s0(empty(fstsplit(s(x),nil)),empty(nil)).  [ur(87,a,261,a,b,86,a)].

given #916 (T,wt=8): 3908 ->*_s0(s(head(cons(x,y))),s(x)).  [ur(87,a,264,a,b,86,a)].

given #917 (T,wt=8): 3946 ->*_s0(tail(head(cons(x,y))),tail(x)).  [ur(87,a,269,a,b,86,a)].

given #918 (T,wt=8): 4016 ->*_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=9): 9746 -->_s0(true,app(app(nil,fstsplit(0,x)),false)) # answer(goal).  [ur(7166,b,138,a,c,9700,a)].

given #921 (F,wt=9): 9801 -->_s0(true,sndsplit(length(tail(cons(x,nil))),false)) # answer(goal).  [resolve(9029,b,557,a)].

given #922 (F,wt=9): 9802 -->_s0(true,sndsplit(length(sndsplit(s(x),nil)),false)) # answer(goal).  [resolve(9029,b,532,a)].

given #923 (F,wt=9): 9805 -->_s0(true,sndsplit(length(head(cons(nil,x))),false)) # answer(goal).  [resolve(9029,b,282,a)].

given #924 (T,wt=8): 4060 ->*_s0(head(head(cons(x,y))),head(x)).  [ur(87,a,283,a,b,86,a)].

given #925 (T,wt=8): 4101 ->*_s0(empty(head(cons(x,y))),empty(x)).  [ur(87,a,286,a,b,86,a)].

given #926 (T,wt=8): 4165 ->*_s0(f(x,length(nil)),f(x,0)).  [ur(87,a,315,a,b,86,a)].

given #927 (T,wt=8): 4192 ->*_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): 9806 -->_s0(true,sndsplit(length(fstsplit(s(x),nil)),false)) # answer(goal).  [resolve(9029,b,257,a)].

given #930 (F,wt=9): 9809 -->_s0(true,sndsplit(tail(cons(x,length(nil))),false)) # answer(goal).  [resolve(9029,b,85,a)].

given #931 (F,wt=9): 9811 -->_s0(true,sndsplit(head(cons(length(nil),x)),false)) # answer(goal).  [resolve(9029,b,67,a)].

given #932 (F,wt=9): 9812 -->_s0(true,sndsplit(length(x),false)) | -->_s0(x,nil) # answer(goal).  [resolve(9029,b,41,b)].

given #933 (T,wt=8): 4219 ->*_s0(cons(x,length(nil)),cons(x,0)).  [ur(87,a,317,a,b,86,a)].

given #934 (T,wt=8): 4279 ->*_s0(cons(length(nil),x),cons(0,x)).  [ur(87,a,318,a,b,86,a)].

given #935 (T,wt=8): 4306 ->*_s0(sndsplit(x,length(nil)),sndsplit(x,0)).  [ur(87,a,320,a,b,86,a)].

given #936 (T,wt=8): 4333 ->*_s0(sndsplit(length(nil),app(nil,x)),x).  [ur(87,a,321,a,b,700,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): 9909 -->_s0(true,empty(fstsplit(s(x),cons(y,z)))) # answer(goal).  [resolve(9030,b,65,a)].

given #939 (F,wt=9): 9910 -->_s0(true,head(fstsplit(s(x),cons(false,y)))) # answer(goal).  [resolve(9031,b,65,a)].

given #940 (F,wt=9): 9911 -->_s0(true,head(cons(x,y))) | -->_s0(x,false) # answer(goal).  [resolve(9031,b,55,b)].

given #941 (F,wt=9): 9912 -->_s0(true,leq(s(x),tail(cons(y,0)))) # answer(goal).  [resolve(9032,b,85,a)].

given #942 (T,wt=8): 4334 ->*_s0(sndsplit(length(nil),fstsplit(0,x)),nil).  [ur(87,a,321,a,b,693,a)].

given #943 (T,wt=8): 4335 ->*_s0(sndsplit(length(nil),leq(0,x)),true).  [ur(87,a,321,a,b,688,a)].

given #944 (T,wt=8): 4336 ->*_s0(sndsplit(length(nil),mapf(x,nil)),nil).  [ur(87,a,321,a,b,645,a)].

given #945 (T,wt=8): 4337 ->*_s0(sndsplit(length(nil),sndsplit(0,x)),x).  [ur(87,a,321,a,b,641,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=9): 9914 -->_s0(true,leq(s(x),head(cons(0,y)))) # answer(goal).  [resolve(9032,b,67,a)].

given #948 (F,wt=9): 9965 -->_s0(true,leq(tail(cons(x,s(y))),0)) # answer(goal).  [resolve(9033,b,85,a)].

given #949 (F,wt=9): 9968 -->_s0(true,leq(head(cons(s(x),y)),0)) # answer(goal).  [resolve(9033,b,67,a)].

given #950 (F,wt=9): 9969 -->_s0(true,tail(cons(x,y))) | -->_s0(y,false) # answer(goal).  [resolve(9073,b,56,b)].

given #951 (T,wt=8): 4341 ->*_s0(sndsplit(length(nil),x),sndsplit(0,x)).  [ur(87,a,321,a,b,86,a)].

given #952 (T,wt=8): 4404 ->*_s0(sndsplit(app(nil,length(nil)),x),x).  [ur(87,a,121,a,b,4340,a)].

given #953 (T,wt=8): 4408 ->*_s0(sndsplit(0,sndsplit(length(nil),x)),x).  [ur(87,a,82,a,b,4340,a)].

given #954 (T,wt=8): 4410 ->*_s0(app(nil,sndsplit(length(nil),x)),x).  [ur(87,a,61,a,b,4340,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): 10276 -->_s0(true,sndsplit(length(nil),sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,321,a,c,4408,a)].

given #957 (F,wt=10): 6873 -->_s0(head(x),nil) | -->_s0(true,y) | -->*_s0(y,false) # answer(goal).  [resolve(6872,a,87,c)].

given #958 (F,wt=10): 7811 -->_s0(true,empty(sndsplit(0,x))) | -->*_s0(empty(x),false) # answer(goal).  [resolve(7166,b,486,a)].

given #959 (F,wt=10): 7812 -->_s0(true,head(sndsplit(0,x))) | -->*_s0(head(x),false) # answer(goal).  [resolve(7166,b,483,a)].

given #960 (T,wt=8): 4429 ->*_s0(mapf(x,length(nil)),mapf(x,0)).  [ur(87,a,328,a,b,86,a)].

given #961 (T,wt=8): 4457 ->*_s0(leq(s(x),app(nil,0)),false).  [ur(87,a,130,a,b,571,a)].

given #962 (T,wt=8): 4485 ->*_s0(mapf(length(nil),x),mapf(0,x)).  [ur(87,a,329,a,b,86,a)].

given #963 (T,wt=8): 4514 ->*_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): 7813 -->_s0(true,length(sndsplit(0,x))) | -->*_s0(length(x),false) # answer(goal).  [resolve(7166,b,482,a)].

given #966 (F,wt=10): 7814 -->_s0(true,tail(sndsplit(0,x))) | -->*_s0(tail(x),false) # answer(goal).  [resolve(7166,b,469,a)].

given #967 (F,wt=10): 7815 -->_s0(true,s(sndsplit(0,x))) | -->*_s0(s(x),false) # answer(goal).  [resolve(7166,b,464,a)].

given #968 (F,wt=10): 7816 -->_s0(true,empty(mapf(x,nil))) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(7166,b,461,a)].

given #969 (T,wt=8): 4556 ->*_s0(leq(length(nil),x),leq(0,x)).  [ur(87,a,331,a,b,86,a)].

given #970 (T,wt=8): 4587 ->*_s0(leq(app(nil,s(x)),0),false).  [ur(87,a,131,a,b,571,a)].

given #971 (T,wt=8): 4620 ->*_s0(leq(app(nil,length(nil)),x),true).  [ur(87,a,131,a,b,4555,a)].

given #972 (T,wt=8): 4622 ->*_s0(sndsplit(0,leq(length(nil),x)),true).  [ur(87,a,82,a,b,4555,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): 7817 -->_s0(true,head(mapf(x,nil))) | -->*_s0(head(nil),false) # answer(goal).  [resolve(7166,b,458,a)].

given #975 (F,wt=10): 7818 -->_s0(true,length(mapf(x,nil))) | -->*_s0(length(nil),false) # answer(goal).  [resolve(7166,b,457,a)].

given #976 (F,wt=10): 7819 -->_s0(true,tail(mapf(x,nil))) | -->*_s0(tail(nil),false) # answer(goal).  [resolve(7166,b,444,a)].

given #977 (F,wt=10): 7820 -->_s0(true,s(mapf(x,nil))) | -->*_s0(s(nil),false) # answer(goal).  [resolve(7166,b,439,a)].

given #978 (T,wt=8): 4623 ->*_s0(leq(s(length(nil)),s(x)),true).  [ur(87,a,72,a,b,4555,a)].

given #979 (T,wt=8): 4625 ->*_s0(app(nil,leq(length(nil),x)),true).  [ur(87,a,61,a,b,4555,a)].

given #980 (T,wt=8): 4639 ->*_s0(fstsplit(x,length(nil)),fstsplit(x,0)).  [ur(87,a,334,a,b,86,a)].

given #981 (T,wt=8): 4667 ->*_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): 7826 -->_s0(true,empty(leq(0,x))) | -->*_s0(empty(true),false) # answer(goal).  [resolve(7166,b,361,a)].

given #984 (F,wt=10): 7827 -->_s0(true,head(leq(0,x))) | -->*_s0(head(true),false) # answer(goal).  [resolve(7166,b,358,a)].

given #985 (F,wt=10): 7828 -->_s0(true,length(leq(0,x))) | -->*_s0(length(true),false) # answer(goal).  [resolve(7166,b,357,a)].

given #986 (F,wt=10): 7829 -->_s0(true,tail(leq(0,x))) | -->*_s0(tail(true),false) # answer(goal).  [resolve(7166,b,344,a)].

given #987 (T,wt=8): 4694 ->*_s0(fstsplit(s(x),app(nil,nil)),nil).  [ur(87,a,134,a,b,576,a)].

given #988 (T,wt=8): 4723 ->*_s0(sndsplit(0,fstsplit(length(nil),x)),nil).  [ur(87,a,82,a,b,4666,a)].

given #989 (T,wt=8): 4725 ->*_s0(app(nil,fstsplit(length(nil),x)),nil).  [ur(87,a,61,a,b,4666,a)].

given #990 (T,wt=8): 4727 ->*_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): 7830 -->_s0(true,s(leq(0,x))) | -->*_s0(s(true),false) # answer(goal).  [resolve(7166,b,339,a)].

given #993 (F,wt=10): 7860 -->_s0(true,empty(fstsplit(0,x))) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(7166,b,211,a)].

given #994 (F,wt=10): 7861 -->_s0(true,head(fstsplit(0,x))) | -->*_s0(head(nil),false) # answer(goal).  [resolve(7166,b,208,a)].

given #995 (F,wt=10): 7862 -->_s0(true,length(fstsplit(0,x))) | -->*_s0(length(nil),false) # answer(goal).  [resolve(7166,b,207,a)].

given #996 (T,wt=8): 4754 ->*_s0(app(length(nil),x),app(0,x)).  [ur(87,a,338,a,b,86,a)].

given #997 (T,wt=8): 4781 ->*_s0(s(leq(s(x),0)),s(false)).  [ur(87,a,364,a,b,86,a)].

given #998 (T,wt=8): 4808 ->*_s0(fstsplit(app(nil,length(nil)),x),nil).  [ur(87,a,135,a,b,4666,a)].

given #999 (T,wt=8): 4810 ->*_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): 7863 -->_s0(true,tail(fstsplit(0,x))) | -->*_s0(tail(nil),false) # answer(goal).  [resolve(7166,b,194,a)].

given #1002 (F,wt=10): 7864 -->_s0(true,s(fstsplit(0,x))) | -->*_s0(s(nil),false) # answer(goal).  [resolve(7166,b,189,a)].

given #1003 (F,wt=10): 7911 -->_s0(true,empty(app(nil,x))) | -->*_s0(empty(x),false) # answer(goal).  [resolve(7166,b,136,a)].

given #1004 (F,wt=10): 7914 -->_s0(true,head(app(nil,x))) | -->*_s0(head(x),false) # answer(goal).  [resolve(7166,b,133,a)].

given #1005 (T,wt=8): 4848 ->*_s0(tail(leq(s(x),0)),tail(false)).  [ur(87,a,369,a,b,86,a)].

given #1006 (T,wt=8): 4875 ->*_s0(length(leq(s(x),0)),length(false)).  [ur(87,a,382,a,b,86,a)].

given #1007 (T,wt=8): 4902 ->*_s0(head(leq(s(x),0)),head(false)).  [ur(87,a,383,a,b,86,a)].

given #1008 (T,wt=8): 4958 ->*_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): 7915 -->_s0(true,length(app(nil,x))) | -->*_s0(length(x),false) # answer(goal).  [resolve(7166,b,132,a)].

given #1011 (F,wt=10): 7928 -->_s0(true,tail(app(nil,x))) | -->*_s0(tail(x),false) # answer(goal).  [resolve(7166,b,119,a)].

given #1012 (F,wt=10): 7933 -->_s0(true,s(app(nil,x))) | -->*_s0(s(x),false) # answer(goal).  [resolve(7166,b,114,a)].

given #1013 (F,wt=10): 8006 -->_s0(true,x) | -->_s0(x,app(app(nil,nil),false)) # answer(goal).  [resolve(7166,c,5074,a)].

given #1014 (T,wt=8): 4985 ->*_s0(s(sndsplit(s(x),nil)),s(nil)).  [ur(87,a,514,a,b,86,a)].

given #1015 (T,wt=8): 5012 ->*_s0(tail(sndsplit(s(x),nil)),tail(nil)).  [ur(87,a,519,a,b,86,a)].

given #1016 (T,wt=8): 5040 ->*_s0(length(sndsplit(s(x),nil)),length(nil)).  [ur(87,a,532,a,b,86,a)].

given #1017 (T,wt=8): 5072 ->*_s0(app(app(nil,nil),empty(nil)),true).  [ur(87,a,138,a,b,636,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): 8007 -->_s0(true,x) | -->_s0(x,leq(s(y),length(nil))) # answer(goal).  [resolve(7166,c,4513,a)].

given #1020 (F,wt=10): 8009 -->_s0(true,x) | -->_s0(x,sndsplit(app(nil,0),false)) # answer(goal).  [resolve(7166,c,3308,a)].

given #1021 (F,wt=10): 8014 -->_s0(true,x) | -->_s0(x,app(nil,app(nil,false))) # answer(goal).  [resolve(7166,c,702,a)].

given #1022 (F,wt=10): 8016 -->_s0(true,x) | -->_s0(x,sndsplit(0,app(nil,false))) # answer(goal).  [resolve(7166,c,700,a)].

given #1023 (T,wt=8): 5073 ->*_s0(app(app(nil,nil),length(nil)),0).  [ur(87,a,138,a,b,630,a)].

given #1024 (T,wt=8): 5141 ->*_s0(head(sndsplit(s(x),nil)),head(nil)).  [ur(87,a,533,a,b,86,a)].

given #1025 (T,wt=8): 5168 ->*_s0(empty(sndsplit(s(x),nil)),empty(nil)).  [ur(87,a,536,a,b,86,a)].

given #1026 (T,wt=8): 5239 ->*_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=10): 8018 -->_s0(true,x) | -->_s0(x,app(nil,sndsplit(0,false))) # answer(goal).  [resolve(7166,c,643,a)].

given #1029 (F,wt=10): 8020 -->_s0(true,x) | -->_s0(x,sndsplit(0,sndsplit(0,false))) # answer(goal).  [resolve(7166,c,641,a)].

given #1030 (F,wt=10): 8039 -->_s0(true,head(sndsplit(0,cons(app(nil,false),x)))) # answer(goal).  [ur(7166,b,483,a,c,701,a)].

given #1031 (F,wt=10): 8040 -->_s0(true,head(sndsplit(0,cons(sndsplit(0,false),x)))) # answer(goal).  [ur(7166,b,483,a,c,642,a)].

given #1032 (T,wt=8): 5276 ->*_s0(tail(tail(cons(x,y))),tail(y)).  [ur(87,a,544,a,b,86,a)].

given #1033 (T,wt=8): 5320 ->*_s0(length(tail(cons(x,y))),length(y)).  [ur(87,a,557,a,b,86,a)].

given #1034 (T,wt=8): 5392 ->*_s0(head(tail(cons(x,y))),head(y)).  [ur(87,a,558,a,b,86,a)].

given #1035 (T,wt=8): 5435 ->*_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): 8042 -->_s0(true,tail(sndsplit(0,cons(x,app(nil,false))))) # answer(goal).  [ur(7166,b,469,a,c,699,a)].

given #1038 (F,wt=10): 8043 -->_s0(true,tail(sndsplit(0,cons(x,sndsplit(0,false))))) # answer(goal).  [ur(7166,b,469,a,c,639,a)].

given #1039 (F,wt=10): 8056 -->_s0(true,app(app(nil,nil),empty(cons(x,y)))) # answer(goal).  [ur(7166,b,162,a,c,5074,a)].

given #1040 (F,wt=10): 8059 -->_s0(true,sndsplit(app(nil,0),empty(cons(x,y)))) # answer(goal).  [ur(7166,b,145,a,c,3308,a)].

given #1041 (T,wt=8): 5690 ->*_s0(tail(app(cons(x,nil),y)),y).  [ur(87,a,94,a,b,699,a)].

given #1042 (T,wt=8): 5742 ->*_s0(s(s(empty(nil))),s(s(true))).  [ur(87,a,704,a,b,86,a)].

given #1043 (T,wt=8): 5769 ->*_s0(tail(s(empty(nil))),tail(s(true))).  [ur(87,a,709,a,b,86,a)].

given #1044 (T,wt=8): 5796 ->*_s0(length(s(empty(nil))),length(s(true))).  [ur(87,a,722,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=10): 8062 -->_s0(true,app(app(nil,nil),tail(cons(x,false)))) # answer(goal).  [ur(7166,b,138,a,c,1068,a)].

given #1047 (F,wt=10): 8065 -->_s0(true,app(nil,app(nil,tail(cons(x,false))))) # answer(goal).  [ur(7166,b,137,a,c,1068,a)].

given #1048 (F,wt=10): 8069 -->_s0(true,head(app(nil,cons(app(nil,false),x)))) # answer(goal).  [ur(7166,b,133,a,c,701,a)].

given #1049 (F,wt=10): 8070 -->_s0(true,head(app(nil,cons(sndsplit(0,false),x)))) # answer(goal).  [ur(7166,b,133,a,c,642,a)].

given #1050 (T,wt=8): 5823 ->*_s0(head(s(empty(nil))),head(s(true))).  [ur(87,a,723,a,b,86,a)].

given #1051 (T,wt=8): 5945 ->*_s0(empty(s(empty(nil))),empty(s(true))).  [ur(87,a,726,a,b,86,a)].

given #1052 (T,wt=8): 5972 ->*_s0(s(tail(empty(nil))),s(tail(true))).  [ur(87,a,762,a,b,86,a)].

given #1053 (T,wt=8): 5999 ->*_s0(tail(tail(empty(nil))),tail(tail(true))).  [ur(87,a,767,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): 8073 -->_s0(true,leq(app(nil,s(s(x))),s(0))) # answer(goal).  [ur(7166,b,131,a,c,1078,a)].

given #1056 (F,wt=10): 8076 -->_s0(true,leq(s(s(x)),app(nil,s(0)))) # answer(goal).  [ur(7166,b,130,a,c,1078,a)].

given #1057 (F,wt=10): 8080 -->_s0(true,sndsplit(app(nil,0),leq(s(x),0))) # answer(goal).  [ur(7166,b,121,a,c,1077,a)].

given #1058 (F,wt=10): 8081 -->_s0(true,sndsplit(app(nil,0),tail(cons(x,false)))) # answer(goal).  [ur(7166,b,121,a,c,1066,a)].

given #1059 (T,wt=8): 6026 ->*_s0(length(tail(empty(nil))),length(tail(true))).  [ur(87,a,780,a,b,86,a)].

given #1060 (T,wt=8): 6084 ->*_s0(head(tail(empty(nil))),head(tail(true))).  [ur(87,a,781,a,b,86,a)].

given #1061 (T,wt=8): 6111 ->*_s0(empty(tail(empty(nil))),empty(tail(true))).  [ur(87,a,784,a,b,86,a)].

given #1062 (T,wt=8): 6138 ->*_s0(s(length(empty(nil))),s(length(true))).  [ur(87,a,788,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): 8084 -->_s0(true,sndsplit(app(nil,s(0)),cons(x,false))) # answer(goal).  [ur(7166,b,121,a,c,640,a)].

given #1065 (F,wt=10): 8085 -->_s0(true,sndsplit(0,app(nil,leq(s(x),0)))) # answer(goal).  [ur(7166,b,120,a,c,1077,a)].

given #1066 (F,wt=10): 8086 -->_s0(true,sndsplit(0,app(nil,tail(cons(x,false))))) # answer(goal).  [ur(7166,b,120,a,c,1066,a)].

given #1067 (F,wt=10): 8089 -->_s0(true,sndsplit(s(0),app(nil,cons(x,false)))) # answer(goal).  [ur(7166,b,120,a,c,640,a)].

given #1068 (T,wt=8): 6165 ->*_s0(tail(length(empty(nil))),tail(length(true))).  [ur(87,a,793,a,b,86,a)].

given #1069 (T,wt=8): 6246 ->*_s0(length(length(empty(nil))),length(length(true))).  [ur(87,a,806,a,b,86,a)].

given #1070 (T,wt=8): 6273 ->*_s0(head(length(empty(nil))),head(length(true))).  [ur(87,a,807,a,b,86,a)].

given #1071 (T,wt=8): 6300 ->*_s0(empty(length(empty(nil))),empty(length(true))).  [ur(87,a,810,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): 8090 -->_s0(true,tail(app(nil,cons(x,app(nil,false))))) # answer(goal).  [ur(7166,b,119,a,c,699,a)].

given #1074 (F,wt=10): 8091 -->_s0(true,tail(app(nil,cons(x,sndsplit(0,false))))) # answer(goal).  [ur(7166,b,119,a,c,639,a)].

given #1075 (F,wt=10): 8093 -->_s0(true,head(app(cons(app(nil,false),x),y))) # answer(goal).  [ur(7166,b,108,a,c,701,a)].

given #1076 (F,wt=10): 8094 -->_s0(true,head(app(cons(sndsplit(0,false),x),y))) # answer(goal).  [ur(7166,b,108,a,c,642,a)].

given #1077 (T,wt=8): 6327 ->*_s0(s(head(empty(nil))),s(head(true))).  [ur(87,a,814,a,b,86,a)].

given #1078 (T,wt=8): 6426 ->*_s0(tail(head(empty(nil))),tail(head(true))).  [ur(87,a,819,a,b,86,a)].

given #1079 (T,wt=8): 6453 ->*_s0(length(head(empty(nil))),length(head(true))).  [ur(87,a,832,a,b,86,a)].

given #1080 (T,wt=8): 6480 ->*_s0(head(head(empty(nil))),head(head(true))).  [ur(87,a,833,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): 8097 -->_s0(true,tail(cons(x,app(app(nil,nil),false)))) # answer(goal).  [ur(7166,b,85,a,c,5074,a)].

given #1083 (F,wt=10): 8098 -->_s0(true,tail(cons(x,leq(s(y),length(nil))))) # answer(goal).  [ur(7166,b,85,a,c,4513,a)].

given #1084 (F,wt=10): 8100 -->_s0(true,tail(cons(x,sndsplit(app(nil,0),false)))) # answer(goal).  [ur(7166,b,85,a,c,3308,a)].

given #1085 (F,wt=10): 8105 -->_s0(true,tail(cons(x,app(nil,app(nil,false))))) # answer(goal).  [ur(7166,b,85,a,c,702,a)].

given #1086 (T,wt=8): 6507 ->*_s0(empty(head(empty(nil))),empty(head(true))).  [ur(87,a,836,a,b,86,a)].

given #1087 (T,wt=8): 6565 ->*_s0(s(empty(empty(nil))),s(empty(true))).  [ur(87,a,840,a,b,86,a)].

given #1088 (T,wt=8): 6592 ->*_s0(tail(empty(empty(nil))),tail(empty(true))).  [ur(87,a,845,a,b,86,a)].

given #1089 (T,wt=8): 6619 ->*_s0(length(empty(empty(nil))),length(empty(true))).  [ur(87,a,858,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=10): 8107 -->_s0(true,tail(cons(x,sndsplit(0,app(nil,false))))) # answer(goal).  [ur(7166,b,85,a,c,700,a)].

given #1092 (F,wt=10): 8109 -->_s0(true,tail(cons(x,app(nil,sndsplit(0,false))))) # answer(goal).  [ur(7166,b,85,a,c,643,a)].

given #1093 (F,wt=10): 8111 -->_s0(true,tail(cons(x,sndsplit(0,sndsplit(0,false))))) # answer(goal).  [ur(7166,b,85,a,c,641,a)].

given #1094 (F,wt=10): 8119 -->_s0(true,sndsplit(s(app(nil,0)),cons(x,false))) # answer(goal).  [ur(7166,b,83,a,c,3308,a)].

given #1095 (T,wt=8): 6646 ->*_s0(head(empty(empty(nil))),head(empty(true))).  [ur(87,a,859,a,b,86,a)].

given #1096 (T,wt=8): 6724 ->*_s0(empty(empty(empty(nil))),empty(empty(true))).  [ur(87,a,862,a,b,86,a)].

given #1097 (T,wt=8): 6751 ->*_s0(s(s(length(nil))),s(s(0))).  [ur(87,a,897,a,b,86,a)].

given #1098 (T,wt=8): 6778 ->*_s0(tail(s(length(nil))),tail(s(0))).  [ur(87,a,902,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): 8122 -->_s0(true,sndsplit(s(0),cons(x,app(nil,false)))) # answer(goal).  [ur(7166,b,83,a,c,700,a)].

given #1101 (F,wt=10): 8123 -->_s0(true,sndsplit(s(0),cons(x,sndsplit(0,false)))) # answer(goal).  [ur(7166,b,83,a,c,641,a)].

given #1102 (F,wt=10): 8129 -->_s0(true,sndsplit(0,leq(s(s(x)),s(0)))) # answer(goal).  [ur(7166,b,82,a,c,1078,a)].

given #1103 (F,wt=10): 8130 -->_s0(true,sndsplit(0,sndsplit(0,leq(s(x),0)))) # answer(goal).  [ur(7166,b,82,a,c,1077,a)].

given #1104 (T,wt=8): 6805 ->*_s0(length(s(length(nil))),length(s(0))).  [ur(87,a,915,a,b,86,a)].

given #1105 (T,wt=8): 6876 ->*_s0(head(s(length(nil))),head(s(0))).  [ur(87,a,916,a,b,86,a)].

given #1106 (T,wt=8): 6903 ->*_s0(empty(s(length(nil))),empty(s(0))).  [ur(87,a,919,a,b,86,a)].

given #1107 (T,wt=8): 6930 ->*_s0(s(tail(length(nil))),s(tail(0))).  [ur(87,a,923,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=10): 8131 -->_s0(true,sndsplit(0,sndsplit(0,tail(cons(x,false))))) # answer(goal).  [ur(7166,b,82,a,c,1066,a)].

given #1110 (F,wt=10): 8132 -->_s0(true,sndsplit(0,head(cons(app(nil,false),x)))) # answer(goal).  [ur(7166,b,82,a,c,701,a)].

given #1111 (F,wt=10): 8134 -->_s0(true,sndsplit(0,tail(cons(x,app(nil,false))))) # answer(goal).  [ur(7166,b,82,a,c,699,a)].

given #1112 (F,wt=10): 8135 -->_s0(true,sndsplit(0,head(cons(sndsplit(0,false),x)))) # answer(goal).  [ur(7166,b,82,a,c,642,a)].

given #1113 (T,wt=8): 6957 ->*_s0(tail(tail(length(nil))),tail(tail(0))).  [ur(87,a,928,a,b,86,a)].

given #1114 (T,wt=8): 7032 ->*_s0(length(tail(length(nil))),length(tail(0))).  [ur(87,a,941,a,b,86,a)].

given #1115 (T,wt=8): 7059 ->*_s0(head(tail(length(nil))),head(tail(0))).  [ur(87,a,942,a,b,86,a)].

given #1116 (T,wt=8): 7086 ->*_s0(empty(tail(length(nil))),empty(tail(0))).  [ur(87,a,945,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): 8137 -->_s0(true,sndsplit(0,sndsplit(s(0),cons(x,false)))) # answer(goal).  [ur(7166,b,82,a,c,640,a)].

given #1119 (F,wt=10): 8138 -->_s0(true,sndsplit(0,tail(cons(x,sndsplit(0,false))))) # answer(goal).  [ur(7166,b,82,a,c,639,a)].

given #1120 (F,wt=10): 8141 -->_s0(true,leq(s(s(s(x))),s(s(0)))) # answer(goal).  [ur(7166,b,72,a,c,1078,a)].

given #1121 (F,wt=10): 8142 -->_s0(true,head(cons(app(app(nil,nil),false),x))) # answer(goal).  [ur(7166,b,67,a,c,5074,a)].

given #1122 (T,wt=8): 7113 ->*_s0(s(length(length(nil))),s(length(0))).  [ur(87,a,949,a,b,86,a)].

given #1123 (T,wt=8): 7168 ->*_s0(tail(length(length(nil))),tail(length(0))).  [ur(87,a,954,a,b,86,a)].

given #1124 (T,wt=8): 7195 ->*_s0(length(length(length(nil))),length(length(0))).  [ur(87,a,967,a,b,86,a)].

given #1125 (T,wt=8): 7222 ->*_s0(head(length(length(nil))),head(length(0))).  [ur(87,a,968,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): 8143 -->_s0(true,head(cons(leq(s(x),length(nil)),y))) # answer(goal).  [ur(7166,b,67,a,c,4513,a)].

given #1128 (F,wt=10): 8145 -->_s0(true,head(cons(sndsplit(app(nil,0),false),x))) # answer(goal).  [ur(7166,b,67,a,c,3308,a)].

given #1129 (F,wt=10): 8150 -->_s0(true,head(cons(app(nil,app(nil,false)),x))) # answer(goal).  [ur(7166,b,67,a,c,702,a)].

given #1130 (F,wt=10): 8152 -->_s0(true,head(cons(sndsplit(0,app(nil,false)),x))) # answer(goal).  [ur(7166,b,67,a,c,700,a)].

given #1131 (T,wt=8): 7249 ->*_s0(empty(length(length(nil))),empty(length(0))).  [ur(87,a,971,a,b,86,a)].

given #1132 (T,wt=8): 7304 ->*_s0(s(head(length(nil))),s(head(0))).  [ur(87,a,975,a,b,86,a)].

given #1133 (T,wt=8): 7331 ->*_s0(tail(head(length(nil))),tail(head(0))).  [ur(87,a,980,a,b,86,a)].

given #1134 (T,wt=8): 7358 ->*_s0(length(head(length(nil))),length(head(0))).  [ur(87,a,993,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): 8154 -->_s0(true,head(cons(app(nil,sndsplit(0,false)),x))) # answer(goal).  [ur(7166,b,67,a,c,643,a)].

given #1137 (F,wt=10): 8156 -->_s0(true,head(cons(sndsplit(0,sndsplit(0,false)),x))) # answer(goal).  [ur(7166,b,67,a,c,641,a)].

given #1138 (F,wt=10): 8167 -->_s0(true,app(nil,leq(s(s(x)),s(0)))) # answer(goal).  [ur(7166,b,61,a,c,1078,a)].

given #1139 (F,wt=10): 8168 -->_s0(true,app(nil,sndsplit(0,leq(s(x),0)))) # answer(goal).  [ur(7166,b,61,a,c,1077,a)].

given #1140 (T,wt=8): 7385 ->*_s0(head(head(length(nil))),head(head(0))).  [ur(87,a,994,a,b,86,a)].

given #1141 (T,wt=8): 7439 ->*_s0(empty(head(length(nil))),empty(head(0))).  [ur(87,a,997,a,b,86,a)].

given #1142 (T,wt=8): 7466 ->*_s0(s(empty(length(nil))),s(empty(0))).  [ur(87,a,1035,a,b,86,a)].

given #1143 (T,wt=8): 7493 ->*_s0(tail(empty(length(nil))),tail(empty(0))).  [ur(87,a,1040,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): 8169 -->_s0(true,app(nil,sndsplit(0,tail(cons(x,false))))) # answer(goal).  [ur(7166,b,61,a,c,1066,a)].

given #1146 (F,wt=10): 8170 -->_s0(true,app(nil,head(cons(app(nil,false),x)))) # answer(goal).  [ur(7166,b,61,a,c,701,a)].

given #1147 (F,wt=10): 8172 -->_s0(true,app(nil,tail(cons(x,app(nil,false))))) # answer(goal).  [ur(7166,b,61,a,c,699,a)].

given #1148 (F,wt=10): 8173 -->_s0(true,app(nil,head(cons(sndsplit(0,false),x)))) # answer(goal).  [ur(7166,b,61,a,c,642,a)].

given #1149 (T,wt=8): 7520 ->*_s0(length(empty(length(nil))),length(empty(0))).  [ur(87,a,1053,a,b,86,a)].

given #1150 (T,wt=8): 7568 ->*_s0(head(empty(length(nil))),head(empty(0))).  [ur(87,a,1054,a,b,86,a)].

given #1151 (T,wt=8): 7595 ->*_s0(empty(empty(length(nil))),empty(empty(0))).  [ur(87,a,1057,a,b,86,a)].

given #1152 (T,wt=8): 8779 ->*_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): 8175 -->_s0(true,app(nil,sndsplit(s(0),cons(x,false)))) # answer(goal).  [ur(7166,b,61,a,c,640,a)].

given #1155 (F,wt=10): 8176 -->_s0(true,app(nil,tail(cons(x,sndsplit(0,false))))) # answer(goal).  [ur(7166,b,61,a,c,639,a)].

given #1156 (F,wt=10): 8191 -->_s0(true,app(app(nil,nil),leq(s(x),0))) # answer(goal).  [ur(7166,b,138,a,c,1080,a)].

given #1157 (F,wt=10): 8192 -->_s0(true,app(nil,app(nil,leq(s(x),0)))) # answer(goal).  [ur(7166,b,137,a,c,1080,a)].

given #1158 (T,wt=8): 9465 ->*_s0(fstsplit(s(x),fstsplit(0,y)),nil).  [ur(87,a,209,a,b,576,a)].

given #1159 (T,wt=8): 9698 ->*_s0(app(fstsplit(0,x),empty(nil)),true).  [ur(87,a,213,a,b,636,a)].

given #1160 (T,wt=8): 9699 ->*_s0(app(fstsplit(0,x),length(nil)),0).  [ur(87,a,213,a,b,630,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): 8217 -->_s0(true,sndsplit(app(nil,0),head(cons(false,x)))) # answer(goal).  [ur(7166,b,121,a,c,1121,a)].

given #1164 (F,wt=10): 8218 -->_s0(true,sndsplit(0,app(nil,head(cons(false,x))))) # answer(goal).  [ur(7166,b,120,a,c,1121,a)].

given #1165 (F,wt=10): 8221 -->_s0(true,sndsplit(0,sndsplit(0,head(cons(false,x))))) # answer(goal).  [ur(7166,b,82,a,c,1121,a)].

given #1166 (F,wt=10): 8223 -->_s0(true,app(nil,sndsplit(0,head(cons(false,x))))) # answer(goal).  [ur(7166,b,61,a,c,1121,a)].

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): 8240 -->_s0(true,app(app(nil,nil),head(cons(false,x)))) # answer(goal).  [ur(7166,b,138,a,c,1123,a)].

given #1173 (F,wt=10): 8241 -->_s0(true,app(nil,app(nil,head(cons(false,x))))) # answer(goal).  [ur(7166,b,137,a,c,1123,a)].

given #1174 (F,wt=10): 8273 -->_s0(true,length(nil)) | -->_s0(0,x) | -->*_s0(x,false) # answer(goal).  [resolve(7973,b,87,c)].

given #1175 (F,wt=7): 11304 -->_s0(true,length(nil)) | -->_s0(0,false) # answer(goal).  [resolve(8273,c,86,a)].

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=9): 11297 -->_s0(true,length(nil)) | -->_s0(0,app(nil,false)) # answer(goal).  [resolve(8273,c,581,a)].

given #1182 (F,wt=9): 11301 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(0,false)) # answer(goal).  [resolve(8273,c,567,a)].

given #1183 (F,wt=10): 8280 -->_s0(true,sndsplit(0,sndsplit(0,empty(cons(x,y))))) # answer(goal).  [resolve(1133,a,7962,b)].

given #1184 (F,wt=10): 8295 -->_s0(true,sndsplit(0,app(nil,empty(cons(x,y))))) # answer(goal).  [ur(7166,b,120,a,c,1133,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): 8299 -->_s0(true,app(nil,sndsplit(0,empty(cons(x,y))))) # answer(goal).  [ur(7166,b,61,a,c,1133,a)].

given #1191 (F,wt=10): 8311 -->_s0(true,app(nil,app(nil,empty(cons(x,y))))) # answer(goal).  [ur(7166,b,137,a,c,1135,a)].

given #1192 (F,wt=10): 8698 -->_s0(true,app(nil,tail(app(nil,cons(x,false))))) # answer(goal).  [resolve(1339,a,7979,b)].

given #1193 (F,wt=10): 8699 -->_s0(true,sndsplit(0,tail(app(nil,cons(x,false))))) # answer(goal).  [resolve(1339,a,7962,b)].

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): 8720 -->_s0(true,tail(sndsplit(0,app(nil,cons(x,false))))) # answer(goal).  [ur(7166,b,469,a,c,1339,a)].

given #1200 (F,wt=10): 8722 -->_s0(true,tail(app(nil,app(nil,cons(x,false))))) # answer(goal).  [ur(7166,b,119,a,c,1339,a)].

given #1201 (F,wt=10): 8822 -->_s0(true,app(nil,head(app(nil,cons(false,x))))) # answer(goal).  [resolve(1516,a,7979,b)].

given #1202 (F,wt=10): 8823 -->_s0(true,sndsplit(0,head(app(nil,cons(false,x))))) # answer(goal).  [resolve(1516,a,7962,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): 11430 ->*_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): 8844 -->_s0(true,head(sndsplit(0,app(nil,cons(false,x))))) # answer(goal).  [ur(7166,b,483,a,c,1516,a)].

given #1209 (F,wt=10): 8846 -->_s0(true,head(app(nil,app(nil,cons(false,x))))) # answer(goal).  [ur(7166,b,133,a,c,1516,a)].

given #1210 (F,wt=10): 8890 -->_s0(true,app(nil,empty(app(nil,cons(x,y))))) # answer(goal).  [resolve(1546,a,7979,b)].

given #1211 (F,wt=10): 8891 -->_s0(true,sndsplit(0,empty(app(nil,cons(x,y))))) # answer(goal).  [resolve(1546,a,7962,b)].

given #1212 (T,wt=8): 11455 ->*_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): 11470 ->*_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): 8910 -->_s0(true,empty(sndsplit(0,app(nil,cons(x,y))))) # answer(goal).  [ur(7166,b,486,a,c,1546,a)].

given #1218 (F,wt=10): 8912 -->_s0(true,empty(app(nil,app(nil,cons(x,y))))) # answer(goal).  [ur(7166,b,136,a,c,1546,a)].

given #1219 (F,wt=10): 9133 -->_s0(true,app(nil,tail(sndsplit(0,cons(x,false))))) # answer(goal).  [resolve(2235,a,7979,b)].

given #1220 (F,wt=10): 9135 -->_s0(true,sndsplit(0,tail(sndsplit(0,cons(x,false))))) # answer(goal).  [resolve(2235,a,7962,b)].

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): 11523 ->*_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): 9155 -->_s0(true,tail(sndsplit(0,sndsplit(0,cons(x,false))))) # answer(goal).  [ur(7166,b,469,a,c,2235,a)].

given #1227 (F,wt=10): 9157 -->_s0(true,tail(app(nil,sndsplit(0,cons(x,false))))) # answer(goal).  [ur(7166,b,119,a,c,2235,a)].

given #1228 (F,wt=10): 9297 -->_s0(true,app(nil,head(sndsplit(0,cons(false,x))))) # answer(goal).  [resolve(2304,a,7979,b)].

given #1229 (F,wt=10): 9299 -->_s0(true,sndsplit(0,head(sndsplit(0,cons(false,x))))) # answer(goal).  [resolve(2304,a,7962,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): 11605 ->*_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=9): 11562 -->_s0(true,app(mapf(x,nil),sndsplit(0,false))) # answer(goal).  [resolve(463,a,8018,b)].

given #1236 (F,wt=9): 11563 -->_s0(true,app(mapf(x,nil),app(nil,false))) # answer(goal).  [resolve(463,a,8014,b)].

given #1237 (F,wt=9): 11618 -->_s0(true,app(nil,app(mapf(x,nil),false))) # answer(goal).  [resolve(11605,a,7979,b)].

given #1238 (F,wt=9): 11620 -->_s0(true,sndsplit(0,app(mapf(x,nil),false))) # answer(goal).  [resolve(11605,a,7962,b)].

given #1239 (T,wt=8): 11603 ->*_s0(app(mapf(x,nil),empty(nil)),true).  [ur(87,a,463,a,b,636,a)].

given #1240 (T,wt=8): 11604 ->*_s0(app(mapf(x,nil),length(nil)),0).  [ur(87,a,463,a,b,630,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=9): 11636 -->_s0(true,app(app(nil,mapf(x,nil)),false)) # answer(goal).  [ur(7166,b,138,a,c,11605,a)].

given #1245 (F,wt=10): 9319 -->_s0(true,head(sndsplit(0,sndsplit(0,cons(false,x))))) # answer(goal).  [ur(7166,b,483,a,c,2304,a)].

given #1246 (F,wt=10): 9321 -->_s0(true,head(app(nil,sndsplit(0,cons(false,x))))) # answer(goal).  [ur(7166,b,133,a,c,2304,a)].

given #1247 (F,wt=10): 9417 -->_s0(true,app(nil,empty(sndsplit(0,cons(x,y))))) # answer(goal).  [resolve(2365,a,7979,b)].

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): 11730 ->*_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): 9419 -->_s0(true,sndsplit(0,empty(sndsplit(0,cons(x,y))))) # answer(goal).  [resolve(2365,a,7962,b)].

given #1254 (F,wt=10): 9437 -->_s0(true,empty(sndsplit(0,sndsplit(0,cons(x,y))))) # answer(goal).  [ur(7166,b,486,a,c,2365,a)].

given #1255 (F,wt=10): 9439 -->_s0(true,empty(app(nil,sndsplit(0,cons(x,y))))) # answer(goal).  [ur(7166,b,136,a,c,2365,a)].

given #1256 (F,wt=10): 9506 -->_s0(true,app(nil,head(app(cons(false,x),y)))) # answer(goal).  [resolve(2492,a,7979,b)].

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): 11815 ->*_s0(sndsplit(sndsplit(0,0),x),x).  [ur(87,a,471,a,b,567,a)].

given #1259 (T,wt=8): 11763 ->*_s0(sndsplit(sndsplit(0,length(nil)),x),x).  [ur(87,a,471,a,b,4340,a)].

given #1260 (T,wt=8): 11813 ->*_s0(sndsplit(sndsplit(0,0),empty(nil)),true).  [ur(87,a,471,a,b,634,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): 11751 -->_s0(true,sndsplit(sndsplit(0,0),sndsplit(0,false))) # answer(goal).  [resolve(471,a,8020,b)].

given #1263 (F,wt=9): 11752 -->_s0(true,sndsplit(sndsplit(0,0),app(nil,false))) # answer(goal).  [resolve(471,a,8016,b)].

given #1264 (F,wt=9): 11753 -->_s0(true,sndsplit(sndsplit(0,app(nil,0)),false)) # answer(goal).  [resolve(471,a,8009,b)].

given #1265 (F,wt=9): 11833 -->_s0(true,app(nil,sndsplit(sndsplit(0,0),false))) # answer(goal).  [resolve(11815,a,7979,b)].

given #1266 (T,wt=8): 11814 ->*_s0(sndsplit(sndsplit(0,0),length(nil)),0).  [ur(87,a,471,a,b,628,a)].

given #1267 (T,wt=8): 11816 ->*_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): 11922 ->*_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=9): 11835 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,0),false))) # answer(goal).  [resolve(11815,a,7962,b)].

given #1272 (F,wt=9): 11853 -->_s0(true,sndsplit(sndsplit(0,sndsplit(0,0)),false)) # answer(goal).  [ur(7166,b,471,a,c,11815,a)].

given #1273 (F,wt=9): 11854 -->_s0(true,sndsplit(app(nil,sndsplit(0,0)),false)) # answer(goal).  [ur(7166,b,121,a,c,11815,a)].

given #1274 (F,wt=10): 9508 -->_s0(true,sndsplit(0,head(app(cons(false,x),y)))) # answer(goal).  [resolve(2492,a,7962,b)].

given #1275 (T,wt=8): 11978 ->*_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): 12028 ->*_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=9): 12016 -->_s0(true,leq(s(x),sndsplit(0,length(nil)))) # answer(goal).  [resolve(480,a,8007,b)].

given #1281 (F,wt=10): 9528 -->_s0(true,head(sndsplit(0,app(cons(false,x),y)))) # answer(goal).  [ur(7166,b,483,a,c,2492,a)].

given #1282 (F,wt=10): 9530 -->_s0(true,head(app(nil,app(cons(false,x),y)))) # answer(goal).  [ur(7166,b,133,a,c,2492,a)].

given #1283 (F,wt=10): 9531 -->_s0(true,app(nil,empty(app(cons(x,y),z)))) # answer(goal).  [resolve(2658,a,7979,b)].

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): 12081 ->*_s0(leq(sndsplit(0,0),x),true).  [ur(87,a,481,a,b,572,a)].

given #1286 (T,wt=8): 12073 ->*_s0(leq(sndsplit(0,length(nil)),x),true).  [ur(87,a,481,a,b,4555,a)].

given #1287 (T,wt=8): 12082 ->*_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=9): 12064 -->_s0(true,leq(sndsplit(0,s(x)),length(nil))) # answer(goal).  [resolve(481,a,8007,b)].

given #1290 (F,wt=10): 9533 -->_s0(true,sndsplit(0,empty(app(cons(x,y),z)))) # answer(goal).  [resolve(2658,a,7962,b)].

given #1291 (F,wt=10): 9551 -->_s0(true,empty(sndsplit(0,app(cons(x,y),z)))) # answer(goal).  [ur(7166,b,486,a,c,2658,a)].

given #1292 (F,wt=10): 9553 -->_s0(true,empty(app(nil,app(cons(x,y),z)))) # answer(goal).  [ur(7166,b,136,a,c,2658,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): 12156 ->*_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): 12182 ->*_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=10): 9721 -->_s0(true,app(fstsplit(0,x),empty(cons(y,z)))) # answer(goal).  [ur(7166,b,213,a,c,1135,a)].

given #1299 (F,wt=10): 9722 -->_s0(true,app(fstsplit(0,x),head(cons(false,y)))) # answer(goal).  [ur(7166,b,213,a,c,1123,a)].

given #1300 (F,wt=10): 9723 -->_s0(true,app(fstsplit(0,x),leq(s(y),0))) # answer(goal).  [ur(7166,b,213,a,c,1080,a)].

given #1301 (F,wt=10): 9724 -->_s0(true,app(fstsplit(0,x),tail(cons(y,false)))) # answer(goal).  [ur(7166,b,213,a,c,1068,a)].

given #1302 (T,wt=8): 12178 ->*_s0(fstsplit(sndsplit(0,length(nil)),x),nil).  [ur(87,a,485,a,b,4666,a)].

given #1303 (T,wt=8): 12183 ->*_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): 12226 -->_s0(true,app(sndsplit(0,nil),sndsplit(0,false))) # answer(goal).  [resolve(488,a,8018,b)].

given #1308 (F,wt=9): 12227 -->_s0(true,app(sndsplit(0,nil),app(nil,false))) # answer(goal).  [resolve(488,a,8014,b)].

given #1309 (F,wt=9): 12228 -->_s0(true,app(sndsplit(0,app(nil,nil)),false)) # answer(goal).  [resolve(488,a,8006,b)].

given #1310 (F,wt=9): 12290 -->_s0(true,app(sndsplit(0,mapf(x,nil)),false)) # answer(goal).  [ur(7166,b,488,a,c,11605,a)].

given #1311 (T,wt=7): 12282 ->*_s0(app(sndsplit(0,nil),x),x).  [ur(87,a,488,a,b,581,a)].

given #1312 (T,wt=8): 12280 ->*_s0(app(sndsplit(0,nil),empty(nil)),true).  [ur(87,a,488,a,b,636,a)].

given #1313 (T,wt=8): 12281 ->*_s0(app(sndsplit(0,nil),length(nil)),0).  [ur(87,a,488,a,b,630,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): 12291 -->_s0(true,app(sndsplit(0,fstsplit(0,x)),false)) # answer(goal).  [ur(7166,b,488,a,c,9700,a)].

given #1317 (F,wt=9): 12304 -->_s0(true,app(nil,app(sndsplit(0,nil),false))) # answer(goal).  [resolve(12282,a,7979,b)].

given #1318 (F,wt=9): 12306 -->_s0(true,sndsplit(0,app(sndsplit(0,nil),false))) # answer(goal).  [resolve(12282,a,7962,b)].

given #1319 (F,wt=9): 12323 -->_s0(true,app(sndsplit(0,sndsplit(0,nil)),false)) # answer(goal).  [ur(7166,b,488,a,c,12282,a)].

given #1320 (T,wt=9): 1065 ->*_s0(tail(cons(x,tail(cons(y,z)))),z).  [ur(87,a,85,a,b,564,a)].

given #1321 (T,wt=9): 1067 ->*_s0(head(cons(tail(cons(x,y)),z)),y).  [ur(87,a,67,a,b,564,a)].

given #1322 (T,wt=9): 1069 ->*_s0(tail(cons(x,sndsplit(s(y),nil))),nil).  [ur(87,a,85,a,b,565,a)].

given #1323 (T,wt=9): 1070 ->*_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=9): 12324 -->_s0(true,app(app(nil,sndsplit(0,nil)),false)) # answer(goal).  [ur(7166,b,138,a,c,12282,a)].

given #1326 (F,wt=10): 9728 -->_s0(true,head(cons(app(fstsplit(0,x),false),y))) # answer(goal).  [resolve(9700,a,7975,b)].

given #1327 (F,wt=10): 9730 -->_s0(true,tail(cons(x,app(fstsplit(0,y),false)))) # answer(goal).  [resolve(9700,a,7959,b)].

given #1328 (F,wt=10): 9731 -->_s0(true,x) | -->_s0(x,app(fstsplit(0,y),false)) # answer(goal).  [resolve(9700,a,7166,c)].

given #1329 (T,wt=8): 12540 ->*_s0(sndsplit(head(cons(0,x)),y),y).  [ur(87,a,271,a,b,567,a)].

given #1330 (T,wt=9): 1072 ->*_s0(head(cons(sndsplit(s(x),nil),y)),nil).  [ur(87,a,67,a,b,565,a)].

given #1331 (T,wt=9): 1076 ->*_s0(tail(cons(x,leq(s(y),0))),false).  [ur(87,a,85,a,b,571,a)].

given #1332 (T,wt=9): 1079 ->*_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): 10143 -->_s0(true,app(nil,sndsplit(length(nil),app(nil,false)))) # answer(goal).  [resolve(4333,a,7979,b)].

given #1335 (F,wt=10): 10145 -->_s0(true,sndsplit(0,sndsplit(length(nil),app(nil,false)))) # answer(goal).  [resolve(4333,a,7962,b)].

given #1336 (F,wt=10): 10163 -->_s0(true,sndsplit(app(nil,length(nil)),app(nil,false))) # answer(goal).  [ur(7166,b,121,a,c,4333,a)].

given #1337 (F,wt=10): 10164 -->_s0(true,sndsplit(length(nil),app(nil,app(nil,false)))) # answer(goal).  [ur(7166,b,120,a,c,4333,a)].

given #1338 (T,wt=9): 1120 ->*_s0(tail(cons(x,head(cons(y,z)))),y).  [ur(87,a,85,a,b,575,a)].

given #1339 (T,wt=9): 1122 ->*_s0(head(cons(head(cons(x,y)),z)),x).  [ur(87,a,67,a,b,575,a)].

given #1340 (T,wt=9): 1124 ->*_s0(tail(cons(x,fstsplit(s(y),nil))),nil).  [ur(87,a,85,a,b,576,a)].

given #1341 (T,wt=9): 1126 ->*_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): 10195 -->_s0(true,app(nil,sndsplit(length(nil),sndsplit(0,false)))) # answer(goal).  [resolve(4337,a,7979,b)].

given #1344 (F,wt=10): 10197 -->_s0(true,sndsplit(0,sndsplit(length(nil),sndsplit(0,false)))) # answer(goal).  [resolve(4337,a,7962,b)].

given #1345 (F,wt=10): 10215 -->_s0(true,sndsplit(app(nil,length(nil)),sndsplit(0,false))) # answer(goal).  [ur(7166,b,121,a,c,4337,a)].

given #1346 (F,wt=10): 10216 -->_s0(true,sndsplit(length(nil),app(nil,sndsplit(0,false)))) # answer(goal).  [ur(7166,b,120,a,c,4337,a)].

given #1347 (T,wt=9): 1132 ->*_s0(tail(cons(x,empty(cons(y,z)))),false).  [ur(87,a,85,a,b,580,a)].

given #1348 (T,wt=9): 1134 ->*_s0(head(cons(empty(cons(x,y)),z)),false).  [ur(87,a,67,a,b,580,a)].

given #1349 (T,wt=9): 1136 ->*_s0(tail(cons(x,sndsplit(0,length(nil)))),0).  [ur(87,a,85,a,b,628,a)].

given #1350 (T,wt=9): 1137 ->*_s0(sndsplit(s(0),cons(x,length(nil))),0).  [ur(87,a,83,a,b,628,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): 10230 -->_s0(true,app(nil,sndsplit(app(nil,length(nil)),false))) # answer(goal).  [resolve(4404,a,7979,b)].

given #1353 (F,wt=10): 10232 -->_s0(true,sndsplit(0,sndsplit(app(nil,length(nil)),false))) # answer(goal).  [resolve(4404,a,7962,b)].

given #1354 (F,wt=10): 10253 -->_s0(true,sndsplit(app(nil,app(nil,length(nil))),false)) # answer(goal).  [ur(7166,b,121,a,c,4404,a)].

given #1355 (F,wt=10): 10255 -->_s0(true,app(nil,sndsplit(0,sndsplit(length(nil),false)))) # answer(goal).  [resolve(4408,a,7979,b)].

given #1356 (T,wt=9): 1139 ->*_s0(head(cons(sndsplit(0,length(nil)),x)),0).  [ur(87,a,67,a,b,628,a)].

given #1357 (T,wt=9): 1168 ->*_s0(tail(cons(x,app(nil,length(nil)))),0).  [ur(87,a,85,a,b,630,a)].

given #1358 (T,wt=9): 1170 ->*_s0(head(cons(app(nil,length(nil)),x)),0).  [ur(87,a,67,a,b,630,a)].

given #1359 (T,wt=9): 1175 ->*_s0(tail(cons(x,sndsplit(0,empty(nil)))),true).  [ur(87,a,85,a,b,634,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): 10257 -->_s0(true,sndsplit(0,sndsplit(0,sndsplit(length(nil),false)))) # answer(goal).  [resolve(4408,a,7962,b)].

given #1362 (F,wt=10): 10277 -->_s0(true,sndsplit(app(nil,0),sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,121,a,c,4408,a)].

given #1363 (F,wt=10): 10278 -->_s0(true,sndsplit(0,app(nil,sndsplit(length(nil),false)))) # answer(goal).  [ur(7166,b,120,a,c,4408,a)].

given #1364 (F,wt=10): 10280 -->_s0(true,app(nil,app(nil,sndsplit(length(nil),false)))) # answer(goal).  [resolve(4410,a,7979,b)].

given #1365 (T,wt=9): 1176 ->*_s0(sndsplit(s(0),cons(x,empty(nil))),true).  [ur(87,a,83,a,b,634,a)].

given #1366 (T,wt=9): 1178 ->*_s0(head(cons(sndsplit(0,empty(nil)),x)),true).  [ur(87,a,67,a,b,634,a)].

given #1367 (T,wt=9): 1183 ->*_s0(tail(cons(x,app(nil,empty(nil)))),true).  [ur(87,a,85,a,b,636,a)].

given #1368 (T,wt=9): 1185 ->*_s0(head(cons(app(nil,empty(nil)),x)),true).  [ur(87,a,67,a,b,636,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): 10297 -->_s0(true,app(fstsplit(0,x),sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,213,a,c,4410,a)].

given #1371 (F,wt=10): 10298 -->_s0(true,app(app(nil,nil),sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,138,a,c,4410,a)].

given #1372 (F,wt=10): 10312 -->_s0(true,app(nil,leq(s(x),app(nil,0)))) # answer(goal).  [resolve(4457,a,7979,b)].

given #1373 (F,wt=10): 10314 -->_s0(true,sndsplit(0,leq(s(x),app(nil,0)))) # answer(goal).  [resolve(4457,a,7962,b)].

given #1374 (T,wt=9): 1187 ->*_s0(tail(cons(x,s(empty(nil)))),s(true)).  [ur(87,a,85,a,b,703,a)].

given #1375 (T,wt=9): 1189 ->*_s0(head(cons(s(empty(nil)),x)),s(true)).  [ur(87,a,67,a,b,703,a)].

given #1376 (T,wt=9): 1219 ->*_s0(tail(cons(x,tail(empty(nil)))),tail(true)).  [ur(87,a,85,a,b,761,a)].

given #1377 (T,wt=9): 1221 ->*_s0(head(cons(tail(empty(nil)),x)),tail(true)).  [ur(87,a,67,a,b,761,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): 10328 -->_s0(true,leq(app(nil,s(x)),app(nil,0))) # answer(goal).  [ur(7166,b,131,a,c,4457,a)].

given #1380 (F,wt=10): 10329 -->_s0(true,leq(s(x),app(nil,app(nil,0)))) # answer(goal).  [ur(7166,b,130,a,c,4457,a)].

given #1381 (F,wt=10): 10330 -->_s0(true,leq(s(s(x)),s(app(nil,0)))) # answer(goal).  [ur(7166,b,72,a,c,4457,a)].

given #1382 (F,wt=10): 10366 -->_s0(true,app(nil,leq(app(nil,s(x)),0))) # answer(goal).  [resolve(4587,a,7979,b)].

given #1383 (T,wt=9): 1223 ->*_s0(tail(cons(x,length(empty(nil)))),length(true)).  [ur(87,a,85,a,b,787,a)].

given #1384 (T,wt=9): 1225 ->*_s0(head(cons(length(empty(nil)),x)),length(true)).  [ur(87,a,67,a,b,787,a)].

given #1385 (T,wt=9): 1227 ->*_s0(tail(cons(x,head(empty(nil)))),head(true)).  [ur(87,a,85,a,b,813,a)].

given #1386 (T,wt=9): 1229 ->*_s0(head(cons(head(empty(nil)),x)),head(true)).  [ur(87,a,67,a,b,813,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): 10368 -->_s0(true,sndsplit(0,leq(app(nil,s(x)),0))) # answer(goal).  [resolve(4587,a,7962,b)].

given #1389 (F,wt=10): 10381 -->_s0(true,leq(app(nil,app(nil,s(x))),0)) # answer(goal).  [ur(7166,b,131,a,c,4587,a)].

given #1390 (F,wt=10): 10382 -->_s0(true,leq(s(app(nil,s(x))),s(0))) # answer(goal).  [ur(7166,b,72,a,c,4587,a)].

given #1391 (F,wt=10): 10562 -->_s0(true,app(app(nil,nil),x)) | -->_s0(x,false) # answer(goal).  [resolve(8006,b,36,b)].

given #1392 (T,wt=8): 12828 ->*_s0(mapf(x,head(cons(nil,y))),nil).  [ur(87,a,278,a,b,568,a)].

given #1393 (T,wt=9): 1231 ->*_s0(tail(cons(x,empty(empty(nil)))),empty(true)).  [ur(87,a,85,a,b,839,a)].

given #1394 (T,wt=9): 1233 ->*_s0(head(cons(empty(empty(nil)),x)),empty(true)).  [ur(87,a,67,a,b,839,a)].

given #1395 (T,wt=9): 1261 ->*_s0(tail(cons(x,s(length(nil)))),s(0)).  [ur(87,a,85,a,b,896,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): 10563 -->_s0(true,app(x,false)) | -->_s0(x,app(nil,nil)) # answer(goal).  [resolve(8006,b,35,b)].

given #1398 (F,wt=9): 12855 -->_s0(true,app(app(sndsplit(0,nil),nil),false)) # answer(goal).  [resolve(10563,b,488,a)].

given #1399 (F,wt=9): 12856 -->_s0(true,app(app(mapf(x,nil),nil),false)) # answer(goal).  [resolve(10563,b,463,a)].

given #1400 (F,wt=9): 12858 -->_s0(true,app(app(fstsplit(0,x),nil),false)) # answer(goal).  [resolve(10563,b,213,a)].

given #1401 (T,wt=9): 1264 ->*_s0(head(cons(s(length(nil)),x)),s(0)).  [ur(87,a,67,a,b,896,a)].

given #1402 (T,wt=9): 1266 ->*_s0(tail(cons(x,tail(length(nil)))),tail(0)).  [ur(87,a,85,a,b,922,a)].

given #1403 (T,wt=9): 1268 ->*_s0(head(cons(tail(length(nil)),x)),tail(0)).  [ur(87,a,67,a,b,922,a)].

given #1404 (T,wt=9): 1270 ->*_s0(tail(cons(x,length(length(nil)))),length(0)).  [ur(87,a,85,a,b,948,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=9): 12859 -->_s0(true,app(app(app(nil,nil),nil),false)) # answer(goal).  [resolve(10563,b,138,a)].

given #1407 (F,wt=10): 10599 -->_s0(true,leq(s(x),y)) | -->_s0(y,length(nil)) # answer(goal).  [resolve(8007,b,43,b)].

given #1408 (F,wt=9): 12903 -->_s0(true,leq(s(x),length(sndsplit(0,nil)))) # answer(goal).  [resolve(10599,b,482,a)].

given #1409 (F,wt=9): 12904 -->_s0(true,leq(s(x),length(mapf(y,nil)))) # answer(goal).  [resolve(10599,b,457,a)].

given #1410 (T,wt=9): 1272 ->*_s0(head(cons(length(length(nil)),x)),length(0)).  [ur(87,a,67,a,b,948,a)].

given #1411 (T,wt=9): 1274 ->*_s0(tail(cons(x,head(length(nil)))),head(0)).  [ur(87,a,85,a,b,974,a)].

given #1412 (T,wt=9): 1276 ->*_s0(head(cons(head(length(nil)),x)),head(0)).  [ur(87,a,67,a,b,974,a)].

given #1413 (T,wt=9): 1305 ->*_s0(tail(cons(x,empty(length(nil)))),empty(0)).  [ur(87,a,85,a,b,1034,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=9): 12907 -->_s0(true,leq(s(x),length(fstsplit(0,y)))) # answer(goal).  [resolve(10599,b,207,a)].

given #1416 (F,wt=9): 12908 -->_s0(true,leq(s(x),length(app(nil,nil)))) # answer(goal).  [resolve(10599,b,132,a)].

given #1417 (F,wt=10): 10600 -->_s0(true,leq(x,length(nil))) | -->_s0(x,s(y)) # answer(goal).  [resolve(8007,b,42,b)].

given #1418 (F,wt=9): 12956 -->_s0(true,leq(length(cons(x,y)),length(nil))) # answer(goal).  [resolve(10600,b,68,a)].

given #1419 (T,wt=8): 12947 ->*_s0(leq(head(cons(0,x)),y),true).  [ur(87,a,281,a,b,572,a)].

given #1420 (T,wt=9): 1307 ->*_s0(head(cons(empty(length(nil)),x)),empty(0)).  [ur(87,a,67,a,b,1034,a)].

given #1421 (T,wt=9): 1312 ->_s0(s(s(app(nil,x))),s(s(x))).  [ur(59,a,114,a)].

given #1422 (T,wt=9): 1317 ->_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): 10601 -->_s0(true,sndsplit(app(nil,0),x)) | -->_s0(x,false) # answer(goal).  [resolve(8009,b,53,b)].

given #1425 (F,wt=10): 10602 -->_s0(true,sndsplit(x,false)) | -->_s0(x,app(nil,0)) # answer(goal).  [resolve(8009,b,52,b)].

given #1426 (F,wt=9): 13007 -->_s0(true,sndsplit(app(sndsplit(0,nil),0),false)) # answer(goal).  [resolve(10602,b,488,a)].

given #1427 (F,wt=9): 13008 -->_s0(true,sndsplit(app(mapf(x,nil),0),false)) # answer(goal).  [resolve(10602,b,463,a)].

given #1428 (T,wt=9): 1330 ->_s0(length(s(app(nil,x))),length(s(x))).  [ur(41,a,114,a)].

given #1429 (T,wt=9): 1331 ->_s0(head(s(app(nil,x))),head(s(x))).  [ur(40,a,114,a)].

given #1430 (T,wt=9): 1334 ->_s0(empty(s(app(nil,x))),empty(s(x))).  [ur(37,a,114,a)].

given #1431 (T,wt=9): 1341 ->_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): 13010 -->_s0(true,sndsplit(app(fstsplit(0,x),0),false)) # answer(goal).  [resolve(10602,b,213,a)].

given #1434 (F,wt=9): 13011 -->_s0(true,sndsplit(app(app(nil,nil),0),false)) # answer(goal).  [resolve(10602,b,138,a)].

given #1435 (F,wt=10): 10603 -->_s0(true,app(nil,x)) | -->_s0(x,app(nil,false)) # answer(goal).  [resolve(8014,b,36,b)].

given #1436 (F,wt=10): 10604 -->_s0(true,app(x,app(nil,false))) | -->_s0(x,nil) # answer(goal).  [resolve(8014,b,35,b)].

given #1437 (T,wt=8): 13068 ->*_s0(fstsplit(head(cons(0,x)),y),nil).  [ur(87,a,285,a,b,578,a)].

given #1438 (T,wt=9): 1346 ->_s0(tail(tail(app(nil,x))),tail(tail(x))).  [ur(54,a,119,a)].

given #1439 (T,wt=9): 1359 ->_s0(length(tail(app(nil,x))),length(tail(x))).  [ur(41,a,119,a)].

given #1440 (T,wt=9): 1360 ->_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): 10605 -->_s0(true,sndsplit(0,x)) | -->_s0(x,app(nil,false)) # answer(goal).  [resolve(8016,b,53,b)].

given #1443 (F,wt=10): 10606 -->_s0(true,sndsplit(x,app(nil,false))) | -->_s0(x,0) # answer(goal).  [resolve(8016,b,52,b)].

given #1444 (F,wt=10): 10639 -->_s0(true,app(nil,x)) | -->_s0(x,sndsplit(0,false)) # answer(goal).  [resolve(8018,b,36,b)].

given #1445 (F,wt=10): 10640 -->_s0(true,app(x,sndsplit(0,false))) | -->_s0(x,nil) # answer(goal).  [resolve(8018,b,35,b)].

given #1446 (T,wt=9): 1363 ->_s0(empty(tail(app(nil,x))),empty(tail(x))).  [ur(37,a,119,a)].

given #1447 (T,wt=9): 1370 ->_s0(s(length(app(nil,x))),s(length(x))).  [ur(59,a,132,a)].

given #1448 (T,wt=8): 13163 ->*_s0(s(length(app(nil,nil))),s(0)).  [ur(87,a,1370,a,b,896,a)].

given #1449 (T,wt=9): 1375 ->_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): 10641 -->_s0(true,sndsplit(0,x)) | -->_s0(x,sndsplit(0,false)) # answer(goal).  [resolve(8020,b,53,b)].

given #1452 (F,wt=10): 10642 -->_s0(true,sndsplit(x,sndsplit(0,false))) | -->_s0(x,0) # answer(goal).  [resolve(8020,b,52,b)].

given #1453 (F,wt=10): 10683 -->_s0(true,app(nil,tail(app(cons(x,nil),false)))) # answer(goal).  [resolve(5690,a,7979,b)].

given #1454 (F,wt=10): 10685 -->_s0(true,sndsplit(0,tail(app(cons(x,nil),false)))) # answer(goal).  [resolve(5690,a,7962,b)].

given #1455 (T,wt=8): 13183 ->*_s0(tail(length(app(nil,nil))),tail(0)).  [ur(87,a,1375,a,b,922,a)].

given #1456 (T,wt=8): 13251 ->*_s0(app(head(cons(nil,x)),y),y).  [ur(87,a,288,a,b,581,a)].

given #1457 (T,wt=9): 1388 ->_s0(length(length(app(nil,x))),length(length(x))).  [ur(41,a,132,a)].

given #1458 (T,wt=8): 13297 ->*_s0(length(length(app(nil,nil))),length(0)).  [ur(87,a,1388,a,b,948,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=10): 10687 -->_s0(true,tail(app(nil,app(cons(x,nil),false)))) # answer(goal).  [resolve(5690,a,7928,b)].

given #1461 (F,wt=10): 10688 -->_s0(true,tail(sndsplit(0,app(cons(x,nil),false)))) # answer(goal).  [resolve(5690,a,7814,b)].

given #1462 (F,wt=10): 11267 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(length(nil),false)) # answer(goal).  [resolve(8273,c,4340,a)].

given #1463 (F,wt=10): 11298 -->_s0(true,length(nil)) | -->_s0(0,empty(cons(x,y))) # answer(goal).  [resolve(8273,c,580,a)].

given #1464 (T,wt=9): 1389 ->_s0(head(length(app(nil,x))),head(length(x))).  [ur(40,a,132,a)].

given #1465 (T,wt=8): 13319 ->*_s0(head(length(app(nil,nil))),head(0)).  [ur(87,a,1389,a,b,974,a)].

given #1466 (T,wt=9): 1392 ->_s0(empty(length(app(nil,x))),empty(length(x))).  [ur(37,a,132,a)].

given #1467 (T,wt=8): 13338 ->*_s0(empty(length(app(nil,nil))),empty(0)).  [ur(87,a,1392,a,b,1034,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): 11299 -->_s0(true,length(nil)) | -->_s0(0,head(cons(false,x))) # answer(goal).  [resolve(8273,c,575,a)].

given #1470 (F,wt=10): 11300 -->_s0(true,length(nil)) | -->_s0(0,leq(s(x),0)) # answer(goal).  [resolve(8273,c,571,a)].

given #1471 (F,wt=10): 11302 -->_s0(true,length(nil)) | -->_s0(0,tail(cons(x,false))) # answer(goal).  [resolve(8273,c,564,a)].

given #1472 (F,wt=10): 11612 -->_s0(true,app(mapf(x,nil),sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,463,a,c,4410,a)].

given #1473 (T,wt=9): 1509 ->*_s0(tail(cons(x,length(app(nil,nil)))),0).  [ur(87,a,85,a,b,1368,a)].

given #1474 (T,wt=9): 1511 ->*_s0(head(cons(length(app(nil,nil)),x)),0).  [ur(87,a,67,a,b,1368,a)].

given #1475 (T,wt=9): 1518 ->_s0(s(head(app(nil,x))),s(head(x))).  [ur(59,a,133,a)].

given #1476 (T,wt=9): 1523 ->_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=10): 11613 -->_s0(true,app(mapf(x,nil),empty(cons(y,z)))) # answer(goal).  [ur(7166,b,463,a,c,1135,a)].

given #1479 (F,wt=10): 11614 -->_s0(true,app(mapf(x,nil),head(cons(false,y)))) # answer(goal).  [ur(7166,b,463,a,c,1123,a)].

given #1480 (F,wt=10): 11615 -->_s0(true,app(mapf(x,nil),leq(s(y),0))) # answer(goal).  [ur(7166,b,463,a,c,1080,a)].

given #1481 (F,wt=10): 11616 -->_s0(true,app(mapf(x,nil),tail(cons(y,false)))) # answer(goal).  [ur(7166,b,463,a,c,1068,a)].

given #1482 (T,wt=9): 1536 ->_s0(length(head(app(nil,x))),length(head(x))).  [ur(41,a,133,a)].

given #1483 (T,wt=9): 1537 ->_s0(head(head(app(nil,x))),head(head(x))).  [ur(40,a,133,a)].

given #1484 (T,wt=9): 1540 ->_s0(empty(head(app(nil,x))),empty(head(x))).  [ur(37,a,133,a)].

given #1485 (T,wt=9): 1549 ->_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): 11619 -->_s0(true,head(cons(app(mapf(x,nil),false),y))) # answer(goal).  [resolve(11605,a,7975,b)].

given #1488 (F,wt=10): 11621 -->_s0(true,tail(cons(x,app(mapf(y,nil),false)))) # answer(goal).  [resolve(11605,a,7959,b)].

given #1489 (F,wt=10): 11622 -->_s0(true,x) | -->_s0(x,app(mapf(y,nil),false)) # answer(goal).  [resolve(11605,a,7166,c)].

given #1490 (F,wt=10): 11737 -->_s0(true,sndsplit(length(nil),sndsplit(0,sndsplit(0,false)))) # answer(goal).  [ur(7166,b,470,a,c,4337,a)].

given #1491 (T,wt=8): 13419 ->*_s0(s(empty(app(nil,nil))),s(true)).  [ur(87,a,1549,a,b,703,a)].

given #1492 (T,wt=9): 1554 ->_s0(tail(empty(app(nil,x))),tail(empty(x))).  [ur(54,a,136,a)].

given #1493 (T,wt=8): 13442 ->*_s0(tail(empty(app(nil,nil))),tail(true)).  [ur(87,a,1554,a,b,761,a)].

given #1494 (T,wt=9): 1567 ->_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): 11738 -->_s0(true,sndsplit(length(nil),sndsplit(0,app(nil,false)))) # answer(goal).  [ur(7166,b,470,a,c,4333,a)].

given #1497 (F,wt=10): 11739 -->_s0(true,sndsplit(s(0),sndsplit(0,cons(x,false)))) # answer(goal).  [ur(7166,b,470,a,c,640,a)].

given #1498 (F,wt=10): 11823 -->_s0(true,sndsplit(sndsplit(0,0),sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,471,a,c,4408,a)].

given #1499 (F,wt=10): 11824 -->_s0(true,sndsplit(sndsplit(0,app(nil,length(nil))),false)) # answer(goal).  [ur(7166,b,471,a,c,4404,a)].

given #1500 (T,wt=8): 13462 ->*_s0(length(empty(app(nil,nil))),length(true)).  [ur(87,a,1567,a,b,787,a)].

given #1501 (T,wt=9): 1568 ->_s0(head(empty(app(nil,x))),head(empty(x))).  [ur(40,a,136,a)].

given #1502 (T,wt=8): 13483 ->*_s0(head(empty(app(nil,nil))),head(true)).  [ur(87,a,1568,a,b,813,a)].

given #1503 (T,wt=9): 1571 ->_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): 11825 -->_s0(true,sndsplit(sndsplit(0,length(nil)),sndsplit(0,false))) # answer(goal).  [ur(7166,b,471,a,c,4337,a)].

given #1506 (F,wt=10): 11826 -->_s0(true,sndsplit(sndsplit(0,length(nil)),app(nil,false))) # answer(goal).  [ur(7166,b,471,a,c,4333,a)].

given #1507 (F,wt=10): 11827 -->_s0(true,sndsplit(sndsplit(0,0),empty(cons(x,y)))) # answer(goal).  [ur(7166,b,471,a,c,1133,a)].

given #1508 (F,wt=10): 11828 -->_s0(true,sndsplit(sndsplit(0,0),head(cons(false,x)))) # answer(goal).  [ur(7166,b,471,a,c,1121,a)].

given #1509 (T,wt=8): 13503 ->*_s0(empty(empty(app(nil,nil))),empty(true)).  [ur(87,a,1571,a,b,839,a)].

given #1510 (T,wt=9): 1578 ->*_s0(tail(cons(x,empty(app(nil,nil)))),true).  [ur(87,a,85,a,b,1547,a)].

given #1511 (T,wt=9): 1580 ->*_s0(head(cons(empty(app(nil,nil)),x)),true).  [ur(87,a,67,a,b,1547,a)].

given #1512 (T,wt=9): 1613 ->_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): 11829 -->_s0(true,sndsplit(sndsplit(0,0),leq(s(x),0))) # answer(goal).  [ur(7166,b,471,a,c,1077,a)].

given #1515 (F,wt=10): 11830 -->_s0(true,sndsplit(sndsplit(0,0),tail(cons(x,false)))) # answer(goal).  [ur(7166,b,471,a,c,1066,a)].

given #1516 (F,wt=10): 11831 -->_s0(true,sndsplit(sndsplit(0,s(0)),cons(x,false))) # answer(goal).  [ur(7166,b,471,a,c,640,a)].

given #1517 (F,wt=10): 11834 -->_s0(true,head(cons(sndsplit(sndsplit(0,0),false),x))) # answer(goal).  [resolve(11815,a,7975,b)].

given #1518 (T,wt=9): 1618 ->_s0(tail(s(fstsplit(0,x))),tail(s(nil))).  [ur(54,a,189,a)].

given #1519 (T,wt=9): 1631 ->_s0(length(s(fstsplit(0,x))),length(s(nil))).  [ur(41,a,189,a)].

given #1520 (T,wt=9): 1632 ->_s0(head(s(fstsplit(0,x))),head(s(nil))).  [ur(40,a,189,a)].

given #1521 (T,wt=9): 1635 ->_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): 11836 -->_s0(true,tail(cons(x,sndsplit(sndsplit(0,0),false)))) # answer(goal).  [resolve(11815,a,7959,b)].

given #1524 (F,wt=10): 11837 -->_s0(true,x) | -->_s0(x,sndsplit(sndsplit(0,0),false)) # answer(goal).  [resolve(11815,a,7166,c)].

given #1525 (F,wt=10): 11855 -->_s0(true,sndsplit(s(sndsplit(0,0)),cons(x,false))) # answer(goal).  [ur(7166,b,83,a,c,11815,a)].

given #1526 (F,wt=10): 11857 -->_s0(true,app(nil,sndsplit(sndsplit(0,length(nil)),false))) # answer(goal).  [resolve(11763,a,7979,b)].

given #1527 (T,wt=8): 13579 ->*_s0(sndsplit(length(cons(x,y)),nil),nil).  [ur(87,a,296,a,b,565,a)].

given #1528 (T,wt=9): 1640 ->_s0(s(tail(fstsplit(0,x))),s(tail(nil))).  [ur(59,a,194,a)].

given #1529 (T,wt=9): 1645 ->_s0(tail(tail(fstsplit(0,x))),tail(tail(nil))).  [ur(54,a,194,a)].

given #1530 (T,wt=9): 1658 ->_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=10): 11859 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,length(nil)),false))) # answer(goal).  [resolve(11763,a,7962,b)].

given #1533 (F,wt=10): 11879 -->_s0(true,sndsplit(sndsplit(0,sndsplit(0,length(nil))),false)) # answer(goal).  [ur(7166,b,471,a,c,11763,a)].

given #1534 (F,wt=10): 11881 -->_s0(true,sndsplit(app(nil,sndsplit(0,length(nil))),false)) # answer(goal).  [ur(7166,b,121,a,c,11763,a)].

given #1535 (F,wt=10): 11935 -->_s0(true,app(fstsplit(s(x),nil),sndsplit(0,false))) # answer(goal).  [resolve(263,a,8018,b)].

given #1536 (T,wt=9): 1659 ->_s0(head(tail(fstsplit(0,x))),head(tail(nil))).  [ur(40,a,194,a)].

given #1537 (T,wt=9): 1662 ->_s0(empty(tail(fstsplit(0,x))),empty(tail(nil))).  [ur(37,a,194,a)].

given #1538 (T,wt=9): 1668 ->_s0(s(length(fstsplit(0,x))),s(length(nil))).  [ur(59,a,207,a)].

given #1539 (T,wt=8): 13629 ->*_s0(s(length(fstsplit(0,x))),s(0)).  [ur(87,a,1668,a,b,896,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): 11936 -->_s0(true,app(fstsplit(s(x),nil),app(nil,false))) # answer(goal).  [resolve(263,a,8014,b)].

given #1542 (F,wt=10): 11986 -->_s0(true,app(nil,app(fstsplit(s(x),nil),false))) # answer(goal).  [resolve(11978,a,7979,b)].

given #1543 (F,wt=10): 11988 -->_s0(true,sndsplit(0,app(fstsplit(s(x),nil),false))) # answer(goal).  [resolve(11978,a,7962,b)].

given #1544 (F,wt=10): 12004 -->_s0(true,app(app(nil,fstsplit(s(x),nil)),false)) # answer(goal).  [ur(7166,b,138,a,c,11978,a)].

given #1545 (T,wt=9): 1673 ->_s0(tail(length(fstsplit(0,x))),tail(length(nil))).  [ur(54,a,207,a)].

given #1546 (T,wt=8): 13648 ->*_s0(tail(length(fstsplit(0,x))),tail(0)).  [ur(87,a,1673,a,b,922,a)].

given #1547 (T,wt=9): 1686 ->_s0(length(length(fstsplit(0,x))),length(length(nil))).  [ur(41,a,207,a)].

given #1548 (T,wt=8): 13665 ->*_s0(length(length(fstsplit(0,x))),length(0)).  [ur(87,a,1686,a,b,948,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): 12035 -->_s0(true,leq(app(nil,s(x)),sndsplit(0,0))) # answer(goal).  [ur(7166,b,480,a,c,4587,a)].

given #1551 (F,wt=10): 12036 -->_s0(true,leq(s(x),sndsplit(0,app(nil,0)))) # answer(goal).  [ur(7166,b,480,a,c,4457,a)].

given #1552 (F,wt=10): 12037 -->_s0(true,leq(s(s(x)),sndsplit(0,s(0)))) # answer(goal).  [ur(7166,b,480,a,c,1078,a)].

given #1553 (F,wt=10): 12039 -->_s0(true,app(nil,leq(s(x),sndsplit(0,0)))) # answer(goal).  [resolve(12028,a,7979,b)].

given #1554 (T,wt=9): 1687 ->_s0(head(length(fstsplit(0,x))),head(length(nil))).  [ur(40,a,207,a)].

given #1555 (T,wt=8): 13683 ->*_s0(head(length(fstsplit(0,x))),head(0)).  [ur(87,a,1687,a,b,974,a)].

given #1556 (T,wt=9): 1690 ->_s0(empty(length(fstsplit(0,x))),empty(length(nil))).  [ur(37,a,207,a)].

given #1557 (T,wt=8): 13700 ->*_s0(empty(length(fstsplit(0,x))),empty(0)).  [ur(87,a,1690,a,b,1034,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=10): 12041 -->_s0(true,sndsplit(0,leq(s(x),sndsplit(0,0)))) # answer(goal).  [resolve(12028,a,7962,b)].

given #1560 (F,wt=10): 12055 -->_s0(true,leq(s(x),sndsplit(0,sndsplit(0,0)))) # answer(goal).  [ur(7166,b,480,a,c,12028,a)].

given #1561 (F,wt=10): 12056 -->_s0(true,leq(s(x),app(nil,sndsplit(0,0)))) # answer(goal).  [ur(7166,b,130,a,c,12028,a)].

given #1562 (F,wt=10): 12057 -->_s0(true,leq(s(s(x)),s(sndsplit(0,0)))) # answer(goal).  [ur(7166,b,72,a,c,12028,a)].

given #1563 (T,wt=9): 1694 ->*_s0(tail(cons(x,length(fstsplit(0,y)))),0).  [ur(87,a,85,a,b,1666,a)].

given #1564 (T,wt=9): 1696 ->*_s0(head(cons(length(fstsplit(0,x)),y)),0).  [ur(87,a,67,a,b,1666,a)].

given #1565 (T,wt=9): 1738 ->_s0(s(head(fstsplit(0,x))),s(head(nil))).  [ur(59,a,208,a)].

given #1566 (T,wt=9): 1743 ->_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): 12089 -->_s0(true,leq(sndsplit(0,s(x)),sndsplit(0,0))) # answer(goal).  [ur(7166,b,481,a,c,12028,a)].

given #1569 (F,wt=10): 12090 -->_s0(true,leq(sndsplit(0,app(nil,s(x))),0)) # answer(goal).  [ur(7166,b,481,a,c,4587,a)].

given #1570 (F,wt=10): 12091 -->_s0(true,leq(sndsplit(0,s(x)),app(nil,0))) # answer(goal).  [ur(7166,b,481,a,c,4457,a)].

given #1571 (F,wt=10): 12092 -->_s0(true,leq(sndsplit(0,s(s(x))),s(0))) # answer(goal).  [ur(7166,b,481,a,c,1078,a)].

given #1572 (T,wt=9): 1756 ->_s0(length(head(fstsplit(0,x))),length(head(nil))).  [ur(41,a,208,a)].

given #1573 (T,wt=9): 1757 ->_s0(head(head(fstsplit(0,x))),head(head(nil))).  [ur(40,a,208,a)].

given #1574 (T,wt=9): 1760 ->_s0(empty(head(fstsplit(0,x))),empty(head(nil))).  [ur(37,a,208,a)].

given #1575 (T,wt=9): 1765 ->_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): 12122 -->_s0(true,app(nil,leq(sndsplit(0,s(x)),0))) # answer(goal).  [resolve(12082,a,7979,b)].

given #1578 (F,wt=10): 12124 -->_s0(true,sndsplit(0,leq(sndsplit(0,s(x)),0))) # answer(goal).  [resolve(12082,a,7962,b)].

given #1579 (F,wt=10): 12138 -->_s0(true,leq(sndsplit(0,sndsplit(0,s(x))),0)) # answer(goal).  [ur(7166,b,481,a,c,12082,a)].

given #1580 (F,wt=10): 12139 -->_s0(true,leq(app(nil,sndsplit(0,s(x))),0)) # answer(goal).  [ur(7166,b,131,a,c,12082,a)].

given #1581 (T,wt=8): 13761 ->*_s0(s(empty(fstsplit(0,x))),s(true)).  [ur(87,a,1765,a,b,703,a)].

given #1582 (T,wt=9): 1770 ->_s0(tail(empty(fstsplit(0,x))),tail(empty(nil))).  [ur(54,a,211,a)].

given #1583 (T,wt=8): 13779 ->*_s0(tail(empty(fstsplit(0,x))),tail(true)).  [ur(87,a,1770,a,b,761,a)].

given #1584 (T,wt=9): 1783 ->_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=10): 12140 -->_s0(true,leq(s(sndsplit(0,s(x))),s(0))) # answer(goal).  [ur(7166,b,72,a,c,12082,a)].

given #1587 (F,wt=10): 12289 -->_s0(true,app(sndsplit(0,fstsplit(s(x),nil)),false)) # answer(goal).  [ur(7166,b,488,a,c,11978,a)].

given #1588 (F,wt=10): 12292 -->_s0(true,app(sndsplit(0,nil),sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,488,a,c,4410,a)].

given #1589 (F,wt=10): 12293 -->_s0(true,app(sndsplit(0,nil),empty(cons(x,y)))) # answer(goal).  [ur(7166,b,488,a,c,1135,a)].

given #1590 (T,wt=8): 13796 ->*_s0(length(empty(fstsplit(0,x))),length(true)).  [ur(87,a,1783,a,b,787,a)].

given #1591 (T,wt=9): 1784 ->_s0(head(empty(fstsplit(0,x))),head(empty(nil))).  [ur(40,a,211,a)].

given #1592 (T,wt=8): 13814 ->*_s0(head(empty(fstsplit(0,x))),head(true)).  [ur(87,a,1784,a,b,813,a)].

given #1593 (T,wt=9): 1787 ->_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): 12294 -->_s0(true,app(sndsplit(0,nil),head(cons(false,x)))) # answer(goal).  [ur(7166,b,488,a,c,1123,a)].

given #1596 (F,wt=10): 12295 -->_s0(true,app(sndsplit(0,nil),leq(s(x),0))) # answer(goal).  [ur(7166,b,488,a,c,1080,a)].

given #1597 (F,wt=10): 12296 -->_s0(true,app(sndsplit(0,nil),tail(cons(x,false)))) # answer(goal).  [ur(7166,b,488,a,c,1068,a)].

given #1598 (F,wt=10): 12305 -->_s0(true,head(cons(app(sndsplit(0,nil),false),x))) # answer(goal).  [resolve(12282,a,7975,b)].

given #1599 (T,wt=8): 13831 ->*_s0(empty(empty(fstsplit(0,x))),empty(true)).  [ur(87,a,1787,a,b,839,a)].

given #1600 (T,wt=9): 1794 ->*_s0(tail(cons(x,empty(fstsplit(0,y)))),true).  [ur(87,a,85,a,b,1763,a)].

given #1601 (T,wt=9): 1796 ->*_s0(head(cons(empty(fstsplit(0,x)),y)),true).  [ur(87,a,67,a,b,1763,a)].

given #1602 (T,wt=9): 1800 ->_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): 12307 -->_s0(true,tail(cons(x,app(sndsplit(0,nil),false)))) # answer(goal).  [resolve(12282,a,7959,b)].

given #1605 (F,wt=10): 12308 -->_s0(true,x) | -->_s0(x,app(sndsplit(0,nil),false)) # answer(goal).  [resolve(12282,a,7166,c)].

given #1606 (F,wt=10): 12471 -->_s0(true,sndsplit(head(cons(0,x)),sndsplit(0,false))) # answer(goal).  [resolve(271,a,8020,b)].

given #1607 (F,wt=10): 12472 -->_s0(true,sndsplit(head(cons(0,x)),app(nil,false))) # answer(goal).  [resolve(271,a,8016,b)].

given #1608 (T,wt=9): 1805 ->_s0(tail(s(leq(0,x))),tail(s(true))).  [ur(54,a,339,a)].

given #1609 (T,wt=9): 1818 ->_s0(length(s(leq(0,x))),length(s(true))).  [ur(41,a,339,a)].

given #1610 (T,wt=9): 1819 ->_s0(head(s(leq(0,x))),head(s(true))).  [ur(40,a,339,a)].

given #1611 (T,wt=9): 1822 ->_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=10): 12473 -->_s0(true,sndsplit(head(cons(app(nil,0),x)),false)) # answer(goal).  [resolve(271,a,8009,b)].

given #1614 (F,wt=10): 12543 -->_s0(true,sndsplit(head(cons(sndsplit(0,0),x)),false)) # answer(goal).  [ur(7166,b,271,a,c,11815,a)].

given #1615 (F,wt=10): 12554 -->_s0(true,app(fstsplit(0,x),y)) | -->_s0(y,false) # answer(goal).  [resolve(9731,b,36,b)].

given #1616 (F,wt=10): 12555 -->_s0(true,app(x,false)) | -->_s0(x,fstsplit(0,y)) # answer(goal).  [resolve(9731,b,35,b)].

given #1617 (T,wt=8): 13910 ->*_s0(leq(length(cons(x,y)),0),false).  [ur(87,a,306,a,b,571,a)].

given #1618 (T,wt=9): 1859 ->_s0(s(tail(leq(0,x))),s(tail(true))).  [ur(59,a,344,a)].

given #1619 (T,wt=9): 1864 ->_s0(tail(tail(leq(0,x))),tail(tail(true))).  [ur(54,a,344,a)].

given #1620 (T,wt=9): 1877 ->_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=8): 13914 -->_s0(true,app(fstsplit(length(nil),x),false)) # answer(goal).  [resolve(12555,b,335,a)].

given #1623 (F,wt=9): 13913 -->_s0(true,app(fstsplit(sndsplit(0,0),x),false)) # answer(goal).  [resolve(12555,b,485,a)].

given #1624 (F,wt=9): 13916 -->_s0(true,app(fstsplit(app(nil,0),x),false)) # answer(goal).  [resolve(12555,b,135,a)].

given #1625 (F,wt=10): 12557 -->_s0(true,app(nil,sndsplit(head(cons(0,x)),false))) # answer(goal).  [resolve(12540,a,7979,b)].

given #1626 (T,wt=9): 1878 ->_s0(head(tail(leq(0,x))),head(tail(true))).  [ur(40,a,344,a)].

given #1627 (T,wt=9): 1881 ->_s0(empty(tail(leq(0,x))),empty(tail(true))).  [ur(37,a,344,a)].

given #1628 (T,wt=9): 1886 ->_s0(s(length(leq(0,x))),s(length(true))).  [ur(59,a,357,a)].

given #1629 (T,wt=9): 1891 ->_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): 12559 -->_s0(true,sndsplit(0,sndsplit(head(cons(0,x)),false))) # answer(goal).  [resolve(12540,a,7962,b)].

given #1632 (F,wt=10): 12578 -->_s0(true,sndsplit(sndsplit(0,head(cons(0,x))),false)) # answer(goal).  [ur(7166,b,471,a,c,12540,a)].

given #1633 (F,wt=10): 12580 -->_s0(true,sndsplit(app(nil,head(cons(0,x))),false)) # answer(goal).  [ur(7166,b,121,a,c,12540,a)].

given #1634 (F,wt=10): 12857 -->_s0(true,app(app(fstsplit(s(x),nil),nil),false)) # answer(goal).  [resolve(10563,b,263,a)].

given #1635 (T,wt=9): 1904 ->_s0(length(length(leq(0,x))),length(length(true))).  [ur(41,a,357,a)].

given #1636 (T,wt=9): 1905 ->_s0(head(length(leq(0,x))),head(length(true))).  [ur(40,a,357,a)].

given #1637 (T,wt=9): 1908 ->_s0(empty(length(leq(0,x))),empty(length(true))).  [ur(37,a,357,a)].

given #1638 (T,wt=9): 1913 ->_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=10): 12860 -->_s0(true,app(tail(cons(x,app(nil,nil))),false)) # answer(goal).  [resolve(10563,b,85,a)].

given #1641 (F,wt=10): 12861 -->_s0(true,app(head(cons(app(nil,nil),x)),false)) # answer(goal).  [resolve(10563,b,67,a)].

given #1642 (F,wt=10): 12862 -->_s0(true,app(app(nil,x),false)) | -->_s0(x,nil) # answer(goal).  [resolve(10563,b,36,b)].

given #1643 (F,wt=10): 12863 -->_s0(true,app(app(x,nil),false)) | -->_s0(x,nil) # answer(goal).  [resolve(10563,b,35,b)].

given #1644 (T,wt=9): 1918 ->_s0(tail(head(leq(0,x))),tail(head(true))).  [ur(54,a,358,a)].

given #1645 (T,wt=9): 1931 ->_s0(length(head(leq(0,x))),length(head(true))).  [ur(41,a,358,a)].

given #1646 (T,wt=9): 1932 ->_s0(head(head(leq(0,x))),head(head(true))).  [ur(40,a,358,a)].

given #1647 (T,wt=9): 1935 ->_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=10): 12880 -->_s0(true,leq(s(x),head(cons(length(nil),y)))) # answer(goal).  [resolve(280,a,8007,b)].

given #1650 (F,wt=10): 12901 -->_s0(true,leq(s(x),length(tail(cons(y,nil))))) # answer(goal).  [resolve(10599,b,557,a)].

given #1651 (F,wt=10): 12902 -->_s0(true,leq(s(x),length(sndsplit(s(y),nil)))) # answer(goal).  [resolve(10599,b,532,a)].

given #1652 (F,wt=10): 12905 -->_s0(true,leq(s(x),length(head(cons(nil,y))))) # answer(goal).  [resolve(10599,b,282,a)].

given #1653 (T,wt=8): 14064 ->*_s0(fstsplit(length(cons(x,y)),nil),nil).  [ur(87,a,310,a,b,576,a)].

given #1654 (T,wt=9): 1940 ->_s0(s(empty(leq(0,x))),s(empty(true))).  [ur(59,a,361,a)].

given #1655 (T,wt=9): 1945 ->_s0(tail(empty(leq(0,x))),tail(empty(true))).  [ur(54,a,361,a)].

given #1656 (T,wt=9): 1958 ->_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=10): 12906 -->_s0(true,leq(s(x),length(fstsplit(s(y),nil)))) # answer(goal).  [resolve(10599,b,257,a)].

given #1659 (F,wt=10): 12909 -->_s0(true,leq(s(x),tail(cons(y,length(nil))))) # answer(goal).  [resolve(10599,b,85,a)].

given #1660 (F,wt=10): 12910 -->_s0(true,leq(s(x),length(y))) | -->_s0(y,nil) # answer(goal).  [resolve(10599,b,41,b)].

given #1661 (F,wt=10): 12927 -->_s0(true,leq(head(cons(s(x),y)),length(nil))) # answer(goal).  [resolve(281,a,8007,b)].

given #1662 (T,wt=9): 1959 ->_s0(head(empty(leq(0,x))),head(empty(true))).  [ur(40,a,361,a)].

given #1663 (T,wt=9): 1962 ->_s0(empty(empty(leq(0,x))),empty(empty(true))).  [ur(37,a,361,a)].

given #1664 (T,wt=9): 1994 ->_s0(s(s(mapf(x,nil))),s(s(nil))).  [ur(59,a,439,a)].

given #1665 (T,wt=9): 1999 ->_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): 12955 -->_s0(true,leq(tail(cons(x,s(y))),length(nil))) # answer(goal).  [resolve(10600,b,85,a)].

given #1668 (F,wt=10): 13009 -->_s0(true,sndsplit(app(fstsplit(s(x),nil),0),false)) # answer(goal).  [resolve(10602,b,263,a)].

given #1669 (F,wt=10): 13012 -->_s0(true,sndsplit(tail(cons(x,app(nil,0))),false)) # answer(goal).  [resolve(10602,b,85,a)].

given #1670 (F,wt=10): 13013 -->_s0(true,sndsplit(app(nil,x),false)) | -->_s0(x,0) # answer(goal).  [resolve(10602,b,36,b)].

given #1671 (T,wt=9): 2012 ->_s0(length(s(mapf(x,nil))),length(s(nil))).  [ur(41,a,439,a)].

given #1672 (T,wt=9): 2013 ->_s0(head(s(mapf(x,nil))),head(s(nil))).  [ur(40,a,439,a)].

given #1673 (T,wt=9): 2016 ->_s0(empty(s(mapf(x,nil))),empty(s(nil))).  [ur(37,a,439,a)].

given #1674 (T,wt=9): 2021 ->_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=10): 13014 -->_s0(true,sndsplit(app(x,0),false)) | -->_s0(x,nil) # answer(goal).  [resolve(10602,b,35,b)].

given #1677 (F,wt=10): 13071 -->_s0(true,app(nil,app(nil,x))) | -->_s0(x,false) # answer(goal).  [resolve(10603,b,36,b)].

given #1678 (F,wt=10): 13072 -->_s0(true,app(nil,app(x,false))) | -->_s0(x,nil) # answer(goal).  [resolve(10603,b,35,b)].

given #1679 (F,wt=10): 13073 -->_s0(true,app(tail(cons(x,nil)),app(nil,false))) # answer(goal).  [resolve(10604,b,85,a)].

given #1680 (T,wt=9): 2026 ->_s0(tail(tail(mapf(x,nil))),tail(tail(nil))).  [ur(54,a,444,a)].

given #1681 (T,wt=9): 2039 ->_s0(length(tail(mapf(x,nil))),length(tail(nil))).  [ur(41,a,444,a)].

given #1682 (T,wt=9): 2040 ->_s0(head(tail(mapf(x,nil))),head(tail(nil))).  [ur(40,a,444,a)].

given #1683 (T,wt=9): 2043 ->_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=10): 13074 -->_s0(true,app(sndsplit(s(x),nil),app(nil,false))) # answer(goal).  [resolve(10604,b,84,a)].

given #1686 (F,wt=10): 13075 -->_s0(true,app(head(cons(nil,x)),app(nil,false))) # answer(goal).  [resolve(10604,b,67,a)].

given #1687 (F,wt=10): 13114 -->_s0(true,app(app(nil,head(cons(nil,x))),false)) # answer(goal).  [resolve(287,a,10563,b)].

given #1688 (F,wt=10): 13141 -->_s0(true,sndsplit(0,app(nil,x))) | -->_s0(x,false) # answer(goal).  [resolve(10605,b,36,b)].

given #1689 (T,wt=9): 2049 ->_s0(s(length(mapf(x,nil))),s(length(nil))).  [ur(59,a,457,a)].

given #1690 (T,wt=8): 14191 ->*_s0(s(length(mapf(x,nil))),s(0)).  [ur(87,a,2049,a,b,896,a)].

given #1691 (T,wt=9): 2054 ->_s0(tail(length(mapf(x,nil))),tail(length(nil))).  [ur(54,a,457,a)].

given #1692 (T,wt=8): 14209 ->*_s0(tail(length(mapf(x,nil))),tail(0)).  [ur(87,a,2054,a,b,922,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=10): 13142 -->_s0(true,sndsplit(0,app(x,false))) | -->_s0(x,nil) # answer(goal).  [resolve(10605,b,35,b)].

given #1695 (F,wt=10): 13143 -->_s0(true,sndsplit(tail(cons(x,0)),app(nil,false))) # answer(goal).  [resolve(10606,b,85,a)].

given #1696 (F,wt=10): 13144 -->_s0(true,app(nil,sndsplit(0,x))) | -->_s0(x,false) # answer(goal).  [resolve(10639,b,53,b)].

given #1697 (F,wt=10): 13145 -->_s0(true,app(nil,sndsplit(x,false))) | -->_s0(x,0) # answer(goal).  [resolve(10639,b,52,b)].

given #1698 (T,wt=9): 2067 ->_s0(length(length(mapf(x,nil))),length(length(nil))).  [ur(41,a,457,a)].

given #1699 (T,wt=8): 14230 ->*_s0(length(length(mapf(x,nil))),length(0)).  [ur(87,a,2067,a,b,948,a)].

given #1700 (T,wt=9): 2068 ->_s0(head(length(mapf(x,nil))),head(length(nil))).  [ur(40,a,457,a)].

given #1701 (T,wt=8): 14247 ->*_s0(head(length(mapf(x,nil))),head(0)).  [ur(87,a,2068,a,b,974,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=10): 13146 -->_s0(true,app(tail(cons(x,nil)),sndsplit(0,false))) # answer(goal).  [resolve(10640,b,85,a)].

given #1704 (F,wt=10): 13147 -->_s0(true,app(sndsplit(s(x),nil),sndsplit(0,false))) # answer(goal).  [resolve(10640,b,84,a)].

given #1705 (F,wt=10): 13148 -->_s0(true,app(head(cons(nil,x)),sndsplit(0,false))) # answer(goal).  [resolve(10640,b,67,a)].

given #1706 (F,wt=10): 13190 -->_s0(true,sndsplit(0,app(head(cons(nil,x)),false))) # answer(goal).  [resolve(288,a,10605,b)].

given #1707 (T,wt=9): 2071 ->_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): 14265 ->*_s0(empty(length(mapf(x,nil))),empty(0)).  [ur(87,a,2071,a,b,1034,a)].

given #1709 (T,wt=9): 2075 ->*_s0(tail(cons(x,length(mapf(y,nil)))),0).  [ur(87,a,85,a,b,2047,a)].

given #1710 (T,wt=9): 2077 ->*_s0(head(cons(length(mapf(x,nil)),y)),0).  [ur(87,a,67,a,b,2047,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=10): 13191 -->_s0(true,app(nil,app(head(cons(nil,x)),false))) # answer(goal).  [resolve(288,a,10603,b)].

given #1713 (F,wt=10): 13192 -->_s0(true,sndsplit(app(head(cons(nil,x)),0),false)) # answer(goal).  [resolve(288,a,10602,b)].

given #1714 (F,wt=10): 13193 -->_s0(true,app(app(head(cons(nil,x)),nil),false)) # answer(goal).  [resolve(288,a,10563,b)].

given #1715 (F,wt=10): 13194 -->_s0(true,app(head(cons(fstsplit(0,x),y)),false)) # answer(goal).  [resolve(288,a,9731,b)].

given #1716 (T,wt=9): 2108 ->_s0(s(head(mapf(x,nil))),s(head(nil))).  [ur(59,a,458,a)].

given #1717 (T,wt=9): 2113 ->_s0(tail(head(mapf(x,nil))),tail(head(nil))).  [ur(54,a,458,a)].

given #1718 (T,wt=9): 2126 ->_s0(length(head(mapf(x,nil))),length(head(nil))).  [ur(41,a,458,a)].

given #1719 (T,wt=9): 2127 ->_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=10): 13253 -->_s0(true,app(head(cons(sndsplit(0,nil),x)),false)) # answer(goal).  [ur(7166,b,288,a,c,12282,a)].

given #1722 (F,wt=10): 13255 -->_s0(true,app(head(cons(mapf(x,nil),y)),false)) # answer(goal).  [ur(7166,b,288,a,c,11605,a)].

given #1723 (F,wt=10): 13261 -->_s0(true,sndsplit(0,sndsplit(0,x))) | -->_s0(x,false) # answer(goal).  [resolve(10641,b,53,b)].

given #1724 (F,wt=10): 13262 -->_s0(true,sndsplit(0,sndsplit(x,false))) | -->_s0(x,0) # answer(goal).  [resolve(10641,b,52,b)].

given #1725 (T,wt=9): 2130 ->_s0(empty(head(mapf(x,nil))),empty(head(nil))).  [ur(37,a,458,a)].

given #1726 (T,wt=9): 2135 ->_s0(s(empty(mapf(x,nil))),s(empty(nil))).  [ur(59,a,461,a)].

given #1727 (T,wt=8): 14286 ->*_s0(s(empty(mapf(x,nil))),s(true)).  [ur(87,a,2135,a,b,703,a)].

given #1728 (T,wt=9): 2140 ->_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=10): 13263 -->_s0(true,sndsplit(tail(cons(x,0)),sndsplit(0,false))) # answer(goal).  [resolve(10642,b,85,a)].

given #1731 (F,wt=10): 13292 -->_s0(true,app(sndsplit(0,head(cons(nil,x))),false)) # answer(goal).  [ur(7166,b,488,a,c,13251,a)].

given #1732 (F,wt=10): 13427 -->_s0(true,app(mapf(x,nil),y)) | -->_s0(y,false) # answer(goal).  [resolve(11622,b,36,b)].

given #1733 (F,wt=10): 13428 -->_s0(true,app(x,false)) | -->_s0(x,mapf(y,nil)) # answer(goal).  [resolve(11622,b,35,b)].

given #1734 (T,wt=8): 14294 ->*_s0(tail(empty(mapf(x,nil))),tail(true)).  [ur(87,a,2140,a,b,761,a)].

given #1735 (T,wt=9): 2153 ->_s0(length(empty(mapf(x,nil))),length(empty(nil))).  [ur(41,a,461,a)].

given #1736 (T,wt=8): 14311 ->*_s0(length(empty(mapf(x,nil))),length(true)).  [ur(87,a,2153,a,b,787,a)].

given #1737 (T,wt=9): 2154 ->_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=9): 14297 -->_s0(true,app(mapf(x,sndsplit(0,nil)),false)) # answer(goal).  [resolve(13428,b,478,a)].

given #1740 (F,wt=9): 14298 -->_s0(true,app(mapf(x,mapf(y,nil)),false)) # answer(goal).  [resolve(13428,b,453,a)].

given #1741 (F,wt=9): 14301 -->_s0(true,app(mapf(x,fstsplit(0,y)),false)) # answer(goal).  [resolve(13428,b,203,a)].

given #1742 (F,wt=9): 14302 -->_s0(true,app(mapf(x,app(nil,nil)),false)) # answer(goal).  [resolve(13428,b,128,a)].

given #1743 (T,wt=8): 14319 ->*_s0(head(empty(mapf(x,nil))),head(true)).  [ur(87,a,2154,a,b,813,a)].

given #1744 (T,wt=9): 2157 ->_s0(empty(empty(mapf(x,nil))),empty(empty(nil))).  [ur(37,a,461,a)].

given #1745 (T,wt=8): 14328 ->*_s0(empty(empty(mapf(x,nil))),empty(true)).  [ur(87,a,2157,a,b,839,a)].

given #1746 (T,wt=9): 2164 ->*_s0(tail(cons(x,empty(mapf(y,nil)))),true).  [ur(87,a,85,a,b,2133,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=10): 13580 -->_s0(true,sndsplit(sndsplit(0,0),x)) | -->_s0(x,false) # answer(goal).  [resolve(11837,b,53,b)].

given #1749 (F,wt=10): 13581 -->_s0(true,sndsplit(x,false)) | -->_s0(x,sndsplit(0,0)) # answer(goal).  [resolve(11837,b,52,b)].

given #1750 (F,wt=8): 14341 -->_s0(true,sndsplit(sndsplit(length(nil),0),false)) # answer(goal).  [resolve(13581,b,321,a)].

given #1751 (F,wt=9): 14340 -->_s0(true,sndsplit(sndsplit(sndsplit(0,0),0),false)) # answer(goal).  [resolve(13581,b,471,a)].

given #1752 (T,wt=9): 2166 ->*_s0(head(cons(empty(mapf(x,nil)),y)),true).  [ur(87,a,67,a,b,2133,a)].

given #1753 (T,wt=9): 2172 ->_s0(s(s(sndsplit(0,x))),s(s(x))).  [ur(59,a,464,a)].

given #1754 (T,wt=9): 2177 ->_s0(tail(s(sndsplit(0,x))),tail(s(x))).  [ur(54,a,464,a)].

given #1755 (T,wt=9): 2190 ->_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=9): 14343 -->_s0(true,sndsplit(sndsplit(app(nil,0),0),false)) # answer(goal).  [resolve(13581,b,121,a)].

given #1758 (F,wt=10): 13874 -->_s0(true,app(sndsplit(0,nil),x)) | -->_s0(x,false) # answer(goal).  [resolve(12308,b,36,b)].

given #1759 (F,wt=10): 13875 -->_s0(true,app(x,false)) | -->_s0(x,sndsplit(0,nil)) # answer(goal).  [resolve(12308,b,35,b)].

given #1760 (F,wt=8): 14366 -->_s0(true,app(sndsplit(length(nil),nil),false)) # answer(goal).  [resolve(13875,b,321,a)].

given #1761 (T,wt=9): 2191 ->_s0(head(s(sndsplit(0,x))),head(s(x))).  [ur(40,a,464,a)].

given #1762 (T,wt=9): 2194 ->_s0(empty(s(sndsplit(0,x))),empty(s(x))).  [ur(37,a,464,a)].

given #1763 (T,wt=9): 2237 ->_s0(s(tail(sndsplit(0,x))),s(tail(x))).  [ur(59,a,469,a)].

given #1764 (T,wt=9): 2242 ->_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=9): 14365 -->_s0(true,app(sndsplit(sndsplit(0,0),nil),false)) # answer(goal).  [resolve(13875,b,471,a)].

given #1767 (F,wt=9): 14368 -->_s0(true,app(sndsplit(app(nil,0),nil),false)) # answer(goal).  [resolve(13875,b,121,a)].

given #1768 (F,wt=10): 13911 -->_s0(true,leq(length(cons(x,y)),sndsplit(0,0))) # answer(goal).  [ur(7166,b,306,a,c,12028,a)].

given #1769 (F,wt=10): 13912 -->_s0(true,leq(length(cons(x,y)),app(nil,0))) # answer(goal).  [ur(7166,b,306,a,c,4457,a)].

given #1770 (T,wt=9): 2255 ->_s0(length(tail(sndsplit(0,x))),length(tail(x))).  [ur(41,a,469,a)].

given #1771 (T,wt=9): 2256 ->_s0(head(tail(sndsplit(0,x))),head(tail(x))).  [ur(40,a,469,a)].

given #1772 (T,wt=9): 2259 ->_s0(empty(tail(sndsplit(0,x))),empty(tail(x))).  [ur(37,a,469,a)].

given #1773 (T,wt=9): 2270 ->_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=10): 13915 -->_s0(true,app(fstsplit(head(cons(0,x)),y),false)) # answer(goal).  [resolve(12555,b,285,a)].

given #1776 (F,wt=10): 13917 -->_s0(true,app(tail(cons(x,fstsplit(0,y))),false)) # answer(goal).  [resolve(12555,b,85,a)].

given #1777 (F,wt=10): 13918 -->_s0(true,app(fstsplit(x,y),false)) | -->_s0(x,0) # answer(goal).  [resolve(12555,b,38,b)].

given #1778 (F,wt=10): 13920 -->_s0(true,app(nil,leq(length(cons(x,y)),0))) # answer(goal).  [resolve(13910,a,7979,b)].

given #1779 (T,wt=8): 14415 ->*_s0(s(length(sndsplit(0,nil))),s(0)).  [ur(87,a,2270,a,b,896,a)].

given #1780 (T,wt=9): 2275 ->_s0(tail(length(sndsplit(0,x))),tail(length(x))).  [ur(54,a,482,a)].

given #1781 (T,wt=8): 14432 ->*_s0(tail(length(sndsplit(0,nil))),tail(0)).  [ur(87,a,2275,a,b,922,a)].

given #1782 (T,wt=9): 2288 ->_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=10): 13922 -->_s0(true,sndsplit(0,leq(length(cons(x,y)),0))) # answer(goal).  [resolve(13910,a,7962,b)].

given #1785 (F,wt=10): 13938 -->_s0(true,leq(sndsplit(0,length(cons(x,y))),0)) # answer(goal).  [ur(7166,b,481,a,c,13910,a)].

given #1786 (F,wt=10): 13941 -->_s0(true,leq(app(nil,length(cons(x,y))),0)) # answer(goal).  [ur(7166,b,131,a,c,13910,a)].

given #1787 (F,wt=10): 13942 -->_s0(true,leq(s(length(cons(x,y))),s(0))) # answer(goal).  [ur(7166,b,72,a,c,13910,a)].

given #1788 (T,wt=8): 14446 ->*_s0(length(length(sndsplit(0,nil))),length(0)).  [ur(87,a,2288,a,b,948,a)].

given #1789 (T,wt=9): 2289 ->_s0(head(length(sndsplit(0,x))),head(length(x))).  [ur(40,a,482,a)].

given #1790 (T,wt=8): 14461 ->*_s0(head(length(sndsplit(0,nil))),head(0)).  [ur(87,a,2289,a,b,974,a)].

given #1791 (T,wt=9): 2292 ->_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=10): 14027 -->_s0(true,app(app(nil,tail(cons(x,nil))),false)) # answer(goal).  [resolve(12862,b,85,a)].

given #1794 (F,wt=10): 14028 -->_s0(true,app(app(nil,sndsplit(s(x),nil)),false)) # answer(goal).  [resolve(12862,b,84,a)].

given #1795 (F,wt=10): 14029 -->_s0(true,app(app(tail(cons(x,nil)),nil),false)) # answer(goal).  [resolve(12863,b,85,a)].

given #1796 (F,wt=10): 14030 -->_s0(true,app(app(sndsplit(s(x),nil),nil),false)) # answer(goal).  [resolve(12863,b,84,a)].

given #1797 (T,wt=8): 14475 ->*_s0(empty(length(sndsplit(0,nil))),empty(0)).  [ur(87,a,2292,a,b,1034,a)].

given #1798 (T,wt=9): 2297 ->*_s0(tail(cons(x,length(sndsplit(0,nil)))),0).  [ur(87,a,85,a,b,2268,a)].

given #1799 (T,wt=9): 2299 ->*_s0(head(cons(length(sndsplit(0,nil)),x)),0).  [ur(87,a,67,a,b,2268,a)].

given #1800 (T,wt=9): 2306 ->_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=10): 14127 -->_s0(true,sndsplit(app(nil,tail(cons(x,0))),false)) # answer(goal).  [resolve(13013,b,85,a)].

given #1803 (F,wt=10): 14157 -->_s0(true,sndsplit(app(tail(cons(x,nil)),0),false)) # answer(goal).  [resolve(13014,b,85,a)].

given #1804 (F,wt=10): 14158 -->_s0(true,sndsplit(app(sndsplit(s(x),nil),0),false)) # answer(goal).  [resolve(13014,b,84,a)].

given #1805 (F,wt=10): 14159 -->_s0(true,app(nil,app(tail(cons(x,nil)),false))) # answer(goal).  [resolve(13072,b,85,a)].

given #1806 (T,wt=9): 2311 ->_s0(tail(head(sndsplit(0,x))),tail(head(x))).  [ur(54,a,483,a)].

given #1807 (T,wt=9): 2324 ->_s0(length(head(sndsplit(0,x))),length(head(x))).  [ur(41,a,483,a)].

given #1808 (T,wt=9): 2325 ->_s0(head(head(sndsplit(0,x))),head(head(x))).  [ur(40,a,483,a)].

given #1809 (T,wt=9): 2328 ->_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=10): 14160 -->_s0(true,app(nil,app(sndsplit(s(x),nil),false))) # answer(goal).  [resolve(13072,b,84,a)].

given #1812 (F,wt=10): 14226 -->_s0(true,sndsplit(0,app(tail(cons(x,nil)),false))) # answer(goal).  [resolve(13142,b,85,a)].

given #1813 (F,wt=10): 14227 -->_s0(true,sndsplit(0,app(sndsplit(s(x),nil),false))) # answer(goal).  [resolve(13142,b,84,a)].

given #1814 (F,wt=10): 14228 -->_s0(true,app(nil,sndsplit(tail(cons(x,0)),false))) # answer(goal).  [resolve(13145,b,85,a)].

given #1815 (T,wt=9): 2368 ->_s0(s(empty(sndsplit(0,x))),s(empty(x))).  [ur(59,a,486,a)].

given #1816 (T,wt=8): 14523 ->*_s0(s(empty(sndsplit(0,nil))),s(true)).  [ur(87,a,2368,a,b,703,a)].

given #1817 (T,wt=9): 2373 ->_s0(tail(empty(sndsplit(0,x))),tail(empty(x))).  [ur(54,a,486,a)].

given #1818 (T,wt=8): 14538 ->*_s0(tail(empty(sndsplit(0,nil))),tail(true)).  [ur(87,a,2373,a,b,761,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=10): 14282 -->_s0(true,sndsplit(0,sndsplit(tail(cons(x,0)),false))) # answer(goal).  [resolve(13262,b,85,a)].

given #1821 (F,wt=10): 14299 -->_s0(true,app(mapf(x,head(cons(nil,y))),false)) # answer(goal).  [resolve(13428,b,278,a)].

given #1822 (F,wt=10): 14300 -->_s0(true,app(mapf(x,fstsplit(s(y),nil)),false)) # answer(goal).  [resolve(13428,b,253,a)].

given #1823 (F,wt=10): 14303 -->_s0(true,app(tail(cons(x,mapf(y,nil))),false)) # answer(goal).  [resolve(13428,b,85,a)].

given #1824 (T,wt=9): 2386 ->_s0(length(empty(sndsplit(0,x))),length(empty(x))).  [ur(41,a,486,a)].

given #1825 (T,wt=8): 14555 ->*_s0(length(empty(sndsplit(0,nil))),length(true)).  [ur(87,a,2386,a,b,787,a)].

given #1826 (T,wt=9): 2387 ->_s0(head(empty(sndsplit(0,x))),head(empty(x))).  [ur(40,a,486,a)].

given #1827 (T,wt=8): 14570 ->*_s0(head(empty(sndsplit(0,nil))),head(true)).  [ur(87,a,2387,a,b,813,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=10): 14304 -->_s0(true,app(mapf(x,y),false)) | -->_s0(y,nil) # answer(goal).  [resolve(13428,b,45,b)].

given #1830 (F,wt=10): 14342 -->_s0(true,sndsplit(sndsplit(head(cons(0,x)),0),false)) # answer(goal).  [resolve(13581,b,271,a)].

given #1831 (F,wt=10): 14344 -->_s0(true,sndsplit(tail(cons(x,sndsplit(0,0))),false)) # answer(goal).  [resolve(13581,b,85,a)].

given #1832 (F,wt=10): 14345 -->_s0(true,sndsplit(sndsplit(s(0),cons(x,0)),false)) # answer(goal).  [resolve(13581,b,83,a)].

given #1833 (T,wt=9): 2390 ->_s0(empty(empty(sndsplit(0,x))),empty(empty(x))).  [ur(37,a,486,a)].

given #1834 (T,wt=8): 14591 ->*_s0(empty(empty(sndsplit(0,nil))),empty(true)).  [ur(87,a,2390,a,b,839,a)].

given #1835 (T,wt=9): 2398 ->*_s0(tail(cons(x,empty(sndsplit(0,nil)))),true).  [ur(87,a,85,a,b,2366,a)].

given #1836 (T,wt=9): 2400 ->*_s0(head(cons(empty(sndsplit(0,nil)),x)),true).  [ur(87,a,67,a,b,2366,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=10): 14346 -->_s0(true,sndsplit(sndsplit(0,x),false)) | -->_s0(x,0) # answer(goal).  [resolve(13581,b,53,b)].

given #1839 (F,wt=10): 14347 -->_s0(true,sndsplit(sndsplit(x,0),false)) | -->_s0(x,0) # answer(goal).  [resolve(13581,b,52,b)].

given #1840 (F,wt=10): 14367 -->_s0(true,app(sndsplit(head(cons(0,x)),nil),false)) # answer(goal).  [resolve(13875,b,271,a)].

given #1841 (F,wt=10): 14369 -->_s0(true,app(tail(cons(x,sndsplit(0,nil))),false)) # answer(goal).  [resolve(13875,b,85,a)].

given #1842 (T,wt=9): 2402 ->*_s0(tail(sndsplit(0,cons(x,length(nil)))),0).  [ur(87,a,469,a,b,627,a)].

given #1843 (T,wt=9): 2403 ->*_s0(tail(app(nil,cons(x,length(nil)))),0).  [ur(87,a,119,a,b,627,a)].

given #1844 (T,wt=9): 2405 ->*_s0(sndsplit(0,tail(cons(x,length(nil)))),0).  [ur(87,a,82,a,b,627,a)].

given #1845 (T,wt=9): 2407 ->*_s0(app(nil,tail(cons(x,length(nil)))),0).  [ur(87,a,61,a,b,627,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=10): 14370 -->_s0(true,app(sndsplit(s(0),cons(x,nil)),false)) # answer(goal).  [resolve(13875,b,83,a)].

given #1848 (F,wt=10): 14371 -->_s0(true,app(sndsplit(0,x),false)) | -->_s0(x,nil) # answer(goal).  [resolve(13875,b,53,b)].

given #1849 (F,wt=10): 14372 -->_s0(true,app(sndsplit(x,nil),false)) | -->_s0(x,0) # answer(goal).  [resolve(13875,b,52,b)].

given #1850 (F,wt=10): 14418 -->_s0(true,app(fstsplit(tail(cons(x,0)),y),false)) # answer(goal).  [resolve(13918,b,85,a)].

given #1851 (T,wt=9): 2408 ->*_s0(head(sndsplit(0,cons(length(nil),x))),0).  [ur(87,a,483,a,b,629,a)].

given #1852 (T,wt=9): 2409 ->*_s0(head(app(nil,cons(length(nil),x))),0).  [ur(87,a,133,a,b,629,a)].

given #1853 (T,wt=9): 2411 ->*_s0(sndsplit(0,head(cons(length(nil),x))),0).  [ur(87,a,82,a,b,629,a)].

given #1854 (T,wt=9): 2413 ->*_s0(app(nil,head(cons(length(nil),x))),0).  [ur(87,a,61,a,b,629,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=10): 14582 -->_s0(true,app(mapf(x,tail(cons(y,nil))),false)) # answer(goal).  [resolve(14304,b,85,a)].

given #1857 (F,wt=10): 14583 -->_s0(true,app(mapf(x,sndsplit(s(y),nil)),false)) # answer(goal).  [resolve(14304,b,84,a)].

given #1858 (F,wt=10): 14609 -->_s0(true,sndsplit(sndsplit(0,tail(cons(x,0))),false)) # answer(goal).  [resolve(14346,b,85,a)].

given #1859 (F,wt=10): 14610 -->_s0(true,sndsplit(sndsplit(tail(cons(x,0)),0),false)) # answer(goal).  [resolve(14347,b,85,a)].

given #1860 (T,wt=9): 2449 ->*_s0(tail(sndsplit(0,cons(x,empty(nil)))),true).  [ur(87,a,469,a,b,633,a)].

given #1861 (T,wt=9): 2450 ->*_s0(tail(app(nil,cons(x,empty(nil)))),true).  [ur(87,a,119,a,b,633,a)].

given #1862 (T,wt=9): 2452 ->*_s0(sndsplit(0,tail(cons(x,empty(nil)))),true).  [ur(87,a,82,a,b,633,a)].

given #1863 (T,wt=9): 2454 ->*_s0(app(nil,tail(cons(x,empty(nil)))),true).  [ur(87,a,61,a,b,633,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=10): 14613 -->_s0(true,app(sndsplit(0,tail(cons(x,nil))),false)) # answer(goal).  [resolve(14371,b,85,a)].

given #1866 (F,wt=10): 14614 -->_s0(true,app(sndsplit(0,sndsplit(s(x),nil)),false)) # answer(goal).  [resolve(14371,b,84,a)].

given #1867 (F,wt=10): 14615 -->_s0(true,app(sndsplit(tail(cons(x,0)),nil),false)) # answer(goal).  [resolve(14372,b,85,a)].

given #1868 (F,wt=11): 6865 -->*_s0(true,false) | -->_s0(mapf(two,head(x)),fstsplit(0,y)) # answer(goal).  [resolve(6383,b,1763,a)].

given #1869 (T,wt=9): 2458 ->*_s0(head(sndsplit(0,cons(empty(nil),x))),true).  [ur(87,a,483,a,b,635,a)].

given #1870 (T,wt=9): 2459 ->*_s0(head(app(nil,cons(empty(nil),x))),true).  [ur(87,a,133,a,b,635,a)].

given #1871 (T,wt=9): 2461 ->*_s0(sndsplit(0,head(cons(empty(nil),x))),true).  [ur(87,a,82,a,b,635,a)].

given #1872 (T,wt=9): 2463 ->*_s0(app(nil,head(cons(empty(nil),x))),true).  [ur(87,a,61,a,b,635,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): 6866 -->*_s0(true,false) | -->_s0(mapf(two,head(x)),app(nil,nil)) # answer(goal).  [resolve(6383,b,1547,a)].

given #1875 (F,wt=11): 7751 -->_s0(true,empty(empty(length(nil)))) | -->*_s0(empty(empty(0)),false) # answer(goal).  [resolve(7166,b,1057,a)].

given #1876 (F,wt=11): 7752 -->_s0(true,head(empty(length(nil)))) | -->*_s0(head(empty(0)),false) # answer(goal).  [resolve(7166,b,1054,a)].

given #1877 (F,wt=11): 7753 -->_s0(true,length(empty(length(nil)))) | -->*_s0(length(empty(0)),false) # answer(goal).  [resolve(7166,b,1053,a)].

given #1878 (T,wt=9): 2474 ->*_s0(sndsplit(0,sndsplit(0,sndsplit(0,x))),x).  [ur(87,a,82,a,b,641,a)].

given #1879 (T,wt=9): 2476 ->*_s0(app(nil,sndsplit(0,sndsplit(0,x))),x).  [ur(87,a,61,a,b,641,a)].

given #1880 (T,wt=9): 2486 ->*_s0(sndsplit(0,app(nil,sndsplit(0,x))),x).  [ur(87,a,82,a,b,643,a)].

given #1881 (T,wt=9): 2488 ->*_s0(app(nil,app(nil,sndsplit(0,x))),x).  [ur(87,a,61,a,b,643,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): 7754 -->_s0(true,tail(empty(length(nil)))) | -->*_s0(tail(empty(0)),false) # answer(goal).  [resolve(7166,b,1040,a)].

given #1884 (F,wt=11): 7755 -->_s0(true,s(empty(length(nil)))) | -->*_s0(s(empty(0)),false) # answer(goal).  [resolve(7166,b,1035,a)].

given #1885 (F,wt=11): 7756 -->_s0(true,empty(head(length(nil)))) | -->*_s0(empty(head(0)),false) # answer(goal).  [resolve(7166,b,997,a)].

given #1886 (F,wt=11): 7757 -->_s0(true,head(head(length(nil)))) | -->*_s0(head(head(0)),false) # answer(goal).  [resolve(7166,b,994,a)].

given #1887 (T,wt=9): 2490 ->*_s0(head(app(cons(empty(nil),x),y)),true).  [ur(87,a,108,a,b,635,a)].

given #1888 (T,wt=9): 2491 ->*_s0(head(app(cons(length(nil),x),y)),0).  [ur(87,a,108,a,b,629,a)].

given #1889 (T,wt=9): 2521 ->*_s0(sndsplit(0,sndsplit(0,mapf(x,nil))),nil).  [ur(87,a,82,a,b,645,a)].

given #1890 (T,wt=9): 2523 ->*_s0(app(nil,sndsplit(0,mapf(x,nil))),nil).  [ur(87,a,61,a,b,645,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): 7758 -->_s0(true,length(head(length(nil)))) | -->*_s0(length(head(0)),false) # answer(goal).  [resolve(7166,b,993,a)].

given #1893 (F,wt=11): 7759 -->_s0(true,tail(head(length(nil)))) | -->*_s0(tail(head(0)),false) # answer(goal).  [resolve(7166,b,980,a)].

given #1894 (F,wt=11): 7760 -->_s0(true,s(head(length(nil)))) | -->*_s0(s(head(0)),false) # answer(goal).  [resolve(7166,b,975,a)].

given #1895 (F,wt=11): 7761 -->_s0(true,empty(length(length(nil)))) | -->*_s0(empty(length(0)),false) # answer(goal).  [resolve(7166,b,971,a)].

given #1896 (T,wt=9): 2525 ->*_s0(sndsplit(0,app(nil,mapf(x,nil))),nil).  [ur(87,a,82,a,b,647,a)].

given #1897 (T,wt=9): 2527 ->*_s0(app(nil,app(nil,mapf(x,nil))),nil).  [ur(87,a,61,a,b,647,a)].

given #1898 (T,wt=9): 2533 ->*_s0(sndsplit(0,sndsplit(0,leq(0,x))),true).  [ur(87,a,82,a,b,688,a)].

given #1899 (T,wt=9): 2535 ->*_s0(app(nil,sndsplit(0,leq(0,x))),true).  [ur(87,a,61,a,b,688,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): 7762 -->_s0(true,head(length(length(nil)))) | -->*_s0(head(length(0)),false) # answer(goal).  [resolve(7166,b,968,a)].

given #1902 (F,wt=11): 7763 -->_s0(true,length(length(length(nil)))) | -->*_s0(length(length(0)),false) # answer(goal).  [resolve(7166,b,967,a)].

given #1903 (F,wt=11): 7764 -->_s0(true,tail(length(length(nil)))) | -->*_s0(tail(length(0)),false) # answer(goal).  [resolve(7166,b,954,a)].

given #1904 (F,wt=11): 7765 -->_s0(true,s(length(length(nil)))) | -->*_s0(s(length(0)),false) # answer(goal).  [resolve(7166,b,949,a)].

given #1905 (T,wt=9): 2540 ->*_s0(sndsplit(0,leq(s(0),s(x))),true).  [ur(87,a,82,a,b,689,a)].

given #1906 (T,wt=9): 2541 ->*_s0(leq(s(s(0)),s(s(x))),true).  [ur(87,a,72,a,b,689,a)].

given #1907 (T,wt=9): 2543 ->*_s0(app(nil,leq(s(0),s(x))),true).  [ur(87,a,61,a,b,689,a)].

given #1908 (T,wt=9): 2575 ->*_s0(sndsplit(0,app(nil,leq(0,x))),true).  [ur(87,a,82,a,b,691,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): 7766 -->_s0(true,empty(tail(length(nil)))) | -->*_s0(empty(tail(0)),false) # answer(goal).  [resolve(7166,b,945,a)].

given #1911 (F,wt=11): 7767 -->_s0(true,head(tail(length(nil)))) | -->*_s0(head(tail(0)),false) # answer(goal).  [resolve(7166,b,942,a)].

given #1912 (F,wt=11): 7768 -->_s0(true,length(tail(length(nil)))) | -->*_s0(length(tail(0)),false) # answer(goal).  [resolve(7166,b,941,a)].

given #1913 (F,wt=11): 7769 -->_s0(true,tail(tail(length(nil)))) | -->*_s0(tail(tail(0)),false) # answer(goal).  [resolve(7166,b,928,a)].

given #1914 (T,wt=9): 2577 ->*_s0(app(nil,app(nil,leq(0,x))),true).  [ur(87,a,61,a,b,691,a)].

given #1915 (T,wt=9): 2580 ->*_s0(sndsplit(0,sndsplit(0,fstsplit(0,x))),nil).  [ur(87,a,82,a,b,693,a)].

given #1916 (T,wt=9): 2582 ->*_s0(app(nil,sndsplit(0,fstsplit(0,x))),nil).  [ur(87,a,61,a,b,693,a)].

given #1917 (T,wt=9): 2584 ->*_s0(sndsplit(0,app(nil,fstsplit(0,x))),nil).  [ur(87,a,82,a,b,695,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): 7770 -->_s0(true,s(tail(length(nil)))) | -->*_s0(s(tail(0)),false) # answer(goal).  [resolve(7166,b,923,a)].

given #1920 (F,wt=11): 7771 -->_s0(true,empty(s(length(nil)))) | -->*_s0(empty(s(0)),false) # answer(goal).  [resolve(7166,b,919,a)].

given #1921 (F,wt=11): 7772 -->_s0(true,head(s(length(nil)))) | -->*_s0(head(s(0)),false) # answer(goal).  [resolve(7166,b,916,a)].

given #1922 (F,wt=11): 7773 -->_s0(true,length(s(length(nil)))) | -->*_s0(length(s(0)),false) # answer(goal).  [resolve(7166,b,915,a)].

given #1923 (T,wt=9): 2586 ->*_s0(app(nil,app(nil,fstsplit(0,x))),nil).  [ur(87,a,61,a,b,695,a)].

given #1924 (T,wt=9): 2597 ->*_s0(sndsplit(0,sndsplit(0,app(nil,x))),x).  [ur(87,a,82,a,b,700,a)].

given #1925 (T,wt=9): 2599 ->*_s0(app(nil,sndsplit(0,app(nil,x))),x).  [ur(87,a,61,a,b,700,a)].

given #1926 (T,wt=9): 2636 ->*_s0(sndsplit(0,app(nil,app(nil,x))),x).  [ur(87,a,82,a,b,702,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): 7774 -->_s0(true,tail(s(length(nil)))) | -->*_s0(tail(s(0)),false) # answer(goal).  [resolve(7166,b,902,a)].

given #1929 (F,wt=11): 7775 -->_s0(true,s(s(length(nil)))) | -->*_s0(s(s(0)),false) # answer(goal).  [resolve(7166,b,897,a)].

given #1930 (F,wt=11): 7776 -->_s0(true,empty(empty(empty(nil)))) | -->*_s0(empty(empty(true)),false) # answer(goal).  [resolve(7166,b,862,a)].

given #1931 (F,wt=11): 7777 -->_s0(true,head(empty(empty(nil)))) | -->*_s0(head(empty(true)),false) # answer(goal).  [resolve(7166,b,859,a)].

given #1932 (T,wt=9): 2638 ->*_s0(app(nil,app(nil,app(nil,x))),x).  [ur(87,a,61,a,b,702,a)].

given #1933 (T,wt=9): 2639 ->*_s0(length(sndsplit(0,cons(x,nil))),s(0)).  [ur(87,a,482,a,b,1263,a)].

given #1934 (T,wt=9): 2640 ->*_s0(length(app(nil,cons(x,nil))),s(0)).  [ur(87,a,132,a,b,1263,a)].

given #1935 (T,wt=9): 2642 ->*_s0(sndsplit(0,length(cons(x,nil))),s(0)).  [ur(87,a,82,a,b,1263,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): 7778 -->_s0(true,length(empty(empty(nil)))) | -->*_s0(length(empty(true)),false) # answer(goal).  [resolve(7166,b,858,a)].

given #1938 (F,wt=11): 7779 -->_s0(true,tail(empty(empty(nil)))) | -->*_s0(tail(empty(true)),false) # answer(goal).  [resolve(7166,b,845,a)].

given #1939 (F,wt=11): 7780 -->_s0(true,s(empty(empty(nil)))) | -->*_s0(s(empty(true)),false) # answer(goal).  [resolve(7166,b,840,a)].

given #1940 (F,wt=11): 7781 -->_s0(true,empty(head(empty(nil)))) | -->*_s0(empty(head(true)),false) # answer(goal).  [resolve(7166,b,836,a)].

given #1941 (T,wt=9): 2644 ->*_s0(app(nil,length(cons(x,nil))),s(0)).  [ur(87,a,61,a,b,1263,a)].

given #1942 (T,wt=9): 2645 ->*_s0(s(sndsplit(0,app(nil,x))),s(x)).  [ur(87,a,464,a,b,1311,a)].

given #1943 (T,wt=9): 2646 ->*_s0(s(app(nil,app(nil,x))),s(x)).  [ur(87,a,114,a,b,1311,a)].

given #1944 (T,wt=9): 2648 ->*_s0(sndsplit(0,s(app(nil,x))),s(x)).  [ur(87,a,82,a,b,1311,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): 7782 -->_s0(true,head(head(empty(nil)))) | -->*_s0(head(head(true)),false) # answer(goal).  [resolve(7166,b,833,a)].

given #1947 (F,wt=11): 7783 -->_s0(true,length(head(empty(nil)))) | -->*_s0(length(head(true)),false) # answer(goal).  [resolve(7166,b,832,a)].

given #1948 (F,wt=11): 7784 -->_s0(true,tail(head(empty(nil)))) | -->*_s0(tail(head(true)),false) # answer(goal).  [resolve(7166,b,819,a)].

given #1949 (F,wt=11): 7785 -->_s0(true,s(head(empty(nil)))) | -->*_s0(s(head(true)),false) # answer(goal).  [resolve(7166,b,814,a)].

given #1950 (T,wt=9): 2650 ->*_s0(app(nil,s(app(nil,x))),s(x)).  [ur(87,a,61,a,b,1311,a)].

given #1951 (T,wt=9): 2651 ->*_s0(tail(sndsplit(0,app(nil,x))),tail(x)).  [ur(87,a,469,a,b,1340,a)].

given #1952 (T,wt=9): 2652 ->*_s0(tail(app(nil,app(nil,x))),tail(x)).  [ur(87,a,119,a,b,1340,a)].

given #1953 (T,wt=9): 2654 ->*_s0(sndsplit(0,tail(app(nil,x))),tail(x)).  [ur(87,a,82,a,b,1340,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): 7786 -->_s0(true,empty(length(empty(nil)))) | -->*_s0(empty(length(true)),false) # answer(goal).  [resolve(7166,b,810,a)].

given #1956 (F,wt=11): 7787 -->_s0(true,head(length(empty(nil)))) | -->*_s0(head(length(true)),false) # answer(goal).  [resolve(7166,b,807,a)].

given #1957 (F,wt=11): 7788 -->_s0(true,length(length(empty(nil)))) | -->*_s0(length(length(true)),false) # answer(goal).  [resolve(7166,b,806,a)].

given #1958 (F,wt=11): 7789 -->_s0(true,tail(length(empty(nil)))) | -->*_s0(tail(length(true)),false) # answer(goal).  [resolve(7166,b,793,a)].

given #1959 (T,wt=9): 2656 ->*_s0(app(nil,tail(app(nil,x))),tail(x)).  [ur(87,a,61,a,b,1340,a)].

given #1960 (T,wt=9): 2687 ->*_s0(length(sndsplit(0,app(nil,x))),length(x)).  [ur(87,a,482,a,b,1369,a)].

given #1961 (T,wt=9): 2688 ->*_s0(length(app(nil,app(nil,x))),length(x)).  [ur(87,a,132,a,b,1369,a)].

given #1962 (T,wt=9): 2690 ->*_s0(sndsplit(0,length(app(nil,x))),length(x)).  [ur(87,a,82,a,b,1369,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): 7790 -->_s0(true,s(length(empty(nil)))) | -->*_s0(s(length(true)),false) # answer(goal).  [resolve(7166,b,788,a)].

given #1965 (F,wt=11): 7791 -->_s0(true,empty(tail(empty(nil)))) | -->*_s0(empty(tail(true)),false) # answer(goal).  [resolve(7166,b,784,a)].

given #1966 (F,wt=11): 7792 -->_s0(true,head(tail(empty(nil)))) | -->*_s0(head(tail(true)),false) # answer(goal).  [resolve(7166,b,781,a)].

given #1967 (F,wt=11): 7793 -->_s0(true,length(tail(empty(nil)))) | -->*_s0(length(tail(true)),false) # answer(goal).  [resolve(7166,b,780,a)].

given #1968 (T,wt=9): 2692 ->*_s0(app(nil,length(app(nil,x))),length(x)).  [ur(87,a,61,a,b,1369,a)].

given #1969 (T,wt=9): 2693 ->*_s0(head(sndsplit(0,app(nil,x))),head(x)).  [ur(87,a,483,a,b,1517,a)].

given #1970 (T,wt=9): 2694 ->*_s0(head(app(nil,app(nil,x))),head(x)).  [ur(87,a,133,a,b,1517,a)].

given #1971 (T,wt=9): 2696 ->*_s0(sndsplit(0,head(app(nil,x))),head(x)).  [ur(87,a,82,a,b,1517,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): 7794 -->_s0(true,tail(tail(empty(nil)))) | -->*_s0(tail(tail(true)),false) # answer(goal).  [resolve(7166,b,767,a)].

given #1974 (F,wt=11): 7795 -->_s0(true,s(tail(empty(nil)))) | -->*_s0(s(tail(true)),false) # answer(goal).  [resolve(7166,b,762,a)].

given #1975 (F,wt=11): 7796 -->_s0(true,empty(s(empty(nil)))) | -->*_s0(empty(s(true)),false) # answer(goal).  [resolve(7166,b,726,a)].

given #1976 (F,wt=11): 7797 -->_s0(true,head(s(empty(nil)))) | -->*_s0(head(s(true)),false) # answer(goal).  [resolve(7166,b,723,a)].

given #1977 (T,wt=9): 2698 ->*_s0(app(nil,head(app(nil,x))),head(x)).  [ur(87,a,61,a,b,1517,a)].

given #1978 (T,wt=9): 2699 ->*_s0(empty(sndsplit(0,app(nil,x))),empty(x)).  [ur(87,a,486,a,b,1548,a)].

given #1979 (T,wt=9): 2700 ->*_s0(empty(app(nil,app(nil,x))),empty(x)).  [ur(87,a,136,a,b,1548,a)].

given #1980 (T,wt=9): 2702 ->*_s0(sndsplit(0,empty(app(nil,x))),empty(x)).  [ur(87,a,82,a,b,1548,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): 7798 -->_s0(true,length(s(empty(nil)))) | -->*_s0(length(s(true)),false) # answer(goal).  [resolve(7166,b,722,a)].

given #1983 (F,wt=11): 7799 -->_s0(true,tail(s(empty(nil)))) | -->*_s0(tail(s(true)),false) # answer(goal).  [resolve(7166,b,709,a)].

given #1984 (F,wt=11): 7800 -->_s0(true,s(s(empty(nil)))) | -->*_s0(s(s(true)),false) # answer(goal).  [resolve(7166,b,704,a)].

given #1985 (F,wt=11): 7801 -->_s0(true,empty(tail(cons(x,y)))) | -->*_s0(empty(y),false) # answer(goal).  [resolve(7166,b,561,a)].

given #1986 (T,wt=9): 2704 ->*_s0(app(nil,empty(app(nil,x))),empty(x)).  [ur(87,a,61,a,b,1548,a)].

given #1987 (T,wt=9): 2705 ->*_s0(s(sndsplit(0,fstsplit(0,x))),s(nil)).  [ur(87,a,464,a,b,1612,a)].

given #1988 (T,wt=9): 2706 ->*_s0(s(app(nil,fstsplit(0,x))),s(nil)).  [ur(87,a,114,a,b,1612,a)].

given #1989 (T,wt=9): 2708 ->*_s0(sndsplit(0,s(fstsplit(0,x))),s(nil)).  [ur(87,a,82,a,b,1612,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): 7802 -->_s0(true,head(tail(cons(x,y)))) | -->*_s0(head(y),false) # answer(goal).  [resolve(7166,b,558,a)].

given #1992 (F,wt=11): 7803 -->_s0(true,length(tail(cons(x,y)))) | -->*_s0(length(y),false) # answer(goal).  [resolve(7166,b,557,a)].

given #1993 (F,wt=11): 7804 -->_s0(true,tail(tail(cons(x,y)))) | -->*_s0(tail(y),false) # answer(goal).  [resolve(7166,b,544,a)].

given #1994 (F,wt=11): 7805 -->_s0(true,s(tail(cons(x,y)))) | -->*_s0(s(y),false) # answer(goal).  [resolve(7166,b,539,a)].

given #1995 (T,wt=9): 2710 ->*_s0(app(nil,s(fstsplit(0,x))),s(nil)).  [ur(87,a,61,a,b,1612,a)].

given #1996 (T,wt=9): 2743 ->*_s0(tail(sndsplit(0,fstsplit(0,x))),tail(nil)).  [ur(87,a,469,a,b,1639,a)].

given #1997 (T,wt=9): 2744 ->*_s0(tail(app(nil,fstsplit(0,x))),tail(nil)).  [ur(87,a,119,a,b,1639,a)].

given #1998 (T,wt=9): 2746 ->*_s0(sndsplit(0,tail(fstsplit(0,x))),tail(nil)).  [ur(87,a,82,a,b,1639,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): 7806 -->_s0(true,empty(sndsplit(s(x),nil))) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(7166,b,536,a)].

given #2001 (F,wt=11): 7807 -->_s0(true,head(sndsplit(s(x),nil))) | -->*_s0(head(nil),false) # answer(goal).  [resolve(7166,b,533,a)].

given #2002 (F,wt=11): 7808 -->_s0(true,length(sndsplit(s(x),nil))) | -->*_s0(length(nil),false) # answer(goal).  [resolve(7166,b,532,a)].

given #2003 (F,wt=11): 7809 -->_s0(true,tail(sndsplit(s(x),nil))) | -->*_s0(tail(nil),false) # answer(goal).  [resolve(7166,b,519,a)].

given #2004 (T,wt=9): 2748 ->*_s0(app(nil,tail(fstsplit(0,x))),tail(nil)).  [ur(87,a,61,a,b,1639,a)].

given #2005 (T,wt=9): 2749 ->*_s0(length(sndsplit(0,fstsplit(0,x))),length(nil)).  [ur(87,a,482,a,b,1667,a)].

given #2006 (T,wt=9): 2750 ->*_s0(length(app(nil,fstsplit(0,x))),length(nil)).  [ur(87,a,132,a,b,1667,a)].

given #2007 (T,wt=9): 2752 ->*_s0(sndsplit(0,length(fstsplit(0,x))),length(nil)).  [ur(87,a,82,a,b,1667,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): 7810 -->_s0(true,s(sndsplit(s(x),nil))) | -->*_s0(s(nil),false) # answer(goal).  [resolve(7166,b,514,a)].

given #2010 (F,wt=11): 7821 -->_s0(true,empty(leq(s(x),0))) | -->*_s0(empty(false),false) # answer(goal).  [resolve(7166,b,386,a)].

given #2011 (F,wt=11): 7822 -->_s0(true,head(leq(s(x),0))) | -->*_s0(head(false),false) # answer(goal).  [resolve(7166,b,383,a)].

given #2012 (F,wt=11): 7823 -->_s0(true,length(leq(s(x),0))) | -->*_s0(length(false),false) # answer(goal).  [resolve(7166,b,382,a)].

given #2013 (T,wt=9): 2754 ->*_s0(app(nil,length(fstsplit(0,x))),length(nil)).  [ur(87,a,61,a,b,1667,a)].

given #2014 (T,wt=9): 2755 ->*_s0(head(sndsplit(0,fstsplit(0,x))),head(nil)).  [ur(87,a,483,a,b,1737,a)].

given #2015 (T,wt=9): 2756 ->*_s0(head(app(nil,fstsplit(0,x))),head(nil)).  [ur(87,a,133,a,b,1737,a)].

given #2016 (T,wt=9): 2758 ->*_s0(sndsplit(0,head(fstsplit(0,x))),head(nil)).  [ur(87,a,82,a,b,1737,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): 7824 -->_s0(true,tail(leq(s(x),0))) | -->*_s0(tail(false),false) # answer(goal).  [resolve(7166,b,369,a)].

given #2019 (F,wt=11): 7825 -->_s0(true,s(leq(s(x),0))) | -->*_s0(s(false),false) # answer(goal).  [resolve(7166,b,364,a)].

given #2020 (F,wt=11): 7831 -->_s0(true,app(length(nil),x)) | -->*_s0(app(0,x),false) # answer(goal).  [resolve(7166,b,338,a)].

given #2021 (F,wt=11): 7832 -->_s0(true,app(x,length(nil))) | -->*_s0(app(x,0),false) # answer(goal).  [resolve(7166,b,337,a)].

given #2022 (T,wt=9): 2760 ->*_s0(app(nil,head(fstsplit(0,x))),head(nil)).  [ur(87,a,61,a,b,1737,a)].

given #2023 (T,wt=9): 2761 ->*_s0(empty(sndsplit(0,fstsplit(0,x))),empty(nil)).  [ur(87,a,486,a,b,1764,a)].

given #2024 (T,wt=9): 2762 ->*_s0(empty(app(nil,fstsplit(0,x))),empty(nil)).  [ur(87,a,136,a,b,1764,a)].

given #2025 (T,wt=9): 2764 ->*_s0(sndsplit(0,empty(fstsplit(0,x))),empty(nil)).  [ur(87,a,82,a,b,1764,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): 7834 -->_s0(true,fstsplit(length(nil),x)) | -->*_s0(fstsplit(0,x),false) # answer(goal).  [resolve(7166,b,335,a)].

given #2028 (F,wt=11): 7835 -->_s0(true,fstsplit(x,length(nil))) | -->*_s0(fstsplit(x,0),false) # answer(goal).  [resolve(7166,b,334,a)].

given #2029 (F,wt=11): 7838 -->_s0(true,leq(length(nil),x)) | -->*_s0(leq(0,x),false) # answer(goal).  [resolve(7166,b,331,a)].

given #2030 (F,wt=11): 7839 -->_s0(true,leq(x,length(nil))) | -->*_s0(leq(x,0),false) # answer(goal).  [resolve(7166,b,330,a)].

given #2031 (T,wt=9): 2766 ->*_s0(app(nil,empty(fstsplit(0,x))),empty(nil)).  [ur(87,a,61,a,b,1764,a)].

given #2032 (T,wt=9): 2798 ->*_s0(s(sndsplit(0,leq(0,x))),s(true)).  [ur(87,a,464,a,b,1799,a)].

given #2033 (T,wt=9): 2799 ->*_s0(s(app(nil,leq(0,x))),s(true)).  [ur(87,a,114,a,b,1799,a)].

given #2034 (T,wt=9): 2801 ->*_s0(sndsplit(0,s(leq(0,x))),s(true)).  [ur(87,a,82,a,b,1799,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): 7840 -->_s0(true,mapf(length(nil),x)) | -->*_s0(mapf(0,x),false) # answer(goal).  [resolve(7166,b,329,a)].

given #2037 (F,wt=11): 7841 -->_s0(true,mapf(x,length(nil))) | -->*_s0(mapf(x,0),false) # answer(goal).  [resolve(7166,b,328,a)].

given #2038 (F,wt=11): 7842 -->_s0(true,sndsplit(length(nil),x)) | -->*_s0(sndsplit(0,x),false) # answer(goal).  [resolve(7166,b,321,a)].

given #2039 (F,wt=11): 7843 -->_s0(true,sndsplit(x,length(nil))) | -->*_s0(sndsplit(x,0),false) # answer(goal).  [resolve(7166,b,320,a)].

given #2040 (T,wt=9): 2803 ->*_s0(app(nil,s(leq(0,x))),s(true)).  [ur(87,a,61,a,b,1799,a)].

given #2041 (T,wt=9): 2804 ->*_s0(tail(sndsplit(0,leq(0,x))),tail(true)).  [ur(87,a,469,a,b,1858,a)].

given #2042 (T,wt=9): 2805 ->*_s0(tail(app(nil,leq(0,x))),tail(true)).  [ur(87,a,119,a,b,1858,a)].

given #2043 (T,wt=9): 2807 ->*_s0(sndsplit(0,tail(leq(0,x))),tail(true)).  [ur(87,a,82,a,b,1858,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): 7845 -->_s0(true,cons(length(nil),x)) | -->*_s0(cons(0,x),false) # answer(goal).  [resolve(7166,b,318,a)].

given #2046 (F,wt=11): 7846 -->_s0(true,cons(x,length(nil))) | -->*_s0(cons(x,0),false) # answer(goal).  [resolve(7166,b,317,a)].

given #2047 (F,wt=11): 7847 -->_s0(true,f(length(nil),x)) | -->*_s0(f(0,x),false) # answer(goal).  [resolve(7166,b,316,a)].

given #2048 (F,wt=11): 7848 -->_s0(true,f(x,length(nil))) | -->*_s0(f(x,0),false) # answer(goal).  [resolve(7166,b,315,a)].

given #2049 (T,wt=9): 2809 ->*_s0(app(nil,tail(leq(0,x))),tail(true)).  [ur(87,a,61,a,b,1858,a)].

given #2050 (T,wt=9): 2810 ->*_s0(length(sndsplit(0,leq(0,x))),length(true)).  [ur(87,a,482,a,b,1885,a)].

given #2051 (T,wt=9): 2811 ->*_s0(length(app(nil,leq(0,x))),length(true)).  [ur(87,a,132,a,b,1885,a)].

given #2052 (T,wt=9): 2813 ->*_s0(sndsplit(0,length(leq(0,x))),length(true)).  [ur(87,a,82,a,b,1885,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): 7850 -->_s0(true,empty(head(cons(x,y)))) | -->*_s0(empty(x),false) # answer(goal).  [resolve(7166,b,286,a)].

given #2055 (F,wt=11): 7851 -->_s0(true,head(head(cons(x,y)))) | -->*_s0(head(x),false) # answer(goal).  [resolve(7166,b,283,a)].

given #2056 (F,wt=11): 7852 -->_s0(true,length(head(cons(x,y)))) | -->*_s0(length(x),false) # answer(goal).  [resolve(7166,b,282,a)].

given #2057 (F,wt=11): 7853 -->_s0(true,tail(head(cons(x,y)))) | -->*_s0(tail(x),false) # answer(goal).  [resolve(7166,b,269,a)].

given #2058 (T,wt=9): 2815 ->*_s0(app(nil,length(leq(0,x))),length(true)).  [ur(87,a,61,a,b,1885,a)].

given #2059 (T,wt=9): 2816 ->*_s0(head(sndsplit(0,leq(0,x))),head(true)).  [ur(87,a,483,a,b,1912,a)].

given #2060 (T,wt=9): 2817 ->*_s0(head(app(nil,leq(0,x))),head(true)).  [ur(87,a,133,a,b,1912,a)].

given #2061 (T,wt=9): 2819 ->*_s0(sndsplit(0,head(leq(0,x))),head(true)).  [ur(87,a,82,a,b,1912,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): 7854 -->_s0(true,s(head(cons(x,y)))) | -->*_s0(s(x),false) # answer(goal).  [resolve(7166,b,264,a)].

given #2064 (F,wt=11): 7855 -->_s0(true,empty(fstsplit(s(x),nil))) | -->*_s0(empty(nil),false) # answer(goal).  [resolve(7166,b,261,a)].

given #2065 (F,wt=11): 7856 -->_s0(true,head(fstsplit(s(x),nil))) | -->*_s0(head(nil),false) # answer(goal).  [resolve(7166,b,258,a)].

given #2066 (F,wt=11): 7857 -->_s0(true,length(fstsplit(s(x),nil))) | -->*_s0(length(nil),false) # answer(goal).  [resolve(7166,b,257,a)].

given #2067 (T,wt=9): 2821 ->*_s0(app(nil,head(leq(0,x))),head(true)).  [ur(87,a,61,a,b,1912,a)].

given #2068 (T,wt=9): 2823 ->*_s0(f(x,app(nil,y)),f(x,y)).  [ur(87,a,115,a,b,86,a)].

given #2069 (T,wt=9): 2869 ->*_s0(empty(sndsplit(0,leq(0,x))),empty(true)).  [ur(87,a,486,a,b,1939,a)].

given #2070 (T,wt=9): 2870 ->*_s0(empty(app(nil,leq(0,x))),empty(true)).  [ur(87,a,136,a,b,1939,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): 7858 -->_s0(true,tail(fstsplit(s(x),nil))) | -->*_s0(tail(nil),false) # answer(goal).  [resolve(7166,b,244,a)].

given #2073 (F,wt=11): 7859 -->_s0(true,s(fstsplit(s(x),nil))) | -->*_s0(s(nil),false) # answer(goal).  [resolve(7166,b,239,a)].

given #2074 (F,wt=11): 7865 -->_s0(true,app(empty(nil),x)) | -->*_s0(app(true,x),false) # answer(goal).  [resolve(7166,b,188,a)].

given #2075 (F,wt=11): 7866 -->_s0(true,app(x,empty(nil))) | -->*_s0(app(x,true),false) # answer(goal).  [resolve(7166,b,187,a)].

given #2076 (T,wt=9): 2872 ->*_s0(sndsplit(0,empty(leq(0,x))),empty(true)).  [ur(87,a,82,a,b,1939,a)].

given #2077 (T,wt=9): 2874 ->*_s0(app(nil,empty(leq(0,x))),empty(true)).  [ur(87,a,61,a,b,1939,a)].

given #2078 (T,wt=9): 2875 ->*_s0(s(sndsplit(0,mapf(x,nil))),s(nil)).  [ur(87,a,464,a,b,1993,a)].

given #2079 (T,wt=9): 2876 ->*_s0(s(app(nil,mapf(x,nil))),s(nil)).  [ur(87,a,114,a,b,1993,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): 7868 -->_s0(true,fstsplit(empty(nil),x)) | -->*_s0(fstsplit(true,x),false) # answer(goal).  [resolve(7166,b,185,a)].

given #2082 (F,wt=11): 7869 -->_s0(true,fstsplit(x,empty(nil))) | -->*_s0(fstsplit(x,true),false) # answer(goal).  [resolve(7166,b,184,a)].

given #2083 (F,wt=11): 7872 -->_s0(true,leq(empty(nil),x)) | -->*_s0(leq(true,x),false) # answer(goal).  [resolve(7166,b,181,a)].

given #2084 (F,wt=11): 7873 -->_s0(true,leq(x,empty(nil))) | -->*_s0(leq(x,true),false) # answer(goal).  [resolve(7166,b,180,a)].

given #2085 (T,wt=9): 2878 ->*_s0(sndsplit(0,s(mapf(x,nil))),s(nil)).  [ur(87,a,82,a,b,1993,a)].

given #2086 (T,wt=9): 2880 ->*_s0(app(nil,s(mapf(x,nil))),s(nil)).  [ur(87,a,61,a,b,1993,a)].

given #2087 (T,wt=9): 2881 ->*_s0(tail(sndsplit(0,mapf(x,nil))),tail(nil)).  [ur(87,a,469,a,b,2020,a)].

given #2088 (T,wt=9): 2882 ->*_s0(tail(app(nil,mapf(x,nil))),tail(nil)).  [ur(87,a,119,a,b,2020,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): 7874 -->_s0(true,mapf(empty(nil),x)) | -->*_s0(mapf(true,x),false) # answer(goal).  [resolve(7166,b,179,a)].

given #2091 (F,wt=11): 7875 -->_s0(true,mapf(x,empty(nil))) | -->*_s0(mapf(x,true),false) # answer(goal).  [resolve(7166,b,178,a)].

given #2092 (F,wt=11): 7876 -->_s0(true,sndsplit(empty(nil),x)) | -->*_s0(sndsplit(true,x),false) # answer(goal).  [resolve(7166,b,171,a)].

given #2093 (F,wt=11): 7877 -->_s0(true,sndsplit(x,empty(nil))) | -->*_s0(sndsplit(x,true),false) # answer(goal).  [resolve(7166,b,170,a)].

given #2094 (T,wt=9): 2884 ->*_s0(sndsplit(0,tail(mapf(x,nil))),tail(nil)).  [ur(87,a,82,a,b,2020,a)].

given #2095 (T,wt=9): 2886 ->*_s0(app(nil,tail(mapf(x,nil))),tail(nil)).  [ur(87,a,61,a,b,2020,a)].

given #2096 (T,wt=9): 2887 ->*_s0(length(sndsplit(0,mapf(x,nil))),length(nil)).  [ur(87,a,482,a,b,2048,a)].

given #2097 (T,wt=9): 2888 ->*_s0(length(app(nil,mapf(x,nil))),length(nil)).  [ur(87,a,132,a,b,2048,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): 7879 -->_s0(true,cons(empty(nil),x)) | -->*_s0(cons(true,x),false) # answer(goal).  [resolve(7166,b,168,a)].

given #2100 (F,wt=11): 7880 -->_s0(true,cons(x,empty(nil))) | -->*_s0(cons(x,true),false) # answer(goal).  [resolve(7166,b,167,a)].

given #2101 (F,wt=11): 7881 -->_s0(true,f(empty(nil),x)) | -->*_s0(f(true,x),false) # answer(goal).  [resolve(7166,b,166,a)].

given #2102 (F,wt=11): 7882 -->_s0(true,f(x,empty(nil))) | -->*_s0(f(x,true),false) # answer(goal).  [resolve(7166,b,165,a)].

given #2103 (T,wt=9): 2890 ->*_s0(sndsplit(0,length(mapf(x,nil))),length(nil)).  [ur(87,a,82,a,b,2048,a)].

given #2104 (T,wt=9): 2892 ->*_s0(app(nil,length(mapf(x,nil))),length(nil)).  [ur(87,a,61,a,b,2048,a)].

given #2105 (T,wt=9): 2894 ->*_s0(f(app(nil,x),y),f(x,y)).  [ur(87,a,116,a,b,86,a)].

given #2106 (T,wt=9): 2927 ->*_s0(head(sndsplit(0,mapf(x,nil))),head(nil)).  [ur(87,a,483,a,b,2107,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): 7886 -->_s0(true,empty(empty(cons(x,y)))) | -->*_s0(empty(false),false) # answer(goal).  [resolve(7166,b,161,a)].

given #2109 (F,wt=11): 7889 -->_s0(true,head(empty(cons(x,y)))) | -->*_s0(head(false),false) # answer(goal).  [resolve(7166,b,158,a)].

given #2110 (F,wt=11): 7890 -->_s0(true,length(empty(cons(x,y)))) | -->*_s0(length(false),false) # answer(goal).  [resolve(7166,b,157,a)].

given #2111 (F,wt=11): 7903 -->_s0(true,tail(empty(cons(x,y)))) | -->*_s0(tail(false),false) # answer(goal).  [resolve(7166,b,144,a)].

given #2112 (T,wt=9): 2928 ->*_s0(head(app(nil,mapf(x,nil))),head(nil)).  [ur(87,a,133,a,b,2107,a)].

given #2113 (T,wt=9): 2930 ->*_s0(sndsplit(0,head(mapf(x,nil))),head(nil)).  [ur(87,a,82,a,b,2107,a)].

given #2114 (T,wt=9): 2932 ->*_s0(app(nil,head(mapf(x,nil))),head(nil)).  [ur(87,a,61,a,b,2107,a)].

given #2115 (T,wt=9): 2933 ->*_s0(empty(sndsplit(0,mapf(x,nil))),empty(nil)).  [ur(87,a,486,a,b,2134,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): 7908 -->_s0(true,s(empty(cons(x,y)))) | -->*_s0(s(false),false) # answer(goal).  [resolve(7166,b,139,a)].

given #2118 (F,wt=11): 7974 -->_s0(true,length(cons(x,y))) | -->*_s0(s(length(y)),false) # answer(goal).  [resolve(7166,b,68,a)].

given #2119 (F,wt=11): 7981 -->_s0(true,s(x)) | -->*_s0(s(y),false) | -->_s0(x,y) # answer(goal).  [resolve(7166,b,59,b)].

given #2120 (F,wt=11): 7986 -->_s0(true,tail(x)) | -->*_s0(tail(y),false) | -->_s0(x,y) # answer(goal).  [resolve(7166,b,54,b)].

given #2121 (T,wt=9): 2934 ->*_s0(empty(app(nil,mapf(x,nil))),empty(nil)).  [ur(87,a,136,a,b,2134,a)].

given #2122 (T,wt=9): 2936 ->*_s0(sndsplit(0,empty(mapf(x,nil))),empty(nil)).  [ur(87,a,82,a,b,2134,a)].

given #2123 (T,wt=9): 2938 ->*_s0(app(nil,empty(mapf(x,nil))),empty(nil)).  [ur(87,a,61,a,b,2134,a)].

given #2124 (T,wt=9): 2939 ->*_s0(s(sndsplit(0,sndsplit(0,x))),s(x)).  [ur(87,a,464,a,b,2171,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=9): 16110 -->_s0(true,tail(sndsplit(length(nil),cons(x,false)))) # answer(goal).  [ur(7986,b,2235,a,c,321,a)].

given #2127 (F,wt=10): 16101 -->_s0(true,tail(app(sndsplit(0,cons(x,nil)),false))) # answer(goal).  [ur(7986,b,5690,a,c,488,a)].

given #2128 (F,wt=10): 16102 -->_s0(true,tail(app(cons(x,nil),sndsplit(0,false)))) # answer(goal).  [ur(7986,b,5690,a,c,487,a)].

given #2129 (F,wt=10): 16107 -->_s0(true,tail(app(app(nil,cons(x,nil)),false))) # answer(goal).  [ur(7986,b,5690,a,c,138,a)].

given #2130 (T,wt=9): 2940 ->*_s0(s(app(nil,sndsplit(0,x))),s(x)).  [ur(87,a,114,a,b,2171,a)].

given #2131 (T,wt=9): 2942 ->*_s0(sndsplit(0,s(sndsplit(0,x))),s(x)).  [ur(87,a,82,a,b,2171,a)].

given #2132 (T,wt=9): 2944 ->*_s0(app(nil,s(sndsplit(0,x))),s(x)).  [ur(87,a,61,a,b,2171,a)].

given #2133 (T,wt=9): 2945 ->*_s0(tail(sndsplit(0,sndsplit(0,x))),tail(x)).  [ur(87,a,469,a,b,2236,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=10): 16108 -->_s0(true,tail(app(cons(x,nil),app(nil,false)))) # answer(goal).  [ur(7986,b,5690,a,c,137,a)].

given #2136 (F,wt=10): 16109 -->_s0(true,tail(sndsplit(sndsplit(0,0),cons(x,false)))) # answer(goal).  [ur(7986,b,2235,a,c,471,a)].

given #2137 (F,wt=10): 16113 -->_s0(true,tail(sndsplit(app(nil,0),cons(x,false)))) # answer(goal).  [ur(7986,b,2235,a,c,121,a)].

given #2138 (F,wt=10): 16115 -->_s0(true,tail(app(sndsplit(0,nil),cons(x,false)))) # answer(goal).  [ur(7986,b,1339,a,c,488,a)].

given #2139 (T,wt=9): 2946 ->*_s0(tail(app(nil,sndsplit(0,x))),tail(x)).  [ur(87,a,119,a,b,2236,a)].

given #2140 (T,wt=9): 2948 ->*_s0(sndsplit(0,tail(sndsplit(0,x))),tail(x)).  [ur(87,a,82,a,b,2236,a)].

given #2141 (T,wt=9): 2950 ->*_s0(app(nil,tail(sndsplit(0,x))),tail(x)).  [ur(87,a,61,a,b,2236,a)].

given #2142 (T,wt=9): 2952 ->*_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=10): 16116 -->_s0(true,tail(app(mapf(x,nil),cons(y,false)))) # answer(goal).  [ur(7986,b,1339,a,c,463,a)].

given #2145 (F,wt=10): 16120 -->_s0(true,tail(app(fstsplit(0,x),cons(y,false)))) # answer(goal).  [ur(7986,b,1339,a,c,213,a)].

given #2146 (F,wt=10): 16121 -->_s0(true,tail(app(app(nil,nil),cons(x,false)))) # answer(goal).  [ur(7986,b,1339,a,c,138,a)].

given #2147 (F,wt=11): 7999 -->_s0(true,length(x)) | -->*_s0(length(y),false) | -->_s0(x,y) # answer(goal).  [resolve(7166,b,41,b)].

given #2148 (T,wt=9): 2981 ->*_s0(length(sndsplit(0,sndsplit(0,x))),length(x)).  [ur(87,a,482,a,b,2269,a)].

given #2149 (T,wt=9): 2982 ->*_s0(length(app(nil,sndsplit(0,x))),length(x)).  [ur(87,a,132,a,b,2269,a)].

given #2150 (T,wt=9): 2984 ->*_s0(sndsplit(0,length(sndsplit(0,x))),length(x)).  [ur(87,a,82,a,b,2269,a)].

given #2151 (T,wt=9): 2986 ->*_s0(app(nil,length(sndsplit(0,x))),length(x)).  [ur(87,a,61,a,b,2269,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): 8000 -->_s0(true,head(x)) | -->*_s0(head(y),false) | -->_s0(x,y) # answer(goal).  [resolve(7166,b,40,b)].

given #2154 (F,wt=9): 17245 -->_s0(true,head(sndsplit(length(nil),cons(false,x)))) # answer(goal).  [ur(8000,b,2304,a,c,321,a)].

given #2155 (F,wt=10): 17239 -->_s0(true,head(app(sndsplit(0,cons(false,x)),y))) # answer(goal).  [ur(8000,b,2492,a,c,488,a)].

given #2156 (F,wt=10): 17242 -->_s0(true,head(app(app(nil,cons(false,x)),y))) # answer(goal).  [ur(8000,b,2492,a,c,138,a)].

given #2157 (T,wt=9): 2987 ->*_s0(head(sndsplit(0,sndsplit(0,x))),head(x)).  [ur(87,a,483,a,b,2305,a)].

given #2158 (T,wt=9): 2988 ->*_s0(head(app(nil,sndsplit(0,x))),head(x)).  [ur(87,a,133,a,b,2305,a)].

given #2159 (T,wt=9): 2990 ->*_s0(sndsplit(0,head(sndsplit(0,x))),head(x)).  [ur(87,a,82,a,b,2305,a)].

given #2160 (T,wt=9): 2992 ->*_s0(app(nil,head(sndsplit(0,x))),head(x)).  [ur(87,a,61,a,b,2305,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=10): 17243 -->_s0(true,head(app(app(cons(false,x),y),z))) # answer(goal).  [ur(8000,b,2492,a,c,113,a)].

given #2163 (F,wt=10): 17244 -->_s0(true,head(sndsplit(sndsplit(0,0),cons(false,x)))) # answer(goal).  [ur(8000,b,2304,a,c,471,a)].

given #2164 (F,wt=10): 17249 -->_s0(true,head(sndsplit(app(nil,0),cons(false,x)))) # answer(goal).  [ur(8000,b,2304,a,c,121,a)].

given #2165 (F,wt=10): 17251 -->_s0(true,head(app(sndsplit(0,nil),cons(false,x)))) # answer(goal).  [ur(8000,b,1516,a,c,488,a)].

given #2166 (T,wt=9): 2993 ->*_s0(empty(sndsplit(0,sndsplit(0,x))),empty(x)).  [ur(87,a,486,a,b,2367,a)].

given #2167 (T,wt=9): 2994 ->*_s0(empty(app(nil,sndsplit(0,x))),empty(x)).  [ur(87,a,136,a,b,2367,a)].

given #2168 (T,wt=9): 2996 ->*_s0(sndsplit(0,empty(sndsplit(0,x))),empty(x)).  [ur(87,a,82,a,b,2367,a)].

given #2169 (T,wt=9): 2998 ->*_s0(app(nil,empty(sndsplit(0,x))),empty(x)).  [ur(87,a,61,a,b,2367,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=10): 17252 -->_s0(true,head(app(mapf(x,nil),cons(false,y)))) # answer(goal).  [ur(8000,b,1516,a,c,463,a)].

given #2172 (F,wt=10): 17257 -->_s0(true,head(app(fstsplit(0,x),cons(false,y)))) # answer(goal).  [ur(8000,b,1516,a,c,213,a)].

given #2173 (F,wt=10): 17258 -->_s0(true,head(app(app(nil,nil),cons(false,x)))) # answer(goal).  [ur(8000,b,1516,a,c,138,a)].

given #2174 (F,wt=11): 8003 -->_s0(true,empty(x)) | -->*_s0(empty(y),false) | -->_s0(x,y) # answer(goal).  [resolve(7166,b,37,b)].

given #2175 (T,wt=9): 3027 ->*_s0(cons(app(nil,x),y),cons(x,y)).  [ur(87,a,118,a,b,86,a)].

given #2176 (T,wt=9): 3166 ->*_s0(sndsplit(x,app(nil,y)),sndsplit(x,y)).  [ur(87,a,120,a,b,86,a)].

given #2177 (T,wt=9): 3301 ->*_s0(sndsplit(app(nil,0),app(nil,x)),x).  [ur(87,a,121,a,b,700,a)].

given #2178 (T,wt=9): 3302 ->*_s0(sndsplit(app(nil,0),fstsplit(0,x)),nil).  [ur(87,a,121,a,b,693,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=9): 17794 -->_s0(true,empty(sndsplit(length(nil),cons(x,y)))) # answer(goal).  [ur(8003,b,2365,a,c,321,a)].

given #2181 (F,wt=10): 17735 -->_s0(true,empty(app(app(cons(x,y),z),u))) # answer(goal).  [resolve(8003,c,113,a),unit_del(b,2658)].

given #2182 (F,wt=10): 17790 -->_s0(true,empty(app(sndsplit(0,cons(x,y)),z))) # answer(goal).  [ur(8003,b,2658,a,c,488,a)].

given #2183 (F,wt=10): 17792 -->_s0(true,empty(app(app(nil,cons(x,y)),z))) # answer(goal).  [ur(8003,b,2658,a,c,138,a)].

given #2184 (T,wt=9): 3303 ->*_s0(sndsplit(app(nil,0),leq(0,x)),true).  [ur(87,a,121,a,b,688,a)].

given #2185 (T,wt=9): 3304 ->*_s0(sndsplit(app(nil,0),mapf(x,nil)),nil).  [ur(87,a,121,a,b,645,a)].

given #2186 (T,wt=9): 3305 ->*_s0(sndsplit(app(nil,0),sndsplit(0,x)),x).  [ur(87,a,121,a,b,641,a)].

given #2187 (T,wt=9): 3310 ->*_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=10): 17793 -->_s0(true,empty(sndsplit(sndsplit(0,0),cons(x,y)))) # answer(goal).  [ur(8003,b,2365,a,c,471,a)].

given #2190 (F,wt=10): 17798 -->_s0(true,empty(sndsplit(app(nil,0),cons(x,y)))) # answer(goal).  [ur(8003,b,2365,a,c,121,a)].

given #2191 (F,wt=10): 17800 -->_s0(true,empty(app(sndsplit(0,nil),cons(x,y)))) # answer(goal).  [ur(8003,b,1546,a,c,488,a)].

given #2192 (F,wt=10): 17801 -->_s0(true,empty(app(mapf(x,nil),cons(y,z)))) # answer(goal).  [ur(8003,b,1546,a,c,463,a)].

given #2193 (T,wt=9): 3346 ->*_s0(sndsplit(app(nil,app(nil,0)),x),x).  [ur(87,a,121,a,b,3308,a)].

given #2194 (T,wt=9): 3350 ->*_s0(sndsplit(0,sndsplit(app(nil,0),x)),x).  [ur(87,a,82,a,b,3308,a)].

given #2195 (T,wt=9): 3352 ->*_s0(app(nil,sndsplit(app(nil,0),x)),x).  [ur(87,a,61,a,b,3308,a)].

given #2196 (T,wt=9): 3799 ->*_s0(length(sndsplit(0,fstsplit(s(x),nil))),0).  [ur(87,a,482,a,b,3772,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): 17806 -->_s0(true,empty(app(fstsplit(0,x),cons(y,z)))) # answer(goal).  [ur(8003,b,1546,a,c,213,a)].

given #2199 (F,wt=10): 17807 -->_s0(true,empty(app(app(nil,nil),cons(x,y)))) # answer(goal).  [ur(8003,b,1546,a,c,138,a)].

given #2200 (F,wt=10): 17888 -->_s0(true,sndsplit(length(nil),sndsplit(app(nil,0),false))) # answer(goal).  [resolve(3350,a,7842,b)].

given #2201 (F,wt=11): 8010 -->_s0(true,x) | -->_s0(x,leq(s(s(y)),s(0))) # answer(goal).  [resolve(7166,c,1078,a)].

given #2202 (T,wt=9): 3800 ->*_s0(length(app(nil,fstsplit(s(x),nil))),0).  [ur(87,a,132,a,b,3772,a)].

given #2203 (T,wt=9): 3802 ->*_s0(sndsplit(0,length(fstsplit(s(x),nil))),0).  [ur(87,a,82,a,b,3772,a)].

given #2204 (T,wt=9): 3804 ->*_s0(app(nil,length(fstsplit(s(x),nil))),0).  [ur(87,a,61,a,b,3772,a)].

given #2205 (T,wt=9): 3894 ->*_s0(empty(sndsplit(0,fstsplit(s(x),nil))),true).  [ur(87,a,486,a,b,3864,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): 8011 -->_s0(true,x) | -->_s0(x,sndsplit(0,leq(s(y),0))) # answer(goal).  [resolve(7166,c,1077,a)].

given #2208 (F,wt=11): 8012 -->_s0(true,x) | -->_s0(x,app(nil,tail(cons(y,false)))) # answer(goal).  [resolve(7166,c,1068,a)].

given #2209 (F,wt=11): 8013 -->_s0(true,x) | -->_s0(x,sndsplit(0,tail(cons(y,false)))) # answer(goal).  [resolve(7166,c,1066,a)].

given #2210 (F,wt=11): 8015 -->_s0(true,x) | -->_s0(x,head(cons(app(nil,false),y))) # answer(goal).  [resolve(7166,c,701,a)].

given #2211 (T,wt=9): 3895 ->*_s0(empty(app(nil,fstsplit(s(x),nil))),true).  [ur(87,a,136,a,b,3864,a)].

given #2212 (T,wt=9): 3897 ->*_s0(sndsplit(0,empty(fstsplit(s(x),nil))),true).  [ur(87,a,82,a,b,3864,a)].

given #2213 (T,wt=9): 3899 ->*_s0(app(nil,empty(fstsplit(s(x),nil))),true).  [ur(87,a,61,a,b,3864,a)].

given #2214 (T,wt=9): 3906 ->*_s0(s(head(cons(length(nil),x))),s(0)).  [ur(87,a,264,a,b,896,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): 8017 -->_s0(true,x) | -->_s0(x,tail(cons(y,app(nil,false)))) # answer(goal).  [resolve(7166,c,699,a)].

given #2217 (F,wt=11): 8019 -->_s0(true,x) | -->_s0(x,head(cons(sndsplit(0,false),y))) # answer(goal).  [resolve(7166,c,642,a)].

given #2218 (F,wt=11): 8021 -->_s0(true,x) | -->_s0(x,sndsplit(s(0),cons(y,false))) # answer(goal).  [resolve(7166,c,640,a)].

given #2219 (F,wt=11): 8022 -->_s0(true,x) | -->_s0(x,tail(cons(y,sndsplit(0,false)))) # answer(goal).  [resolve(7166,c,639,a)].

given #2220 (T,wt=9): 3907 ->*_s0(s(head(cons(empty(nil),x))),s(true)).  [ur(87,a,264,a,b,703,a)].

given #2221 (T,wt=9): 3941 ->*_s0(tail(head(cons(length(nil),x))),tail(0)).  [ur(87,a,269,a,b,922,a)].

given #2222 (T,wt=9): 3942 ->*_s0(tail(head(cons(empty(nil),x))),tail(true)).  [ur(87,a,269,a,b,761,a)].

given #2223 (T,wt=9): 3945 ->*_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): 8032 -->_s0(true,head(tail(cons(x,cons(app(nil,false),y))))) # answer(goal).  [ur(7166,b,558,a,c,701,a)].

given #2226 (F,wt=11): 8033 -->_s0(true,head(tail(cons(x,cons(sndsplit(0,false),y))))) # answer(goal).  [ur(7166,b,558,a,c,642,a)].

given #2227 (F,wt=11): 8035 -->_s0(true,tail(tail(cons(x,cons(y,app(nil,false)))))) # answer(goal).  [ur(7166,b,544,a,c,699,a)].

given #2228 (F,wt=11): 8036 -->_s0(true,tail(tail(cons(x,cons(y,sndsplit(0,false)))))) # answer(goal).  [ur(7166,b,544,a,c,639,a)].

given #2229 (T,wt=9): 4004 ->*_s0(length(head(cons(sndsplit(0,nil),x))),0).  [ur(87,a,282,a,b,2268,a)].

given #2230 (T,wt=9): 4006 ->*_s0(length(head(cons(mapf(x,nil),y))),0).  [ur(87,a,282,a,b,2047,a)].

given #2231 (T,wt=9): 4009 ->*_s0(length(head(cons(fstsplit(0,x),y))),0).  [ur(87,a,282,a,b,1666,a)].

given #2232 (T,wt=9): 4011 ->*_s0(length(head(cons(app(nil,nil),x))),0).  [ur(87,a,282,a,b,1368,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): 8050 -->_s0(true,head(head(cons(cons(app(nil,false),x),y)))) # answer(goal).  [ur(7166,b,283,a,c,701,a)].

given #2235 (F,wt=11): 8051 -->_s0(true,head(head(cons(cons(sndsplit(0,false),x),y)))) # answer(goal).  [ur(7166,b,283,a,c,642,a)].

given #2236 (F,wt=11): 8053 -->_s0(true,tail(head(cons(cons(x,app(nil,false)),y)))) # answer(goal).  [ur(7166,b,269,a,c,699,a)].

given #2237 (F,wt=11): 8054 -->_s0(true,tail(head(cons(cons(x,sndsplit(0,false)),y)))) # answer(goal).  [ur(7166,b,269,a,c,639,a)].

given #2238 (T,wt=9): 4013 ->*_s0(length(head(cons(length(nil),x))),length(0)).  [ur(87,a,282,a,b,948,a)].

given #2239 (T,wt=9): 4014 ->*_s0(length(head(cons(empty(nil),x))),length(true)).  [ur(87,a,282,a,b,787,a)].

given #2240 (T,wt=9): 4042 ->*_s0(length(sndsplit(0,head(cons(nil,x)))),0).  [ur(87,a,482,a,b,4015,a)].

given #2241 (T,wt=9): 4044 ->*_s0(length(app(nil,head(cons(nil,x)))),0).  [ur(87,a,132,a,b,4015,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): 8101 -->_s0(true,tail(cons(x,leq(s(s(y)),s(0))))) # answer(goal).  [ur(7166,b,85,a,c,1078,a)].

given #2244 (F,wt=11): 8102 -->_s0(true,tail(cons(x,sndsplit(0,leq(s(y),0))))) # answer(goal).  [ur(7166,b,85,a,c,1077,a)].

given #2245 (F,wt=11): 8103 -->_s0(true,tail(cons(x,app(nil,tail(cons(y,false)))))) # answer(goal).  [ur(7166,b,85,a,c,1068,a)].

given #2246 (F,wt=11): 8104 -->_s0(true,tail(cons(x,sndsplit(0,tail(cons(y,false)))))) # answer(goal).  [ur(7166,b,85,a,c,1066,a)].

given #2247 (T,wt=9): 4046 ->*_s0(sndsplit(0,length(head(cons(nil,x)))),0).  [ur(87,a,82,a,b,4015,a)].

given #2248 (T,wt=9): 4048 ->*_s0(app(nil,length(head(cons(nil,x)))),0).  [ur(87,a,61,a,b,4015,a)].

given #2249 (T,wt=9): 4055 ->*_s0(head(head(cons(length(nil),x))),head(0)).  [ur(87,a,283,a,b,974,a)].

given #2250 (T,wt=9): 4056 ->*_s0(head(head(cons(empty(nil),x))),head(true)).  [ur(87,a,283,a,b,813,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): 8106 -->_s0(true,tail(cons(x,head(cons(app(nil,false),y))))) # answer(goal).  [ur(7166,b,85,a,c,701,a)].

given #2253 (F,wt=11): 8108 -->_s0(true,tail(cons(x,tail(cons(y,app(nil,false)))))) # answer(goal).  [ur(7166,b,85,a,c,699,a)].

given #2254 (F,wt=11): 8110 -->_s0(true,tail(cons(x,head(cons(sndsplit(0,false),y))))) # answer(goal).  [ur(7166,b,85,a,c,642,a)].

given #2255 (F,wt=11): 8112 -->_s0(true,tail(cons(x,sndsplit(s(0),cons(y,false))))) # answer(goal).  [ur(7166,b,85,a,c,640,a)].

given #2256 (T,wt=9): 4059 ->*_s0(head(head(cons(cons(x,y),z))),x).  [ur(87,a,283,a,b,575,a)].

given #2257 (T,wt=9): 4089 ->*_s0(empty(head(cons(sndsplit(0,nil),x))),true).  [ur(87,a,286,a,b,2366,a)].

given #2258 (T,wt=9): 4091 ->*_s0(empty(head(cons(mapf(x,nil),y))),true).  [ur(87,a,286,a,b,2133,a)].

given #2259 (T,wt=9): 4094 ->*_s0(empty(head(cons(fstsplit(0,x),y))),true).  [ur(87,a,286,a,b,1763,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): 8113 -->_s0(true,tail(cons(x,tail(cons(y,sndsplit(0,false)))))) # answer(goal).  [ur(7166,b,85,a,c,639,a)].

given #2262 (F,wt=11): 8120 -->_s0(true,sndsplit(s(0),cons(x,leq(s(y),0)))) # answer(goal).  [ur(7166,b,83,a,c,1077,a)].

given #2263 (F,wt=11): 8121 -->_s0(true,sndsplit(s(0),cons(x,tail(cons(y,false))))) # answer(goal).  [ur(7166,b,83,a,c,1066,a)].

given #2264 (F,wt=11): 8124 -->_s0(true,sndsplit(s(s(0)),cons(x,cons(y,false)))) # answer(goal).  [ur(7166,b,83,a,c,640,a)].

given #2265 (T,wt=9): 4096 ->*_s0(empty(head(cons(app(nil,nil),x))),true).  [ur(87,a,286,a,b,1547,a)].

given #2266 (T,wt=9): 4097 ->*_s0(empty(head(cons(length(nil),x))),empty(0)).  [ur(87,a,286,a,b,1034,a)].

given #2267 (T,wt=9): 4098 ->*_s0(empty(head(cons(empty(nil),x))),empty(true)).  [ur(87,a,286,a,b,839,a)].

given #2268 (T,wt=9): 4099 ->*_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): 8146 -->_s0(true,head(cons(leq(s(s(x)),s(0)),y))) # answer(goal).  [ur(7166,b,67,a,c,1078,a)].

given #2271 (F,wt=11): 8147 -->_s0(true,head(cons(sndsplit(0,leq(s(x),0)),y))) # answer(goal).  [ur(7166,b,67,a,c,1077,a)].

given #2272 (F,wt=11): 8148 -->_s0(true,head(cons(app(nil,tail(cons(x,false))),y))) # answer(goal).  [ur(7166,b,67,a,c,1068,a)].

given #2273 (F,wt=11): 8149 -->_s0(true,head(cons(sndsplit(0,tail(cons(x,false))),y))) # answer(goal).  [ur(7166,b,67,a,c,1066,a)].

given #2274 (T,wt=9): 4157 ->*_s0(empty(sndsplit(0,head(cons(nil,x)))),true).  [ur(87,a,486,a,b,4100,a)].

given #2275 (T,wt=9): 4159 ->*_s0(empty(app(nil,head(cons(nil,x)))),true).  [ur(87,a,136,a,b,4100,a)].

given #2276 (T,wt=9): 4161 ->*_s0(sndsplit(0,empty(head(cons(nil,x)))),true).  [ur(87,a,82,a,b,4100,a)].

given #2277 (T,wt=9): 4163 ->*_s0(app(nil,empty(head(cons(nil,x)))),true).  [ur(87,a,61,a,b,4100,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): 8151 -->_s0(true,head(cons(head(cons(app(nil,false),x)),y))) # answer(goal).  [ur(7166,b,67,a,c,701,a)].

given #2280 (F,wt=11): 8153 -->_s0(true,head(cons(tail(cons(x,app(nil,false))),y))) # answer(goal).  [ur(7166,b,67,a,c,699,a)].

given #2281 (F,wt=11): 8155 -->_s0(true,head(cons(head(cons(sndsplit(0,false),x)),y))) # answer(goal).  [ur(7166,b,67,a,c,642,a)].

given #2282 (F,wt=11): 8157 -->_s0(true,head(cons(sndsplit(s(0),cons(x,false)),y))) # answer(goal).  [ur(7166,b,67,a,c,640,a)].

given #2283 (T,wt=9): 4247 ->*_s0(mapf(x,app(nil,y)),mapf(x,y)).  [ur(87,a,128,a,b,86,a)].

given #2284 (T,wt=9): 4273 ->*_s0(mapf(x,app(nil,app(nil,nil))),nil).  [ur(87,a,128,a,b,4246,a)].

given #2285 (T,wt=9): 4275 ->*_s0(sndsplit(0,mapf(x,app(nil,nil))),nil).  [ur(87,a,82,a,b,4246,a)].

given #2286 (T,wt=9): 4277 ->*_s0(app(nil,mapf(x,app(nil,nil))),nil).  [ur(87,a,61,a,b,4246,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): 8158 -->_s0(true,head(cons(tail(cons(x,sndsplit(0,false))),y))) # answer(goal).  [ur(7166,b,67,a,c,639,a)].

given #2289 (F,wt=11): 8179 -->_s0(true,x) | -->_s0(x,app(nil,leq(s(y),0))) # answer(goal).  [resolve(1080,a,7166,c)].

given #2290 (F,wt=11): 8193 -->_s0(true,tail(cons(x,app(nil,leq(s(y),0))))) # answer(goal).  [ur(7166,b,85,a,c,1080,a)].

given #2291 (F,wt=11): 8194 -->_s0(true,head(cons(app(nil,leq(s(x),0)),y))) # answer(goal).  [ur(7166,b,67,a,c,1080,a)].

given #2292 (T,wt=9): 4368 ->*_s0(mapf(app(nil,x),y),mapf(x,y)).  [ur(87,a,129,a,b,86,a)].

given #2293 (T,wt=9): 4406 ->*_s0(tail(cons(x,sndsplit(length(nil),y))),y).  [ur(87,a,85,a,b,4340,a)].

given #2294 (T,wt=9): 4407 ->*_s0(sndsplit(s(length(nil)),cons(x,y)),y).  [ur(87,a,83,a,b,4340,a)].

given #2295 (T,wt=9): 4409 ->*_s0(head(cons(sndsplit(length(nil),x),y)),x).  [ur(87,a,67,a,b,4340,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): 18156 -->_s0(true,sndsplit(length(cons(x,nil)),cons(y,false))) # answer(goal).  [ur(7166,b,296,a,c,4407,a)].

given #2298 (F,wt=11): 8195 -->_s0(true,x) | -->_s0(x,sndsplit(0,head(cons(false,y)))) # answer(goal).  [resolve(1121,a,7166,c)].

given #2299 (F,wt=11): 8219 -->_s0(true,tail(cons(x,sndsplit(0,head(cons(false,y)))))) # answer(goal).  [ur(7166,b,85,a,c,1121,a)].

given #2300 (F,wt=11): 8220 -->_s0(true,sndsplit(s(0),cons(x,head(cons(false,y))))) # answer(goal).  [ur(7166,b,83,a,c,1121,a)].

given #2301 (T,wt=9): 4414 ->*_s0(sndsplit(app(nil,length(nil)),empty(nil)),true).  [ur(87,a,121,a,b,4338,a)].

given #2302 (T,wt=9): 4415 ->*_s0(sndsplit(length(nil),app(nil,empty(nil))),true).  [ur(87,a,120,a,b,4338,a)].

given #2303 (T,wt=9): 4418 ->*_s0(sndsplit(0,sndsplit(length(nil),empty(nil))),true).  [ur(87,a,82,a,b,4338,a)].

given #2304 (T,wt=9): 4420 ->*_s0(app(nil,sndsplit(length(nil),empty(nil))),true).  [ur(87,a,61,a,b,4338,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): 8222 -->_s0(true,head(cons(sndsplit(0,head(cons(false,x))),y))) # answer(goal).  [ur(7166,b,67,a,c,1121,a)].

given #2307 (F,wt=11): 8224 -->_s0(true,x) | -->_s0(x,app(nil,head(cons(false,y)))) # answer(goal).  [resolve(1123,a,7166,c)].

given #2308 (F,wt=11): 8242 -->_s0(true,tail(cons(x,app(nil,head(cons(false,y)))))) # answer(goal).  [ur(7166,b,85,a,c,1123,a)].

given #2309 (F,wt=11): 8243 -->_s0(true,head(cons(app(nil,head(cons(false,x))),y))) # answer(goal).  [ur(7166,b,67,a,c,1123,a)].

given #2310 (T,wt=9): 4421 ->*_s0(sndsplit(app(nil,length(nil)),length(nil)),0).  [ur(87,a,121,a,b,4339,a)].

given #2311 (T,wt=9): 4422 ->*_s0(sndsplit(length(nil),app(nil,length(nil))),0).  [ur(87,a,120,a,b,4339,a)].

given #2312 (T,wt=9): 4425 ->*_s0(sndsplit(0,sndsplit(length(nil),length(nil))),0).  [ur(87,a,82,a,b,4339,a)].

given #2313 (T,wt=9): 4427 ->*_s0(app(nil,sndsplit(length(nil),length(nil))),0).  [ur(87,a,61,a,b,4339,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): 8274 -->_s0(true,sndsplit(0,x)) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal).  [resolve(7962,b,87,c)].

given #2316 (F,wt=9): 18795 -->_s0(true,sndsplit(0,length(nil))) | -->*_s0(0,false) # answer(goal).  [resolve(8274,b,69,a)].

given #2317 (F,wt=10): 18784 -->_s0(true,sndsplit(0,sndsplit(0,x))) | -->*_s0(x,false) # answer(goal).  [resolve(8274,b,82,a)].

given #2318 (F,wt=10): 18792 -->_s0(true,sndsplit(0,mapf(x,nil))) | -->*_s0(nil,false) # answer(goal).  [resolve(8274,b,74,a)].

given #2319 (T,wt=9): 4456 ->*_s0(leq(s(0),app(nil,s(x))),true).  [ur(87,a,130,a,b,689,a)].

given #2320 (T,wt=9): 4458 ->*_s0(leq(x,app(nil,y)),leq(x,y)).  [ur(87,a,130,a,b,86,a)].

given #2321 (T,wt=9): 4547 ->*_s0(leq(s(x),app(nil,length(nil))),false).  [ur(87,a,130,a,b,4513,a)].

given #2322 (T,wt=9): 4549 ->*_s0(sndsplit(0,leq(s(x),length(nil))),false).  [ur(87,a,82,a,b,4513,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): 18800 -->_s0(true,sndsplit(0,fstsplit(0,x))) | -->*_s0(nil,false) # answer(goal).  [resolve(8274,b,64,a)].

given #2325 (F,wt=10): 18801 -->_s0(true,sndsplit(0,app(nil,x))) | -->*_s0(x,false) # answer(goal).  [resolve(8274,b,61,a)].

given #2326 (F,wt=10): 19632 -->_s0(true,sndsplit(length(nil),leq(s(x),length(nil)))) # answer(goal).  [resolve(4549,a,7842,b)].

given #2327 (F,wt=11): 8275 -->_s0(true,mapf(x,nil)) | -->_s0(nil,y) | -->*_s0(y,false) # answer(goal).  [resolve(7970,b,87,c)].

given #2328 (T,wt=9): 4550 ->*_s0(leq(s(s(x)),s(length(nil))),false).  [ur(87,a,72,a,b,4513,a)].

given #2329 (T,wt=9): 4552 ->*_s0(app(nil,leq(s(x),length(nil))),false).  [ur(87,a,61,a,b,4513,a)].

given #2330 (T,wt=9): 4584 ->*_s0(leq(app(nil,s(x)),length(nil)),false).  [ur(87,a,131,a,b,4513,a)].

given #2331 (T,wt=9): 4585 ->*_s0(leq(app(nil,s(0)),s(x)),true).  [ur(87,a,131,a,b,689,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=8): 19742 -->_s0(true,mapf(x,nil)) | -->_s0(nil,false) # answer(goal).  [resolve(8275,c,86,a)].

given #2334 (F,wt=10): 19735 -->_s0(true,mapf(x,nil)) | -->_s0(nil,app(nil,false)) # answer(goal).  [resolve(8275,c,581,a)].

given #2335 (F,wt=10): 19739 -->_s0(true,mapf(x,nil)) | -->_s0(nil,sndsplit(0,false)) # answer(goal).  [resolve(8275,c,567,a)].

given #2336 (F,wt=10): 19768 -->_s0(true,leq(s(s(x)),length(cons(y,nil)))) # answer(goal).  [ur(7166,b,305,a,c,4550,a)].

given #2337 (T,wt=9): 4588 ->*_s0(leq(app(nil,x),y),leq(x,y)).  [ur(87,a,131,a,b,86,a)].

given #2338 (T,wt=9): 4621 ->*_s0(tail(cons(x,leq(length(nil),y))),true).  [ur(87,a,85,a,b,4555,a)].

given #2339 (T,wt=9): 4624 ->*_s0(head(cons(leq(length(nil),x),y)),true).  [ur(87,a,67,a,b,4555,a)].

given #2340 (T,wt=9): 4632 ->*_s0(leq(app(nil,app(nil,0)),x),true).  [ur(87,a,131,a,b,4586,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): 8281 -->_s0(true,x) | -->_s0(x,sndsplit(0,empty(cons(y,z)))) # answer(goal).  [resolve(1133,a,7166,c)].

given #2343 (F,wt=11): 8296 -->_s0(true,tail(cons(x,sndsplit(0,empty(cons(y,z)))))) # answer(goal).  [ur(7166,b,85,a,c,1133,a)].

given #2344 (F,wt=11): 8297 -->_s0(true,sndsplit(s(0),cons(x,empty(cons(y,z))))) # answer(goal).  [ur(7166,b,83,a,c,1133,a)].

given #2345 (F,wt=11): 8298 -->_s0(true,head(cons(sndsplit(0,empty(cons(x,y))),z))) # answer(goal).  [ur(7166,b,67,a,c,1133,a)].

given #2346 (T,wt=9): 4634 ->*_s0(sndsplit(0,leq(app(nil,0),x)),true).  [ur(87,a,82,a,b,4586,a)].

given #2347 (T,wt=9): 4635 ->*_s0(leq(s(app(nil,0)),s(x)),true).  [ur(87,a,72,a,b,4586,a)].

given #2348 (T,wt=9): 4637 ->*_s0(app(nil,leq(app(nil,0),x)),true).  [ur(87,a,61,a,b,4586,a)].

given #2349 (T,wt=9): 4695 ->*_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): 8300 -->_s0(true,x) | -->_s0(x,app(nil,empty(cons(y,z)))) # answer(goal).  [resolve(1135,a,7166,c)].

given #2352 (F,wt=11): 8312 -->_s0(true,tail(cons(x,app(nil,empty(cons(y,z)))))) # answer(goal).  [ur(7166,b,85,a,c,1135,a)].

given #2353 (F,wt=11): 8313 -->_s0(true,head(cons(app(nil,empty(cons(x,y))),z))) # answer(goal).  [ur(7166,b,67,a,c,1135,a)].

given #2354 (F,wt=11): 8343 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,y) | -->*_s0(y,false) # answer(goal).  [resolve(7978,b,87,c)].

given #2355 (T,wt=9): 4722 ->*_s0(tail(cons(x,fstsplit(length(nil),y))),nil).  [ur(87,a,85,a,b,4666,a)].

given #2356 (T,wt=9): 4724 ->*_s0(head(cons(fstsplit(length(nil),x),y)),nil).  [ur(87,a,67,a,b,4666,a)].

given #2357 (T,wt=9): 4811 ->*_s0(fstsplit(app(nil,x),y),fstsplit(x,y)).  [ur(87,a,135,a,b,86,a)].

given #2358 (T,wt=9): 4842 ->*_s0(fstsplit(app(nil,app(nil,0)),x),nil).  [ur(87,a,135,a,b,4809,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=8): 19941 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,false) # answer(goal).  [resolve(8343,c,86,a)].

given #2361 (F,wt=10): 19934 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,app(nil,false)) # answer(goal).  [resolve(8343,c,581,a)].

given #2362 (F,wt=10): 19938 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,sndsplit(0,false)) # answer(goal).  [resolve(8343,c,567,a)].

given #2363 (F,wt=11): 8344 -->_s0(true,app(nil,x)) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal).  [resolve(7979,b,87,c)].

given #2364 (T,wt=9): 4844 ->*_s0(sndsplit(0,fstsplit(app(nil,0),x)),nil).  [ur(87,a,82,a,b,4809,a)].

given #2365 (T,wt=9): 4846 ->*_s0(app(nil,fstsplit(app(nil,0),x)),nil).  [ur(87,a,61,a,b,4809,a)].

given #2366 (T,wt=9): 4929 ->*_s0(app(x,app(nil,y)),app(x,y)).  [ur(87,a,137,a,b,86,a)].

given #2367 (T,wt=9): 5067 ->*_s0(app(app(nil,nil),app(nil,x)),x).  [ur(87,a,138,a,b,702,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=9): 20395 -->_s0(true,app(nil,length(nil))) | -->*_s0(0,false) # answer(goal).  [resolve(8344,b,69,a)].

given #2370 (F,wt=10): 20391 -->_s0(true,app(nil,sndsplit(0,x))) | -->*_s0(x,false) # answer(goal).  [resolve(8344,b,82,a)].

given #2371 (F,wt=10): 20392 -->_s0(true,app(nil,mapf(x,nil))) | -->*_s0(nil,false) # answer(goal).  [resolve(8344,b,74,a)].

given #2372 (F,wt=10): 20400 -->_s0(true,app(nil,fstsplit(0,x))) | -->*_s0(nil,false) # answer(goal).  [resolve(8344,b,64,a)].

given #2373 (T,wt=9): 5068 ->*_s0(app(app(nil,nil),fstsplit(0,x)),nil).  [ur(87,a,138,a,b,695,a)].

given #2374 (T,wt=9): 5069 ->*_s0(app(app(nil,nil),leq(0,x)),true).  [ur(87,a,138,a,b,691,a)].

given #2375 (T,wt=9): 5070 ->*_s0(app(app(nil,nil),mapf(x,nil)),nil).  [ur(87,a,138,a,b,647,a)].

given #2376 (T,wt=9): 5071 ->*_s0(app(app(nil,nil),sndsplit(0,x)),x).  [ur(87,a,138,a,b,643,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=10): 20401 -->_s0(true,app(nil,app(nil,x))) | -->*_s0(x,false) # answer(goal).  [resolve(8344,b,61,a)].

given #2379 (F,wt=11): 8700 -->_s0(true,x) | -->_s0(x,tail(app(nil,cons(y,false)))) # answer(goal).  [resolve(1339,a,7166,c)].

given #2380 (F,wt=11): 8719 -->_s0(true,tail(tail(cons(x,app(nil,cons(y,false)))))) # answer(goal).  [ur(7166,b,544,a,c,1339,a)].

given #2381 (F,wt=11): 8721 -->_s0(true,tail(head(cons(app(nil,cons(x,false)),y)))) # answer(goal).  [ur(7166,b,269,a,c,1339,a)].

given #2382 (T,wt=9): 5075 ->*_s0(app(app(nil,x),y),app(x,y)).  [ur(87,a,138,a,b,86,a)].

given #2383 (T,wt=9): 5117 ->*_s0(length(sndsplit(0,sndsplit(s(x),nil))),0).  [ur(87,a,482,a,b,5039,a)].

given #2384 (T,wt=9): 5119 ->*_s0(length(app(nil,sndsplit(s(x),nil))),0).  [ur(87,a,132,a,b,5039,a)].

given #2385 (T,wt=9): 5121 ->*_s0(sndsplit(0,length(sndsplit(s(x),nil))),0).  [ur(87,a,82,a,b,5039,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): 8723 -->_s0(true,tail(cons(x,tail(app(nil,cons(y,false)))))) # answer(goal).  [ur(7166,b,85,a,c,1339,a)].

given #2388 (F,wt=11): 8724 -->_s0(true,head(cons(tail(app(nil,cons(x,false))),y))) # answer(goal).  [ur(7166,b,67,a,c,1339,a)].

given #2389 (F,wt=11): 8824 -->_s0(true,x) | -->_s0(x,head(app(nil,cons(false,y)))) # answer(goal).  [resolve(1516,a,7166,c)].

given #2390 (F,wt=11): 8843 -->_s0(true,head(tail(cons(x,app(nil,cons(false,y)))))) # answer(goal).  [ur(7166,b,558,a,c,1516,a)].

given #2391 (T,wt=9): 5123 ->*_s0(app(nil,length(sndsplit(s(x),nil))),0).  [ur(87,a,61,a,b,5039,a)].

given #2392 (T,wt=9): 5134 ->*_s0(app(app(nil,app(nil,nil)),x),x).  [ur(87,a,138,a,b,5074,a)].

given #2393 (T,wt=9): 5137 ->*_s0(sndsplit(0,app(app(nil,nil),x)),x).  [ur(87,a,82,a,b,5074,a)].

given #2394 (T,wt=9): 5139 ->*_s0(app(nil,app(app(nil,nil),x)),x).  [ur(87,a,61,a,b,5074,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): 21356 -->_s0(true,sndsplit(length(nil),app(app(nil,nil),false))) # answer(goal).  [resolve(5137,a,7842,b)].

given #2397 (F,wt=11): 8845 -->_s0(true,head(head(cons(app(nil,cons(false,x)),y)))) # answer(goal).  [ur(7166,b,283,a,c,1516,a)].

given #2398 (F,wt=11): 8847 -->_s0(true,tail(cons(x,head(app(nil,cons(false,y)))))) # answer(goal).  [ur(7166,b,85,a,c,1516,a)].

given #2399 (F,wt=11): 8848 -->_s0(true,head(cons(head(app(nil,cons(false,x))),y))) # answer(goal).  [ur(7166,b,67,a,c,1516,a)].

given #2400 (T,wt=9): 5224 ->*_s0(empty(sndsplit(0,sndsplit(s(x),nil))),true).  [ur(87,a,486,a,b,5167,a)].

given #2401 (T,wt=9): 5226 ->*_s0(empty(app(nil,sndsplit(s(x),nil))),true).  [ur(87,a,136,a,b,5167,a)].

given #2402 (T,wt=9): 5228 ->*_s0(sndsplit(0,empty(sndsplit(s(x),nil))),true).  [ur(87,a,82,a,b,5167,a)].

given #2403 (T,wt=9): 5230 ->*_s0(app(nil,empty(sndsplit(s(x),nil))),true).  [ur(87,a,61,a,b,5167,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): 8892 -->_s0(true,x) | -->_s0(x,empty(app(nil,cons(y,z)))) # answer(goal).  [resolve(1546,a,7166,c)].

given #2406 (F,wt=11): 8909 -->_s0(true,empty(tail(cons(x,app(nil,cons(y,z)))))) # answer(goal).  [ur(7166,b,561,a,c,1546,a)].

given #2407 (F,wt=11): 8911 -->_s0(true,empty(head(cons(app(nil,cons(x,y)),z)))) # answer(goal).  [ur(7166,b,286,a,c,1546,a)].

given #2408 (F,wt=11): 8913 -->_s0(true,tail(cons(x,empty(app(nil,cons(y,z)))))) # answer(goal).  [ur(7166,b,85,a,c,1546,a)].

given #2409 (T,wt=9): 5237 ->*_s0(s(tail(cons(x,length(nil)))),s(0)).  [ur(87,a,539,a,b,896,a)].

given #2410 (T,wt=9): 5238 ->*_s0(s(tail(cons(x,empty(nil)))),s(true)).  [ur(87,a,539,a,b,703,a)].

given #2411 (T,wt=9): 5271 ->*_s0(tail(tail(cons(x,length(nil)))),tail(0)).  [ur(87,a,544,a,b,922,a)].

given #2412 (T,wt=9): 5272 ->*_s0(tail(tail(cons(x,empty(nil)))),tail(true)).  [ur(87,a,544,a,b,761,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): 8914 -->_s0(true,head(cons(empty(app(nil,cons(x,y))),z))) # answer(goal).  [ur(7166,b,67,a,c,1546,a)].

given #2415 (F,wt=11): 9134 -->_s0(true,head(cons(tail(sndsplit(0,cons(x,false))),y))) # answer(goal).  [resolve(2235,a,7975,b)].

given #2416 (F,wt=11): 9136 -->_s0(true,tail(cons(x,tail(sndsplit(0,cons(y,false)))))) # answer(goal).  [resolve(2235,a,7959,b)].

given #2417 (F,wt=11): 9137 -->_s0(true,x) | -->_s0(x,tail(sndsplit(0,cons(y,false)))) # answer(goal).  [resolve(2235,a,7166,c)].

given #2418 (T,wt=9): 5275 ->*_s0(tail(tail(cons(x,cons(y,z)))),z).  [ur(87,a,544,a,b,564,a)].

given #2419 (T,wt=9): 5308 ->*_s0(length(tail(cons(x,sndsplit(0,nil)))),0).  [ur(87,a,557,a,b,2268,a)].

given #2420 (T,wt=9): 5310 ->*_s0(length(tail(cons(x,mapf(y,nil)))),0).  [ur(87,a,557,a,b,2047,a)].

given #2421 (T,wt=9): 5313 ->*_s0(length(tail(cons(x,fstsplit(0,y)))),0).  [ur(87,a,557,a,b,1666,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): 9154 -->_s0(true,tail(tail(cons(x,sndsplit(0,cons(y,false)))))) # answer(goal).  [ur(7166,b,544,a,c,2235,a)].

given #2424 (F,wt=11): 9156 -->_s0(true,tail(head(cons(sndsplit(0,cons(x,false)),y)))) # answer(goal).  [ur(7166,b,269,a,c,2235,a)].

given #2425 (F,wt=11): 9298 -->_s0(true,head(cons(head(sndsplit(0,cons(false,x))),y))) # answer(goal).  [resolve(2304,a,7975,b)].

given #2426 (F,wt=11): 9300 -->_s0(true,tail(cons(x,head(sndsplit(0,cons(false,y)))))) # answer(goal).  [resolve(2304,a,7959,b)].

given #2427 (T,wt=9): 5315 ->*_s0(length(tail(cons(x,app(nil,nil)))),0).  [ur(87,a,557,a,b,1368,a)].

given #2428 (T,wt=9): 5317 ->*_s0(length(tail(cons(x,length(nil)))),length(0)).  [ur(87,a,557,a,b,948,a)].

given #2429 (T,wt=9): 5318 ->*_s0(length(tail(cons(x,empty(nil)))),length(true)).  [ur(87,a,557,a,b,787,a)].

given #2430 (T,wt=9): 5374 ->*_s0(length(sndsplit(0,tail(cons(x,nil)))),0).  [ur(87,a,482,a,b,5319,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): 9301 -->_s0(true,x) | -->_s0(x,head(sndsplit(0,cons(false,y)))) # answer(goal).  [resolve(2304,a,7166,c)].

given #2433 (F,wt=11): 9318 -->_s0(true,head(tail(cons(x,sndsplit(0,cons(false,y)))))) # answer(goal).  [ur(7166,b,558,a,c,2304,a)].

given #2434 (F,wt=11): 9320 -->_s0(true,head(head(cons(sndsplit(0,cons(false,x)),y)))) # answer(goal).  [ur(7166,b,283,a,c,2304,a)].

given #2435 (F,wt=11): 9418 -->_s0(true,head(cons(empty(sndsplit(0,cons(x,y))),z))) # answer(goal).  [resolve(2365,a,7975,b)].

given #2436 (T,wt=9): 5376 ->*_s0(length(app(nil,tail(cons(x,nil)))),0).  [ur(87,a,132,a,b,5319,a)].

given #2437 (T,wt=9): 5378 ->*_s0(sndsplit(0,length(tail(cons(x,nil)))),0).  [ur(87,a,82,a,b,5319,a)].

given #2438 (T,wt=9): 5380 ->*_s0(app(nil,length(tail(cons(x,nil)))),0).  [ur(87,a,61,a,b,5319,a)].

given #2439 (T,wt=9): 5387 ->*_s0(head(tail(cons(x,length(nil)))),head(0)).  [ur(87,a,558,a,b,974,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): 9420 -->_s0(true,tail(cons(x,empty(sndsplit(0,cons(y,z)))))) # answer(goal).  [resolve(2365,a,7959,b)].

given #2442 (F,wt=11): 9421 -->_s0(true,x) | -->_s0(x,empty(sndsplit(0,cons(y,z)))) # answer(goal).  [resolve(2365,a,7166,c)].

given #2443 (F,wt=11): 9436 -->_s0(true,empty(tail(cons(x,sndsplit(0,cons(y,z)))))) # answer(goal).  [ur(7166,b,561,a,c,2365,a)].

given #2444 (F,wt=11): 9438 -->_s0(true,empty(head(cons(sndsplit(0,cons(x,y)),z)))) # answer(goal).  [ur(7166,b,286,a,c,2365,a)].

given #2445 (T,wt=9): 5388 ->*_s0(head(tail(cons(x,empty(nil)))),head(true)).  [ur(87,a,558,a,b,813,a)].

given #2446 (T,wt=9): 5391 ->*_s0(head(tail(cons(x,cons(y,z)))),y).  [ur(87,a,558,a,b,575,a)].

given #2447 (T,wt=9): 5423 ->*_s0(empty(tail(cons(x,sndsplit(0,nil)))),true).  [ur(87,a,561,a,b,2366,a)].

given #2448 (T,wt=9): 5425 ->*_s0(empty(tail(cons(x,mapf(y,nil)))),true).  [ur(87,a,561,a,b,2133,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): 9507 -->_s0(true,head(cons(head(app(cons(false,x),y)),z))) # answer(goal).  [resolve(2492,a,7975,b)].

given #2451 (F,wt=11): 9509 -->_s0(true,tail(cons(x,head(app(cons(false,y),z))))) # answer(goal).  [resolve(2492,a,7959,b)].

given #2452 (F,wt=11): 9510 -->_s0(true,x) | -->_s0(x,head(app(cons(false,y),z))) # answer(goal).  [resolve(2492,a,7166,c)].

given #2453 (F,wt=11): 9527 -->_s0(true,head(tail(cons(x,app(cons(false,y),z))))) # answer(goal).  [ur(7166,b,558,a,c,2492,a)].

given #2454 (T,wt=9): 5428 ->*_s0(empty(tail(cons(x,fstsplit(0,y)))),true).  [ur(87,a,561,a,b,1763,a)].

given #2455 (T,wt=9): 5430 ->*_s0(empty(tail(cons(x,app(nil,nil)))),true).  [ur(87,a,561,a,b,1547,a)].

given #2456 (T,wt=9): 5431 ->*_s0(empty(tail(cons(x,length(nil)))),empty(0)).  [ur(87,a,561,a,b,1034,a)].

given #2457 (T,wt=9): 5432 ->*_s0(empty(tail(cons(x,empty(nil)))),empty(true)).  [ur(87,a,561,a,b,839,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): 9529 -->_s0(true,head(head(cons(app(cons(false,x),y),z)))) # answer(goal).  [ur(7166,b,283,a,c,2492,a)].

given #2460 (F,wt=11): 9532 -->_s0(true,head(cons(empty(app(cons(x,y),z)),u))) # answer(goal).  [resolve(2658,a,7975,b)].

given #2461 (F,wt=11): 9534 -->_s0(true,tail(cons(x,empty(app(cons(y,z),u))))) # answer(goal).  [resolve(2658,a,7959,b)].

given #2462 (F,wt=11): 9535 -->_s0(true,x) | -->_s0(x,empty(app(cons(y,z),u))) # answer(goal).  [resolve(2658,a,7166,c)].

given #2463 (T,wt=9): 5433 ->*_s0(empty(tail(cons(x,cons(y,z)))),false).  [ur(87,a,561,a,b,580,a)].

given #2464 (T,wt=9): 5465 ->*_s0(empty(sndsplit(0,tail(cons(x,nil)))),true).  [ur(87,a,486,a,b,5434,a)].

given #2465 (T,wt=9): 5467 ->*_s0(empty(app(nil,tail(cons(x,nil)))),true).  [ur(87,a,136,a,b,5434,a)].

given #2466 (T,wt=9): 5469 ->*_s0(sndsplit(0,empty(tail(cons(x,nil)))),true).  [ur(87,a,82,a,b,5434,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): 9550 -->_s0(true,empty(tail(cons(x,app(cons(y,z),u))))) # answer(goal).  [ur(7166,b,561,a,c,2658,a)].

given #2469 (F,wt=11): 9552 -->_s0(true,empty(head(cons(app(cons(x,y),z),u)))) # answer(goal).  [ur(7166,b,286,a,c,2658,a)].

given #2470 (F,wt=11): 10144 -->_s0(true,head(cons(sndsplit(length(nil),app(nil,false)),x))) # answer(goal).  [resolve(4333,a,7975,b)].

given #2471 (F,wt=11): 10146 -->_s0(true,tail(cons(x,sndsplit(length(nil),app(nil,false))))) # answer(goal).  [resolve(4333,a,7959,b)].

given #2472 (T,wt=9): 5471 ->*_s0(app(nil,empty(tail(cons(x,nil)))),true).  [ur(87,a,61,a,b,5434,a)].

given #2473 (T,wt=9): 5631 ->*_s0(sndsplit(length(nil),empty(cons(x,y))),false).  [ur(87,a,145,a,b,4340,a)].

given #2474 (T,wt=9): 7635 ->*_s0(sndsplit(length(nil),tail(cons(x,y))),y).  [ur(87,a,321,a,b,1066,a)].

given #2475 (T,wt=9): 7683 ->*_s0(sndsplit(length(nil),sndsplit(s(x),nil)),nil).  [ur(87,a,321,a,b,1071,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): 10147 -->_s0(true,x) | -->_s0(x,sndsplit(length(nil),app(nil,false))) # answer(goal).  [resolve(4333,a,7166,c)].

given #2478 (F,wt=11): 10165 -->_s0(true,sndsplit(s(length(nil)),cons(x,app(nil,false)))) # answer(goal).  [ur(7166,b,83,a,c,4333,a)].

given #2479 (F,wt=11): 10196 -->_s0(true,head(cons(sndsplit(length(nil),sndsplit(0,false)),x))) # answer(goal).  [resolve(4337,a,7975,b)].

given #2480 (F,wt=11): 10198 -->_s0(true,tail(cons(x,sndsplit(length(nil),sndsplit(0,false))))) # answer(goal).  [resolve(4337,a,7959,b)].

given #2481 (T,wt=9): 7705 ->*_s0(sndsplit(length(nil),leq(s(x),0)),false).  [ur(87,a,321,a,b,1077,a)].

given #2482 (T,wt=9): 8208 ->*_s0(sndsplit(length(nil),head(cons(x,y))),x).  [ur(87,a,321,a,b,1121,a)].

given #2483 (T,wt=9): 8244 ->*_s0(sndsplit(length(nil),fstsplit(s(x),nil)),nil).  [ur(87,a,321,a,b,1125,a)].

given #2484 (T,wt=9): 8314 ->*_s0(sndsplit(length(nil),sndsplit(0,length(nil))),0).  [ur(87,a,321,a,b,1138,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): 10199 -->_s0(true,x) | -->_s0(x,sndsplit(length(nil),sndsplit(0,false))) # answer(goal).  [resolve(4337,a,7166,c)].

given #2487 (F,wt=11): 10217 -->_s0(true,sndsplit(s(length(nil)),cons(x,sndsplit(0,false)))) # answer(goal).  [ur(7166,b,83,a,c,4337,a)].

given #2488 (F,wt=11): 10231 -->_s0(true,head(cons(sndsplit(app(nil,length(nil)),false),x))) # answer(goal).  [resolve(4404,a,7975,b)].

given #2489 (F,wt=11): 10233 -->_s0(true,tail(cons(x,sndsplit(app(nil,length(nil)),false)))) # answer(goal).  [resolve(4404,a,7959,b)].

given #2490 (T,wt=9): 8368 ->*_s0(sndsplit(length(nil),sndsplit(0,empty(nil))),true).  [ur(87,a,321,a,b,1177,a)].

given #2491 (T,wt=9): 8424 ->*_s0(sndsplit(length(nil),s(empty(nil))),s(true)).  [ur(87,a,321,a,b,1188,a)].

given #2492 (T,wt=9): 8457 ->*_s0(sndsplit(length(nil),tail(empty(nil))),tail(true)).  [ur(87,a,321,a,b,1220,a)].

given #2493 (T,wt=9): 8469 ->*_s0(sndsplit(length(nil),length(empty(nil))),length(true)).  [ur(87,a,321,a,b,1224,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): 10234 -->_s0(true,x) | -->_s0(x,sndsplit(app(nil,length(nil)),false)) # answer(goal).  [resolve(4404,a,7166,c)].

given #2496 (F,wt=11): 10252 -->_s0(true,sndsplit(app(nil,length(nil)),empty(cons(x,y)))) # answer(goal).  [ur(7166,b,145,a,c,4404,a)].

given #2497 (F,wt=11): 10254 -->_s0(true,sndsplit(s(app(nil,length(nil))),cons(x,false))) # answer(goal).  [ur(7166,b,83,a,c,4404,a)].

given #2498 (F,wt=11): 10256 -->_s0(true,head(cons(sndsplit(0,sndsplit(length(nil),false)),x))) # answer(goal).  [resolve(4408,a,7975,b)].

given #2499 (T,wt=9): 8502 ->*_s0(sndsplit(length(nil),head(empty(nil))),head(true)).  [ur(87,a,321,a,b,1228,a)].

given #2500 (T,wt=9): 8514 ->*_s0(sndsplit(length(nil),empty(empty(nil))),empty(true)).  [ur(87,a,321,a,b,1232,a)].

given #2501 (T,wt=9): 8533 ->*_s0(sndsplit(length(nil),s(length(nil))),s(0)).  [ur(87,a,321,a,b,1262,a)].

given #2502 (T,wt=9): 8545 ->*_s0(sndsplit(length(nil),tail(length(nil))),tail(0)).  [ur(87,a,321,a,b,1267,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): 10258 -->_s0(true,tail(cons(x,sndsplit(0,sndsplit(length(nil),false))))) # answer(goal).  [resolve(4408,a,7959,b)].

given #2505 (F,wt=11): 10259 -->_s0(true,x) | -->_s0(x,sndsplit(0,sndsplit(length(nil),false))) # answer(goal).  [resolve(4408,a,7166,c)].

given #2506 (F,wt=11): 10279 -->_s0(true,sndsplit(s(0),cons(x,sndsplit(length(nil),false)))) # answer(goal).  [ur(7166,b,83,a,c,4408,a)].

given #2507 (F,wt=11): 10281 -->_s0(true,head(cons(app(nil,sndsplit(length(nil),false)),x))) # answer(goal).  [resolve(4410,a,7975,b)].

given #2508 (T,wt=9): 8554 ->*_s0(f(x,fstsplit(0,y)),f(x,nil)).  [ur(87,a,190,a,b,86,a)].

given #2509 (T,wt=9): 8578 ->*_s0(sndsplit(length(nil),length(length(nil))),length(0)).  [ur(87,a,321,a,b,1271,a)].

given #2510 (T,wt=9): 8590 ->*_s0(sndsplit(length(nil),head(length(nil))),head(0)).  [ur(87,a,321,a,b,1275,a)].

given #2511 (T,wt=9): 8599 ->*_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): 10282 -->_s0(true,tail(cons(x,app(nil,sndsplit(length(nil),false))))) # answer(goal).  [resolve(4410,a,7959,b)].

given #2514 (F,wt=11): 10283 -->_s0(true,x) | -->_s0(x,app(nil,sndsplit(length(nil),false))) # answer(goal).  [resolve(4410,a,7166,c)].

given #2515 (F,wt=11): 10313 -->_s0(true,head(cons(leq(s(x),app(nil,0)),y))) # answer(goal).  [resolve(4457,a,7975,b)].

given #2516 (F,wt=11): 10315 -->_s0(true,tail(cons(x,leq(s(y),app(nil,0))))) # answer(goal).  [resolve(4457,a,7959,b)].

given #2517 (T,wt=9): 8630 ->*_s0(sndsplit(length(nil),empty(length(nil))),empty(0)).  [ur(87,a,321,a,b,1306,a)].

given #2518 (T,wt=9): 8651 ->*_s0(cons(x,fstsplit(0,y)),cons(x,nil)).  [ur(87,a,192,a,b,86,a)].

given #2519 (T,wt=9): 8726 ->*_s0(cons(fstsplit(0,x),y),cons(nil,y)).  [ur(87,a,193,a,b,86,a)].

given #2520 (T,wt=9): 8770 ->*_s0(sndsplit(length(nil),length(app(nil,nil))),0).  [ur(87,a,321,a,b,1510,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): 10316 -->_s0(true,x) | -->_s0(x,leq(s(y),app(nil,0))) # answer(goal).  [resolve(4457,a,7166,c)].

given #2523 (F,wt=11): 10367 -->_s0(true,head(cons(leq(app(nil,s(x)),0),y))) # answer(goal).  [resolve(4587,a,7975,b)].

given #2524 (F,wt=11): 10369 -->_s0(true,tail(cons(x,leq(app(nil,s(y)),0)))) # answer(goal).  [resolve(4587,a,7959,b)].

given #2525 (F,wt=11): 10370 -->_s0(true,x) | -->_s0(x,leq(app(nil,s(y)),0)) # answer(goal).  [resolve(4587,a,7166,c)].

given #2526 (T,wt=9): 8780 ->*_s0(sndsplit(x,fstsplit(0,y)),sndsplit(x,nil)).  [ur(87,a,195,a,b,86,a)].

given #2527 (T,wt=9): 8850 ->*_s0(sndsplit(fstsplit(0,x),y),sndsplit(nil,y)).  [ur(87,a,196,a,b,86,a)].

given #2528 (T,wt=9): 8942 ->*_s0(sndsplit(length(nil),empty(app(nil,nil))),true).  [ur(87,a,321,a,b,1579,a)].

given #2529 (T,wt=9): 8966 ->*_s0(sndsplit(length(nil),length(fstsplit(0,x))),0).  [ur(87,a,321,a,b,1695,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): 10684 -->_s0(true,head(cons(tail(app(cons(x,nil),false)),y))) # answer(goal).  [resolve(5690,a,7975,b)].

given #2532 (F,wt=11): 10686 -->_s0(true,tail(cons(x,tail(app(cons(y,nil),false))))) # answer(goal).  [resolve(5690,a,7959,b)].

given #2533 (F,wt=11): 10689 -->_s0(true,x) | -->_s0(x,tail(app(cons(y,nil),false))) # answer(goal).  [resolve(5690,a,7166,c)].

given #2534 (F,wt=11): 10706 -->_s0(true,tail(tail(cons(x,app(cons(y,nil),false))))) # answer(goal).  [ur(7166,b,544,a,c,5690,a)].

given #2535 (T,wt=9): 9005 ->*_s0(sndsplit(length(nil),empty(fstsplit(0,x))),true).  [ur(87,a,321,a,b,1795,a)].

given #2536 (T,wt=9): 9042 ->*_s0(sndsplit(length(nil),length(mapf(x,nil))),0).  [ur(87,a,321,a,b,2076,a)].

given #2537 (T,wt=9): 9078 ->*_s0(sndsplit(length(nil),empty(mapf(x,nil))),true).  [ur(87,a,321,a,b,2165,a)].

given #2538 (T,wt=9): 9207 ->*_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): 10707 -->_s0(true,tail(head(cons(app(cons(x,nil),false),y)))) # answer(goal).  [ur(7166,b,269,a,c,5690,a)].

given #2541 (F,wt=11): 10742 -->_s0(true,head(fstsplit(s(x),cons(app(nil,false),y)))) # answer(goal).  [ur(7166,b,233,a,c,701,a)].

given #2542 (F,wt=11): 10743 -->_s0(true,head(fstsplit(s(x),cons(sndsplit(0,false),y)))) # answer(goal).  [ur(7166,b,233,a,c,642,a)].

given #2543 (F,wt=11): 11258 -->_s0(true,length(nil)) | -->_s0(0,app(fstsplit(0,x),false)) # answer(goal).  [resolve(8273,c,9700,a)].

given #2544 (T,wt=9): 9227 ->*_s0(mapf(x,app(nil,fstsplit(0,y))),nil).  [ur(87,a,128,a,b,9206,a)].

given #2545 (T,wt=9): 9229 ->*_s0(sndsplit(0,mapf(x,fstsplit(0,y))),nil).  [ur(87,a,82,a,b,9206,a)].

given #2546 (T,wt=9): 9231 ->*_s0(app(nil,mapf(x,fstsplit(0,y))),nil).  [ur(87,a,61,a,b,9206,a)].

given #2547 (T,wt=9): 9248 ->*_s0(sndsplit(length(nil),length(sndsplit(0,nil))),0).  [ur(87,a,321,a,b,2298,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): 11260 -->_s0(true,length(nil)) | -->_s0(0,app(app(nil,nil),false)) # answer(goal).  [resolve(8273,c,5074,a)].

given #2550 (F,wt=11): 11262 -->_s0(true,length(nil)) | -->_s0(0,leq(s(x),length(nil))) # answer(goal).  [resolve(8273,c,4513,a)].

given #2551 (F,wt=11): 11270 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(app(nil,0),false)) # answer(goal).  [resolve(8273,c,3308,a)].

given #2552 (F,wt=11): 11288 -->_s0(true,length(nil)) | -->_s0(0,app(nil,app(nil,false))) # answer(goal).  [resolve(8273,c,702,a)].

given #2553 (T,wt=9): 9257 ->*_s0(mapf(fstsplit(0,x),y),mapf(nil,y)).  [ur(87,a,204,a,b,86,a)].

given #2554 (T,wt=9): 9323 ->*_s0(leq(x,fstsplit(0,y)),leq(x,nil)).  [ur(87,a,205,a,b,86,a)].

given #2555 (T,wt=9): 9389 ->*_s0(leq(fstsplit(0,x),y),leq(nil,y)).  [ur(87,a,206,a,b,86,a)].

given #2556 (T,wt=9): 9466 ->*_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): 11290 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(0,app(nil,false))) # answer(goal).  [resolve(8273,c,700,a)].

given #2559 (F,wt=11): 11292 -->_s0(true,length(nil)) | -->_s0(0,app(nil,sndsplit(0,false))) # answer(goal).  [resolve(8273,c,643,a)].

given #2560 (F,wt=11): 11294 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(0,sndsplit(0,false))) # answer(goal).  [resolve(8273,c,641,a)].

given #2561 (F,wt=11): 11617 -->_s0(true,length(nil)) | -->_s0(0,app(mapf(x,nil),false)) # answer(goal).  [resolve(11605,a,8273,c)].

given #2562 (T,wt=9): 9490 ->*_s0(sndsplit(length(nil),empty(sndsplit(0,nil))),true).  [ur(87,a,321,a,b,2399,a)].

given #2563 (T,wt=9): 9555 ->*_s0(fstsplit(fstsplit(0,x),y),fstsplit(nil,y)).  [ur(87,a,210,a,b,86,a)].

given #2564 (T,wt=9): 9608 ->*_s0(app(x,fstsplit(0,y)),app(x,nil)).  [ur(87,a,212,a,b,86,a)].

given #2565 (T,wt=9): 9643 ->*_s0(f(length(nil),empty(nil)),f(0,true)).  [ur(87,a,316,a,b,3193,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): 11832 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(sndsplit(0,0),false)) # answer(goal).  [resolve(11815,a,8273,c)].

given #2568 (F,wt=11): 11858 -->_s0(true,head(cons(sndsplit(sndsplit(0,length(nil)),false),x))) # answer(goal).  [resolve(11763,a,7975,b)].

given #2569 (F,wt=11): 11860 -->_s0(true,tail(cons(x,sndsplit(sndsplit(0,length(nil)),false)))) # answer(goal).  [resolve(11763,a,7959,b)].

given #2570 (F,wt=11): 11861 -->_s0(true,x) | -->_s0(x,sndsplit(sndsplit(0,length(nil)),false)) # answer(goal).  [resolve(11763,a,7166,c)].

given #2571 (T,wt=9): 9645 ->*_s0(f(empty(nil),empty(nil)),f(true,true)).  [ur(87,a,166,a,b,3193,a)].

given #2572 (T,wt=9): 9654 ->*_s0(f(empty(nil),length(nil)),f(true,0)).  [ur(87,a,315,a,b,3220,a)].

given #2573 (T,wt=9): 9693 ->*_s0(app(fstsplit(0,x),app(nil,y)),y).  [ur(87,a,213,a,b,702,a)].

given #2574 (T,wt=9): 9694 ->*_s0(app(fstsplit(0,x),fstsplit(0,y)),nil).  [ur(87,a,213,a,b,695,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): 11880 -->_s0(true,sndsplit(sndsplit(0,length(nil)),empty(cons(x,y)))) # answer(goal).  [ur(7166,b,145,a,c,11763,a)].

given #2577 (F,wt=11): 11882 -->_s0(true,sndsplit(s(sndsplit(0,length(nil))),cons(x,false))) # answer(goal).  [ur(7166,b,83,a,c,11763,a)].

given #2578 (F,wt=11): 11980 -->_s0(true,app(fstsplit(s(x),nil),sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,263,a,c,4410,a)].

given #2579 (F,wt=11): 11981 -->_s0(true,app(fstsplit(s(x),nil),empty(cons(y,z)))) # answer(goal).  [ur(7166,b,263,a,c,1135,a)].

given #2580 (T,wt=9): 9695 ->*_s0(app(fstsplit(0,x),leq(0,y)),true).  [ur(87,a,213,a,b,691,a)].

given #2581 (T,wt=9): 9696 ->*_s0(app(fstsplit(0,x),mapf(y,nil)),nil).  [ur(87,a,213,a,b,647,a)].

given #2582 (T,wt=9): 9697 ->*_s0(app(fstsplit(0,x),sndsplit(0,y)),y).  [ur(87,a,213,a,b,643,a)].

given #2583 (T,wt=9): 9701 ->*_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): 11982 -->_s0(true,app(fstsplit(s(x),nil),head(cons(false,y)))) # answer(goal).  [ur(7166,b,263,a,c,1123,a)].

given #2586 (F,wt=11): 11983 -->_s0(true,app(fstsplit(s(x),nil),leq(s(y),0))) # answer(goal).  [ur(7166,b,263,a,c,1080,a)].

given #2587 (F,wt=11): 11984 -->_s0(true,app(fstsplit(s(x),nil),tail(cons(y,false)))) # answer(goal).  [ur(7166,b,263,a,c,1068,a)].

given #2588 (F,wt=11): 11987 -->_s0(true,head(cons(app(fstsplit(s(x),nil),false),y))) # answer(goal).  [resolve(11978,a,7975,b)].

given #2589 (T,wt=9): 9740 ->*_s0(app(app(nil,fstsplit(0,x)),y),y).  [ur(87,a,138,a,b,9700,a)].

given #2590 (T,wt=9): 9743 ->*_s0(sndsplit(0,app(fstsplit(0,x),y)),y).  [ur(87,a,82,a,b,9700,a)].

given #2591 (T,wt=9): 9745 ->*_s0(app(nil,app(fstsplit(0,x),y)),y).  [ur(87,a,61,a,b,9700,a)].

given #2592 (T,wt=9): 9747 ->*_s0(cons(length(nil),empty(nil)),cons(0,true)).  [ur(87,a,318,a,b,3247,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): 21880 -->_s0(true,sndsplit(length(nil),app(fstsplit(0,x),false))) # answer(goal).  [resolve(9743,a,7842,b)].

given #2595 (F,wt=11): 11989 -->_s0(true,tail(cons(x,app(fstsplit(s(y),nil),false)))) # answer(goal).  [resolve(11978,a,7959,b)].

given #2596 (F,wt=11): 11990 -->_s0(true,x) | -->_s0(x,app(fstsplit(s(y),nil),false)) # answer(goal).  [resolve(11978,a,7166,c)].

given #2597 (F,wt=11): 12040 -->_s0(true,head(cons(leq(s(x),sndsplit(0,0)),y))) # answer(goal).  [resolve(12028,a,7975,b)].

given #2598 (T,wt=9): 9749 ->*_s0(cons(empty(nil),empty(nil)),cons(true,true)).  [ur(87,a,168,a,b,3247,a)].

given #2599 (T,wt=9): 9758 ->*_s0(cons(empty(nil),length(nil)),cons(true,0)).  [ur(87,a,317,a,b,3274,a)].

given #2600 (T,wt=9): 9826 ->*_s0(sndsplit(length(nil),empty(nil)),sndsplit(0,true)).  [ur(87,a,321,a,b,3354,a)].

given #2601 (T,wt=9): 9828 ->*_s0(sndsplit(empty(nil),empty(nil)),sndsplit(true,true)).  [ur(87,a,171,a,b,3354,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): 12042 -->_s0(true,tail(cons(x,leq(s(y),sndsplit(0,0))))) # answer(goal).  [resolve(12028,a,7959,b)].

given #2604 (F,wt=11): 12043 -->_s0(true,x) | -->_s0(x,leq(s(y),sndsplit(0,0))) # answer(goal).  [resolve(12028,a,7166,c)].

given #2605 (F,wt=11): 12123 -->_s0(true,head(cons(leq(sndsplit(0,s(x)),0),y))) # answer(goal).  [resolve(12082,a,7975,b)].

given #2606 (F,wt=11): 12125 -->_s0(true,tail(cons(x,leq(sndsplit(0,s(y)),0)))) # answer(goal).  [resolve(12082,a,7959,b)].

given #2607 (T,wt=9): 9838 ->*_s0(sndsplit(empty(nil),length(nil)),sndsplit(true,0)).  [ur(87,a,320,a,b,3381,a)].

given #2608 (T,wt=9): 9857 ->*_s0(mapf(length(nil),empty(nil)),mapf(0,true)).  [ur(87,a,329,a,b,3408,a)].

given #2609 (T,wt=9): 9859 ->*_s0(mapf(empty(nil),empty(nil)),mapf(true,true)).  [ur(87,a,179,a,b,3408,a)].

given #2610 (T,wt=9): 9868 ->*_s0(mapf(empty(nil),length(nil)),mapf(true,0)).  [ur(87,a,328,a,b,3462,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): 12126 -->_s0(true,x) | -->_s0(x,leq(sndsplit(0,s(y)),0)) # answer(goal).  [resolve(12082,a,7166,c)].

given #2613 (F,wt=11): 12303 -->_s0(true,length(nil)) | -->_s0(0,app(sndsplit(0,nil),false)) # answer(goal).  [resolve(12282,a,8273,c)].

given #2614 (F,wt=11): 12406 -->_s0(true,sndsplit(sndsplit(0,length(nil)),head(cons(false,x)))) # answer(goal).  [ur(7166,b,270,a,c,11763,a)].

given #2615 (F,wt=11): 12407 -->_s0(true,sndsplit(0,head(cons(sndsplit(length(nil),false),x)))) # answer(goal).  [ur(7166,b,270,a,c,4408,a)].

given #2616 (T,wt=9): 9878 ->*_s0(leq(length(nil),empty(nil)),leq(0,true)).  [ur(87,a,331,a,b,3489,a)].

given #2617 (T,wt=9): 9880 ->*_s0(leq(empty(nil),empty(nil)),leq(true,true)).  [ur(87,a,181,a,b,3489,a)].

given #2618 (T,wt=9): 9890 ->*_s0(leq(empty(nil),length(nil)),leq(true,0)).  [ur(87,a,330,a,b,3517,a)].

given #2619 (T,wt=9): 9915 ->*_s0(fstsplit(length(nil),empty(nil)),fstsplit(0,true)).  [ur(87,a,335,a,b,3544,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): 12408 -->_s0(true,sndsplit(app(nil,length(nil)),head(cons(false,x)))) # answer(goal).  [ur(7166,b,270,a,c,4404,a)].

given #2622 (F,wt=11): 12409 -->_s0(true,sndsplit(length(nil),head(cons(sndsplit(0,false),x)))) # answer(goal).  [ur(7166,b,270,a,c,4337,a)].

given #2623 (F,wt=11): 12410 -->_s0(true,sndsplit(length(nil),head(cons(app(nil,false),x)))) # answer(goal).  [ur(7166,b,270,a,c,4333,a)].

given #2624 (F,wt=11): 12411 -->_s0(true,sndsplit(0,head(cons(empty(cons(x,y)),z)))) # answer(goal).  [ur(7166,b,270,a,c,1133,a)].

given #2625 (T,wt=9): 9917 ->*_s0(fstsplit(empty(nil),empty(nil)),fstsplit(true,true)).  [ur(87,a,185,a,b,3544,a)].

given #2626 (T,wt=9): 9926 ->*_s0(fstsplit(empty(nil),length(nil)),fstsplit(true,0)).  [ur(87,a,334,a,b,3598,a)].

given #2627 (T,wt=9): 9936 ->*_s0(app(length(nil),empty(nil)),app(0,true)).  [ur(87,a,338,a,b,3625,a)].

given #2628 (T,wt=9): 9938 ->*_s0(app(empty(nil),empty(nil)),app(true,true)).  [ur(87,a,188,a,b,3625,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): 12412 -->_s0(true,sndsplit(0,head(cons(head(cons(false,x)),y)))) # answer(goal).  [ur(7166,b,270,a,c,1121,a)].

given #2631 (F,wt=11): 12413 -->_s0(true,sndsplit(0,head(cons(leq(s(x),0),y)))) # answer(goal).  [ur(7166,b,270,a,c,1077,a)].

given #2632 (F,wt=11): 12414 -->_s0(true,sndsplit(0,head(cons(tail(cons(x,false)),y)))) # answer(goal).  [ur(7166,b,270,a,c,1066,a)].

given #2633 (F,wt=11): 12415 -->_s0(true,sndsplit(s(0),head(cons(cons(x,false),y)))) # answer(goal).  [ur(7166,b,270,a,c,640,a)].

given #2634 (T,wt=9): 9947 ->*_s0(app(empty(nil),length(nil)),app(true,0)).  [ur(87,a,337,a,b,3652,a)].

given #2635 (T,wt=9): 10043 ->*_s0(tail(fstsplit(s(0),cons(x,y))),nil).  [ur(87,a,219,a,b,692,a)].

given #2636 (T,wt=9): 10081 ->*_s0(f(length(nil),length(nil)),f(0,0)).  [ur(87,a,316,a,b,4165,a)].

given #2637 (T,wt=9): 10109 ->*_s0(cons(length(nil),length(nil)),cons(0,0)).  [ur(87,a,318,a,b,4219,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): 12417 -->_s0(true,app(nil,tail(cons(x,tail(cons(y,false)))))) # answer(goal).  [resolve(1065,a,7979,b)].

given #2640 (F,wt=11): 12419 -->_s0(true,sndsplit(0,tail(cons(x,tail(cons(y,false)))))) # answer(goal).  [resolve(1065,a,7962,b)].

given #2641 (F,wt=11): 12421 -->_s0(true,tail(app(nil,cons(x,tail(cons(y,false)))))) # answer(goal).  [resolve(1065,a,7928,b)].

given #2642 (F,wt=11): 12422 -->_s0(true,tail(sndsplit(0,cons(x,tail(cons(y,false)))))) # answer(goal).  [resolve(1065,a,7814,b)].

given #2643 (T,wt=9): 10132 ->*_s0(sndsplit(length(nil),length(nil)),sndsplit(0,0)).  [ur(87,a,321,a,b,4306,a)].

given #2644 (T,wt=9): 10268 ->*_s0(sndsplit(length(nil),sndsplit(length(nil),x)),x).  [ur(87,a,321,a,b,4408,a)].

given #2645 (T,wt=9): 10302 ->*_s0(mapf(length(nil),length(nil)),mapf(0,0)).  [ur(87,a,329,a,b,4429,a)].

given #2646 (T,wt=9): 10340 ->*_s0(leq(length(nil),length(nil)),leq(0,0)).  [ur(87,a,331,a,b,4514,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): 12439 -->_s0(true,app(nil,head(cons(tail(cons(x,false)),y)))) # answer(goal).  [resolve(1067,a,7979,b)].

given #2649 (F,wt=11): 12442 -->_s0(true,head(app(nil,cons(tail(cons(x,false)),y)))) # answer(goal).  [resolve(1067,a,7914,b)].

given #2650 (F,wt=11): 12443 -->_s0(true,head(sndsplit(0,cons(tail(cons(x,false)),y)))) # answer(goal).  [resolve(1067,a,7812,b)].

given #2651 (F,wt=11): 12460 -->_s0(true,head(app(cons(tail(cons(x,false)),y),z))) # answer(goal).  [ur(7166,b,108,a,c,1067,a)].

given #2652 (T,wt=9): 10400 ->*_s0(sndsplit(length(nil),leq(length(nil),x)),true).  [ur(87,a,321,a,b,4622,a)].

given #2653 (T,wt=9): 10433 ->*_s0(fstsplit(length(nil),length(nil)),fstsplit(0,0)).  [ur(87,a,335,a,b,4639,a)].

given #2654 (T,wt=9): 10463 ->*_s0(sndsplit(length(nil),fstsplit(length(nil),x)),nil).  [ur(87,a,321,a,b,4723,a)].

given #2655 (T,wt=9): 10476 ->*_s0(app(length(nil),length(nil)),app(0,0)).  [ur(87,a,338,a,b,4727,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): 12544 -->_s0(true,sndsplit(head(cons(sndsplit(0,length(nil)),x)),false)) # answer(goal).  [ur(7166,b,271,a,c,11763,a)].

given #2658 (F,wt=11): 12545 -->_s0(true,sndsplit(head(cons(0,x)),sndsplit(length(nil),false))) # answer(goal).  [ur(7166,b,271,a,c,4408,a)].

given #2659 (F,wt=11): 12546 -->_s0(true,sndsplit(head(cons(app(nil,length(nil)),x)),false)) # answer(goal).  [ur(7166,b,271,a,c,4404,a)].

given #2660 (F,wt=11): 12547 -->_s0(true,sndsplit(head(cons(length(nil),x)),sndsplit(0,false))) # answer(goal).  [ur(7166,b,271,a,c,4337,a)].

given #2661 (T,wt=9): 10740 ->*_s0(head(fstsplit(s(x),cons(y,z))),y).  [ur(87,a,233,a,b,575,a)].

given #2662 (T,wt=9): 10807 ->*_s0(length(cons(x,empty(nil))),s(length(true))).  [ur(87,a,68,a,b,6138,a)].

given #2663 (T,wt=9): 10843 ->*_s0(empty(fstsplit(s(x),cons(y,z))),false).  [ur(87,a,236,a,b,580,a)].

given #2664 (T,wt=9): 11040 ->*_s0(length(cons(x,length(nil))),s(length(0))).  [ur(87,a,68,a,b,7113,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): 22094 -->*_s0(empty(mapf(two,head(x))),true) # answer(goal).  [ur(584,b,10843,a,c,305,a,d,4635,a)].

given #2667 (F,wt=7): 22303 -->_s0(empty(mapf(two,head(x))),true) # answer(goal).  [ur(87,b,86,a,c,22094,a)].

given #2668 (F,wt=8): 22298 -->_s0(empty(mapf(two,head(x))),empty(nil)) # answer(goal).  [ur(87,b,579,a,c,22094,a)].

given #2669 (F,wt=6): 22304 -->_s0(mapf(two,head(x)),nil) # answer(goal).  [resolve(22298,a,37,b)].

given #2670 (T,wt=9): 11113 ->*_s0(sndsplit(s(x),fstsplit(s(y),nil)),nil).  [ur(87,a,245,a,b,565,a)].

given #2671 (T,wt=9): 11214 ->*_s0(f(x,leq(0,y)),f(x,true)).  [ur(87,a,340,a,b,86,a)].

given #2672 (T,wt=9): 11224 ->*_s0(f(leq(0,x),y),f(true,y)).  [ur(87,a,341,a,b,86,a)].

given #2673 (T,wt=9): 11233 ->*_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): 22297 -->_s0(empty(mapf(two,head(x))),app(nil,true)) # answer(goal).  [ur(87,b,581,a,c,22094,a)].

given #2676 (F,wt=9): 22300 -->_s0(empty(mapf(two,head(x))),leq(0,y)) # answer(goal).  [ur(87,b,572,a,c,22094,a)].

given #2677 (F,wt=9): 22301 -->_s0(empty(mapf(two,head(x))),sndsplit(0,true)) # answer(goal).  [ur(87,b,567,a,c,22094,a)].

given #2678 (F,wt=10): 22072 -->_s0(mapf(two,head(x)),nil) | -->_s0(0,s(y)) # answer(goal).  [resolve(10843,a,895,b)].

given #2679 (T,wt=9): 11242 ->*_s0(cons(leq(0,x),y),cons(true,y)).  [ur(87,a,343,a,b,86,a)].

given #2680 (T,wt=9): 11251 ->*_s0(sndsplit(x,leq(0,y)),sndsplit(x,true)).  [ur(87,a,345,a,b,86,a)].

given #2681 (T,wt=9): 11308 ->*_s0(sndsplit(leq(0,x),y),sndsplit(true,y)).  [ur(87,a,346,a,b,86,a)].

given #2682 (T,wt=9): 11317 ->*_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): 22095 -->_s0(empty(mapf(two,head(x))),y) | -->*_s0(y,true) # answer(goal).  [resolve(22094,a,87,c)].

given #2685 (F,wt=10): 22164 -->_s0(empty(mapf(two,head(x))),leq(length(nil),y)) # answer(goal).  [ur(87,b,4555,a,c,22094,a)].

given #2686 (F,wt=10): 22176 -->_s0(empty(mapf(two,head(x))),sndsplit(length(nil),true)) # answer(goal).  [ur(87,b,4340,a,c,22094,a)].

given #2687 (F,wt=10): 22236 -->_s0(empty(mapf(two,head(x))),empty(sndsplit(0,nil))) # answer(goal).  [ur(87,b,2366,a,c,22094,a)].

given #2688 (T,wt=9): 11326 ->*_s0(mapf(leq(0,x),y),mapf(true,y)).  [ur(87,a,354,a,b,86,a)].

given #2689 (T,wt=9): 11335 ->*_s0(leq(x,leq(0,y)),leq(x,true)).  [ur(87,a,355,a,b,86,a)].

given #2690 (T,wt=9): 11346 ->*_s0(leq(leq(0,x),y),leq(true,y)).  [ur(87,a,356,a,b,86,a)].

given #2691 (T,wt=9): 11355 ->*_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): 22324 -->_s0(mapf(two,head(x)),sndsplit(0,nil)) # answer(goal).  [resolve(22236,a,37,b)].

given #2694 (F,wt=10): 22247 -->_s0(empty(mapf(two,head(x))),empty(mapf(y,nil))) # answer(goal).  [ur(87,b,2133,a,c,22094,a)].

============================== PROOF =================================

% Proof 1 at 0.44 (+ 0.04) 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(empty(mapf(two,head(x13))),true) & ->*_s0(leq(x14,length(x15)),true) & ->*_s0(empty(fstsplit(x14,x15)),false))) # label(goal) # label(non_clause) # label(goal).  [goal].
37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence).  [clausify(3)].
42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence).  [clausify(8)].
43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence).  [clausify(9)].
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(empty(mapf(two,head(x))),true) | -->*_s0(leq(y,length(z)),true) | -->*_s0(empty(fstsplit(y,z)),false) # label(goal) # answer(goal).  [deny(34)].
131 ->_s0(leq(app(nil,x),y),leq(x,y)).  [ur(42,a,61,a)].
236 ->_s0(empty(fstsplit(s(x),cons(y,z))),empty(cons(y,fstsplit(x,z)))).  [ur(37,a,65,a)].
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)].
584 -->*_s0(empty(mapf(two,head(x))),true) | -->*_s0(empty(fstsplit(y,z)),false) | -->_s0(leq(y,length(z)),u) | -->*_s0(u,true) # answer(goal).  [resolve(88,b,87,c)].
2133 ->*_s0(empty(mapf(x,nil)),true).  [ur(87,a,461,a,b,579,a)].
4586 ->*_s0(leq(app(nil,0),x),true).  [ur(87,a,131,a,b,572,a)].
4635 ->*_s0(leq(s(app(nil,0)),s(x)),true).  [ur(87,a,72,a,b,4586,a)].
10843 ->*_s0(empty(fstsplit(s(x),cons(y,z))),false).  [ur(87,a,236,a,b,580,a)].
22094 -->*_s0(empty(mapf(two,head(x))),true) # answer(goal).  [ur(584,b,10843,a,c,305,a,d,4635,a)].
22247 -->_s0(empty(mapf(two,head(x))),empty(mapf(y,nil))) # answer(goal).  [ur(87,b,2133,a,c,22094,a)].
22328 -->_s0(mapf(two,head(x)),mapf(y,nil)) # answer(goal).  [resolve(22247,a,37,b)].
22329 $F # answer(goal).  [resolve(22328,a,278,a)].

============================== end of proof ==========================

============================== STATISTICS ============================

Given=2694. Generated=46446. Kept=22294. proofs=1.
Usable=2694. Sos=19599. Demods=0. Limbo=0, Disabled=54. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=9250. Back_subsumed=0.
Sos_limit_deleted=14902. 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=64668. Nonunit_bsub_feature_tests=1082.
Megabytes=45.04.
User_CPU=0.44, System_CPU=0.04, Wall_clock=0.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 3343811 exit (max_proofs) Tue Jul 30 09:38:55 2024


The problem is feasible.