NO Problem 1: Infeasibility Problem: [(VAR vNonEmpty x n h t m pid st1 in2 st2 in3 st3 vNonEmpty x6 x1 x3) (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(fstsplit(x6,x1)) ->* false, leq(x6,length(x3)) ->* true, empty(fstsplit(x6,x3)) ->* false Problem 1: Obtaining a proof using Prover9: -> Prover9 Output: ============================== Prover9 =============================== Prover9 (64) version 2009-11A, November 2009. Process 3157870 was started by sandbox on z005.star.cs.uiowa.edu, Tue Jul 30 08:24:40 2024 The command was "./prover9 -f /tmp/prover93157863-0.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file /tmp/prover93157863-0.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(fstsplit(x13,x14)),false) & ->*_s0(leq(x13,length(x15)),true) & ->*_s0(empty(fstsplit(x13,x15)),false))) # label(goal). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 ->_s0(x1,y) -> ->_s0(app(x1,x2),app(y,x2)) # label(congruence) # label(non_clause). [assumption]. 2 ->_s0(x2,y) -> ->_s0(app(x1,x2),app(x1,y)) # label(congruence) # label(non_clause). [assumption]. 3 ->_s0(x1,y) -> ->_s0(empty(x1),empty(y)) # label(congruence) # label(non_clause). [assumption]. 4 ->_s0(x1,y) -> ->_s0(fstsplit(x1,x2),fstsplit(y,x2)) # label(congruence) # label(non_clause). [assumption]. 5 ->_s0(x2,y) -> ->_s0(fstsplit(x1,x2),fstsplit(x1,y)) # label(congruence) # label(non_clause). [assumption]. 6 ->_s0(x1,y) -> ->_s0(head(x1),head(y)) # label(congruence) # label(non_clause). [assumption]. 7 ->_s0(x1,y) -> ->_s0(length(x1),length(y)) # label(congruence) # label(non_clause). [assumption]. 8 ->_s0(x1,y) -> ->_s0(leq(x1,x2),leq(y,x2)) # label(congruence) # label(non_clause). [assumption]. 9 ->_s0(x2,y) -> ->_s0(leq(x1,x2),leq(x1,y)) # label(congruence) # label(non_clause). [assumption]. 10 ->_s0(x1,y) -> ->_s0(mapf(x1,x2),mapf(y,x2)) # label(congruence) # label(non_clause). [assumption]. 11 ->_s0(x2,y) -> ->_s0(mapf(x1,x2),mapf(x1,y)) # label(congruence) # label(non_clause). [assumption]. 12 ->_s0(x1,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(y,x2,x3,x4,x5,x6)) # label(congruence) # label(non_clause). [assumption]. 13 ->_s0(x2,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,y,x3,x4,x5,x6)) # label(congruence) # label(non_clause). [assumption]. 14 ->_s0(x3,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,y,x4,x5,x6)) # label(congruence) # label(non_clause). [assumption]. 15 ->_s0(x4,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,y,x5,x6)) # label(congruence) # label(non_clause). [assumption]. 16 ->_s0(x5,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,x4,y,x6)) # label(congruence) # label(non_clause). [assumption]. 17 ->_s0(x6,y) -> ->_s0(ring(x1,x2,x3,x4,x5,x6),ring(x1,x2,x3,x4,x5,y)) # label(congruence) # label(non_clause). [assumption]. 18 ->_s0(x1,y) -> ->_s0(sndsplit(x1,x2),sndsplit(y,x2)) # label(congruence) # label(non_clause). [assumption]. 19 ->_s0(x2,y) -> ->_s0(sndsplit(x1,x2),sndsplit(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20 ->_s0(x1,y) -> ->_s0(tail(x1),tail(y)) # label(congruence) # label(non_clause). [assumption]. 21 ->_s0(x1,y) -> ->_s0(cons(x1,x2),cons(y,x2)) # label(congruence) # label(non_clause). [assumption]. 22 ->_s0(x2,y) -> ->_s0(cons(x1,x2),cons(x1,y)) # label(congruence) # label(non_clause). [assumption]. 23 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 24 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 26 ->*_s0(empty(fstsplit(x5,x7)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(sndsplit(x5,x7),cons(fstsplit(x5,x7),x8),x9,x10,x11,x5)) # label(replacement) # label(non_clause). [assumption]. 27 ->*_s0(leq(x5,length(x9)),false) & ->*_s0(empty(fstsplit(x5,app(mapf(two,head(x8)),x9))),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,tail(x8),sndsplit(x5,app(mapf(two,head(x8)),x9)),cons(fstsplit(x5,app(mapf(two,head(x8)),x9)),x10),x11,x5)) # label(replacement) # label(non_clause). [assumption]. 28 ->*_s0(empty(mapf(two,head(x8))),true) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,tail(x8),x9,x10,x11,x5)) # label(replacement) # label(non_clause). [assumption]. 29 ->*_s0(leq(x5,length(x9)),true) & ->*_s0(empty(fstsplit(x5,x9)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,sndsplit(x5,x9),cons(fstsplit(x5,x9),x10),x11,x5)) # label(replacement) # label(non_clause). [assumption]. 30 ->*_s0(leq(x5,length(x11)),false) & ->*_s0(empty(fstsplit(x5,app(mapf(three,head(x10)),x11))),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,tail(x10),sndsplit(x5,app(mapf(three,head(x10)),x11)),x5)) # label(replacement) # label(non_clause). [assumption]. 31 ->*_s0(empty(mapf(three,head(x10))),true) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,tail(x10),x11,x5)) # label(replacement) # label(non_clause). [assumption]. 32 ->*_s0(leq(x5,length(x11)),true) & ->*_s0(empty(fstsplit(x5,x11)),false) -> ->_s0(ring(x7,x8,x9,x10,x11,x5),ring(x7,x8,x9,x10,sndsplit(x5,x11),x5)) # label(replacement) # label(non_clause). [assumption]. 33 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 34 (exists x13 exists x14 exists x15 (->*_s0(empty(fstsplit(x13,x14)),false) & ->*_s0(leq(x13,length(x15)),true) & ->*_s0(empty(fstsplit(x13,x15)),false))) # label(goal) # label(non_clause) # label(goal). [goal]. ============================== end of process non-clausal formulas === ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence). [clausify(1)]. -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence). [clausify(2)]. -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)]. -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence). [clausify(4)]. -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence). [clausify(5)]. -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence). [clausify(6)]. -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence). [clausify(7)]. -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence). [clausify(8)]. -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)]. -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence). [clausify(10)]. -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence). [clausify(11)]. -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence). [clausify(12)]. -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence). [clausify(13)]. -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence). [clausify(14)]. -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence). [clausify(15)]. -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence). [clausify(16)]. -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence). [clausify(17)]. -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence). [clausify(18)]. -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence). [clausify(19)]. -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence). [clausify(20)]. -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence). [clausify(21)]. -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence). [clausify(22)]. -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(23)]. -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(24)]. -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(25)]. ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement). [assumption]. ->_s0(app(nil,x),x) # label(replacement). [assumption]. ->_s0(empty(cons(x,y)),false) # label(replacement). [assumption]. ->_s0(empty(nil),true) # label(replacement). [assumption]. ->_s0(fstsplit(0,x),nil) # label(replacement). [assumption]. ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption]. ->_s0(fstsplit(s(x),nil),nil) # label(replacement). [assumption]. ->_s0(head(cons(x,y)),x) # label(replacement). [assumption]. ->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption]. ->_s0(length(nil),0) # label(replacement). [assumption]. ->_s0(leq(0,x),true) # label(replacement). [assumption]. ->_s0(leq(s(x),0),false) # label(replacement). [assumption]. ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption]. ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement). [assumption]. ->_s0(mapf(x,nil),nil) # label(replacement). [assumption]. -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement). [clausify(26)]. -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement). [clausify(27)]. -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement). [clausify(28)]. -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement). [clausify(29)]. -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement). [clausify(30)]. -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement). [clausify(31)]. -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement). [clausify(32)]. ->_s0(sndsplit(0,x),x) # label(replacement). [assumption]. ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement). [assumption]. ->_s0(sndsplit(s(x),nil),nil) # label(replacement). [assumption]. ->_s0(tail(cons(x,y)),y) # label(replacement). [assumption]. ->*_s0(x,x) # label(reflexivity). [assumption]. -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)]. -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal). [deny(34)]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination ============= Auto_denials: % copying label goal to answer in negative clause Term ordering decisions: Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). Function symbol precedence: function_order([ nil, false, true, 0, two, three, cons, fstsplit, mapf, sndsplit, app, leq, f, empty, s, head, length, tail, ring ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(neg_binary_resolution). % (HNE depth_diff=-26) % clear(ordered_res). % (HNE depth_diff=-26) % set(ur_resolution). % (HNE depth_diff=-26) % set(ur_resolution) -> set(pos_ur_resolution). % set(ur_resolution) -> set(neg_ur_resolution). Auto_process settings: % set(unit_deletion). % (Horn set with negative nonunits) kept: 35 -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence). [clausify(1)]. kept: 36 -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence). [clausify(2)]. kept: 37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)]. kept: 38 -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence). [clausify(4)]. kept: 39 -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence). [clausify(5)]. kept: 40 -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence). [clausify(6)]. kept: 41 -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence). [clausify(7)]. kept: 42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence). [clausify(8)]. kept: 43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)]. kept: 44 -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence). [clausify(10)]. kept: 45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence). [clausify(11)]. kept: 46 -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence). [clausify(12)]. kept: 47 -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence). [clausify(13)]. kept: 48 -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence). [clausify(14)]. kept: 49 -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence). [clausify(15)]. kept: 50 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence). [clausify(16)]. kept: 51 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence). [clausify(17)]. kept: 52 -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence). [clausify(18)]. kept: 53 -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence). [clausify(19)]. kept: 54 -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence). [clausify(20)]. kept: 55 -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence). [clausify(21)]. kept: 56 -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence). [clausify(22)]. kept: 57 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(23)]. kept: 58 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(24)]. kept: 59 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(25)]. kept: 60 ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement). [assumption]. kept: 61 ->_s0(app(nil,x),x) # label(replacement). [assumption]. kept: 62 ->_s0(empty(cons(x,y)),false) # label(replacement). [assumption]. kept: 63 ->_s0(empty(nil),true) # label(replacement). [assumption]. kept: 64 ->_s0(fstsplit(0,x),nil) # label(replacement). [assumption]. kept: 65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption]. kept: 66 ->_s0(fstsplit(s(x),nil),nil) # label(replacement). [assumption]. kept: 67 ->_s0(head(cons(x,y)),x) # label(replacement). [assumption]. kept: 68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption]. kept: 69 ->_s0(length(nil),0) # label(replacement). [assumption]. kept: 70 ->_s0(leq(0,x),true) # label(replacement). [assumption]. kept: 71 ->_s0(leq(s(x),0),false) # label(replacement). [assumption]. kept: 72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption]. kept: 73 ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement). [assumption]. kept: 74 ->_s0(mapf(x,nil),nil) # label(replacement). [assumption]. kept: 75 -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement). [clausify(26)]. kept: 76 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement). [clausify(27)]. kept: 77 -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement). [clausify(28)]. kept: 78 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement). [clausify(29)]. kept: 79 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement). [clausify(30)]. kept: 80 -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement). [clausify(31)]. kept: 81 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement). [clausify(32)]. kept: 82 ->_s0(sndsplit(0,x),x) # label(replacement). [assumption]. kept: 83 ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement). [assumption]. kept: 84 ->_s0(sndsplit(s(x),nil),nil) # label(replacement). [assumption]. kept: 85 ->_s0(tail(cons(x,y)),y) # label(replacement). [assumption]. kept: 86 ->*_s0(x,x) # label(reflexivity). [assumption]. kept: 87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)]. kept: 88 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal) # answer(goal). [deny(34)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 35 -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence). [clausify(1)]. 36 -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence). [clausify(2)]. 37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)]. 38 -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence). [clausify(4)]. 39 -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence). [clausify(5)]. 40 -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence). [clausify(6)]. 41 -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence). [clausify(7)]. 42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence). [clausify(8)]. 43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)]. 44 -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence). [clausify(10)]. 45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence). [clausify(11)]. 46 -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence). [clausify(12)]. 47 -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence). [clausify(13)]. 48 -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence). [clausify(14)]. 49 -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence). [clausify(15)]. 50 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence). [clausify(16)]. 51 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence). [clausify(17)]. 52 -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence). [clausify(18)]. 53 -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence). [clausify(19)]. 54 -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence). [clausify(20)]. 55 -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence). [clausify(21)]. 56 -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence). [clausify(22)]. 57 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(23)]. 58 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(24)]. 59 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(25)]. 60 ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement). [assumption]. 61 ->_s0(app(nil,x),x) # label(replacement). [assumption]. 62 ->_s0(empty(cons(x,y)),false) # label(replacement). [assumption]. 63 ->_s0(empty(nil),true) # label(replacement). [assumption]. 64 ->_s0(fstsplit(0,x),nil) # label(replacement). [assumption]. 65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption]. 66 ->_s0(fstsplit(s(x),nil),nil) # label(replacement). [assumption]. 67 ->_s0(head(cons(x,y)),x) # label(replacement). [assumption]. 68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption]. 69 ->_s0(length(nil),0) # label(replacement). [assumption]. 70 ->_s0(leq(0,x),true) # label(replacement). [assumption]. 71 ->_s0(leq(s(x),0),false) # label(replacement). [assumption]. 72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption]. 73 ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement). [assumption]. 74 ->_s0(mapf(x,nil),nil) # label(replacement). [assumption]. 75 -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement). [clausify(26)]. 76 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement). [clausify(27)]. 77 -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement). [clausify(28)]. 78 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement). [clausify(29)]. 79 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement). [clausify(30)]. 80 -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement). [clausify(31)]. 81 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement). [clausify(32)]. 82 ->_s0(sndsplit(0,x),x) # label(replacement). [assumption]. 83 ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement). [assumption]. 84 ->_s0(sndsplit(s(x),nil),nil) # label(replacement). [assumption]. 85 ->_s0(tail(cons(x,y)),y) # label(replacement). [assumption]. 86 ->*_s0(x,x) # label(reflexivity). [assumption]. 87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)]. 88 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal) # answer(goal). [deny(34)]. end_of_list. formulas(demodulators). end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.01 seconds. given #1 (I,wt=10): 35 -->_s0(x,y) | ->_s0(app(x,z),app(y,z)) # label(congruence). [clausify(1)]. given #2 (I,wt=10): 36 -->_s0(x,y) | ->_s0(app(z,x),app(z,y)) # label(congruence). [clausify(2)]. given #3 (I,wt=8): 37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)]. given #4 (I,wt=10): 38 -->_s0(x,y) | ->_s0(fstsplit(x,z),fstsplit(y,z)) # label(congruence). [clausify(4)]. given #5 (I,wt=10): 39 -->_s0(x,y) | ->_s0(fstsplit(z,x),fstsplit(z,y)) # label(congruence). [clausify(5)]. given #6 (I,wt=8): 40 -->_s0(x,y) | ->_s0(head(x),head(y)) # label(congruence). [clausify(6)]. given #7 (I,wt=8): 41 -->_s0(x,y) | ->_s0(length(x),length(y)) # label(congruence). [clausify(7)]. given #8 (I,wt=10): 42 -->_s0(x,y) | ->_s0(leq(x,z),leq(y,z)) # label(congruence). [clausify(8)]. given #9 (I,wt=10): 43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)]. given #10 (I,wt=10): 44 -->_s0(x,y) | ->_s0(mapf(x,z),mapf(y,z)) # label(congruence). [clausify(10)]. given #11 (I,wt=10): 45 -->_s0(x,y) | ->_s0(mapf(z,x),mapf(z,y)) # label(congruence). [clausify(11)]. given #12 (I,wt=18): 46 -->_s0(x,y) | ->_s0(ring(x,z,u,w,v5,v6),ring(y,z,u,w,v5,v6)) # label(congruence). [clausify(12)]. given #13 (I,wt=18): 47 -->_s0(x,y) | ->_s0(ring(z,x,u,w,v5,v6),ring(z,y,u,w,v5,v6)) # label(congruence). [clausify(13)]. given #14 (I,wt=18): 48 -->_s0(x,y) | ->_s0(ring(z,u,x,w,v5,v6),ring(z,u,y,w,v5,v6)) # label(congruence). [clausify(14)]. given #15 (I,wt=18): 49 -->_s0(x,y) | ->_s0(ring(z,u,w,x,v5,v6),ring(z,u,w,y,v5,v6)) # label(congruence). [clausify(15)]. given #16 (I,wt=18): 50 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,x,v6),ring(z,u,w,v5,y,v6)) # label(congruence). [clausify(16)]. given #17 (I,wt=18): 51 -->_s0(x,y) | ->_s0(ring(z,u,w,v5,v6,x),ring(z,u,w,v5,v6,y)) # label(congruence). [clausify(17)]. given #18 (I,wt=10): 52 -->_s0(x,y) | ->_s0(sndsplit(x,z),sndsplit(y,z)) # label(congruence). [clausify(18)]. given #19 (I,wt=10): 53 -->_s0(x,y) | ->_s0(sndsplit(z,x),sndsplit(z,y)) # label(congruence). [clausify(19)]. given #20 (I,wt=8): 54 -->_s0(x,y) | ->_s0(tail(x),tail(y)) # label(congruence). [clausify(20)]. given #21 (I,wt=10): 55 -->_s0(x,y) | ->_s0(cons(x,z),cons(y,z)) # label(congruence). [clausify(21)]. given #22 (I,wt=10): 56 -->_s0(x,y) | ->_s0(cons(z,x),cons(z,y)) # label(congruence). [clausify(22)]. given #23 (I,wt=10): 57 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(23)]. given #24 (I,wt=10): 58 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(24)]. given #25 (I,wt=8): 59 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(25)]. given #26 (I,wt=11): 60 ->_s0(app(cons(x,y),z),cons(x,app(y,z))) # label(replacement). [assumption]. given #27 (I,wt=5): 61 ->_s0(app(nil,x),x) # label(replacement). [assumption]. given #28 (I,wt=6): 62 ->_s0(empty(cons(x,y)),false) # label(replacement). [assumption]. given #29 (I,wt=4): 63 ->_s0(empty(nil),true) # label(replacement). [assumption]. given #30 (I,wt=5): 64 ->_s0(fstsplit(0,x),nil) # label(replacement). [assumption]. given #31 (I,wt=12): 65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption]. given #32 (I,wt=6): 66 ->_s0(fstsplit(s(x),nil),nil) # label(replacement). [assumption]. given #33 (I,wt=6): 67 ->_s0(head(cons(x,y)),x) # label(replacement). [assumption]. given #34 (I,wt=8): 68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption]. given #35 (I,wt=4): 69 ->_s0(length(nil),0) # label(replacement). [assumption]. given #36 (I,wt=5): 70 ->_s0(leq(0,x),true) # label(replacement). [assumption]. given #37 (I,wt=6): 71 ->_s0(leq(s(x),0),false) # label(replacement). [assumption]. given #38 (I,wt=9): 72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption]. given #39 (I,wt=13): 73 ->_s0(mapf(x,cons(y,z)),app(f(x,y),mapf(x,z))) # label(replacement). [assumption]. given #40 (I,wt=5): 74 ->_s0(mapf(x,nil),nil) # label(replacement). [assumption]. given #41 (I,wt=27): 75 -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(y,z,u,w,v5,x),ring(sndsplit(x,y),cons(fstsplit(x,y),z),u,w,v5,x)) # label(replacement). [clausify(26)]. given #42 (I,wt=49): 76 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(two,head(z)),y))),false) | ->_s0(ring(u,z,y,w,v5,x),ring(u,tail(z),sndsplit(x,app(mapf(two,head(z)),y)),cons(fstsplit(x,app(mapf(two,head(z)),y)),w),v5,x)) # label(replacement). [clausify(27)]. given #43 (I,wt=23): 77 -->*_s0(empty(mapf(two,head(x))),true) | ->_s0(ring(y,x,z,u,w,v5),ring(y,tail(x),z,u,w,v5)) # label(replacement). [clausify(28)]. given #44 (I,wt=33): 78 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,y,w,v5,x),ring(z,u,sndsplit(x,y),cons(fstsplit(x,y),w),v5,x)) # label(replacement). [clausify(29)]. given #45 (I,wt=40): 79 -->*_s0(leq(x,length(y)),false) | -->*_s0(empty(fstsplit(x,app(mapf(three,head(z)),y))),false) | ->_s0(ring(u,w,v5,z,y,x),ring(u,w,v5,tail(z),sndsplit(x,app(mapf(three,head(z)),y)),x)) # label(replacement). [clausify(30)]. given #46 (I,wt=23): 80 -->*_s0(empty(mapf(three,head(x))),true) | ->_s0(ring(y,z,u,x,w,v5),ring(y,z,u,tail(x),w,v5)) # label(replacement). [clausify(31)]. given #47 (I,wt=29): 81 -->*_s0(leq(x,length(y)),true) | -->*_s0(empty(fstsplit(x,y)),false) | ->_s0(ring(z,u,w,v5,y,x),ring(z,u,w,v5,sndsplit(x,y),x)) # label(replacement). [clausify(32)]. given #48 (I,wt=5): 82 ->_s0(sndsplit(0,x),x) # label(replacement). [assumption]. given #49 (I,wt=10): 83 ->_s0(sndsplit(s(x),cons(y,z)),sndsplit(x,z)) # label(replacement). [assumption]. given #50 (I,wt=6): 84 ->_s0(sndsplit(s(x),nil),nil) # label(replacement). [assumption]. given #51 (I,wt=6): 85 ->_s0(tail(cons(x,y)),y) # label(replacement). [assumption]. given #52 (I,wt=3): 86 ->*_s0(x,x) # label(reflexivity). [assumption]. given #53 (I,wt=9): 87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)]. given #54 (I,wt=18): 88 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal) # answer(goal). [deny(34)]. given #55 (A,wt=13): 89 ->_s0(s(app(cons(x,y),z)),s(cons(x,app(y,z)))). [ur(59,a,60,a)]. given #56 (F,wt=21): 583 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(empty(fstsplit(x,z)),false) | -->_s0(leq(x,length(z)),u) | -->*_s0(u,true) # answer(goal). [resolve(88,b,87,c)]. given #57 (F,wt=12): 612 -->*_s0(empty(fstsplit(0,x)),false) | -->*_s0(empty(fstsplit(0,y)),false) # answer(goal). [resolve(583,c,70,a),unit_del(c,86)]. given #58 (F,wt=18): 616 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(empty(fstsplit(x,z)),false) | -->_s0(leq(x,length(z)),true) # answer(goal). [resolve(583,d,86,a)]. given #59 (F,wt=21): 584 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->_s0(empty(fstsplit(x,z)),u) | -->*_s0(u,false) # answer(goal). [resolve(88,c,87,c)]. 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=18): 621 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->_s0(empty(fstsplit(x,z)),false) # answer(goal). [resolve(584,d,86,a)]. given #66 (F,wt=19): 626 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(empty(fstsplit(x,z)),false) | -->_s0(leq(x,length(z)),empty(nil)) # answer(goal). [resolve(579,a,583,d)]. given #67 (F,wt=20): 631 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->_s0(empty(fstsplit(x,z)),sndsplit(0,false)) # answer(goal). [resolve(567,a,584,d)]. given #68 (F,wt=20): 632 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(empty(fstsplit(x,z)),false) | -->_s0(leq(x,length(z)),sndsplit(0,true)) # answer(goal). [resolve(567,a,583,d)]. given #69 (T,wt=5): 572 ->*_s0(leq(0,x),true). [ur(87,a,70,a,b,86,a)]. given #70 (T,wt=5): 578 ->*_s0(fstsplit(0,x),nil). [ur(87,a,64,a,b,86,a)]. given #71 (T,wt=5): 581 ->*_s0(app(nil,x),x). [ur(87,a,61,a,b,86,a)]. given #72 (T,wt=6): 164 ->_s0(s(empty(nil)),s(true)). [ur(59,a,63,a)]. given #73 (A,wt=15): 91 ->_s0(f(app(cons(x,y),z),u),f(cons(x,app(y,z)),u)). [ur(57,a,60,a)]. given #74 (F,wt=12): 675 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(fstsplit(0,y)),false) # answer(goal). [resolve(572,a,621,b)]. given #75 (F,wt=14): 674 -->*_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(fstsplit(0,y)),sndsplit(0,false)) # answer(goal). [resolve(572,a,631,b)]. given #76 (F,wt=15): 744 -->_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(fstsplit(0,y)),z) | -->*_s0(z,false) # answer(goal). [resolve(675,a,87,c)]. given #77 (F,wt=12): 750 -->_s0(empty(fstsplit(0,x)),false) | -->_s0(empty(fstsplit(0,y)),false) # answer(goal). [resolve(744,c,86,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=17): 745 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(fstsplit(0,y)),z) | -->*_s0(z,false) # answer(goal). [resolve(674,a,87,c)]. given #84 (F,wt=16): 882 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(fstsplit(0,y)),app(nil,false)) # answer(goal). [resolve(745,c,581,a)]. given #85 (F,wt=16): 883 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(fstsplit(0,y)),sndsplit(0,false)) # answer(goal). [resolve(745,c,567,a)]. given #86 (F,wt=17): 881 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->*_s0(empty(y),false) | -->_s0(fstsplit(0,z),y) # answer(goal). [resolve(745,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=12): 886 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->*_s0(empty(nil),false) # answer(goal). [resolve(881,c,64,a)]. given #93 (F,wt=15): 1018 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(nil),y) | -->*_s0(y,false) # answer(goal). [resolve(886,b,87,c)]. given #94 (F,wt=11): 1019 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->*_s0(true,false) # answer(goal). [resolve(1018,b,63,a)]. given #95 (F,wt=12): 1024 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(nil),false) # answer(goal). [resolve(1018,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=14): 1021 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(nil),app(nil,false)) # answer(goal). [resolve(1018,c,581,a)]. given #102 (F,wt=14): 1022 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(nil),sndsplit(0,false)) # answer(goal). [resolve(1018,c,567,a)]. given #103 (F,wt=14): 1025 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,y) | -->*_s0(y,false) # answer(goal). [resolve(1019,b,87,c)]. given #104 (F,wt=11): 1105 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,false) # answer(goal). [resolve(1025,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): 623 ->*_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=13): 1100 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,app(nil,false)) # answer(goal). [resolve(1025,c,581,a)]. given #111 (F,wt=13): 1102 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,sndsplit(0,false)) # answer(goal). [resolve(1025,c,567,a)]. given #112 (F,wt=14): 1101 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,leq(s(y),0)) # answer(goal). [resolve(1025,c,571,a)]. given #113 (F,wt=14): 1103 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,tail(cons(y,false))) # answer(goal). [resolve(1025,c,564,a)]. given #114 (T,wt=6): 625 ->*_s0(app(nil,length(nil)),0). [ur(87,a,61,a,b,573,a)]. given #115 (T,wt=6): 628 ->*_s0(sndsplit(0,empty(nil)),true). [ur(87,a,82,a,b,579,a)]. given #116 (T,wt=6): 630 ->*_s0(app(nil,empty(nil)),true). [ur(87,a,61,a,b,579,a)]. given #117 (T,wt=6): 692 ->*_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=14): 1106 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,head(cons(false,y))) # answer(goal). [resolve(575,a,1025,c)]. given #120 (F,wt=14): 1119 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,empty(cons(y,z))) # answer(goal). [resolve(580,a,1025,c)]. given #121 (F,wt=15): 1020 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->*_s0(empty(y),false) | -->_s0(nil,y) # answer(goal). [resolve(1018,b,37,b)]. given #122 (F,wt=13): 1205 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(nil,cons(y,z)) # answer(goal). [resolve(1020,b,580,a)]. given #123 (T,wt=6): 751 ->*_s0(tail(empty(nil)),tail(true)). [ur(87,a,169,a,b,86,a)]. given #124 (T,wt=6): 777 ->*_s0(length(empty(nil)),length(true)). [ur(87,a,182,a,b,86,a)]. given #125 (T,wt=6): 803 ->*_s0(head(empty(nil)),head(true)). [ur(87,a,183,a,b,86,a)]. given #126 (T,wt=6): 829 ->*_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=15): 1052 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(nil),tail(cons(y,false))) # answer(goal). [resolve(564,a,1018,c)]. given #129 (F,wt=15): 1065 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(nil),leq(s(y),0)) # answer(goal). [resolve(571,a,1018,c)]. given #130 (F,wt=15): 1107 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(nil),head(cons(false,y))) # answer(goal). [resolve(575,a,1018,c)]. given #131 (F,wt=15): 1120 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(nil),empty(cons(y,z))) # answer(goal). [resolve(580,a,1018,c)]. given #132 (T,wt=6): 888 ->*_s0(s(length(nil)),s(0)). [ur(87,a,314,a,b,86,a)]. given #133 (T,wt=6): 914 ->*_s0(tail(length(nil)),tail(0)). [ur(87,a,319,a,b,86,a)]. given #134 (T,wt=6): 940 ->*_s0(length(length(nil)),length(0)). [ur(87,a,332,a,b,86,a)]. given #135 (T,wt=6): 966 ->*_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=15): 1121 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(fstsplit(0,y),cons(z,u)) # answer(goal). [resolve(580,a,881,b)]. given #138 (F,wt=17): 887 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->*_s0(empty(fstsplit(y,z)),false) | -->_s0(0,y) # answer(goal). [resolve(881,c,38,b)]. given #139 (F,wt=17): 1053 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(fstsplit(0,y)),tail(cons(z,false))) # answer(goal). [resolve(564,a,745,c)]. given #140 (F,wt=17): 1066 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(empty(fstsplit(0,y)),leq(s(z),0)) # answer(goal). [resolve(571,a,745,c)]. given #141 (T,wt=6): 1026 ->*_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=17): 1104 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,y) | -->_s0(y,z) | -->*_s0(z,false) # answer(goal). [resolve(1025,c,87,c)]. given #147 (F,wt=14): 1485 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,y) | -->_s0(y,false) # answer(goal). [resolve(1104,d,86,a)]. given #148 (F,wt=15): 1445 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,length(nil)) | -->*_s0(0,false) # answer(goal). [resolve(1104,c,69,a)]. given #149 (F,wt=16): 1436 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,sndsplit(0,y)) | -->*_s0(y,false) # answer(goal). [resolve(1104,c,82,a)]. given #150 (T,wt=6): 1356 ->*_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): 1533 ->*_s0(empty(app(nil,nil)),true). [ur(87,a,136,a,b,579,a)]. given #154 (A,wt=23): 100 ->_s0(ring(x,y,app(cons(z,u),w),v5,v6,v7),ring(x,y,cons(z,app(u,w)),v5,v6,v7)). [ur(48,a,60,a)]. given #155 (F,wt=15): 1487 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,sndsplit(0,app(nil,false))) # answer(goal). [resolve(1436,c,581,a)]. given #156 (F,wt=15): 1491 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,sndsplit(0,sndsplit(0,false))) # answer(goal). [resolve(1436,c,567,a)]. given #157 (F,wt=16): 1442 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,mapf(y,nil)) | -->*_s0(nil,false) # answer(goal). [resolve(1104,c,74,a)]. given #158 (F,wt=16): 1450 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,fstsplit(0,y)) | -->*_s0(nil,false) # answer(goal). [resolve(1104,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): 1650 ->*_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=16): 1451 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,app(nil,y)) | -->*_s0(y,false) # answer(goal). [resolve(1104,c,61,a)]. given #165 (F,wt=15): 1709 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,app(nil,app(nil,false))) # answer(goal). [resolve(1451,c,581,a)]. given #166 (F,wt=15): 1713 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,app(nil,sndsplit(0,false))) # answer(goal). [resolve(1451,c,567,a)]. given #167 (F,wt=16): 1478 -->_s0(empty(fstsplit(0,x)),sndsplit(0,false)) | -->_s0(true,y) | -->_s0(y,app(nil,false)) # answer(goal). [resolve(1104,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): 1748 ->*_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=10): 1747 -->*_s0(empty(fstsplit(0,x)),false) | -->*_s0(empty(nil),false) # answer(goal). [resolve(211,a,584,c),unit_del(b,572)]. given #174 (F,wt=13): 1835 -->*_s0(empty(nil),false) | -->_s0(empty(fstsplit(0,x)),y) | -->*_s0(y,false) # answer(goal). [resolve(1747,a,87,c)]. given #175 (F,wt=4): 1838 -->*_s0(empty(nil),false) # answer(goal). [resolve(1835,b,211,a),merge(b)]. given #176 (F,wt=3): 1847 -->*_s0(true,false) # answer(goal). [ur(87,a,63,a,c,1838,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=3): 1855 -->_s0(true,false) # answer(goal). [ur(87,b,86,a,c,1847,a)]. given #183 (F,wt=4): 1846 -->_s0(empty(nil),false) # answer(goal). [ur(87,b,86,a,c,1838,a)]. given #184 (F,wt=5): 1849 -->_s0(true,app(nil,false)) # answer(goal). [ur(87,b,581,a,c,1847,a)]. given #185 (F,wt=5): 1853 -->_s0(true,sndsplit(0,false)) # answer(goal). [ur(87,b,567,a,c,1847,a)]. given #186 (T,wt=7): 439 ->_s0(s(mapf(x,nil)),s(nil)). [ur(59,a,74,a)]. given #187 (T,wt=7): 444 ->_s0(tail(mapf(x,nil)),tail(nil)). [ur(54,a,74,a)]. given #188 (T,wt=7): 457 ->_s0(length(mapf(x,nil)),length(nil)). [ur(41,a,74,a)]. given #189 (T,wt=6): 2046 ->*_s0(length(mapf(x,nil)),0). [ur(87,a,457,a,b,573,a)]. given #190 (A,wt=15): 104 ->_s0(mapf(app(cons(x,y),z),u),mapf(cons(x,app(y,z)),u)). [ur(44,a,60,a)]. given #191 (F,wt=6): 1840 -->_s0(empty(nil),app(nil,false)) # answer(goal). [ur(87,b,581,a,c,1838,a)]. given #192 (F,wt=6): 1844 -->_s0(empty(nil),sndsplit(0,false)) # answer(goal). [ur(87,b,567,a,c,1838,a)]. given #193 (F,wt=6): 1848 -->_s0(true,x) | -->*_s0(x,false) # answer(goal). [resolve(1847,a,87,c)]. given #194 (F,wt=6): 1850 -->_s0(true,empty(cons(x,y))) # answer(goal). [ur(87,b,580,a,c,1847,a)]. given #195 (T,wt=7): 458 ->_s0(head(mapf(x,nil)),head(nil)). [ur(40,a,74,a)]. given #196 (T,wt=7): 461 ->_s0(empty(mapf(x,nil)),empty(nil)). [ur(37,a,74,a)]. given #197 (T,wt=6): 2132 ->*_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=6): 1851 -->_s0(true,head(cons(false,x))) # answer(goal). [ur(87,b,575,a,c,1847,a)]. given #201 (F,wt=6): 1852 -->_s0(true,leq(s(x),0)) # answer(goal). [ur(87,b,571,a,c,1847,a)]. given #202 (F,wt=6): 1854 -->_s0(true,tail(cons(x,false))) # answer(goal). [ur(87,b,564,a,c,1847,a)]. given #203 (F,wt=7): 1839 -->_s0(empty(nil),x) | -->*_s0(x,false) # answer(goal). [resolve(1838,a,87,c)]. 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): 2255 ->*_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=7): 1841 -->_s0(empty(nil),empty(cons(x,y))) # answer(goal). [ur(87,b,580,a,c,1838,a)]. given #210 (F,wt=5): 2344 -->_s0(nil,cons(x,y)) # answer(goal). [resolve(1841,a,37,b)]. given #211 (F,wt=7): 1842 -->_s0(empty(nil),head(cons(false,x))) # answer(goal). [ur(87,b,575,a,c,1838,a)]. given #212 (F,wt=7): 1843 -->_s0(empty(nil),leq(s(x),0)) # answer(goal). [ur(87,b,571,a,c,1838,a)]. given #213 (T,wt=7): 486 ->_s0(empty(sndsplit(0,x)),empty(x)). [ur(37,a,82,a)]. given #214 (T,wt=6): 2351 ->*_s0(empty(sndsplit(0,nil)),true). [ur(87,a,486,a,b,579,a)]. given #215 (T,wt=7): 622 ->*_s0(tail(cons(x,length(nil))),0). [ur(87,a,85,a,b,573,a)]. given #216 (T,wt=7): 624 ->*_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=7): 1845 -->_s0(empty(nil),tail(cons(x,false))) # answer(goal). [ur(87,b,564,a,c,1838,a)]. given #219 (F,wt=7): 2219 -->*_s0(empty(x),false) | -->_s0(nil,x) # answer(goal). [resolve(1839,a,37,b)]. given #220 (F,wt=9): 2105 -->_s0(true,x) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal). [resolve(1848,b,87,c)]. given #221 (F,wt=6): 2530 -->_s0(true,x) | -->_s0(x,false) # answer(goal). [resolve(2105,c,86,a)]. given #222 (T,wt=7): 627 ->*_s0(tail(cons(x,empty(nil))),true). [ur(87,a,85,a,b,579,a)]. given #223 (T,wt=7): 629 ->*_s0(head(cons(empty(nil),x)),true). [ur(87,a,67,a,b,579,a)]. given #224 (T,wt=7): 635 ->*_s0(sndsplit(0,sndsplit(0,x)),x). [ur(87,a,82,a,b,567,a)]. given #225 (T,wt=7): 637 ->*_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=7): 2490 -->_s0(true,length(nil)) | -->*_s0(0,false) # answer(goal). [resolve(2105,b,69,a)]. given #228 (F,wt=7): 2544 -->_s0(true,sndsplit(0,app(nil,false))) # answer(goal). [ur(2105,b,82,a,c,581,a)]. given #229 (F,wt=7): 2548 -->_s0(true,sndsplit(0,sndsplit(0,false))) # answer(goal). [ur(2105,b,82,a,c,567,a)]. given #230 (F,wt=7): 2557 -->_s0(true,app(nil,app(nil,false))) # answer(goal). [ur(2105,b,61,a,c,581,a)]. given #231 (T,wt=7): 639 ->*_s0(sndsplit(0,mapf(x,nil)),nil). [ur(87,a,82,a,b,568,a)]. given #232 (T,wt=7): 641 ->*_s0(app(nil,mapf(x,nil)),nil). [ur(87,a,61,a,b,568,a)]. given #233 (T,wt=7): 678 ->*_s0(sndsplit(0,leq(0,x)),true). [ur(87,a,82,a,b,572,a)]. given #234 (T,wt=7): 679 ->*_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=7): 2561 -->_s0(true,app(nil,sndsplit(0,false))) # answer(goal). [ur(2105,b,61,a,c,567,a)]. given #237 (F,wt=8): 2479 -->_s0(true,sndsplit(0,x)) | -->*_s0(x,false) # answer(goal). [resolve(2105,b,82,a)]. given #238 (F,wt=8): 2487 -->_s0(true,mapf(x,nil)) | -->*_s0(nil,false) # answer(goal). [resolve(2105,b,74,a)]. given #239 (F,wt=8): 2495 -->_s0(true,fstsplit(0,x)) | -->*_s0(nil,false) # answer(goal). [resolve(2105,b,64,a)]. given #240 (T,wt=7): 681 ->*_s0(app(nil,leq(0,x)),true). [ur(87,a,61,a,b,572,a)]. given #241 (T,wt=7): 683 ->*_s0(sndsplit(0,fstsplit(0,x)),nil). [ur(87,a,82,a,b,578,a)]. given #242 (T,wt=7): 685 ->*_s0(app(nil,fstsplit(0,x)),nil). [ur(87,a,61,a,b,578,a)]. given #243 (T,wt=7): 689 ->*_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=8): 2496 -->_s0(true,app(nil,x)) | -->*_s0(x,false) # answer(goal). [resolve(2105,b,61,a)]. given #246 (F,wt=8): 2523 -->_s0(true,x) | -->_s0(x,app(nil,false)) # answer(goal). [resolve(2105,c,581,a)]. given #247 (F,wt=8): 2527 -->_s0(true,x) | -->_s0(x,sndsplit(0,false)) # answer(goal). [resolve(2105,c,567,a)]. given #248 (F,wt=8): 2531 -->_s0(true,empty(sndsplit(0,cons(x,y)))) # answer(goal). [ur(2105,b,486,a,c,580,a)]. given #249 (T,wt=7): 691 ->*_s0(app(nil,app(nil,x)),x). [ur(87,a,61,a,b,581,a)]. given #250 (T,wt=7): 1251 ->*_s0(length(cons(x,nil)),s(0)). [ur(87,a,68,a,b,888,a)]. given #251 (T,wt=7): 1299 ->*_s0(s(app(nil,x)),s(x)). [ur(87,a,114,a,b,86,a)]. given #252 (T,wt=7): 1328 ->*_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=8): 2532 -->_s0(true,head(sndsplit(0,cons(false,x)))) # answer(goal). [ur(2105,b,483,a,c,575,a)]. given #255 (F,wt=8): 2533 -->_s0(true,tail(sndsplit(0,cons(x,false)))) # answer(goal). [ur(2105,b,469,a,c,564,a)]. given #256 (F,wt=8): 2534 -->_s0(true,empty(app(nil,cons(x,y)))) # answer(goal). [ur(2105,b,136,a,c,580,a)]. given #257 (F,wt=8): 2535 -->_s0(true,head(app(nil,cons(false,x)))) # answer(goal). [ur(2105,b,133,a,c,575,a)]. given #258 (T,wt=7): 1357 ->*_s0(length(app(nil,x)),length(x)). [ur(87,a,132,a,b,86,a)]. given #259 (T,wt=7): 1503 ->*_s0(head(app(nil,x)),head(x)). [ur(87,a,133,a,b,86,a)]. given #260 (T,wt=7): 1534 ->*_s0(empty(app(nil,x)),empty(x)). [ur(87,a,136,a,b,86,a)]. given #261 (T,wt=7): 1596 ->*_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=8): 2536 -->_s0(true,tail(app(nil,cons(x,false)))) # answer(goal). [ur(2105,b,119,a,c,564,a)]. given #264 (F,wt=8): 2537 -->_s0(true,tail(cons(x,app(nil,false)))) # answer(goal). [ur(2105,b,85,a,c,581,a)]. given #265 (F,wt=8): 2541 -->_s0(true,tail(cons(x,sndsplit(0,false)))) # answer(goal). [ur(2105,b,85,a,c,567,a)]. given #266 (F,wt=8): 2543 -->_s0(true,sndsplit(s(0),cons(x,false))) # answer(goal). [ur(2105,b,83,a,c,567,a)]. given #267 (T,wt=7): 1623 ->*_s0(tail(fstsplit(0,x)),tail(nil)). [ur(87,a,194,a,b,86,a)]. given #268 (T,wt=7): 1651 ->*_s0(length(fstsplit(0,x)),length(nil)). [ur(87,a,207,a,b,86,a)]. given #269 (T,wt=7): 1721 ->*_s0(head(fstsplit(0,x)),head(nil)). [ur(87,a,208,a,b,86,a)]. given #270 (T,wt=7): 1749 ->*_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=8): 2545 -->_s0(true,sndsplit(0,empty(cons(x,y)))) # answer(goal). [ur(2105,b,82,a,c,580,a)]. given #273 (F,wt=8): 2546 -->_s0(true,sndsplit(0,head(cons(false,x)))) # answer(goal). [ur(2105,b,82,a,c,575,a)]. given #274 (F,wt=8): 2547 -->_s0(true,sndsplit(0,leq(s(x),0))) # answer(goal). [ur(2105,b,82,a,c,571,a)]. given #275 (F,wt=8): 2549 -->_s0(true,sndsplit(0,tail(cons(x,false)))) # answer(goal). [ur(2105,b,82,a,c,564,a)]. given #276 (T,wt=7): 1782 ->*_s0(s(leq(0,x)),s(true)). [ur(87,a,339,a,b,86,a)]. given #277 (T,wt=7): 1857 ->*_s0(tail(leq(0,x)),tail(true)). [ur(87,a,344,a,b,86,a)]. given #278 (T,wt=7): 1884 ->*_s0(length(leq(0,x)),length(true)). [ur(87,a,357,a,b,86,a)]. given #279 (T,wt=7): 1911 ->*_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=8): 2550 -->_s0(true,leq(s(s(x)),s(0))) # answer(goal). [ur(2105,b,72,a,c,571,a)]. given #282 (F,wt=8): 2551 -->_s0(true,head(cons(app(nil,false),x))) # answer(goal). [ur(2105,b,67,a,c,581,a)]. given #283 (F,wt=8): 2555 -->_s0(true,head(cons(sndsplit(0,false),x))) # answer(goal). [ur(2105,b,67,a,c,567,a)]. given #284 (F,wt=8): 2558 -->_s0(true,app(nil,empty(cons(x,y)))) # answer(goal). [ur(2105,b,61,a,c,580,a)]. given #285 (T,wt=7): 1938 ->*_s0(empty(leq(0,x)),empty(true)). [ur(87,a,361,a,b,86,a)]. given #286 (T,wt=7): 1992 ->*_s0(s(mapf(x,nil)),s(nil)). [ur(87,a,439,a,b,86,a)]. given #287 (T,wt=7): 2019 ->*_s0(tail(mapf(x,nil)),tail(nil)). [ur(87,a,444,a,b,86,a)]. given #288 (T,wt=7): 2047 ->*_s0(length(mapf(x,nil)),length(nil)). [ur(87,a,457,a,b,86,a)]. given #289 (A,wt=9): 116 ->_s0(f(app(nil,x),y),f(x,y)). [ur(57,a,61,a)]. given #290 (F,wt=8): 2559 -->_s0(true,app(nil,head(cons(false,x)))) # answer(goal). [ur(2105,b,61,a,c,575,a)]. given #291 (F,wt=8): 2560 -->_s0(true,app(nil,leq(s(x),0))) # answer(goal). [ur(2105,b,61,a,c,571,a)]. given #292 (F,wt=8): 2562 -->_s0(true,app(nil,tail(cons(x,false)))) # answer(goal). [ur(2105,b,61,a,c,564,a)]. given #293 (F,wt=8): 2578 -->_s0(empty(nil),sndsplit(0,sndsplit(0,false))) # answer(goal). [resolve(635,a,1839,b)]. given #294 (T,wt=7): 2106 ->*_s0(head(mapf(x,nil)),head(nil)). [ur(87,a,458,a,b,86,a)]. given #295 (T,wt=7): 2133 ->*_s0(empty(mapf(x,nil)),empty(nil)). [ur(87,a,461,a,b,86,a)]. given #296 (T,wt=7): 2167 ->*_s0(s(sndsplit(0,x)),s(x)). [ur(87,a,464,a,b,86,a)]. given #297 (T,wt=7): 2224 ->*_s0(tail(sndsplit(0,x)),tail(x)). [ur(87,a,469,a,b,86,a)]. given #298 (A,wt=9): 117 ->_s0(cons(x,app(nil,y)),cons(x,y)). [ur(56,a,61,a)]. given #299 (F,wt=8): 2592 -->_s0(empty(nil),app(nil,sndsplit(0,false))) # answer(goal). [resolve(637,a,1839,b)]. given #300 (F,wt=8): 2633 -->_s0(true,head(app(cons(false,x),y))) # answer(goal). [ur(2105,b,108,a,c,575,a)]. given #301 (F,wt=8): 2702 -->_s0(empty(nil),sndsplit(0,app(nil,false))) # answer(goal). [resolve(689,a,1839,b)]. given #302 (F,wt=8): 2742 -->_s0(true,app(nil,x)) | -->_s0(x,false) # answer(goal). [resolve(2523,b,36,b)]. given #303 (T,wt=7): 2256 ->*_s0(length(sndsplit(0,x)),length(x)). [ur(87,a,482,a,b,86,a)]. given #304 (T,wt=7): 2291 ->*_s0(head(sndsplit(0,x)),head(x)). [ur(87,a,483,a,b,86,a)]. given #305 (T,wt=7): 2352 ->*_s0(empty(sndsplit(0,x)),empty(x)). [ur(87,a,486,a,b,86,a)]. given #306 (T,wt=8): 139 ->_s0(s(empty(cons(x,y))),s(false)). [ur(59,a,62,a)]. given #307 (A,wt=9): 118 ->_s0(cons(app(nil,x),y),cons(x,y)). [ur(55,a,61,a)]. given #308 (F,wt=8): 2743 -->_s0(true,app(x,false)) | -->_s0(x,nil) # answer(goal). [resolve(2523,b,35,b)]. given #309 (F,wt=7): 3135 -->_s0(true,app(sndsplit(0,nil),false)) # answer(goal). [resolve(2743,b,82,a)]. given #310 (F,wt=7): 3136 -->_s0(true,app(mapf(x,nil),false)) # answer(goal). [resolve(2743,b,74,a)]. given #311 (F,wt=7): 3139 -->_s0(true,app(fstsplit(0,x),false)) # answer(goal). [resolve(2743,b,64,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=7): 3140 -->_s0(true,app(app(nil,nil),false)) # answer(goal). [resolve(2743,b,61,a)]. given #318 (F,wt=8): 2744 -->_s0(true,sndsplit(0,x)) | -->_s0(x,false) # answer(goal). [resolve(2527,b,53,b)]. given #319 (F,wt=8): 2745 -->_s0(true,sndsplit(x,false)) | -->_s0(x,0) # answer(goal). [resolve(2527,b,52,b)]. given #320 (F,wt=6): 3279 -->_s0(true,sndsplit(length(nil),false)) # answer(goal). [resolve(2745,b,69,a)]. given #321 (T,wt=8): 165 ->_s0(f(x,empty(nil)),f(x,true)). [ur(58,a,63,a)]. given #322 (T,wt=8): 166 ->_s0(f(empty(nil),x),f(true,x)). [ur(57,a,63,a)]. given #323 (T,wt=8): 167 ->_s0(cons(x,empty(nil)),cons(x,true)). [ur(56,a,63,a)]. given #324 (T,wt=8): 168 ->_s0(cons(empty(nil),x),cons(true,x)). [ur(55,a,63,a)]. given #325 (A,wt=9): 121 ->_s0(sndsplit(app(nil,x),y),sndsplit(x,y)). [ur(52,a,61,a)]. given #326 (F,wt=7): 3278 -->_s0(true,sndsplit(sndsplit(0,0),false)) # answer(goal). [resolve(2745,b,82,a)]. given #327 (F,wt=7): 3281 -->_s0(true,sndsplit(app(nil,0),false)) # answer(goal). [resolve(2745,b,61,a)]. given #328 (F,wt=8): 2749 -->_s0(empty(nil),app(nil,app(nil,false))) # answer(goal). [resolve(691,a,1839,b)]. given #329 (F,wt=8): 2777 -->_s0(true,empty(app(cons(x,y),z))) # answer(goal). [resolve(111,a,2105,b),unit_del(b,580)]. given #330 (T,wt=7): 3398 ->*_s0(sndsplit(app(nil,0),x),x). [ur(87,a,121,a,b,567,a)]. given #331 (T,wt=8): 170 ->_s0(sndsplit(x,empty(nil)),sndsplit(x,true)). [ur(53,a,63,a)]. given #332 (T,wt=8): 171 ->_s0(sndsplit(empty(nil),x),sndsplit(true,x)). [ur(52,a,63,a)]. given #333 (T,wt=8): 178 ->_s0(mapf(x,empty(nil)),mapf(x,true)). [ur(45,a,63,a)]. given #334 (A,wt=17): 122 ->_s0(ring(x,y,z,u,w,app(nil,v5)),ring(x,y,z,u,w,v5)). [ur(51,a,61,a)]. given #335 (F,wt=8): 3133 -->_s0(true,app(tail(cons(x,nil)),false)) # answer(goal). [resolve(2743,b,85,a)]. given #336 (F,wt=8): 3134 -->_s0(true,app(sndsplit(s(x),nil),false)) # answer(goal). [resolve(2743,b,84,a)]. given #337 (F,wt=8): 3137 -->_s0(true,app(head(cons(nil,x)),false)) # answer(goal). [resolve(2743,b,67,a)]. given #338 (F,wt=8): 3138 -->_s0(true,app(fstsplit(s(x),nil),false)) # answer(goal). [resolve(2743,b,66,a)]. given #339 (T,wt=8): 179 ->_s0(mapf(empty(nil),x),mapf(true,x)). [ur(44,a,63,a)]. given #340 (T,wt=8): 180 ->_s0(leq(x,empty(nil)),leq(x,true)). [ur(43,a,63,a)]. given #341 (T,wt=8): 181 ->_s0(leq(empty(nil),x),leq(true,x)). [ur(42,a,63,a)]. given #342 (T,wt=8): 184 ->_s0(fstsplit(x,empty(nil)),fstsplit(x,true)). [ur(39,a,63,a)]. given #343 (A,wt=17): 123 ->_s0(ring(x,y,z,u,app(nil,w),v5),ring(x,y,z,u,w,v5)). [ur(50,a,61,a)]. given #344 (F,wt=8): 3277 -->_s0(true,sndsplit(tail(cons(x,0)),false)) # answer(goal). [resolve(2745,b,85,a)]. given #345 (F,wt=8): 3280 -->_s0(true,sndsplit(head(cons(0,x)),false)) # answer(goal). [resolve(2745,b,67,a)]. given #346 (F,wt=8): 3431 -->_s0(empty(nil),sndsplit(app(nil,0),false)) # answer(goal). [resolve(3398,a,1839,b)]. given #347 (F,wt=9): 2438 -->_s0(true,empty(length(nil))) | -->*_s0(empty(0),false) # answer(goal). [resolve(2105,b,336,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=9): 2439 -->_s0(true,head(length(nil))) | -->*_s0(head(0),false) # answer(goal). [resolve(2105,b,333,a)]. given #354 (F,wt=9): 2440 -->_s0(true,length(length(nil))) | -->*_s0(length(0),false) # answer(goal). [resolve(2105,b,332,a)]. given #355 (F,wt=9): 2441 -->_s0(true,tail(length(nil))) | -->*_s0(tail(0),false) # answer(goal). [resolve(2105,b,319,a)]. given #356 (F,wt=9): 2442 -->_s0(true,s(length(nil))) | -->*_s0(s(0),false) # answer(goal). [resolve(2105,b,314,a)]. given #357 (T,wt=8): 244 ->_s0(tail(fstsplit(s(x),nil)),tail(nil)). [ur(54,a,66,a)]. given #358 (T,wt=8): 257 ->_s0(length(fstsplit(s(x),nil)),length(nil)). [ur(41,a,66,a)]. given #359 (T,wt=7): 3857 ->*_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=9): 2447 -->_s0(true,empty(empty(nil))) | -->*_s0(empty(true),false) # answer(goal). [resolve(2105,b,186,a)]. given #363 (F,wt=9): 2448 -->_s0(true,head(empty(nil))) | -->*_s0(head(true),false) # answer(goal). [resolve(2105,b,183,a)]. given #364 (F,wt=9): 2449 -->_s0(true,length(empty(nil))) | -->*_s0(length(true),false) # answer(goal). [resolve(2105,b,182,a)]. given #365 (F,wt=9): 2450 -->_s0(true,tail(empty(nil))) | -->*_s0(tail(true),false) # answer(goal). [resolve(2105,b,169,a)]. given #366 (T,wt=8): 261 ->_s0(empty(fstsplit(s(x),nil)),empty(nil)). [ur(37,a,66,a)]. given #367 (T,wt=7): 3948 ->*_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=9): 2451 -->_s0(true,s(empty(nil))) | -->*_s0(s(true),false) # answer(goal). [resolve(2105,b,164,a)]. given #372 (F,wt=9): 2476 -->_s0(true,tail(cons(x,y))) | -->*_s0(y,false) # answer(goal). [resolve(2105,b,85,a)]. given #373 (F,wt=9): 2477 -->_s0(true,sndsplit(s(x),nil)) | -->*_s0(nil,false) # answer(goal). [resolve(2105,b,84,a)]. given #374 (F,wt=9): 2492 -->_s0(true,head(cons(x,y))) | -->*_s0(x,false) # answer(goal). [resolve(2105,b,67,a)]. given #375 (T,wt=8): 282 ->_s0(length(head(cons(x,y))),length(x)). [ur(41,a,67,a)]. given #376 (T,wt=7): 4099 ->*_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=9): 2493 -->_s0(true,fstsplit(s(x),nil)) | -->*_s0(nil,false) # answer(goal). [resolve(2105,b,66,a)]. given #381 (F,wt=9): 2524 -->_s0(true,x) | -->_s0(x,empty(cons(y,z))) # answer(goal). [resolve(2105,c,580,a)]. given #382 (F,wt=9): 2525 -->_s0(true,x) | -->_s0(x,head(cons(false,y))) # answer(goal). [resolve(2105,c,575,a)]. given #383 (F,wt=9): 2526 -->_s0(true,x) | -->_s0(x,leq(s(y),0)) # answer(goal). [resolve(2105,c,571,a)]. given #384 (T,wt=7): 4185 ->*_s0(empty(head(cons(nil,x))),true). [ur(87,a,286,a,b,579,a)]. given #385 (T,wt=8): 315 ->_s0(f(x,length(nil)),f(x,0)). [ur(58,a,69,a)]. given #386 (T,wt=8): 316 ->_s0(f(length(nil),x),f(0,x)). [ur(57,a,69,a)]. given #387 (T,wt=8): 317 ->_s0(cons(x,length(nil)),cons(x,0)). [ur(56,a,69,a)]. given #388 (A,wt=9): 128 ->_s0(mapf(x,app(nil,y)),mapf(x,y)). [ur(45,a,61,a)]. given #389 (F,wt=9): 2528 -->_s0(true,x) | -->_s0(x,tail(cons(y,false))) # answer(goal). [resolve(2105,c,564,a)]. given #390 (F,wt=9): 2538 -->_s0(true,tail(cons(x,empty(cons(y,z))))) # answer(goal). [ur(2105,b,85,a,c,580,a)]. given #391 (F,wt=9): 2539 -->_s0(true,tail(cons(x,head(cons(false,y))))) # answer(goal). [ur(2105,b,85,a,c,575,a)]. given #392 (F,wt=9): 2540 -->_s0(true,tail(cons(x,leq(s(y),0)))) # answer(goal). [ur(2105,b,85,a,c,571,a)]. given #393 (T,wt=7): 4335 ->*_s0(mapf(x,app(nil,nil)),nil). [ur(87,a,128,a,b,568,a)]. given #394 (T,wt=8): 318 ->_s0(cons(length(nil),x),cons(0,x)). [ur(55,a,69,a)]. given #395 (T,wt=8): 320 ->_s0(sndsplit(x,length(nil)),sndsplit(x,0)). [ur(53,a,69,a)]. given #396 (T,wt=8): 321 ->_s0(sndsplit(length(nil),x),sndsplit(0,x)). [ur(52,a,69,a)]. given #397 (A,wt=9): 129 ->_s0(mapf(app(nil,x),y),mapf(x,y)). [ur(44,a,61,a)]. given #398 (F,wt=8): 4457 -->_s0(true,sndsplit(length(nil),app(nil,false))) # answer(goal). [ur(2105,b,321,a,c,689,a)]. given #399 (F,wt=8): 4458 -->_s0(true,sndsplit(length(nil),sndsplit(0,false))) # answer(goal). [ur(2105,b,321,a,c,635,a)]. given #400 (F,wt=9): 2542 -->_s0(true,tail(cons(x,tail(cons(y,false))))) # answer(goal). [ur(2105,b,85,a,c,564,a)]. given #401 (F,wt=9): 2552 -->_s0(true,head(cons(empty(cons(x,y)),z))) # answer(goal). [ur(2105,b,67,a,c,580,a)]. given #402 (T,wt=6): 4430 ->*_s0(sndsplit(length(nil),x),x). [ur(87,a,321,a,b,567,a)]. given #403 (T,wt=7): 4428 ->*_s0(sndsplit(length(nil),empty(nil)),true). [ur(87,a,321,a,b,628,a)]. given #404 (T,wt=7): 4429 ->*_s0(sndsplit(length(nil),length(nil)),0). [ur(87,a,321,a,b,623,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=7): 4491 -->_s0(empty(nil),sndsplit(length(nil),false)) # answer(goal). [resolve(4430,a,1839,b)]. given #408 (F,wt=8): 4486 -->_s0(true,app(nil,sndsplit(length(nil),false))) # answer(goal). [resolve(4430,a,2496,b)]. given #409 (F,wt=8): 4488 -->_s0(true,sndsplit(0,sndsplit(length(nil),false))) # answer(goal). [resolve(4430,a,2479,b)]. given #410 (F,wt=8): 4502 -->_s0(true,sndsplit(app(nil,length(nil)),false)) # answer(goal). [ur(2105,b,121,a,c,4430,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): 4606 ->*_s0(leq(s(x),length(nil)),false). [ur(87,a,330,a,b,571,a)]. given #414 (T,wt=8): 331 ->_s0(leq(length(nil),x),leq(0,x)). [ur(42,a,69,a)]. given #415 (A,wt=9): 131 ->_s0(leq(app(nil,x),y),leq(x,y)). [ur(42,a,61,a)]. given #416 (F,wt=7): 4603 -->_s0(true,leq(s(x),length(nil))) # answer(goal). [resolve(330,a,2526,b)]. given #417 (F,wt=8): 4546 -->_s0(true,leq(s(x),app(nil,0))) # answer(goal). [resolve(130,a,2526,b)]. given #418 (F,wt=8): 4638 -->_s0(empty(nil),leq(s(x),length(nil))) # answer(goal). [resolve(4606,a,1839,b)]. given #419 (F,wt=8): 4678 -->_s0(true,leq(app(nil,s(x)),0)) # answer(goal). [resolve(131,a,2526,b)]. given #420 (T,wt=6): 4651 ->*_s0(leq(length(nil),x),true). [ur(87,a,331,a,b,572,a)]. given #421 (T,wt=7): 4683 ->*_s0(leq(app(nil,0),x),true). [ur(87,a,131,a,b,572,a)]. given #422 (T,wt=8): 334 ->_s0(fstsplit(x,length(nil)),fstsplit(x,0)). [ur(39,a,69,a)]. given #423 (T,wt=8): 335 ->_s0(fstsplit(length(nil),x),fstsplit(0,x)). [ur(38,a,69,a)]. given #424 (A,wt=9): 134 ->_s0(fstsplit(x,app(nil,y)),fstsplit(x,y)). [ur(39,a,61,a)]. given #425 (F,wt=9): 2553 -->_s0(true,head(cons(head(cons(false,x)),y))) # answer(goal). [ur(2105,b,67,a,c,575,a)]. given #426 (F,wt=9): 2554 -->_s0(true,head(cons(leq(s(x),0),y))) # answer(goal). [ur(2105,b,67,a,c,571,a)]. given #427 (F,wt=9): 2556 -->_s0(true,head(cons(tail(cons(x,false)),y))) # answer(goal). [ur(2105,b,67,a,c,564,a)]. given #428 (F,wt=9): 2588 -->_s0(true,sndsplit(0,sndsplit(0,sndsplit(0,false)))) # answer(goal). [ur(2105,b,82,a,c,635,a)]. given #429 (T,wt=6): 4760 ->*_s0(fstsplit(length(nil),x),nil). [ur(87,a,335,a,b,578,a)]. given #430 (T,wt=8): 337 ->_s0(app(x,length(nil)),app(x,0)). [ur(36,a,69,a)]. given #431 (T,wt=8): 338 ->_s0(app(length(nil),x),app(0,x)). [ur(35,a,69,a)]. given #432 (T,wt=8): 364 ->_s0(s(leq(s(x),0)),s(false)). [ur(59,a,71,a)]. given #433 (A,wt=9): 135 ->_s0(fstsplit(app(nil,x),y),fstsplit(x,y)). [ur(38,a,61,a)]. given #434 (F,wt=9): 2590 -->_s0(true,app(nil,sndsplit(0,sndsplit(0,false)))) # answer(goal). [ur(2105,b,61,a,c,635,a)]. given #435 (F,wt=9): 2600 -->_s0(true,sndsplit(0,app(nil,sndsplit(0,false)))) # answer(goal). [ur(2105,b,82,a,c,637,a)]. given #436 (F,wt=9): 2602 -->_s0(true,app(nil,app(nil,sndsplit(0,false)))) # answer(goal). [ur(2105,b,61,a,c,637,a)]. given #437 (F,wt=9): 2700 -->_s0(true,sndsplit(0,sndsplit(0,app(nil,false)))) # answer(goal). [resolve(689,a,2479,b)]. given #438 (T,wt=7): 4902 ->*_s0(fstsplit(app(nil,0),x),nil). [ur(87,a,135,a,b,578,a)]. given #439 (T,wt=8): 369 ->_s0(tail(leq(s(x),0)),tail(false)). [ur(54,a,71,a)]. given #440 (T,wt=8): 382 ->_s0(length(leq(s(x),0)),length(false)). [ur(41,a,71,a)]. given #441 (T,wt=8): 383 ->_s0(head(leq(s(x),0)),head(false)). [ur(40,a,71,a)]. given #442 (A,wt=9): 137 ->_s0(app(x,app(nil,y)),app(x,y)). [ur(36,a,61,a)]. given #443 (F,wt=9): 2713 -->_s0(true,app(nil,sndsplit(0,app(nil,false)))) # answer(goal). [ur(2105,b,61,a,c,689,a)]. given #444 (F,wt=9): 2746 -->_s0(true,app(nil,app(nil,app(nil,false)))) # answer(goal). [resolve(691,a,2496,b)]. given #445 (F,wt=9): 2747 -->_s0(true,sndsplit(0,app(nil,app(nil,false)))) # answer(goal). [resolve(691,a,2479,b)]. given #446 (F,wt=9): 3426 -->_s0(true,sndsplit(app(nil,0),app(nil,false))) # answer(goal). [ur(2105,b,121,a,c,689,a)]. given #447 (T,wt=8): 386 ->_s0(empty(leq(s(x),0)),empty(false)). [ur(37,a,71,a)]. given #448 (T,wt=8): 514 ->_s0(s(sndsplit(s(x),nil)),s(nil)). [ur(59,a,84,a)]. given #449 (T,wt=8): 519 ->_s0(tail(sndsplit(s(x),nil)),tail(nil)). [ur(54,a,84,a)]. given #450 (T,wt=8): 532 ->_s0(length(sndsplit(s(x),nil)),length(nil)). [ur(41,a,84,a)]. given #451 (A,wt=9): 138 ->_s0(app(app(nil,x),y),app(x,y)). [ur(35,a,61,a)]. given #452 (F,wt=9): 3427 -->_s0(true,sndsplit(app(nil,0),sndsplit(0,false))) # answer(goal). [ur(2105,b,121,a,c,635,a)]. given #453 (F,wt=9): 3428 -->_s0(true,app(nil,sndsplit(app(nil,0),false))) # answer(goal). [resolve(3398,a,2496,b)]. given #454 (F,wt=9): 3429 -->_s0(true,sndsplit(0,sndsplit(app(nil,0),false))) # answer(goal). [resolve(3398,a,2479,b)]. given #455 (F,wt=9): 3441 -->_s0(true,sndsplit(app(nil,app(nil,0)),false)) # answer(goal). [ur(2105,b,121,a,c,3398,a)]. given #456 (T,wt=7): 5125 ->*_s0(length(sndsplit(s(x),nil)),0). [ur(87,a,532,a,b,573,a)]. given #457 (T,wt=7): 5160 ->*_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=8): 5201 -->_s0(empty(nil),app(app(nil,nil),false)) # answer(goal). [resolve(5160,a,1839,b)]. given #462 (F,wt=9): 4053 -->_s0(true,tail(head(cons(cons(x,false),y)))) # answer(goal). [ur(2105,b,269,a,c,564,a)]. given #463 (F,wt=9): 4170 -->_s0(true,head(head(cons(cons(false,x),y)))) # answer(goal). [ur(2105,b,283,a,c,575,a)]. given #464 (F,wt=9): 4212 -->_s0(true,empty(head(cons(cons(x,y),z)))) # answer(goal). [ur(2105,b,286,a,c,580,a)]. given #465 (T,wt=7): 5239 ->*_s0(empty(sndsplit(s(x),nil)),true). [ur(87,a,536,a,b,579,a)]. given #466 (T,wt=8): 539 ->_s0(s(tail(cons(x,y))),s(y)). [ur(59,a,85,a)]. given #467 (T,wt=8): 544 ->_s0(tail(tail(cons(x,y))),tail(y)). [ur(54,a,85,a)]. given #468 (T,wt=8): 557 ->_s0(length(tail(cons(x,y))),length(y)). [ur(41,a,85,a)]. given #469 (A,wt=10): 141 ->_s0(f(empty(cons(x,y)),z),f(false,z)). [ur(57,a,62,a)]. given #470 (F,wt=9): 4241 -->_s0(true,empty(x)) | -->_s0(x,cons(y,z)) # answer(goal). [resolve(2524,b,37,b)]. given #471 (F,wt=9): 4242 -->_s0(true,head(x)) | -->_s0(x,cons(false,y)) # answer(goal). [resolve(2525,b,40,b)]. given #472 (F,wt=9): 4243 -->_s0(true,leq(s(x),y)) | -->_s0(y,0) # answer(goal). [resolve(2526,b,43,b)]. given #473 (F,wt=8): 5449 -->_s0(true,leq(s(x),sndsplit(0,0))) # answer(goal). [resolve(4243,b,82,a)]. given #474 (T,wt=7): 5389 ->*_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): 5512 ->*_s0(empty(tail(cons(x,nil))),true). [ur(87,a,561,a,b,579,a)]. given #478 (A,wt=10): 142 ->_s0(cons(x,empty(cons(y,z))),cons(x,false)). [ur(56,a,62,a)]. given #479 (F,wt=9): 4244 -->_s0(true,leq(x,0)) | -->_s0(x,s(y)) # answer(goal). [resolve(2526,b,42,b)]. given #480 (F,wt=8): 5576 -->_s0(true,leq(sndsplit(0,s(x)),0)) # answer(goal). [resolve(4244,b,82,a)]. given #481 (F,wt=8): 5577 -->_s0(true,leq(length(cons(x,y)),0)) # answer(goal). [resolve(4244,b,68,a)]. given #482 (F,wt=9): 4362 -->_s0(true,tail(x)) | -->_s0(x,cons(y,false)) # answer(goal). [resolve(2528,b,54,b)]. 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): 633 ->*_s0(tail(cons(x,sndsplit(0,y))),y). [ur(87,a,85,a,b,567,a)]. given #485 (T,wt=8): 634 ->*_s0(sndsplit(s(0),cons(x,y)),y). [ur(87,a,83,a,b,567,a)]. given #486 (T,wt=8): 636 ->*_s0(head(cons(sndsplit(0,x),y)),x). [ur(87,a,67,a,b,567,a)]. given #487 (A,wt=10): 143 ->_s0(cons(empty(cons(x,y)),z),cons(false,z)). [ur(55,a,62,a)]. given #488 (F,wt=9): 4487 -->_s0(true,head(cons(sndsplit(length(nil),false),x))) # answer(goal). [resolve(4430,a,2492,b)]. given #489 (F,wt=9): 4489 -->_s0(true,tail(cons(x,sndsplit(length(nil),false)))) # answer(goal). [resolve(4430,a,2476,b)]. given #490 (F,wt=9): 4490 -->_s0(true,x) | -->_s0(x,sndsplit(length(nil),false)) # answer(goal). [resolve(4430,a,2105,c)]. given #491 (F,wt=9): 4503 -->_s0(true,sndsplit(s(length(nil)),cons(x,false))) # answer(goal). [ur(2105,b,83,a,c,4430,a)]. given #492 (T,wt=8): 638 ->*_s0(tail(cons(x,mapf(y,nil))),nil). [ur(87,a,85,a,b,568,a)]. given #493 (T,wt=8): 640 ->*_s0(head(cons(mapf(x,nil),y)),nil). [ur(87,a,67,a,b,568,a)]. given #494 (T,wt=8): 677 ->*_s0(tail(cons(x,leq(0,y))),true). [ur(87,a,85,a,b,572,a)]. given #495 (T,wt=8): 680 ->*_s0(head(cons(leq(0,x),y)),true). [ur(87,a,67,a,b,572,a)]. given #496 (A,wt=10): 145 ->_s0(sndsplit(x,empty(cons(y,z))),sndsplit(x,false)). [ur(53,a,62,a)]. given #497 (F,wt=9): 4633 -->_s0(true,app(nil,leq(s(x),length(nil)))) # answer(goal). [resolve(4606,a,2496,b)]. given #498 (F,wt=9): 4635 -->_s0(true,sndsplit(0,leq(s(x),length(nil)))) # answer(goal). [resolve(4606,a,2479,b)]. given #499 (F,wt=9): 4647 -->_s0(true,leq(s(x),app(nil,length(nil)))) # answer(goal). [ur(2105,b,130,a,c,4606,a)]. NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 0.10 sec). given #500 (F,wt=9): 4648 -->_s0(true,leq(s(s(x)),s(length(nil)))) # answer(goal). [ur(2105,b,72,a,c,4606,a)]. given #501 (T,wt=8): 682 ->*_s0(tail(cons(x,fstsplit(0,y))),nil). [ur(87,a,85,a,b,578,a)]. given #502 (T,wt=8): 684 ->*_s0(head(cons(fstsplit(0,x),y)),nil). [ur(87,a,67,a,b,578,a)]. given #503 (T,wt=8): 688 ->*_s0(tail(cons(x,app(nil,y))),y). [ur(87,a,85,a,b,581,a)]. given #504 (T,wt=8): 690 ->*_s0(head(cons(app(nil,x),y)),x). [ur(87,a,67,a,b,581,a)]. given #505 (A,wt=10): 146 ->_s0(sndsplit(empty(cons(x,y)),z),sndsplit(false,z)). [ur(52,a,62,a)]. given #506 (F,wt=8): 5785 -->_s0(true,tail(app(cons(x,nil),false))) # answer(goal). [ur(2105,b,94,a,c,688,a)]. given #507 (F,wt=9): 4711 -->_s0(true,leq(app(nil,s(x)),length(nil))) # answer(goal). [ur(2105,b,131,a,c,4606,a)]. given #508 (F,wt=9): 5187 -->_s0(true,app(app(nil,nil),app(nil,false))) # answer(goal). [ur(2105,b,138,a,c,691,a)]. given #509 (F,wt=9): 5188 -->_s0(true,app(app(nil,nil),sndsplit(0,false))) # answer(goal). [ur(2105,b,138,a,c,637,a)]. given #510 (T,wt=8): 693 ->_s0(s(s(empty(nil))),s(s(true))). [ur(59,a,164,a)]. given #511 (T,wt=8): 698 ->_s0(tail(s(empty(nil))),tail(s(true))). [ur(54,a,164,a)]. given #512 (T,wt=8): 711 ->_s0(length(s(empty(nil))),length(s(true))). [ur(41,a,164,a)]. given #513 (T,wt=8): 712 ->_s0(head(s(empty(nil))),head(s(true))). [ur(40,a,164,a)]. given #514 (A,wt=18): 147 ->_s0(ring(x,y,z,u,w,empty(cons(v5,v6))),ring(x,y,z,u,w,false)). [ur(51,a,62,a)]. given #515 (F,wt=9): 5196 -->_s0(true,app(nil,app(app(nil,nil),false))) # answer(goal). [resolve(5160,a,2496,b)]. given #516 (F,wt=9): 5198 -->_s0(true,sndsplit(0,app(app(nil,nil),false))) # answer(goal). [resolve(5160,a,2479,b)]. given #517 (F,wt=9): 5211 -->_s0(true,app(app(nil,app(nil,nil)),false)) # answer(goal). [ur(2105,b,138,a,c,5160,a)]. given #518 (F,wt=9): 5335 -->_s0(true,tail(tail(cons(x,cons(y,false))))) # answer(goal). [resolve(544,a,2528,b)]. given #519 (T,wt=8): 715 ->_s0(empty(s(empty(nil))),empty(s(true))). [ur(37,a,164,a)]. given #520 (T,wt=8): 752 ->_s0(s(tail(empty(nil))),s(tail(true))). [ur(59,a,169,a)]. given #521 (T,wt=8): 757 ->_s0(tail(tail(empty(nil))),tail(tail(true))). [ur(54,a,169,a)]. given #522 (T,wt=8): 770 ->_s0(length(tail(empty(nil))),length(tail(true))). [ur(41,a,169,a)]. given #523 (A,wt=18): 148 ->_s0(ring(x,y,z,u,empty(cons(w,v5)),v6),ring(x,y,z,u,false,v6)). [ur(50,a,62,a)]. given #524 (F,wt=9): 5443 -->_s0(true,empty(tail(cons(x,cons(y,z))))) # answer(goal). [resolve(4241,b,85,a)]. given #525 (F,wt=9): 5444 -->_s0(true,empty(fstsplit(s(x),cons(y,z)))) # answer(goal). [resolve(4241,b,65,a)]. given #526 (F,wt=9): 5445 -->_s0(true,head(tail(cons(x,cons(false,y))))) # answer(goal). [resolve(4242,b,85,a)]. given #527 (F,wt=9): 5446 -->_s0(true,head(fstsplit(s(x),cons(false,y)))) # answer(goal). [resolve(4242,b,65,a)]. given #528 (T,wt=8): 771 ->_s0(head(tail(empty(nil))),head(tail(true))). [ur(40,a,169,a)]. given #529 (T,wt=8): 774 ->_s0(empty(tail(empty(nil))),empty(tail(true))). [ur(37,a,169,a)]. given #530 (T,wt=8): 778 ->_s0(s(length(empty(nil))),s(length(true))). [ur(59,a,182,a)]. given #531 (T,wt=8): 783 ->_s0(tail(length(empty(nil))),tail(length(true))). [ur(54,a,182,a)]. given #532 (A,wt=18): 149 ->_s0(ring(x,y,z,empty(cons(u,w)),v5,v6),ring(x,y,z,false,v5,v6)). [ur(49,a,62,a)]. given #533 (F,wt=9): 5447 -->_s0(true,head(cons(x,y))) | -->_s0(x,false) # answer(goal). [resolve(4242,b,55,b)]. given #534 (F,wt=9): 5448 -->_s0(true,leq(s(x),tail(cons(y,0)))) # answer(goal). [resolve(4243,b,85,a)]. given #535 (F,wt=9): 5450 -->_s0(true,leq(s(x),head(cons(0,y)))) # answer(goal). [resolve(4243,b,67,a)]. given #536 (F,wt=9): 5575 -->_s0(true,leq(tail(cons(x,s(y))),0)) # answer(goal). [resolve(4244,b,85,a)]. given #537 (T,wt=8): 796 ->_s0(length(length(empty(nil))),length(length(true))). [ur(41,a,182,a)]. given #538 (T,wt=8): 797 ->_s0(head(length(empty(nil))),head(length(true))). [ur(40,a,182,a)]. given #539 (T,wt=8): 800 ->_s0(empty(length(empty(nil))),empty(length(true))). [ur(37,a,182,a)]. given #540 (T,wt=8): 804 ->_s0(s(head(empty(nil))),s(head(true))). [ur(59,a,183,a)]. given #541 (A,wt=18): 150 ->_s0(ring(x,y,empty(cons(z,u)),w,v5,v6),ring(x,y,false,w,v5,v6)). [ur(48,a,62,a)]. given #542 (F,wt=9): 5578 -->_s0(true,leq(head(cons(s(x),y)),0)) # answer(goal). [resolve(4244,b,67,a)]. given #543 (F,wt=9): 5579 -->_s0(true,tail(cons(x,y))) | -->_s0(y,false) # answer(goal). [resolve(4362,b,56,b)]. given #544 (F,wt=9): 5594 -->_s0(empty(nil),tail(cons(x,sndsplit(0,false)))) # answer(goal). [resolve(633,a,1839,b)]. given #545 (F,wt=9): 5614 -->_s0(empty(nil),sndsplit(s(0),cons(x,false))) # answer(goal). [resolve(634,a,1839,b)]. given #546 (T,wt=8): 809 ->_s0(tail(head(empty(nil))),tail(head(true))). [ur(54,a,183,a)]. given #547 (T,wt=8): 822 ->_s0(length(head(empty(nil))),length(head(true))). [ur(41,a,183,a)]. given #548 (T,wt=8): 823 ->_s0(head(head(empty(nil))),head(head(true))). [ur(40,a,183,a)]. given #549 (T,wt=8): 826 ->_s0(empty(head(empty(nil))),empty(head(true))). [ur(37,a,183,a)]. given #550 (A,wt=18): 151 ->_s0(ring(x,empty(cons(y,z)),u,w,v5,v6),ring(x,false,u,w,v5,v6)). [ur(47,a,62,a)]. given #551 (F,wt=9): 5633 -->_s0(empty(nil),head(cons(sndsplit(0,false),x))) # answer(goal). [resolve(636,a,1839,b)]. given #552 (F,wt=9): 5677 -->_s0(true,sndsplit(length(nil),x)) | -->_s0(x,false) # answer(goal). [resolve(4490,b,53,b)]. given #553 (F,wt=9): 5678 -->_s0(true,sndsplit(x,false)) | -->_s0(x,length(nil)) # answer(goal). [resolve(4490,b,52,b)]. given #554 (F,wt=8): 6516 -->_s0(true,sndsplit(length(sndsplit(0,nil)),false)) # answer(goal). [resolve(5678,b,482,a)]. given #555 (T,wt=8): 830 ->_s0(s(empty(empty(nil))),s(empty(true))). [ur(59,a,186,a)]. given #556 (T,wt=8): 835 ->_s0(tail(empty(empty(nil))),tail(empty(true))). [ur(54,a,186,a)]. given #557 (T,wt=8): 848 ->_s0(length(empty(empty(nil))),length(empty(true))). [ur(41,a,186,a)]. given #558 (T,wt=8): 849 ->_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=8): 6517 -->_s0(true,sndsplit(length(mapf(x,nil)),false)) # answer(goal). [resolve(5678,b,457,a)]. given #561 (F,wt=8): 6520 -->_s0(true,sndsplit(length(fstsplit(0,x)),false)) # answer(goal). [resolve(5678,b,207,a)]. given #562 (F,wt=8): 6521 -->_s0(true,sndsplit(length(app(nil,nil)),false)) # answer(goal). [resolve(5678,b,132,a)]. given #563 (F,wt=8): 6523 -->_s0(true,sndsplit(sndsplit(0,length(nil)),false)) # answer(goal). [resolve(5678,b,82,a)]. given #564 (T,wt=8): 852 ->_s0(empty(empty(empty(nil))),empty(empty(true))). [ur(37,a,186,a)]. given #565 (T,wt=8): 889 ->_s0(s(s(length(nil))),s(s(0))). [ur(59,a,314,a)]. given #566 (T,wt=8): 894 ->_s0(tail(s(length(nil))),tail(s(0))). [ur(54,a,314,a)]. given #567 (T,wt=8): 907 ->_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=9): 5715 -->_s0(true,sndsplit(length(nil),empty(cons(x,y)))) # answer(goal). [resolve(145,a,4490,b)]. given #570 (F,wt=9): 5768 -->_s0(empty(nil),tail(cons(x,app(nil,false)))) # answer(goal). [resolve(688,a,1839,b)]. given #571 (F,wt=9): 5791 -->_s0(empty(nil),head(cons(app(nil,false),x))) # answer(goal). [resolve(690,a,1839,b)]. given #572 (F,wt=9): 6511 -->_s0(true,sndsplit(length(nil),tail(cons(x,false)))) # answer(goal). [resolve(5677,b,85,a)]. given #573 (T,wt=8): 908 ->_s0(head(s(length(nil))),head(s(0))). [ur(40,a,314,a)]. given #574 (T,wt=8): 911 ->_s0(empty(s(length(nil))),empty(s(0))). [ur(37,a,314,a)]. given #575 (T,wt=8): 915 ->_s0(s(tail(length(nil))),s(tail(0))). [ur(59,a,319,a)]. given #576 (T,wt=8): 920 ->_s0(tail(tail(length(nil))),tail(tail(0))). [ur(54,a,319,a)]. given #577 (A,wt=10): 154 ->_s0(mapf(empty(cons(x,y)),z),mapf(false,z)). [ur(44,a,62,a)]. given #578 (F,wt=9): 6512 -->_s0(true,sndsplit(length(nil),leq(s(x),0))) # answer(goal). [resolve(5677,b,71,a)]. given #579 (F,wt=9): 6513 -->_s0(true,sndsplit(length(nil),head(cons(false,x)))) # answer(goal). [resolve(5677,b,67,a)]. given #580 (F,wt=9): 6514 -->_s0(true,sndsplit(length(tail(cons(x,nil))),false)) # answer(goal). [resolve(5678,b,557,a)]. given #581 (F,wt=9): 6515 -->_s0(true,sndsplit(length(sndsplit(s(x),nil)),false)) # answer(goal). [resolve(5678,b,532,a)]. given #582 (T,wt=8): 933 ->_s0(length(tail(length(nil))),length(tail(0))). [ur(41,a,319,a)]. given #583 (T,wt=8): 934 ->_s0(head(tail(length(nil))),head(tail(0))). [ur(40,a,319,a)]. given #584 (T,wt=8): 937 ->_s0(empty(tail(length(nil))),empty(tail(0))). [ur(37,a,319,a)]. given #585 (T,wt=8): 941 ->_s0(s(length(length(nil))),s(length(0))). [ur(59,a,332,a)]. given #586 (A,wt=10): 155 ->_s0(leq(x,empty(cons(y,z))),leq(x,false)). [ur(43,a,62,a)]. given #587 (F,wt=9): 6518 -->_s0(true,sndsplit(length(head(cons(nil,x))),false)) # answer(goal). [resolve(5678,b,282,a)]. given #588 (F,wt=9): 6519 -->_s0(true,sndsplit(length(fstsplit(s(x),nil)),false)) # answer(goal). [resolve(5678,b,257,a)]. given #589 (F,wt=9): 6522 -->_s0(true,sndsplit(tail(cons(x,length(nil))),false)) # answer(goal). [resolve(5678,b,85,a)]. given #590 (F,wt=9): 6524 -->_s0(true,sndsplit(head(cons(length(nil),x)),false)) # answer(goal). [resolve(5678,b,67,a)]. given #591 (T,wt=8): 946 ->_s0(tail(length(length(nil))),tail(length(0))). [ur(54,a,332,a)]. given #592 (T,wt=8): 959 ->_s0(length(length(length(nil))),length(length(0))). [ur(41,a,332,a)]. given #593 (T,wt=8): 960 ->_s0(head(length(length(nil))),head(length(0))). [ur(40,a,332,a)]. given #594 (T,wt=8): 963 ->_s0(empty(length(length(nil))),empty(length(0))). [ur(37,a,332,a)]. given #595 (A,wt=10): 156 ->_s0(leq(empty(cons(x,y)),z),leq(false,z)). [ur(42,a,62,a)]. given #596 (F,wt=9): 6525 -->_s0(true,sndsplit(length(x),false)) | -->_s0(x,nil) # answer(goal). [resolve(5678,b,41,b)]. given #597 (F,wt=10): 2220 -->_s0(empty(nil),x) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal). [resolve(1839,b,87,c)]. given #598 (F,wt=7): 7458 -->_s0(empty(nil),x) | -->_s0(x,false) # answer(goal). [resolve(2220,c,86,a)]. given #599 (F,wt=7): 7583 -->_s0(empty(x),false) | -->_s0(nil,x) # answer(goal). [resolve(7458,a,37,b)]. given #600 (T,wt=8): 967 ->_s0(s(head(length(nil))),s(head(0))). [ur(59,a,333,a)]. given #601 (T,wt=8): 972 ->_s0(tail(head(length(nil))),tail(head(0))). [ur(54,a,333,a)]. given #602 (T,wt=8): 985 ->_s0(length(head(length(nil))),length(head(0))). [ur(41,a,333,a)]. given #603 (T,wt=8): 986 ->_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=8): 7405 -->_s0(empty(nil),length(nil)) | -->*_s0(0,false) # answer(goal). [resolve(2220,b,69,a)]. given #606 (F,wt=9): 7369 -->_s0(empty(nil),empty(app(cons(x,y),z))) # answer(goal). [resolve(2220,b,111,a),unit_del(b,580)]. given #607 (F,wt=7): 7725 -->_s0(nil,app(cons(x,y),z)) # answer(goal). [resolve(7369,a,37,b)]. given #608 (F,wt=9): 7395 -->_s0(empty(nil),sndsplit(0,x)) | -->*_s0(x,false) # answer(goal). [resolve(2220,b,82,a)]. given #609 (T,wt=8): 989 ->_s0(empty(head(length(nil))),empty(head(0))). [ur(37,a,333,a)]. given #610 (T,wt=8): 1027 ->_s0(s(empty(length(nil))),s(empty(0))). [ur(59,a,336,a)]. given #611 (T,wt=8): 1032 ->_s0(tail(empty(length(nil))),tail(empty(0))). [ur(54,a,336,a)]. given #612 (T,wt=8): 1045 ->_s0(length(empty(length(nil))),length(empty(0))). [ur(41,a,336,a)]. given #613 (A,wt=10): 160 ->_s0(fstsplit(empty(cons(x,y)),z),fstsplit(false,z)). [ur(38,a,62,a)]. Low Water (keep): wt=22.000, iters=6667 given #614 (F,wt=9): 7402 -->_s0(empty(nil),mapf(x,nil)) | -->*_s0(nil,false) # answer(goal). [resolve(2220,b,74,a)]. given #615 (F,wt=9): 7410 -->_s0(empty(nil),fstsplit(0,x)) | -->*_s0(nil,false) # answer(goal). [resolve(2220,b,64,a)]. given #616 (F,wt=9): 7411 -->_s0(empty(nil),app(nil,x)) | -->*_s0(x,false) # answer(goal). [resolve(2220,b,61,a)]. given #617 (F,wt=9): 7451 -->_s0(empty(nil),x) | -->_s0(x,app(nil,false)) # answer(goal). [resolve(2220,c,581,a)]. given #618 (T,wt=8): 1046 ->_s0(head(empty(length(nil))),head(empty(0))). [ur(40,a,336,a)]. given #619 (T,wt=8): 1049 ->_s0(empty(empty(length(nil))),empty(empty(0))). [ur(37,a,336,a)]. given #620 (T,wt=8): 1057 ->*_s0(sndsplit(0,tail(cons(x,y))),y). [ur(87,a,82,a,b,564,a)]. given #621 (T,wt=8): 1059 ->*_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=9): 7455 -->_s0(empty(nil),x) | -->_s0(x,sndsplit(0,false)) # answer(goal). [resolve(2220,c,567,a)]. given #624 (F,wt=9): 7466 -->_s0(empty(nil),empty(sndsplit(0,cons(x,y)))) # answer(goal). [ur(2220,b,486,a,c,580,a)]. given #625 (F,wt=7): 7995 -->_s0(nil,sndsplit(0,cons(x,y))) # answer(goal). [resolve(7466,a,37,b)]. given #626 (F,wt=9): 7469 -->_s0(empty(nil),head(sndsplit(0,cons(false,x)))) # answer(goal). [ur(2220,b,483,a,c,575,a)]. given #627 (T,wt=8): 1062 ->*_s0(sndsplit(0,sndsplit(s(x),nil)),nil). [ur(87,a,82,a,b,565,a)]. given #628 (T,wt=8): 1064 ->*_s0(app(nil,sndsplit(s(x),nil)),nil). [ur(87,a,61,a,b,565,a)]. given #629 (T,wt=8): 1069 ->*_s0(sndsplit(0,leq(s(x),0)),false). [ur(87,a,82,a,b,571,a)]. given #630 (T,wt=8): 1070 ->*_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=9): 7472 -->_s0(empty(nil),tail(sndsplit(0,cons(x,false)))) # answer(goal). [ur(2220,b,469,a,c,564,a)]. given #633 (F,wt=9): 7473 -->_s0(empty(nil),sndsplit(length(nil),app(nil,false))) # answer(goal). [ur(2220,b,321,a,c,689,a)]. given #634 (F,wt=9): 7474 -->_s0(empty(nil),sndsplit(length(nil),sndsplit(0,false))) # answer(goal). [ur(2220,b,321,a,c,635,a)]. given #635 (F,wt=9): 7484 -->_s0(empty(nil),sndsplit(0,empty(cons(x,y)))) # answer(goal). [ur(2220,b,145,a,c,567,a)]. given #636 (T,wt=8): 1072 ->*_s0(app(nil,leq(s(x),0)),false). [ur(87,a,61,a,b,571,a)]. given #637 (T,wt=8): 1112 ->*_s0(sndsplit(0,head(cons(x,y))),x). [ur(87,a,82,a,b,575,a)]. given #638 (T,wt=8): 1114 ->*_s0(app(nil,head(cons(x,y))),x). [ur(87,a,61,a,b,575,a)]. given #639 (T,wt=8): 1116 ->*_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=9): 7490 -->_s0(empty(nil),empty(app(nil,cons(x,y)))) # answer(goal). [ur(2220,b,136,a,c,580,a)]. given #642 (F,wt=7): 8172 -->_s0(nil,app(nil,cons(x,y))) # answer(goal). [resolve(7490,a,37,b)]. given #643 (F,wt=9): 7493 -->_s0(empty(nil),head(app(nil,cons(false,x)))) # answer(goal). [ur(2220,b,133,a,c,575,a)]. given #644 (F,wt=9): 7495 -->_s0(empty(nil),leq(app(nil,s(x)),0)) # answer(goal). [ur(2220,b,131,a,c,571,a)]. given #645 (T,wt=8): 1118 ->*_s0(app(nil,fstsplit(s(x),nil)),nil). [ur(87,a,61,a,b,576,a)]. given #646 (T,wt=8): 1125 ->*_s0(sndsplit(0,empty(cons(x,y))),false). [ur(87,a,82,a,b,580,a)]. given #647 (T,wt=8): 1127 ->*_s0(app(nil,empty(cons(x,y))),false). [ur(87,a,61,a,b,580,a)]. given #648 (T,wt=8): 1130 ->*_s0(sndsplit(0,sndsplit(0,length(nil))),0). [ur(87,a,82,a,b,623,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=9): 7497 -->_s0(empty(nil),leq(s(x),app(nil,0))) # answer(goal). [ur(2220,b,130,a,c,571,a)]. given #651 (F,wt=9): 7498 -->_s0(empty(nil),sndsplit(app(nil,length(nil)),false)) # answer(goal). [ur(2220,b,121,a,c,4430,a)]. given #652 (F,wt=9): 7508 -->_s0(empty(nil),tail(app(nil,cons(x,false)))) # answer(goal). [ur(2220,b,119,a,c,564,a)]. given #653 (F,wt=9): 7511 -->_s0(empty(nil),head(app(cons(false,x),y))) # answer(goal). [ur(2220,b,108,a,c,575,a)]. given #654 (T,wt=8): 1132 ->*_s0(app(nil,sndsplit(0,length(nil))),0). [ur(87,a,61,a,b,623,a)]. given #655 (T,wt=8): 1161 ->*_s0(sndsplit(0,app(nil,length(nil))),0). [ur(87,a,82,a,b,625,a)]. given #656 (T,wt=8): 1163 ->*_s0(app(nil,app(nil,length(nil))),0). [ur(87,a,61,a,b,625,a)]. given #657 (T,wt=8): 1167 ->*_s0(sndsplit(0,sndsplit(0,empty(nil))),true). [ur(87,a,82,a,b,628,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=9): 7512 -->_s0(empty(nil),tail(app(cons(x,nil),false))) # answer(goal). [ur(2220,b,94,a,c,688,a)]. given #660 (F,wt=9): 7537 -->_s0(empty(nil),sndsplit(0,sndsplit(length(nil),false))) # answer(goal). [ur(2220,b,82,a,c,4430,a)]. given #661 (F,wt=9): 7546 -->_s0(empty(nil),sndsplit(0,head(cons(false,x)))) # answer(goal). [ur(2220,b,82,a,c,575,a)]. given #662 (F,wt=9): 7547 -->_s0(empty(nil),sndsplit(0,leq(s(x),0))) # answer(goal). [ur(2220,b,82,a,c,571,a)]. given #663 (T,wt=8): 1169 ->*_s0(app(nil,sndsplit(0,empty(nil))),true). [ur(87,a,61,a,b,628,a)]. given #664 (T,wt=8): 1172 ->*_s0(sndsplit(0,app(nil,empty(nil))),true). [ur(87,a,82,a,b,630,a)]. given #665 (T,wt=8): 1174 ->*_s0(app(nil,app(nil,empty(nil))),true). [ur(87,a,61,a,b,630,a)]. given #666 (T,wt=8): 1176 ->*_s0(sndsplit(0,s(empty(nil))),s(true)). [ur(87,a,82,a,b,692,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=9): 7548 -->_s0(empty(nil),sndsplit(0,tail(cons(x,false)))) # answer(goal). [ur(2220,b,82,a,c,564,a)]. given #669 (F,wt=9): 7550 -->_s0(empty(nil),leq(s(s(x)),s(0))) # answer(goal). [ur(2220,b,72,a,c,571,a)]. given #670 (F,wt=9): 7570 -->_s0(empty(nil),app(nil,sndsplit(length(nil),false))) # answer(goal). [ur(2220,b,61,a,c,4430,a)]. given #671 (F,wt=9): 7579 -->_s0(empty(nil),app(nil,empty(cons(x,y)))) # answer(goal). [ur(2220,b,61,a,c,580,a)]. given #672 (T,wt=8): 1178 ->*_s0(app(nil,s(empty(nil))),s(true)). [ur(87,a,61,a,b,692,a)]. given #673 (T,wt=8): 1208 ->*_s0(sndsplit(0,tail(empty(nil))),tail(true)). [ur(87,a,82,a,b,751,a)]. given #674 (T,wt=8): 1210 ->*_s0(app(nil,tail(empty(nil))),tail(true)). [ur(87,a,61,a,b,751,a)]. given #675 (T,wt=8): 1212 ->*_s0(sndsplit(0,length(empty(nil))),length(true)). [ur(87,a,82,a,b,777,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=9): 7580 -->_s0(empty(nil),app(nil,head(cons(false,x)))) # answer(goal). [ur(2220,b,61,a,c,575,a)]. given #678 (F,wt=9): 7581 -->_s0(empty(nil),app(nil,leq(s(x),0))) # answer(goal). [ur(2220,b,61,a,c,571,a)]. given #679 (F,wt=9): 7582 -->_s0(empty(nil),app(nil,tail(cons(x,false)))) # answer(goal). [ur(2220,b,61,a,c,564,a)]. given #680 (F,wt=9): 7864 -->_s0(empty(x),app(nil,false)) | -->_s0(nil,x) # answer(goal). [resolve(7451,a,37,b)]. given #681 (T,wt=8): 1214 ->*_s0(app(nil,length(empty(nil))),length(true)). [ur(87,a,61,a,b,777,a)]. given #682 (T,wt=8): 1216 ->*_s0(sndsplit(0,head(empty(nil))),head(true)). [ur(87,a,82,a,b,803,a)]. given #683 (T,wt=8): 1218 ->*_s0(app(nil,head(empty(nil))),head(true)). [ur(87,a,61,a,b,803,a)]. given #684 (T,wt=8): 1220 ->*_s0(sndsplit(0,empty(empty(nil))),empty(true)). [ur(87,a,82,a,b,829,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=9): 7865 -->_s0(empty(nil),app(nil,x)) | -->_s0(x,false) # answer(goal). [resolve(7451,b,36,b)]. given #687 (F,wt=9): 7866 -->_s0(empty(nil),app(x,false)) | -->_s0(x,nil) # answer(goal). [resolve(7451,b,35,b)]. given #688 (F,wt=8): 8416 -->_s0(empty(nil),app(sndsplit(0,nil),false)) # answer(goal). [resolve(7866,b,82,a)]. given #689 (F,wt=8): 8417 -->_s0(empty(nil),app(mapf(x,nil),false)) # answer(goal). [resolve(7866,b,74,a)]. given #690 (T,wt=8): 1222 ->*_s0(app(nil,empty(empty(nil))),empty(true)). [ur(87,a,61,a,b,829,a)]. given #691 (T,wt=8): 1250 ->*_s0(sndsplit(0,s(length(nil))),s(0)). [ur(87,a,82,a,b,888,a)]. given #692 (T,wt=8): 1253 ->*_s0(app(nil,s(length(nil))),s(0)). [ur(87,a,61,a,b,888,a)]. given #693 (T,wt=8): 1255 ->*_s0(sndsplit(0,tail(length(nil))),tail(0)). [ur(87,a,82,a,b,914,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): 8420 -->_s0(empty(nil),app(fstsplit(0,x),false)) # answer(goal). [resolve(7866,b,64,a)]. given #696 (F,wt=9): 7992 -->_s0(empty(x),sndsplit(0,false)) | -->_s0(nil,x) # answer(goal). [resolve(7455,a,37,b)]. given #697 (F,wt=9): 7993 -->_s0(empty(nil),sndsplit(0,x)) | -->_s0(x,false) # answer(goal). [resolve(7455,b,53,b)]. given #698 (F,wt=9): 7994 -->_s0(empty(nil),sndsplit(x,false)) | -->_s0(x,0) # answer(goal). [resolve(7455,b,52,b)]. given #699 (T,wt=8): 1257 ->*_s0(app(nil,tail(length(nil))),tail(0)). [ur(87,a,61,a,b,914,a)]. given #700 (T,wt=8): 1259 ->*_s0(sndsplit(0,length(length(nil))),length(0)). [ur(87,a,82,a,b,940,a)]. given #701 (T,wt=8): 1261 ->*_s0(app(nil,length(length(nil))),length(0)). [ur(87,a,61,a,b,940,a)]. given #702 (T,wt=8): 1263 ->*_s0(sndsplit(0,head(length(nil))),head(0)). [ur(87,a,82,a,b,966,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): 8468 -->_s0(empty(nil),sndsplit(sndsplit(0,0),false)) # answer(goal). [resolve(7994,b,82,a)]. given #705 (F,wt=9): 8414 -->_s0(empty(nil),app(tail(cons(x,nil)),false)) # answer(goal). [resolve(7866,b,85,a)]. given #706 (F,wt=9): 8415 -->_s0(empty(nil),app(sndsplit(s(x),nil),false)) # answer(goal). [resolve(7866,b,84,a)]. given #707 (F,wt=9): 8418 -->_s0(empty(nil),app(head(cons(nil,x)),false)) # answer(goal). [resolve(7866,b,67,a)]. given #708 (T,wt=8): 1265 ->*_s0(app(nil,head(length(nil))),head(0)). [ur(87,a,61,a,b,966,a)]. given #709 (T,wt=8): 1294 ->*_s0(sndsplit(0,empty(length(nil))),empty(0)). [ur(87,a,82,a,b,1026,a)]. given #710 (T,wt=8): 1296 ->*_s0(app(nil,empty(length(nil))),empty(0)). [ur(87,a,61,a,b,1026,a)]. given #711 (T,wt=8): 1297 ->*_s0(s(app(nil,length(nil))),s(0)). [ur(87,a,114,a,b,888,a)]. given #712 (A,wt=9): 192 ->_s0(cons(x,fstsplit(0,y)),cons(x,nil)). [ur(56,a,64,a)]. given #713 (F,wt=9): 8419 -->_s0(empty(nil),app(fstsplit(s(x),nil),false)) # answer(goal). [resolve(7866,b,66,a)]. given #714 (F,wt=9): 8467 -->_s0(empty(nil),sndsplit(tail(cons(x,0)),false)) # answer(goal). [resolve(7994,b,85,a)]. given #715 (F,wt=9): 8469 -->_s0(empty(nil),sndsplit(head(cons(0,x)),false)) # answer(goal). [resolve(7994,b,67,a)]. given #716 (F,wt=10): 2423 -->_s0(nil,x) | -->_s0(empty(x),y) | -->*_s0(y,false) # answer(goal). [resolve(2219,a,87,c)]. given #717 (T,wt=8): 1298 ->*_s0(s(app(nil,empty(nil))),s(true)). [ur(87,a,114,a,b,692,a)]. given #718 (T,wt=8): 1325 ->*_s0(tail(app(nil,length(nil))),tail(0)). [ur(87,a,119,a,b,914,a)]. given #719 (T,wt=8): 1326 ->*_s0(tail(app(nil,empty(nil))),tail(true)). [ur(87,a,119,a,b,751,a)]. given #720 (T,wt=8): 1327 ->*_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): 8576 -->_s0(nil,length(nil)) | -->*_s0(empty(0),false) # answer(goal). [resolve(2423,b,336,a)]. given #723 (F,wt=8): 8578 -->_s0(nil,empty(nil)) | -->*_s0(empty(true),false) # answer(goal). [resolve(2423,b,186,a)]. given #724 (F,wt=8): 8609 -->_s0(nil,tail(cons(x,cons(y,z)))) # answer(goal). [ur(2423,b,561,a,c,580,a)]. given #725 (F,wt=8): 8610 -->_s0(nil,head(cons(cons(x,y),z))) # answer(goal). [ur(2423,b,286,a,c,580,a)]. given #726 (T,wt=8): 1354 ->*_s0(length(app(nil,length(nil))),length(0)). [ur(87,a,132,a,b,940,a)]. given #727 (T,wt=8): 1355 ->*_s0(length(app(nil,empty(nil))),length(true)). [ur(87,a,132,a,b,777,a)]. given #728 (T,wt=8): 1494 ->*_s0(length(app(nil,app(nil,nil))),0). [ur(87,a,132,a,b,1356,a)]. given #729 (T,wt=8): 1496 ->*_s0(sndsplit(0,length(app(nil,nil))),0). [ur(87,a,82,a,b,1356,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=9): 8573 -->_s0(nil,sndsplit(0,x)) | -->*_s0(empty(x),false) # answer(goal). [resolve(2423,b,486,a)]. given #732 (F,wt=9): 8575 -->_s0(nil,leq(0,x)) | -->*_s0(empty(true),false) # answer(goal). [resolve(2423,b,361,a)]. given #733 (F,wt=9): 8580 -->_s0(nil,app(nil,x)) | -->*_s0(empty(x),false) # answer(goal). [resolve(2423,b,136,a)]. given #734 (F,wt=10): 2424 -->_s0(true,empty(sndsplit(0,x))) | -->*_s0(empty(x),false) # answer(goal). [resolve(2105,b,486,a)]. given #735 (T,wt=8): 1498 ->*_s0(app(nil,length(app(nil,nil))),0). [ur(87,a,61,a,b,1356,a)]. given #736 (T,wt=8): 1500 ->*_s0(head(app(nil,length(nil))),head(0)). [ur(87,a,133,a,b,966,a)]. given #737 (T,wt=8): 1501 ->*_s0(head(app(nil,empty(nil))),head(true)). [ur(87,a,133,a,b,803,a)]. given #738 (T,wt=8): 1502 ->*_s0(head(app(nil,cons(x,y))),x). [ur(87,a,133,a,b,575,a)]. given #739 (A,wt=9): 196 ->_s0(sndsplit(fstsplit(0,x),y),sndsplit(nil,y)). [ur(52,a,64,a)]. given #740 (F,wt=10): 2425 -->_s0(true,head(sndsplit(0,x))) | -->*_s0(head(x),false) # answer(goal). [resolve(2105,b,483,a)]. given #741 (F,wt=10): 2426 -->_s0(true,length(sndsplit(0,x))) | -->*_s0(length(x),false) # answer(goal). [resolve(2105,b,482,a)]. given #742 (F,wt=10): 2427 -->_s0(true,tail(sndsplit(0,x))) | -->*_s0(tail(x),false) # answer(goal). [resolve(2105,b,469,a)]. given #743 (F,wt=10): 2428 -->_s0(true,s(sndsplit(0,x))) | -->*_s0(s(x),false) # answer(goal). [resolve(2105,b,464,a)]. given #744 (T,wt=8): 1530 ->*_s0(empty(app(nil,length(nil))),empty(0)). [ur(87,a,136,a,b,1026,a)]. given #745 (T,wt=8): 1531 ->*_s0(empty(app(nil,empty(nil))),empty(true)). [ur(87,a,136,a,b,829,a)]. given #746 (T,wt=8): 1532 ->*_s0(empty(app(nil,cons(x,y))),false). [ur(87,a,136,a,b,580,a)]. given #747 (T,wt=8): 1561 ->*_s0(empty(app(nil,app(nil,nil))),true). [ur(87,a,136,a,b,1533,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): 8840 -->_s0(nil,app(nil,app(nil,cons(x,y)))) # answer(goal). [resolve(1532,a,8580,b)]. given #750 (F,wt=9): 8841 -->_s0(nil,sndsplit(0,app(nil,cons(x,y)))) # answer(goal). [resolve(1532,a,8573,b)]. given #751 (F,wt=10): 2429 -->_s0(true,head(mapf(x,nil))) | -->*_s0(head(nil),false) # answer(goal). [resolve(2105,b,458,a)]. given #752 (F,wt=10): 2430 -->_s0(true,length(mapf(x,nil))) | -->*_s0(length(nil),false) # answer(goal). [resolve(2105,b,457,a)]. given #753 (T,wt=8): 1563 ->*_s0(sndsplit(0,empty(app(nil,nil))),true). [ur(87,a,82,a,b,1533,a)]. given #754 (T,wt=8): 1565 ->*_s0(app(nil,empty(app(nil,nil))),true). [ur(87,a,61,a,b,1533,a)]. given #755 (T,wt=8): 1677 ->*_s0(length(app(nil,fstsplit(0,x))),0). [ur(87,a,132,a,b,1650,a)]. given #756 (T,wt=8): 1679 ->*_s0(sndsplit(0,length(fstsplit(0,x))),0). [ur(87,a,82,a,b,1650,a)]. given #757 (A,wt=17): 198 ->_s0(ring(x,y,z,u,fstsplit(0,w),v5),ring(x,y,z,u,nil,v5)). [ur(50,a,64,a)]. given #758 (F,wt=10): 2431 -->_s0(true,tail(mapf(x,nil))) | -->*_s0(tail(nil),false) # answer(goal). [resolve(2105,b,444,a)]. given #759 (F,wt=10): 2432 -->_s0(true,s(mapf(x,nil))) | -->*_s0(s(nil),false) # answer(goal). [resolve(2105,b,439,a)]. given #760 (F,wt=10): 2433 -->_s0(true,empty(leq(0,x))) | -->*_s0(empty(true),false) # answer(goal). [resolve(2105,b,361,a)]. given #761 (F,wt=10): 2434 -->_s0(true,head(leq(0,x))) | -->*_s0(head(true),false) # answer(goal). [resolve(2105,b,358,a)]. given #762 (T,wt=8): 1681 ->*_s0(app(nil,length(fstsplit(0,x))),0). [ur(87,a,61,a,b,1650,a)]. given #763 (T,wt=8): 1776 ->*_s0(empty(app(nil,fstsplit(0,x))),true). [ur(87,a,136,a,b,1748,a)]. given #764 (T,wt=8): 1778 ->*_s0(sndsplit(0,empty(fstsplit(0,x))),true). [ur(87,a,82,a,b,1748,a)]. given #765 (T,wt=8): 1780 ->*_s0(app(nil,empty(fstsplit(0,x))),true). [ur(87,a,61,a,b,1748,a)]. given #766 (A,wt=17): 199 ->_s0(ring(x,y,z,fstsplit(0,u),w,v5),ring(x,y,z,nil,w,v5)). [ur(49,a,64,a)]. given #767 (F,wt=10): 2435 -->_s0(true,length(leq(0,x))) | -->*_s0(length(true),false) # answer(goal). [resolve(2105,b,357,a)]. given #768 (F,wt=10): 2436 -->_s0(true,tail(leq(0,x))) | -->*_s0(tail(true),false) # answer(goal). [resolve(2105,b,344,a)]. given #769 (F,wt=10): 2437 -->_s0(true,s(leq(0,x))) | -->*_s0(s(true),false) # answer(goal). [resolve(2105,b,339,a)]. given #770 (F,wt=10): 2443 -->_s0(true,head(fstsplit(0,x))) | -->*_s0(head(nil),false) # answer(goal). [resolve(2105,b,208,a)]. given #771 (T,wt=8): 2073 ->*_s0(length(app(nil,mapf(x,nil))),0). [ur(87,a,132,a,b,2046,a)]. given #772 (T,wt=8): 2075 ->*_s0(sndsplit(0,length(mapf(x,nil))),0). [ur(87,a,82,a,b,2046,a)]. given #773 (T,wt=8): 2077 ->*_s0(app(nil,length(mapf(x,nil))),0). [ur(87,a,61,a,b,2046,a)]. given #774 (T,wt=8): 2160 ->*_s0(empty(app(nil,mapf(x,nil))),true). [ur(87,a,136,a,b,2132,a)]. given #775 (A,wt=17): 200 ->_s0(ring(x,y,fstsplit(0,z),u,w,v5),ring(x,y,nil,u,w,v5)). [ur(48,a,64,a)]. given #776 (F,wt=10): 2444 -->_s0(true,length(fstsplit(0,x))) | -->*_s0(length(nil),false) # answer(goal). [resolve(2105,b,207,a)]. given #777 (F,wt=10): 2445 -->_s0(true,tail(fstsplit(0,x))) | -->*_s0(tail(nil),false) # answer(goal). [resolve(2105,b,194,a)]. given #778 (F,wt=10): 2446 -->_s0(true,s(fstsplit(0,x))) | -->*_s0(s(nil),false) # answer(goal). [resolve(2105,b,189,a)]. given #779 (F,wt=10): 2452 -->_s0(true,empty(app(nil,x))) | -->*_s0(empty(x),false) # answer(goal). [resolve(2105,b,136,a)]. given #780 (T,wt=8): 2162 ->*_s0(sndsplit(0,empty(mapf(x,nil))),true). [ur(87,a,82,a,b,2132,a)]. given #781 (T,wt=8): 2164 ->*_s0(app(nil,empty(mapf(x,nil))),true). [ur(87,a,61,a,b,2132,a)]. given #782 (T,wt=8): 2165 ->*_s0(s(sndsplit(0,length(nil))),s(0)). [ur(87,a,464,a,b,888,a)]. given #783 (T,wt=8): 2166 ->*_s0(s(sndsplit(0,empty(nil))),s(true)). [ur(87,a,464,a,b,692,a)]. given #784 (A,wt=17): 201 ->_s0(ring(x,fstsplit(0,y),z,u,w,v5),ring(x,nil,z,u,w,v5)). [ur(47,a,64,a)]. given #785 (F,wt=10): 2453 -->_s0(true,head(app(nil,x))) | -->*_s0(head(x),false) # answer(goal). [resolve(2105,b,133,a)]. given #786 (F,wt=10): 2454 -->_s0(true,length(app(nil,x))) | -->*_s0(length(x),false) # answer(goal). [resolve(2105,b,132,a)]. given #787 (F,wt=10): 2455 -->_s0(true,tail(app(nil,x))) | -->*_s0(tail(x),false) # answer(goal). [resolve(2105,b,119,a)]. given #788 (F,wt=10): 2456 -->_s0(true,s(app(nil,x))) | -->*_s0(s(x),false) # answer(goal). [resolve(2105,b,114,a)]. given #789 (T,wt=8): 2221 ->*_s0(tail(sndsplit(0,length(nil))),tail(0)). [ur(87,a,469,a,b,914,a)]. given #790 (T,wt=8): 2222 ->*_s0(tail(sndsplit(0,empty(nil))),tail(true)). [ur(87,a,469,a,b,751,a)]. given #791 (T,wt=8): 2223 ->*_s0(tail(sndsplit(0,cons(x,y))),y). [ur(87,a,469,a,b,564,a)]. given #792 (T,wt=8): 2250 ->*_s0(length(sndsplit(0,mapf(x,nil))),0). [ur(87,a,482,a,b,2046,a)]. given #793 (A,wt=17): 202 ->_s0(ring(fstsplit(0,x),y,z,u,w,v5),ring(nil,y,z,u,w,v5)). [ur(46,a,64,a)]. given #794 (F,wt=10): 2577 -->_s0(true,x) | -->_s0(x,sndsplit(0,sndsplit(0,false))) # answer(goal). [resolve(635,a,2105,c)]. given #795 (F,wt=10): 2586 -->_s0(true,tail(cons(x,sndsplit(0,sndsplit(0,false))))) # answer(goal). [ur(2105,b,85,a,c,635,a)]. given #796 (F,wt=10): 2587 -->_s0(true,sndsplit(s(0),cons(x,sndsplit(0,false)))) # answer(goal). [ur(2105,b,83,a,c,635,a)]. given #797 (F,wt=10): 2589 -->_s0(true,head(cons(sndsplit(0,sndsplit(0,false)),x))) # answer(goal). [ur(2105,b,67,a,c,635,a)]. given #798 (T,wt=8): 2251 ->*_s0(length(sndsplit(0,fstsplit(0,x))),0). [ur(87,a,482,a,b,1650,a)]. given #799 (T,wt=8): 2252 ->*_s0(length(sndsplit(0,app(nil,nil))),0). [ur(87,a,482,a,b,1356,a)]. given #800 (T,wt=8): 2253 ->*_s0(length(sndsplit(0,length(nil))),length(0)). [ur(87,a,482,a,b,940,a)]. given #801 (T,wt=8): 2254 ->*_s0(length(sndsplit(0,empty(nil))),length(true)). [ur(87,a,482,a,b,777,a)]. given #802 (A,wt=9): 203 ->_s0(mapf(x,fstsplit(0,y)),mapf(x,nil)). [ur(45,a,64,a)]. given #803 (F,wt=10): 2591 -->_s0(true,x) | -->_s0(x,app(nil,sndsplit(0,false))) # answer(goal). [resolve(637,a,2105,c)]. given #804 (F,wt=10): 2599 -->_s0(true,tail(cons(x,app(nil,sndsplit(0,false))))) # answer(goal). [ur(2105,b,85,a,c,637,a)]. given #805 (F,wt=10): 2601 -->_s0(true,head(cons(app(nil,sndsplit(0,false)),x))) # answer(goal). [ur(2105,b,67,a,c,637,a)]. given #806 (F,wt=10): 2634 -->_s0(true,length(nil)) | -->_s0(0,x) | -->*_s0(x,false) # answer(goal). [resolve(2490,b,87,c)]. given #807 (T,wt=7): 9154 ->*_s0(mapf(x,fstsplit(0,y)),nil). [ur(87,a,203,a,b,568,a)]. given #808 (T,wt=8): 2282 ->*_s0(length(sndsplit(0,sndsplit(0,nil))),0). [ur(87,a,482,a,b,2255,a)]. given #809 (T,wt=8): 2283 ->*_s0(length(app(nil,sndsplit(0,nil))),0). [ur(87,a,132,a,b,2255,a)]. given #810 (T,wt=8): 2285 ->*_s0(sndsplit(0,length(sndsplit(0,nil))),0). [ur(87,a,82,a,b,2255,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=7): 9210 -->_s0(true,length(nil)) | -->_s0(0,false) # answer(goal). [resolve(2634,c,86,a)]. given #813 (F,wt=9): 9203 -->_s0(true,length(nil)) | -->_s0(0,app(nil,false)) # answer(goal). [resolve(2634,c,581,a)]. given #814 (F,wt=9): 9207 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(0,false)) # answer(goal). [resolve(2634,c,567,a)]. given #815 (F,wt=10): 2701 -->_s0(true,x) | -->_s0(x,sndsplit(0,app(nil,false))) # answer(goal). [resolve(689,a,2105,c)]. given #816 (T,wt=8): 2287 ->*_s0(app(nil,length(sndsplit(0,nil))),0). [ur(87,a,61,a,b,2255,a)]. given #817 (T,wt=8): 2288 ->*_s0(head(sndsplit(0,length(nil))),head(0)). [ur(87,a,483,a,b,966,a)]. given #818 (T,wt=8): 2289 ->*_s0(head(sndsplit(0,empty(nil))),head(true)). [ur(87,a,483,a,b,803,a)]. given #819 (T,wt=8): 2290 ->*_s0(head(sndsplit(0,cons(x,y))),x). [ur(87,a,483,a,b,575,a)]. given #820 (A,wt=9): 205 ->_s0(leq(x,fstsplit(0,y)),leq(x,nil)). [ur(43,a,64,a)]. given #821 (F,wt=10): 2710 -->_s0(true,tail(cons(x,sndsplit(0,app(nil,false))))) # answer(goal). [ur(2105,b,85,a,c,689,a)]. given #822 (F,wt=10): 2711 -->_s0(true,sndsplit(s(0),cons(x,app(nil,false)))) # answer(goal). [ur(2105,b,83,a,c,689,a)]. given #823 (F,wt=10): 2712 -->_s0(true,head(cons(sndsplit(0,app(nil,false)),x))) # answer(goal). [ur(2105,b,67,a,c,689,a)]. given #824 (F,wt=10): 2748 -->_s0(true,x) | -->_s0(x,app(nil,app(nil,false))) # answer(goal). [resolve(691,a,2105,c)]. given #825 (T,wt=8): 2345 ->*_s0(empty(sndsplit(0,mapf(x,nil))),true). [ur(87,a,486,a,b,2132,a)]. given #826 (T,wt=8): 2346 ->*_s0(empty(sndsplit(0,fstsplit(0,x))),true). [ur(87,a,486,a,b,1748,a)]. given #827 (T,wt=8): 2347 ->*_s0(empty(sndsplit(0,app(nil,nil))),true). [ur(87,a,486,a,b,1533,a)]. given #828 (T,wt=8): 2348 ->*_s0(empty(sndsplit(0,length(nil))),empty(0)). [ur(87,a,486,a,b,1026,a)]. given #829 (A,wt=9): 206 ->_s0(leq(fstsplit(0,x),y),leq(nil,y)). [ur(42,a,64,a)]. given #830 (F,wt=10): 2757 -->_s0(true,tail(cons(x,app(nil,app(nil,false))))) # answer(goal). [ur(2105,b,85,a,c,691,a)]. given #831 (F,wt=10): 2758 -->_s0(true,head(cons(app(nil,app(nil,false)),x))) # answer(goal). [ur(2105,b,67,a,c,691,a)]. given #832 (F,wt=10): 3430 -->_s0(true,x) | -->_s0(x,sndsplit(app(nil,0),false)) # answer(goal). [resolve(3398,a,2105,c)]. given #833 (F,wt=10): 3442 -->_s0(true,tail(cons(x,sndsplit(app(nil,0),false)))) # answer(goal). [ur(2105,b,85,a,c,3398,a)]. given #834 (T,wt=8): 2349 ->*_s0(empty(sndsplit(0,empty(nil))),empty(true)). [ur(87,a,486,a,b,829,a)]. given #835 (T,wt=8): 2350 ->*_s0(empty(sndsplit(0,cons(x,y))),false). [ur(87,a,486,a,b,580,a)]. given #836 (T,wt=8): 2379 ->*_s0(empty(sndsplit(0,sndsplit(0,nil))),true). [ur(87,a,486,a,b,2351,a)]. given #837 (T,wt=8): 2380 ->*_s0(empty(app(nil,sndsplit(0,nil))),true). [ur(87,a,136,a,b,2351,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): 9406 -->_s0(nil,app(nil,sndsplit(0,cons(x,y)))) # answer(goal). [resolve(2350,a,8580,b)]. given #840 (F,wt=9): 9407 -->_s0(nil,sndsplit(0,sndsplit(0,cons(x,y)))) # answer(goal). [resolve(2350,a,8573,b)]. given #841 (F,wt=10): 3443 -->_s0(true,sndsplit(s(app(nil,0)),cons(x,false))) # answer(goal). [ur(2105,b,83,a,c,3398,a)]. given #842 (F,wt=10): 3444 -->_s0(true,head(cons(sndsplit(app(nil,0),false),x))) # answer(goal). [ur(2105,b,67,a,c,3398,a)]. given #843 (T,wt=8): 2382 ->*_s0(sndsplit(0,empty(sndsplit(0,nil))),true). [ur(87,a,82,a,b,2351,a)]. given #844 (T,wt=8): 2384 ->*_s0(app(nil,empty(sndsplit(0,nil))),true). [ur(87,a,61,a,b,2351,a)]. given #845 (T,wt=8): 2606 ->*_s0(head(app(cons(x,y),z)),x). [ur(87,a,108,a,b,575,a)]. given #846 (T,wt=8): 2778 ->*_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): 9527 -->_s0(nil,app(nil,app(cons(x,y),z))) # answer(goal). [resolve(2778,a,8580,b)]. given #849 (F,wt=9): 9528 -->_s0(nil,sndsplit(0,app(cons(x,y),z))) # answer(goal). [resolve(2778,a,8573,b)]. given #850 (F,wt=10): 4634 -->_s0(true,head(cons(leq(s(x),length(nil)),y))) # answer(goal). [resolve(4606,a,2492,b)]. given #851 (F,wt=10): 4636 -->_s0(true,tail(cons(x,leq(s(y),length(nil))))) # answer(goal). [resolve(4606,a,2476,b)]. given #852 (T,wt=8): 3080 ->*_s0(s(empty(cons(x,y))),s(false)). [ur(87,a,139,a,b,86,a)]. given #853 (T,wt=8): 3142 ->*_s0(tail(empty(cons(x,y))),tail(false)). [ur(87,a,144,a,b,86,a)]. given #854 (T,wt=8): 3169 ->*_s0(length(empty(cons(x,y))),length(false)). [ur(87,a,157,a,b,86,a)]. given #855 (T,wt=8): 3196 ->*_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=10): 4637 -->_s0(true,x) | -->_s0(x,leq(s(y),length(nil))) # answer(goal). [resolve(4606,a,2105,c)]. given #858 (F,wt=10): 5197 -->_s0(true,head(cons(app(app(nil,nil),false),x))) # answer(goal). [resolve(5160,a,2492,b)]. given #859 (F,wt=10): 5199 -->_s0(true,tail(cons(x,app(app(nil,nil),false)))) # answer(goal). [resolve(5160,a,2476,b)]. given #860 (F,wt=10): 5200 -->_s0(true,x) | -->_s0(x,app(app(nil,nil),false)) # answer(goal). [resolve(5160,a,2105,c)]. given #861 (T,wt=8): 3223 ->*_s0(empty(empty(cons(x,y))),empty(false)). [ur(87,a,161,a,b,86,a)]. given #862 (T,wt=8): 3250 ->*_s0(sndsplit(s(x),app(nil,nil)),nil). [ur(87,a,120,a,b,565,a)]. given #863 (T,wt=8): 3283 ->*_s0(f(x,empty(nil)),f(x,true)). [ur(87,a,165,a,b,86,a)]. given #864 (T,wt=8): 3310 ->*_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): 9678 -->_s0(true,app(fstsplit(0,x),app(nil,false))) # answer(goal). [resolve(213,a,2748,b)]. given #867 (F,wt=9): 9679 -->_s0(true,app(fstsplit(0,x),sndsplit(0,false))) # answer(goal). [resolve(213,a,2591,b)]. given #868 (F,wt=10): 5589 -->_s0(true,app(nil,tail(cons(x,sndsplit(0,false))))) # answer(goal). [resolve(633,a,2496,b)]. given #869 (F,wt=10): 5591 -->_s0(true,sndsplit(0,tail(cons(x,sndsplit(0,false))))) # answer(goal). [resolve(633,a,2479,b)]. given #870 (T,wt=7): 9717 ->*_s0(app(fstsplit(0,x),y),y). [ur(87,a,213,a,b,581,a)]. given #871 (T,wt=8): 3337 ->*_s0(cons(x,empty(nil)),cons(x,true)). [ur(87,a,167,a,b,86,a)]. given #872 (T,wt=8): 3364 ->*_s0(cons(empty(nil),x),cons(true,x)). [ur(87,a,168,a,b,86,a)]. given #873 (T,wt=8): 3396 ->*_s0(sndsplit(app(nil,0),empty(nil)),true). [ur(87,a,121,a,b,628,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): 9751 -->_s0(true,app(nil,app(fstsplit(0,x),false))) # answer(goal). [resolve(9717,a,2496,b)]. given #876 (F,wt=9): 9753 -->_s0(true,sndsplit(0,app(fstsplit(0,x),false))) # answer(goal). [resolve(9717,a,2479,b)]. given #877 (F,wt=9): 9770 -->_s0(true,app(app(nil,fstsplit(0,x)),false)) # answer(goal). [ur(2105,b,138,a,c,9717,a)]. given #878 (F,wt=10): 5606 -->_s0(true,tail(sndsplit(0,cons(x,sndsplit(0,false))))) # answer(goal). [ur(2105,b,469,a,c,633,a)]. given #879 (T,wt=8): 3397 ->*_s0(sndsplit(app(nil,0),length(nil)),0). [ur(87,a,121,a,b,623,a)]. given #880 (T,wt=8): 3399 ->*_s0(sndsplit(app(nil,s(x)),nil),nil). [ur(87,a,121,a,b,565,a)]. given #881 (T,wt=8): 3446 ->*_s0(sndsplit(x,empty(nil)),sndsplit(x,true)). [ur(87,a,170,a,b,86,a)]. given #882 (T,wt=8): 3473 ->*_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=10): 5608 -->_s0(true,tail(app(nil,cons(x,sndsplit(0,false))))) # answer(goal). [ur(2105,b,119,a,c,633,a)]. given #885 (F,wt=10): 5609 -->_s0(true,app(nil,sndsplit(s(0),cons(x,false)))) # answer(goal). [resolve(634,a,2496,b)]. given #886 (F,wt=10): 5611 -->_s0(true,sndsplit(0,sndsplit(s(0),cons(x,false)))) # answer(goal). [resolve(634,a,2479,b)]. given #887 (F,wt=10): 5625 -->_s0(true,sndsplit(app(nil,s(0)),cons(x,false))) # answer(goal). [ur(2105,b,121,a,c,634,a)]. given #888 (T,wt=8): 3500 ->*_s0(mapf(x,empty(nil)),mapf(x,true)). [ur(87,a,178,a,b,86,a)]. given #889 (T,wt=8): 3554 ->*_s0(mapf(empty(nil),x),mapf(true,x)). [ur(87,a,179,a,b,86,a)]. given #890 (T,wt=8): 3581 ->*_s0(leq(x,empty(nil)),leq(x,true)). [ur(87,a,180,a,b,86,a)]. given #891 (T,wt=8): 3609 ->*_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=10): 5626 -->_s0(true,sndsplit(s(0),app(nil,cons(x,false)))) # answer(goal). [ur(2105,b,120,a,c,634,a)]. given #894 (F,wt=10): 5628 -->_s0(true,app(nil,head(cons(sndsplit(0,false),x)))) # answer(goal). [resolve(636,a,2496,b)]. given #895 (F,wt=10): 5630 -->_s0(true,sndsplit(0,head(cons(sndsplit(0,false),x)))) # answer(goal). [resolve(636,a,2479,b)]. given #896 (F,wt=10): 5646 -->_s0(true,head(sndsplit(0,cons(sndsplit(0,false),x)))) # answer(goal). [ur(2105,b,483,a,c,636,a)]. given #897 (T,wt=8): 3636 ->*_s0(fstsplit(x,empty(nil)),fstsplit(x,true)). [ur(87,a,184,a,b,86,a)]. given #898 (T,wt=8): 3691 ->*_s0(fstsplit(empty(nil),x),fstsplit(true,x)). [ur(87,a,185,a,b,86,a)]. given #899 (T,wt=8): 3718 ->*_s0(app(x,empty(nil)),app(x,true)). [ur(87,a,187,a,b,86,a)]. given #900 (T,wt=8): 3745 ->*_s0(app(empty(nil),x),app(true,x)). [ur(87,a,188,a,b,86,a)]. given #901 (A,wt=16): 217 ->_s0(cons(x,fstsplit(s(y),cons(z,u))),cons(x,cons(z,fstsplit(y,u)))). [ur(56,a,65,a)]. given #902 (F,wt=10): 5648 -->_s0(true,head(app(nil,cons(sndsplit(0,false),x)))) # answer(goal). [ur(2105,b,133,a,c,636,a)]. given #903 (F,wt=10): 5649 -->_s0(true,head(app(cons(sndsplit(0,false),x),y))) # answer(goal). [ur(2105,b,108,a,c,636,a)]. given #904 (F,wt=10): 5745 -->_s0(true,sndsplit(app(nil,0),empty(cons(x,y)))) # answer(goal). [ur(2105,b,145,a,c,3398,a)]. given #905 (F,wt=10): 5763 -->_s0(true,app(nil,tail(cons(x,app(nil,false))))) # answer(goal). [resolve(688,a,2496,b)]. given #906 (T,wt=8): 3772 ->*_s0(s(fstsplit(s(x),nil)),s(nil)). [ur(87,a,239,a,b,86,a)]. given #907 (T,wt=8): 3830 ->*_s0(tail(fstsplit(s(x),nil)),tail(nil)). [ur(87,a,244,a,b,86,a)]. given #908 (T,wt=8): 3858 ->*_s0(length(fstsplit(s(x),nil)),length(nil)). [ur(87,a,257,a,b,86,a)]. given #909 (T,wt=8): 3891 ->*_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=10): 5765 -->_s0(true,sndsplit(0,tail(cons(x,app(nil,false))))) # answer(goal). [resolve(688,a,2479,b)]. given #912 (F,wt=10): 5782 -->_s0(true,tail(sndsplit(0,cons(x,app(nil,false))))) # answer(goal). [ur(2105,b,469,a,c,688,a)]. given #913 (F,wt=10): 5784 -->_s0(true,tail(app(nil,cons(x,app(nil,false))))) # answer(goal). [ur(2105,b,119,a,c,688,a)]. given #914 (F,wt=10): 5786 -->_s0(true,app(nil,head(cons(app(nil,false),x)))) # answer(goal). [resolve(690,a,2496,b)]. given #915 (T,wt=8): 3949 ->*_s0(empty(fstsplit(s(x),nil)),empty(nil)). [ur(87,a,261,a,b,86,a)]. given #916 (T,wt=8): 3990 ->*_s0(s(head(cons(x,y))),s(x)). [ur(87,a,264,a,b,86,a)]. given #917 (T,wt=8): 4027 ->*_s0(tail(head(cons(x,y))),tail(x)). [ur(87,a,269,a,b,86,a)]. given #918 (T,wt=8): 4100 ->*_s0(length(head(cons(x,y))),length(x)). [ur(87,a,282,a,b,86,a)]. given #919 (A,wt=14): 219 ->_s0(tail(fstsplit(s(x),cons(y,z))),tail(cons(y,fstsplit(x,z)))). [ur(54,a,65,a)]. given #920 (F,wt=10): 5788 -->_s0(true,sndsplit(0,head(cons(app(nil,false),x)))) # answer(goal). [resolve(690,a,2479,b)]. given #921 (F,wt=10): 5805 -->_s0(true,head(sndsplit(0,cons(app(nil,false),x)))) # answer(goal). [ur(2105,b,483,a,c,690,a)]. given #922 (F,wt=10): 5807 -->_s0(true,head(app(nil,cons(app(nil,false),x)))) # answer(goal). [ur(2105,b,133,a,c,690,a)]. given #923 (F,wt=10): 5808 -->_s0(true,head(app(cons(app(nil,false),x),y))) # answer(goal). [ur(2105,b,108,a,c,690,a)]. given #924 (T,wt=8): 4144 ->*_s0(head(head(cons(x,y))),head(x)). [ur(87,a,283,a,b,86,a)]. given #925 (T,wt=8): 4186 ->*_s0(empty(head(cons(x,y))),empty(x)). [ur(87,a,286,a,b,86,a)]. given #926 (T,wt=8): 4254 ->*_s0(f(x,length(nil)),f(x,0)). [ur(87,a,315,a,b,86,a)]. given #927 (T,wt=8): 4281 ->*_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=10): 7272 -->_s0(empty(nil),empty(length(nil))) | -->*_s0(empty(0),false) # answer(goal). [resolve(2220,b,336,a)]. given #930 (F,wt=10): 7275 -->_s0(empty(nil),head(length(nil))) | -->*_s0(head(0),false) # answer(goal). [resolve(2220,b,333,a)]. given #931 (F,wt=10): 7276 -->_s0(empty(nil),length(length(nil))) | -->*_s0(length(0),false) # answer(goal). [resolve(2220,b,332,a)]. given #932 (F,wt=10): 7283 -->_s0(empty(nil),tail(length(nil))) | -->*_s0(tail(0),false) # answer(goal). [resolve(2220,b,319,a)]. given #933 (T,wt=8): 4308 ->*_s0(cons(x,length(nil)),cons(x,0)). [ur(87,a,317,a,b,86,a)]. given #934 (T,wt=8): 4369 ->*_s0(cons(length(nil),x),cons(0,x)). [ur(87,a,318,a,b,86,a)]. given #935 (T,wt=8): 4396 ->*_s0(sndsplit(x,length(nil)),sndsplit(x,0)). [ur(87,a,320,a,b,86,a)]. given #936 (T,wt=8): 4423 ->*_s0(sndsplit(length(nil),app(nil,x)),x). [ur(87,a,321,a,b,689,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=10): 7288 -->_s0(empty(nil),s(length(nil))) | -->*_s0(s(0),false) # answer(goal). [resolve(2220,b,314,a)]. given #939 (F,wt=10): 7304 -->_s0(empty(nil),empty(empty(nil))) | -->*_s0(empty(true),false) # answer(goal). [resolve(2220,b,186,a)]. given #940 (F,wt=10): 7307 -->_s0(empty(nil),head(empty(nil))) | -->*_s0(head(true),false) # answer(goal). [resolve(2220,b,183,a)]. given #941 (F,wt=10): 7308 -->_s0(empty(nil),length(empty(nil))) | -->*_s0(length(true),false) # answer(goal). [resolve(2220,b,182,a)]. given #942 (T,wt=8): 4424 ->*_s0(sndsplit(length(nil),fstsplit(0,x)),nil). [ur(87,a,321,a,b,683,a)]. given #943 (T,wt=8): 4425 ->*_s0(sndsplit(length(nil),leq(0,x)),true). [ur(87,a,321,a,b,678,a)]. given #944 (T,wt=8): 4426 ->*_s0(sndsplit(length(nil),mapf(x,nil)),nil). [ur(87,a,321,a,b,639,a)]. given #945 (T,wt=8): 4427 ->*_s0(sndsplit(length(nil),sndsplit(0,x)),x). [ur(87,a,321,a,b,635,a)]. given #946 (A,wt=24): 222 ->_s0(ring(x,y,z,u,w,fstsplit(s(v5),cons(v6,v7))),ring(x,y,z,u,w,cons(v6,fstsplit(v5,v7)))). [ur(51,a,65,a)]. given #947 (F,wt=10): 7315 -->_s0(empty(nil),tail(empty(nil))) | -->*_s0(tail(true),false) # answer(goal). [resolve(2220,b,169,a)]. given #948 (F,wt=10): 7320 -->_s0(empty(nil),s(empty(nil))) | -->*_s0(s(true),false) # answer(goal). [resolve(2220,b,164,a)]. given #949 (F,wt=10): 7392 -->_s0(empty(nil),tail(cons(x,y))) | -->*_s0(y,false) # answer(goal). [resolve(2220,b,85,a)]. given #950 (F,wt=10): 7393 -->_s0(empty(nil),sndsplit(s(x),nil)) | -->*_s0(nil,false) # answer(goal). [resolve(2220,b,84,a)]. given #951 (T,wt=8): 4431 ->*_s0(sndsplit(length(nil),x),sndsplit(0,x)). [ur(87,a,321,a,b,86,a)]. given #952 (T,wt=8): 4495 ->*_s0(sndsplit(app(nil,length(nil)),x),x). [ur(87,a,121,a,b,4430,a)]. given #953 (T,wt=8): 4499 ->*_s0(sndsplit(0,sndsplit(length(nil),x)),x). [ur(87,a,82,a,b,4430,a)]. given #954 (T,wt=8): 4501 ->*_s0(app(nil,sndsplit(length(nil),x)),x). [ur(87,a,61,a,b,4430,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): 10311 -->_s0(true,sndsplit(length(nil),sndsplit(length(nil),false))) # answer(goal). [ur(2105,b,321,a,c,4499,a)]. given #957 (F,wt=10): 7407 -->_s0(empty(nil),head(cons(x,y))) | -->*_s0(x,false) # answer(goal). [resolve(2220,b,67,a)]. given #958 (F,wt=10): 7408 -->_s0(empty(nil),fstsplit(s(x),nil)) | -->*_s0(nil,false) # answer(goal). [resolve(2220,b,66,a)]. given #959 (F,wt=10): 7440 -->_s0(empty(nil),x) | -->_s0(x,sndsplit(length(nil),false)) # answer(goal). [resolve(2220,c,4430,a)]. given #960 (T,wt=8): 4520 ->*_s0(mapf(x,length(nil)),mapf(x,0)). [ur(87,a,328,a,b,86,a)]. given #961 (T,wt=8): 4549 ->*_s0(leq(s(x),app(nil,0)),false). [ur(87,a,130,a,b,571,a)]. given #962 (T,wt=8): 4577 ->*_s0(mapf(length(nil),x),mapf(0,x)). [ur(87,a,329,a,b,86,a)]. given #963 (T,wt=8): 4607 ->*_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): 7452 -->_s0(empty(nil),x) | -->_s0(x,empty(cons(y,z))) # answer(goal). [resolve(2220,c,580,a)]. given #966 (F,wt=10): 7453 -->_s0(empty(nil),x) | -->_s0(x,head(cons(false,y))) # answer(goal). [resolve(2220,c,575,a)]. given #967 (F,wt=10): 7454 -->_s0(empty(nil),x) | -->_s0(x,leq(s(y),0)) # answer(goal). [resolve(2220,c,571,a)]. given #968 (F,wt=10): 7456 -->_s0(empty(nil),x) | -->_s0(x,tail(cons(y,false))) # answer(goal). [resolve(2220,c,564,a)]. given #969 (T,wt=8): 4652 ->*_s0(leq(length(nil),x),leq(0,x)). [ur(87,a,331,a,b,86,a)]. given #970 (T,wt=8): 4684 ->*_s0(leq(app(nil,s(x)),0),false). [ur(87,a,131,a,b,571,a)]. given #971 (T,wt=8): 4715 ->*_s0(leq(app(nil,length(nil)),x),true). [ur(87,a,131,a,b,4651,a)]. given #972 (T,wt=8): 4717 ->*_s0(sndsplit(0,leq(length(nil),x)),true). [ur(87,a,82,a,b,4651,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): 7459 -->_s0(empty(nil),empty(tail(cons(x,cons(y,z))))) # answer(goal). [ur(2220,b,561,a,c,580,a)]. given #975 (F,wt=10): 7462 -->_s0(empty(nil),head(tail(cons(x,cons(false,y))))) # answer(goal). [ur(2220,b,558,a,c,575,a)]. given #976 (F,wt=10): 7465 -->_s0(empty(nil),tail(tail(cons(x,cons(y,false))))) # answer(goal). [ur(2220,b,544,a,c,564,a)]. given #977 (F,wt=10): 7475 -->_s0(empty(nil),empty(head(cons(cons(x,y),z)))) # answer(goal). [ur(2220,b,286,a,c,580,a)]. given #978 (T,wt=8): 4718 ->*_s0(leq(s(length(nil)),s(x)),true). [ur(87,a,72,a,b,4651,a)]. given #979 (T,wt=8): 4720 ->*_s0(app(nil,leq(length(nil),x)),true). [ur(87,a,61,a,b,4651,a)]. given #980 (T,wt=8): 4733 ->*_s0(fstsplit(x,length(nil)),fstsplit(x,0)). [ur(87,a,334,a,b,86,a)]. given #981 (T,wt=8): 4761 ->*_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): 7478 -->_s0(empty(nil),head(head(cons(cons(false,x),y)))) # answer(goal). [ur(2220,b,283,a,c,575,a)]. given #984 (F,wt=10): 7481 -->_s0(empty(nil),tail(head(cons(cons(x,false),y)))) # answer(goal). [ur(2220,b,269,a,c,564,a)]. given #985 (F,wt=10): 7482 -->_s0(empty(nil),sndsplit(length(nil),empty(cons(x,y)))) # answer(goal). [ur(2220,b,145,a,c,4430,a)]. given #986 (F,wt=10): 7485 -->_s0(empty(nil),app(app(nil,app(nil,nil)),false)) # answer(goal). [ur(2220,b,138,a,c,5160,a)]. given #987 (T,wt=8): 4788 ->*_s0(fstsplit(s(x),app(nil,nil)),nil). [ur(87,a,134,a,b,576,a)]. given #988 (T,wt=8): 4816 ->*_s0(sndsplit(0,fstsplit(length(nil),x)),nil). [ur(87,a,82,a,b,4760,a)]. given #989 (T,wt=8): 4818 ->*_s0(app(nil,fstsplit(length(nil),x)),nil). [ur(87,a,61,a,b,4760,a)]. given #990 (T,wt=8): 4820 ->*_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): 7486 -->_s0(empty(nil),app(app(nil,nil),app(nil,false))) # answer(goal). [ur(2220,b,138,a,c,691,a)]. given #993 (F,wt=10): 7487 -->_s0(empty(nil),app(app(nil,nil),sndsplit(0,false))) # answer(goal). [ur(2220,b,138,a,c,637,a)]. given #994 (F,wt=10): 7488 -->_s0(empty(nil),app(nil,app(nil,app(nil,false)))) # answer(goal). [ur(2220,b,137,a,c,691,a)]. given #995 (F,wt=10): 7489 -->_s0(empty(nil),app(nil,app(nil,sndsplit(0,false)))) # answer(goal). [ur(2220,b,137,a,c,637,a)]. given #996 (T,wt=8): 4847 ->*_s0(app(length(nil),x),app(0,x)). [ur(87,a,338,a,b,86,a)]. given #997 (T,wt=8): 4874 ->*_s0(s(leq(s(x),0)),s(false)). [ur(87,a,364,a,b,86,a)]. given #998 (T,wt=8): 4901 ->*_s0(fstsplit(app(nil,length(nil)),x),nil). [ur(87,a,135,a,b,4760,a)]. given #999 (T,wt=8): 4903 ->*_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): 7494 -->_s0(empty(nil),leq(app(nil,s(x)),length(nil))) # answer(goal). [ur(2220,b,131,a,c,4606,a)]. given #1002 (F,wt=10): 7496 -->_s0(empty(nil),leq(s(x),app(nil,length(nil)))) # answer(goal). [ur(2220,b,130,a,c,4606,a)]. given #1003 (F,wt=10): 7499 -->_s0(empty(nil),sndsplit(app(nil,app(nil,0)),false)) # answer(goal). [ur(2220,b,121,a,c,3398,a)]. given #1004 (F,wt=10): 7500 -->_s0(empty(nil),sndsplit(app(nil,0),app(nil,false))) # answer(goal). [ur(2220,b,121,a,c,689,a)]. given #1005 (T,wt=8): 4936 ->*_s0(tail(leq(s(x),0)),tail(false)). [ur(87,a,369,a,b,86,a)]. given #1006 (T,wt=8): 4963 ->*_s0(length(leq(s(x),0)),length(false)). [ur(87,a,382,a,b,86,a)]. given #1007 (T,wt=8): 4990 ->*_s0(head(leq(s(x),0)),head(false)). [ur(87,a,383,a,b,86,a)]. given #1008 (T,wt=8): 5044 ->*_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): 7501 -->_s0(empty(nil),sndsplit(app(nil,0),sndsplit(0,false))) # answer(goal). [ur(2220,b,121,a,c,635,a)]. given #1011 (F,wt=10): 7503 -->_s0(empty(nil),sndsplit(0,app(nil,app(nil,false)))) # answer(goal). [ur(2220,b,120,a,c,689,a)]. given #1012 (F,wt=10): 7504 -->_s0(empty(nil),sndsplit(0,app(nil,sndsplit(0,false)))) # answer(goal). [ur(2220,b,120,a,c,635,a)]. given #1013 (F,wt=10): 7515 -->_s0(empty(nil),tail(cons(x,sndsplit(length(nil),false)))) # answer(goal). [ur(2220,b,85,a,c,4430,a)]. given #1014 (T,wt=8): 5071 ->*_s0(s(sndsplit(s(x),nil)),s(nil)). [ur(87,a,514,a,b,86,a)]. given #1015 (T,wt=8): 5098 ->*_s0(tail(sndsplit(s(x),nil)),tail(nil)). [ur(87,a,519,a,b,86,a)]. given #1016 (T,wt=8): 5126 ->*_s0(length(sndsplit(s(x),nil)),length(nil)). [ur(87,a,532,a,b,86,a)]. given #1017 (T,wt=8): 5158 ->*_s0(app(app(nil,nil),empty(nil)),true). [ur(87,a,138,a,b,630,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): 7526 -->_s0(empty(nil),tail(cons(x,empty(cons(y,z))))) # answer(goal). [ur(2220,b,85,a,c,580,a)]. given #1020 (F,wt=10): 7527 -->_s0(empty(nil),tail(cons(x,head(cons(false,y))))) # answer(goal). [ur(2220,b,85,a,c,575,a)]. given #1021 (F,wt=10): 7528 -->_s0(empty(nil),tail(cons(x,leq(s(y),0)))) # answer(goal). [ur(2220,b,85,a,c,571,a)]. given #1022 (F,wt=10): 7529 -->_s0(empty(nil),tail(cons(x,tail(cons(y,false))))) # answer(goal). [ur(2220,b,85,a,c,564,a)]. given #1023 (T,wt=8): 5159 ->*_s0(app(app(nil,nil),length(nil)),0). [ur(87,a,138,a,b,625,a)]. given #1024 (T,wt=8): 5213 ->*_s0(head(sndsplit(s(x),nil)),head(nil)). [ur(87,a,533,a,b,86,a)]. given #1025 (T,wt=8): 5240 ->*_s0(empty(sndsplit(s(x),nil)),empty(nil)). [ur(87,a,536,a,b,86,a)]. given #1026 (T,wt=8): 5309 ->*_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): 7530 -->_s0(empty(nil),sndsplit(s(length(nil)),cons(x,false))) # answer(goal). [ur(2220,b,83,a,c,4430,a)]. given #1029 (F,wt=10): 7535 -->_s0(empty(nil),sndsplit(0,app(app(nil,nil),false))) # answer(goal). [ur(2220,b,82,a,c,5160,a)]. given #1030 (F,wt=10): 7536 -->_s0(empty(nil),sndsplit(0,leq(s(x),length(nil)))) # answer(goal). [ur(2220,b,82,a,c,4606,a)]. given #1031 (F,wt=10): 7538 -->_s0(empty(nil),sndsplit(0,sndsplit(app(nil,0),false))) # answer(goal). [ur(2220,b,82,a,c,3398,a)]. given #1032 (T,wt=8): 5347 ->*_s0(tail(tail(cons(x,y))),tail(y)). [ur(87,a,544,a,b,86,a)]. given #1033 (T,wt=8): 5390 ->*_s0(length(tail(cons(x,y))),length(y)). [ur(87,a,557,a,b,86,a)]. given #1034 (T,wt=8): 5470 ->*_s0(head(tail(cons(x,y))),head(y)). [ur(87,a,558,a,b,86,a)]. given #1035 (T,wt=8): 5513 ->*_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): 7540 -->_s0(empty(nil),sndsplit(0,sndsplit(0,app(nil,false)))) # answer(goal). [ur(2220,b,82,a,c,689,a)]. given #1038 (F,wt=10): 7543 -->_s0(empty(nil),sndsplit(0,sndsplit(0,sndsplit(0,false)))) # answer(goal). [ur(2220,b,82,a,c,635,a)]. given #1039 (F,wt=10): 7549 -->_s0(empty(nil),leq(s(s(x)),s(length(nil)))) # answer(goal). [ur(2220,b,72,a,c,4606,a)]. given #1040 (F,wt=10): 7553 -->_s0(empty(nil),head(cons(sndsplit(length(nil),false),x))) # answer(goal). [ur(2220,b,67,a,c,4430,a)]. given #1041 (T,wt=8): 5776 ->*_s0(tail(app(cons(x,nil),y)),y). [ur(87,a,94,a,b,688,a)]. given #1042 (T,wt=8): 5837 ->*_s0(s(s(empty(nil))),s(s(true))). [ur(87,a,693,a,b,86,a)]. given #1043 (T,wt=8): 5864 ->*_s0(tail(s(empty(nil))),tail(s(true))). [ur(87,a,698,a,b,86,a)]. given #1044 (T,wt=8): 5891 ->*_s0(length(s(empty(nil))),length(s(true))). [ur(87,a,711,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): 7564 -->_s0(empty(nil),head(cons(empty(cons(x,y)),z))) # answer(goal). [ur(2220,b,67,a,c,580,a)]. given #1047 (F,wt=10): 7565 -->_s0(empty(nil),head(cons(head(cons(false,x)),y))) # answer(goal). [ur(2220,b,67,a,c,575,a)]. given #1048 (F,wt=10): 7566 -->_s0(empty(nil),head(cons(leq(s(x),0),y))) # answer(goal). [ur(2220,b,67,a,c,571,a)]. given #1049 (F,wt=10): 7567 -->_s0(empty(nil),head(cons(tail(cons(x,false)),y))) # answer(goal). [ur(2220,b,67,a,c,564,a)]. given #1050 (T,wt=8): 5918 ->*_s0(head(s(empty(nil))),head(s(true))). [ur(87,a,712,a,b,86,a)]. given #1051 (T,wt=8): 5972 ->*_s0(empty(s(empty(nil))),empty(s(true))). [ur(87,a,715,a,b,86,a)]. given #1052 (T,wt=8): 5999 ->*_s0(s(tail(empty(nil))),s(tail(true))). [ur(87,a,752,a,b,86,a)]. given #1053 (T,wt=8): 6026 ->*_s0(tail(tail(empty(nil))),tail(tail(true))). [ur(87,a,757,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): 7568 -->_s0(empty(nil),app(nil,app(app(nil,nil),false))) # answer(goal). [ur(2220,b,61,a,c,5160,a)]. given #1056 (F,wt=10): 7569 -->_s0(empty(nil),app(nil,leq(s(x),length(nil)))) # answer(goal). [ur(2220,b,61,a,c,4606,a)]. given #1057 (F,wt=10): 7571 -->_s0(empty(nil),app(nil,sndsplit(app(nil,0),false))) # answer(goal). [ur(2220,b,61,a,c,3398,a)]. given #1058 (F,wt=10): 7573 -->_s0(empty(nil),app(nil,sndsplit(0,app(nil,false)))) # answer(goal). [ur(2220,b,61,a,c,689,a)]. given #1059 (T,wt=8): 6053 ->*_s0(length(tail(empty(nil))),length(tail(true))). [ur(87,a,770,a,b,86,a)]. given #1060 (T,wt=8): 6107 ->*_s0(head(tail(empty(nil))),head(tail(true))). [ur(87,a,771,a,b,86,a)]. given #1061 (T,wt=8): 6134 ->*_s0(empty(tail(empty(nil))),empty(tail(true))). [ur(87,a,774,a,b,86,a)]. given #1062 (T,wt=8): 6161 ->*_s0(s(length(empty(nil))),s(length(true))). [ur(87,a,778,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): 7576 -->_s0(empty(nil),app(nil,sndsplit(0,sndsplit(0,false)))) # answer(goal). [ur(2220,b,61,a,c,635,a)]. given #1065 (F,wt=10): 7925 -->_s0(true,app(nil,sndsplit(0,tail(cons(x,false))))) # answer(goal). [resolve(1057,a,2496,b)]. given #1066 (F,wt=10): 7927 -->_s0(true,sndsplit(0,sndsplit(0,tail(cons(x,false))))) # answer(goal). [resolve(1057,a,2479,b)]. given #1067 (F,wt=10): 7941 -->_s0(empty(nil),sndsplit(length(nil),tail(cons(x,false)))) # answer(goal). [ur(2220,b,321,a,c,1057,a)]. given #1068 (T,wt=8): 6188 ->*_s0(tail(length(empty(nil))),tail(length(true))). [ur(87,a,783,a,b,86,a)]. given #1069 (T,wt=8): 6242 ->*_s0(length(length(empty(nil))),length(length(true))). [ur(87,a,796,a,b,86,a)]. given #1070 (T,wt=8): 6269 ->*_s0(head(length(empty(nil))),head(length(true))). [ur(87,a,797,a,b,86,a)]. given #1071 (T,wt=8): 6296 ->*_s0(empty(length(empty(nil))),empty(length(true))). [ur(87,a,800,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=8): 10875 -->_s0(nil,fstsplit(s(x),cons(y,z))) # answer(goal). [resolve(236,a,2423,b),unit_del(b,580)]. given #1074 (F,wt=10): 7947 -->_s0(true,sndsplit(app(nil,0),tail(cons(x,false)))) # answer(goal). [ur(2105,b,121,a,c,1057,a)]. given #1075 (F,wt=10): 7948 -->_s0(true,sndsplit(0,app(nil,tail(cons(x,false))))) # answer(goal). [ur(2105,b,120,a,c,1057,a)]. given #1076 (F,wt=10): 7951 -->_s0(true,app(nil,app(nil,tail(cons(x,false))))) # answer(goal). [resolve(1059,a,2496,b)]. given #1077 (T,wt=8): 6323 ->*_s0(s(head(empty(nil))),s(head(true))). [ur(87,a,804,a,b,86,a)]. given #1078 (T,wt=8): 6377 ->*_s0(tail(head(empty(nil))),tail(head(true))). [ur(87,a,809,a,b,86,a)]. given #1079 (T,wt=8): 6404 ->*_s0(length(head(empty(nil))),length(head(true))). [ur(87,a,822,a,b,86,a)]. given #1080 (T,wt=8): 6431 ->*_s0(head(head(empty(nil))),head(head(true))). [ur(87,a,823,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): 7966 -->_s0(true,app(app(nil,nil),tail(cons(x,false)))) # answer(goal). [ur(2105,b,138,a,c,1059,a)]. given #1083 (F,wt=10): 7991 -->_s0(true,app(app(nil,nil),empty(cons(x,y)))) # answer(goal). [ur(2105,b,162,a,c,5160,a)]. given #1084 (F,wt=10): 8010 -->_s0(true,app(nil,sndsplit(0,leq(s(x),0)))) # answer(goal). [resolve(1069,a,2496,b)]. given #1085 (F,wt=10): 8012 -->_s0(true,sndsplit(0,sndsplit(0,leq(s(x),0)))) # answer(goal). [resolve(1069,a,2479,b)]. given #1086 (T,wt=8): 6458 ->*_s0(empty(head(empty(nil))),empty(head(true))). [ur(87,a,826,a,b,86,a)]. given #1087 (T,wt=8): 6527 ->*_s0(s(empty(empty(nil))),s(empty(true))). [ur(87,a,830,a,b,86,a)]. given #1088 (T,wt=8): 6554 ->*_s0(tail(empty(empty(nil))),tail(empty(true))). [ur(87,a,835,a,b,86,a)]. given #1089 (T,wt=8): 6581 ->*_s0(length(empty(empty(nil))),length(empty(true))). [ur(87,a,848,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): 8026 -->_s0(empty(nil),sndsplit(length(nil),leq(s(x),0))) # answer(goal). [ur(2220,b,321,a,c,1069,a)]. given #1092 (F,wt=10): 8032 -->_s0(true,sndsplit(app(nil,0),leq(s(x),0))) # answer(goal). [ur(2105,b,121,a,c,1069,a)]. given #1093 (F,wt=10): 8033 -->_s0(true,sndsplit(0,app(nil,leq(s(x),0)))) # answer(goal). [ur(2105,b,120,a,c,1069,a)]. given #1094 (F,wt=10): 8037 -->_s0(true,app(nil,leq(s(s(x)),s(0)))) # answer(goal). [resolve(1070,a,2496,b)]. given #1095 (T,wt=8): 6608 ->*_s0(head(empty(empty(nil))),head(empty(true))). [ur(87,a,849,a,b,86,a)]. given #1096 (T,wt=8): 6662 ->*_s0(empty(empty(empty(nil))),empty(empty(true))). [ur(87,a,852,a,b,86,a)]. given #1097 (T,wt=8): 6689 ->*_s0(s(s(length(nil))),s(s(0))). [ur(87,a,889,a,b,86,a)]. given #1098 (T,wt=8): 6716 ->*_s0(tail(s(length(nil))),tail(s(0))). [ur(87,a,894,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): 8039 -->_s0(true,sndsplit(0,leq(s(s(x)),s(0)))) # answer(goal). [resolve(1070,a,2479,b)]. given #1101 (F,wt=10): 8057 -->_s0(true,leq(app(nil,s(s(x))),s(0))) # answer(goal). [ur(2105,b,131,a,c,1070,a)]. given #1102 (F,wt=10): 8058 -->_s0(true,leq(s(s(x)),app(nil,s(0)))) # answer(goal). [ur(2105,b,130,a,c,1070,a)]. given #1103 (F,wt=10): 8059 -->_s0(true,leq(s(s(s(x))),s(s(0)))) # answer(goal). [ur(2105,b,72,a,c,1070,a)]. given #1104 (T,wt=8): 6743 ->*_s0(length(s(length(nil))),length(s(0))). [ur(87,a,907,a,b,86,a)]. given #1105 (T,wt=8): 6797 ->*_s0(head(s(length(nil))),head(s(0))). [ur(87,a,908,a,b,86,a)]. given #1106 (T,wt=8): 6824 ->*_s0(empty(s(length(nil))),empty(s(0))). [ur(87,a,911,a,b,86,a)]. given #1107 (T,wt=8): 6851 ->*_s0(s(tail(length(nil))),s(tail(0))). [ur(87,a,915,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): 8083 -->_s0(true,app(nil,app(nil,leq(s(x),0)))) # answer(goal). [resolve(1072,a,2496,b)]. given #1110 (F,wt=10): 8097 -->_s0(true,app(app(nil,nil),leq(s(x),0))) # answer(goal). [ur(2105,b,138,a,c,1072,a)]. given #1111 (F,wt=10): 8100 -->_s0(true,app(nil,sndsplit(0,head(cons(false,x))))) # answer(goal). [resolve(1112,a,2496,b)]. given #1112 (F,wt=10): 8102 -->_s0(true,sndsplit(0,sndsplit(0,head(cons(false,x))))) # answer(goal). [resolve(1112,a,2479,b)]. given #1113 (T,wt=8): 6878 ->*_s0(tail(tail(length(nil))),tail(tail(0))). [ur(87,a,920,a,b,86,a)]. given #1114 (T,wt=8): 6932 ->*_s0(length(tail(length(nil))),length(tail(0))). [ur(87,a,933,a,b,86,a)]. given #1115 (T,wt=8): 6959 ->*_s0(head(tail(length(nil))),head(tail(0))). [ur(87,a,934,a,b,86,a)]. given #1116 (T,wt=8): 6986 ->*_s0(empty(tail(length(nil))),empty(tail(0))). [ur(87,a,937,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): 8116 -->_s0(empty(nil),sndsplit(length(nil),head(cons(false,x)))) # answer(goal). [ur(2220,b,321,a,c,1112,a)]. given #1119 (F,wt=10): 8122 -->_s0(true,sndsplit(app(nil,0),head(cons(false,x)))) # answer(goal). [ur(2105,b,121,a,c,1112,a)]. given #1120 (F,wt=10): 8123 -->_s0(true,sndsplit(0,app(nil,head(cons(false,x))))) # answer(goal). [ur(2105,b,120,a,c,1112,a)]. given #1121 (F,wt=10): 8126 -->_s0(true,app(nil,app(nil,head(cons(false,x))))) # answer(goal). [resolve(1114,a,2496,b)]. given #1122 (T,wt=8): 7013 ->*_s0(s(length(length(nil))),s(length(0))). [ur(87,a,941,a,b,86,a)]. given #1123 (T,wt=8): 7067 ->*_s0(tail(length(length(nil))),tail(length(0))). [ur(87,a,946,a,b,86,a)]. given #1124 (T,wt=8): 7094 ->*_s0(length(length(length(nil))),length(length(0))). [ur(87,a,959,a,b,86,a)]. given #1125 (T,wt=8): 7121 ->*_s0(head(length(length(nil))),head(length(0))). [ur(87,a,960,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): 8141 -->_s0(true,app(app(nil,nil),head(cons(false,x)))) # answer(goal). [ur(2105,b,138,a,c,1114,a)]. given #1128 (F,wt=10): 8179 -->_s0(true,app(nil,sndsplit(0,empty(cons(x,y))))) # answer(goal). [resolve(1125,a,2496,b)]. given #1129 (F,wt=10): 8181 -->_s0(true,sndsplit(0,sndsplit(0,empty(cons(x,y))))) # answer(goal). [resolve(1125,a,2479,b)]. given #1130 (F,wt=10): 8197 -->_s0(true,sndsplit(0,app(nil,empty(cons(x,y))))) # answer(goal). [ur(2105,b,120,a,c,1125,a)]. given #1131 (T,wt=8): 7148 ->*_s0(empty(length(length(nil))),empty(length(0))). [ur(87,a,963,a,b,86,a)]. given #1132 (T,wt=8): 7586 ->*_s0(s(head(length(nil))),s(head(0))). [ur(87,a,967,a,b,86,a)]. given #1133 (T,wt=8): 7614 ->*_s0(tail(head(length(nil))),tail(head(0))). [ur(87,a,972,a,b,86,a)]. given #1134 (T,wt=8): 7642 ->*_s0(length(head(length(nil))),length(head(0))). [ur(87,a,985,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): 8200 -->_s0(true,app(nil,app(nil,empty(cons(x,y))))) # answer(goal). [resolve(1127,a,2496,b)]. given #1137 (F,wt=10): 8562 -->_s0(nil,empty(length(nil))) | -->*_s0(empty(empty(0)),false) # answer(goal). [resolve(2423,b,1049,a)]. given #1138 (F,wt=10): 8563 -->_s0(nil,head(length(nil))) | -->*_s0(empty(head(0)),false) # answer(goal). [resolve(2423,b,989,a)]. given #1139 (F,wt=10): 8564 -->_s0(nil,length(length(nil))) | -->*_s0(empty(length(0)),false) # answer(goal). [resolve(2423,b,963,a)]. given #1140 (T,wt=8): 7670 ->*_s0(head(head(length(nil))),head(head(0))). [ur(87,a,986,a,b,86,a)]. given #1141 (T,wt=8): 7729 ->*_s0(empty(head(length(nil))),empty(head(0))). [ur(87,a,989,a,b,86,a)]. given #1142 (T,wt=8): 7757 ->*_s0(s(empty(length(nil))),s(empty(0))). [ur(87,a,1027,a,b,86,a)]. given #1143 (T,wt=8): 7785 ->*_s0(tail(empty(length(nil))),tail(empty(0))). [ur(87,a,1032,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): 8565 -->_s0(nil,tail(length(nil))) | -->*_s0(empty(tail(0)),false) # answer(goal). [resolve(2423,b,937,a)]. given #1146 (F,wt=10): 8566 -->_s0(nil,s(length(nil))) | -->*_s0(empty(s(0)),false) # answer(goal). [resolve(2423,b,911,a)]. given #1147 (F,wt=10): 8567 -->_s0(nil,empty(empty(nil))) | -->*_s0(empty(empty(true)),false) # answer(goal). [resolve(2423,b,852,a)]. given #1148 (F,wt=10): 8568 -->_s0(nil,head(empty(nil))) | -->*_s0(empty(head(true)),false) # answer(goal). [resolve(2423,b,826,a)]. given #1149 (T,wt=8): 7813 ->*_s0(length(empty(length(nil))),length(empty(0))). [ur(87,a,1045,a,b,86,a)]. given #1150 (T,wt=8): 7869 ->*_s0(head(empty(length(nil))),head(empty(0))). [ur(87,a,1046,a,b,86,a)]. given #1151 (T,wt=8): 7897 ->*_s0(empty(empty(length(nil))),empty(empty(0))). [ur(87,a,1049,a,b,86,a)]. given #1152 (T,wt=8): 8723 ->*_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): 8569 -->_s0(nil,length(empty(nil))) | -->*_s0(empty(length(true)),false) # answer(goal). [resolve(2423,b,800,a)]. given #1155 (F,wt=10): 8570 -->_s0(nil,tail(empty(nil))) | -->*_s0(empty(tail(true)),false) # answer(goal). [resolve(2423,b,774,a)]. given #1156 (F,wt=10): 8571 -->_s0(nil,s(empty(nil))) | -->*_s0(empty(s(true)),false) # answer(goal). [resolve(2423,b,715,a)]. given #1157 (F,wt=10): 8572 -->_s0(nil,tail(cons(x,y))) | -->*_s0(empty(y),false) # answer(goal). [resolve(2423,b,561,a)]. given #1158 (T,wt=8): 9461 ->*_s0(fstsplit(s(x),fstsplit(0,y)),nil). [ur(87,a,209,a,b,576,a)]. given #1159 (T,wt=8): 9715 ->*_s0(app(fstsplit(0,x),empty(nil)),true). [ur(87,a,213,a,b,630,a)]. given #1160 (T,wt=8): 9716 ->*_s0(app(fstsplit(0,x),length(nil)),0). [ur(87,a,213,a,b,625,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): 8574 -->_s0(nil,leq(s(x),0)) | -->*_s0(empty(false),false) # answer(goal). [resolve(2423,b,386,a)]. given #1164 (F,wt=10): 8577 -->_s0(nil,head(cons(x,y))) | -->*_s0(empty(x),false) # answer(goal). [resolve(2423,b,286,a)]. given #1165 (F,wt=10): 8579 -->_s0(nil,empty(cons(x,y))) | -->*_s0(empty(false),false) # answer(goal). [resolve(2423,b,161,a)]. given #1166 (F,wt=10): 8581 -->_s0(nil,x) | -->*_s0(empty(y),false) | -->_s0(x,y) # answer(goal). [resolve(2423,b,37,b)]. given #1167 (T,wt=9): 341 ->_s0(f(leq(0,x),y),f(true,y)). [ur(57,a,70,a)]. given #1168 (T,wt=9): 342 ->_s0(cons(x,leq(0,y)),cons(x,true)). [ur(56,a,70,a)]. given #1169 (T,wt=9): 343 ->_s0(cons(leq(0,x),y),cons(true,y)). [ur(55,a,70,a)]. given #1170 (T,wt=9): 345 ->_s0(sndsplit(x,leq(0,y)),sndsplit(x,true)). [ur(53,a,70,a)]. given #1171 (A,wt=18): 249 ->_s0(ring(x,y,z,fstsplit(s(u),nil),w,v5),ring(x,y,z,nil,w,v5)). [ur(49,a,66,a)]. given #1172 (F,wt=8): 11280 -->_s0(nil,x) | -->_s0(x,cons(y,z)) # answer(goal). [resolve(8581,b,580,a)]. given #1173 (F,wt=8): 11558 -->_s0(nil,sndsplit(length(nil),cons(x,y))) # answer(goal). [ur(8581,b,2350,a,c,321,a)]. given #1174 (F,wt=9): 11501 -->_s0(nil,app(app(cons(x,y),z),u)) # answer(goal). [resolve(8581,c,113,a),unit_del(b,2778)]. given #1175 (F,wt=9): 11557 -->_s0(nil,app(app(nil,cons(x,y)),z)) # answer(goal). [ur(8581,b,2778,a,c,138,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): 11560 -->_s0(nil,sndsplit(app(nil,0),cons(x,y))) # answer(goal). [ur(8581,b,2350,a,c,121,a)]. given #1182 (F,wt=9): 11563 -->_s0(nil,app(fstsplit(0,x),cons(y,z))) # answer(goal). [ur(8581,b,1532,a,c,213,a)]. given #1183 (F,wt=9): 11564 -->_s0(nil,app(app(nil,nil),cons(x,y))) # answer(goal). [ur(8581,b,1532,a,c,138,a)]. given #1184 (F,wt=10): 8584 -->_s0(nil,x) | -->_s0(empty(x),sndsplit(length(nil),false)) # answer(goal). [resolve(2423,c,4430,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): 8604 -->_s0(nil,x) | -->_s0(empty(x),empty(cons(y,z))) # answer(goal). [resolve(2423,c,580,a)]. given #1191 (F,wt=10): 8605 -->_s0(nil,x) | -->_s0(empty(x),head(cons(false,y))) # answer(goal). [resolve(2423,c,575,a)]. given #1192 (F,wt=10): 8606 -->_s0(nil,x) | -->_s0(empty(x),leq(s(y),0)) # answer(goal). [resolve(2423,c,571,a)]. given #1193 (F,wt=10): 8607 -->_s0(nil,x) | -->_s0(empty(x),tail(cons(y,false))) # answer(goal). [resolve(2423,c,564,a)]. given #1194 (T,wt=9): 363 ->_s0(app(leq(0,x),y),app(true,y)). [ur(35,a,70,a)]. given #1195 (T,wt=9): 440 ->_s0(f(x,mapf(y,nil)),f(x,nil)). [ur(58,a,74,a)]. given #1196 (T,wt=9): 441 ->_s0(f(mapf(x,nil),y),f(nil,y)). [ur(57,a,74,a)]. given #1197 (T,wt=9): 442 ->_s0(cons(x,mapf(y,nil)),cons(x,nil)). [ur(56,a,74,a)]. given #1198 (A,wt=18): 252 ->_s0(ring(fstsplit(s(x),nil),y,z,u,w,v5),ring(nil,y,z,u,w,v5)). [ur(46,a,66,a)]. given #1199 (F,wt=10): 8637 -->_s0(true,app(nil,tail(app(nil,cons(x,false))))) # answer(goal). [resolve(1327,a,2496,b)]. given #1200 (F,wt=10): 8639 -->_s0(true,sndsplit(0,tail(app(nil,cons(x,false))))) # answer(goal). [resolve(1327,a,2479,b)]. given #1201 (F,wt=10): 8662 -->_s0(true,tail(sndsplit(0,app(nil,cons(x,false))))) # answer(goal). [ur(2105,b,469,a,c,1327,a)]. given #1202 (F,wt=10): 8664 -->_s0(true,tail(app(nil,app(nil,cons(x,false))))) # answer(goal). [ur(2105,b,119,a,c,1327,a)]. 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): 11767 ->*_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): 8770 -->_s0(true,app(nil,head(app(nil,cons(false,x))))) # answer(goal). [resolve(1502,a,2496,b)]. given #1209 (F,wt=10): 8772 -->_s0(true,sndsplit(0,head(app(nil,cons(false,x))))) # answer(goal). [resolve(1502,a,2479,b)]. given #1210 (F,wt=10): 8795 -->_s0(true,head(sndsplit(0,app(nil,cons(false,x))))) # answer(goal). [ur(2105,b,483,a,c,1502,a)]. given #1211 (F,wt=10): 8797 -->_s0(true,head(app(nil,app(nil,cons(false,x))))) # answer(goal). [ur(2105,b,133,a,c,1502,a)]. given #1212 (T,wt=8): 11796 ->*_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): 11813 ->*_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): 8844 -->_s0(true,app(nil,empty(app(nil,cons(x,y))))) # answer(goal). [resolve(1532,a,2496,b)]. given #1218 (F,wt=10): 8846 -->_s0(true,sndsplit(0,empty(app(nil,cons(x,y))))) # answer(goal). [resolve(1532,a,2479,b)]. given #1219 (F,wt=10): 8848 -->_s0(true,empty(sndsplit(0,app(nil,cons(x,y))))) # answer(goal). [resolve(1532,a,2424,b)]. given #1220 (F,wt=10): 8863 -->_s0(nil,tail(cons(x,app(nil,cons(y,z))))) # answer(goal). [ur(2423,b,561,a,c,1532,a)]. given #1221 (T,wt=9): 455 ->_s0(leq(x,mapf(y,nil)),leq(x,nil)). [ur(43,a,74,a)]. given #1222 (T,wt=9): 456 ->_s0(leq(mapf(x,nil),y),leq(nil,y)). [ur(42,a,74,a)]. given #1223 (T,wt=9): 459 ->_s0(fstsplit(x,mapf(y,nil)),fstsplit(x,nil)). [ur(39,a,74,a)]. given #1224 (T,wt=8): 11876 ->*_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): 8864 -->_s0(nil,head(cons(app(nil,cons(x,y)),z))) # answer(goal). [ur(2423,b,286,a,c,1532,a)]. given #1227 (F,wt=10): 8873 -->_s0(true,empty(app(nil,app(nil,cons(x,y))))) # answer(goal). [ur(2105,b,136,a,c,1532,a)]. given #1228 (F,wt=10): 9075 -->_s0(true,app(nil,tail(sndsplit(0,cons(x,false))))) # answer(goal). [resolve(2223,a,2496,b)]. given #1229 (F,wt=10): 9077 -->_s0(true,sndsplit(0,tail(sndsplit(0,cons(x,false))))) # answer(goal). [resolve(2223,a,2479,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): 11966 ->*_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): 11922 -->_s0(true,app(mapf(x,nil),app(nil,false))) # answer(goal). [resolve(463,a,2748,b)]. given #1236 (F,wt=9): 11923 -->_s0(true,app(mapf(x,nil),sndsplit(0,false))) # answer(goal). [resolve(463,a,2591,b)]. given #1237 (F,wt=9): 11973 -->_s0(nil,app(mapf(x,nil),cons(y,z))) # answer(goal). [ur(8581,b,1532,a,c,463,a)]. given #1238 (F,wt=9): 11991 -->_s0(true,app(nil,app(mapf(x,nil),false))) # answer(goal). [resolve(11966,a,2496,b)]. given #1239 (T,wt=8): 11964 ->*_s0(app(mapf(x,nil),empty(nil)),true). [ur(87,a,463,a,b,630,a)]. given #1240 (T,wt=8): 11965 ->*_s0(app(mapf(x,nil),length(nil)),0). [ur(87,a,463,a,b,625,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): 11993 -->_s0(true,sndsplit(0,app(mapf(x,nil),false))) # answer(goal). [resolve(11966,a,2479,b)]. given #1245 (F,wt=9): 12007 -->_s0(true,app(app(nil,mapf(x,nil)),false)) # answer(goal). [ur(2105,b,138,a,c,11966,a)]. given #1246 (F,wt=10): 9079 -->_s0(true,tail(app(nil,sndsplit(0,cons(x,false))))) # answer(goal). [resolve(2223,a,2455,b)]. given #1247 (F,wt=10): 9080 -->_s0(true,tail(sndsplit(0,sndsplit(0,cons(x,false))))) # answer(goal). [resolve(2223,a,2427,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): 12110 ->*_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): 9118 -->_s0(true,sndsplit(0,x)) | -->_s0(x,sndsplit(0,false)) # answer(goal). [resolve(2577,b,53,b)]. given #1254 (F,wt=10): 9119 -->_s0(true,sndsplit(x,sndsplit(0,false))) | -->_s0(x,0) # answer(goal). [resolve(2577,b,52,b)]. given #1255 (F,wt=9): 12139 -->_s0(true,sndsplit(sndsplit(0,0),sndsplit(0,false))) # answer(goal). [resolve(9119,b,82,a)]. given #1256 (F,wt=10): 9175 -->_s0(true,app(nil,x)) | -->_s0(x,sndsplit(0,false)) # answer(goal). [resolve(2591,b,36,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): 12211 ->*_s0(sndsplit(sndsplit(0,0),x),x). [ur(87,a,471,a,b,567,a)]. given #1259 (T,wt=8): 12159 ->*_s0(sndsplit(sndsplit(0,length(nil)),x),x). [ur(87,a,471,a,b,4430,a)]. given #1260 (T,wt=8): 12209 ->*_s0(sndsplit(sndsplit(0,0),empty(nil)),true). [ur(87,a,471,a,b,628,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): 12143 -->_s0(true,app(nil,sndsplit(sndsplit(0,0),false))) # answer(goal). [resolve(471,a,9175,b)]. given #1263 (F,wt=9): 12144 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,0),false))) # answer(goal). [resolve(471,a,9118,b)]. given #1264 (F,wt=9): 12146 -->_s0(empty(nil),sndsplit(sndsplit(0,length(nil)),false)) # answer(goal). [resolve(471,a,7440,b)]. given #1265 (F,wt=9): 12147 -->_s0(true,sndsplit(sndsplit(0,app(nil,0)),false)) # answer(goal). [resolve(471,a,3430,b)]. given #1266 (T,wt=8): 12210 ->*_s0(sndsplit(sndsplit(0,0),length(nil)),0). [ur(87,a,471,a,b,623,a)]. given #1267 (T,wt=8): 12212 ->*_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): 12337 ->*_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): 12148 -->_s0(true,sndsplit(sndsplit(0,0),app(nil,false))) # answer(goal). [resolve(471,a,2701,b)]. given #1272 (F,wt=9): 12219 -->_s0(nil,sndsplit(sndsplit(0,0),cons(x,y))) # answer(goal). [ur(8581,b,2350,a,c,471,a)]. given #1273 (F,wt=9): 12263 -->_s0(true,sndsplit(sndsplit(0,sndsplit(0,0)),false)) # answer(goal). [ur(2105,b,471,a,c,12211,a)]. given #1274 (F,wt=9): 12264 -->_s0(true,sndsplit(app(nil,sndsplit(0,0)),false)) # answer(goal). [ur(2105,b,121,a,c,12211,a)]. given #1275 (T,wt=8): 12395 ->*_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): 12460 ->*_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): 12446 -->_s0(empty(nil),leq(s(x),sndsplit(0,0))) # answer(goal). [resolve(480,a,7454,b)]. given #1281 (F,wt=9): 12447 -->_s0(true,leq(s(x),sndsplit(0,length(nil)))) # answer(goal). [resolve(480,a,4637,b)]. given #1282 (F,wt=10): 9176 -->_s0(true,app(x,sndsplit(0,false))) | -->_s0(x,nil) # answer(goal). [resolve(2591,b,35,b)]. given #1283 (F,wt=9): 12511 -->_s0(true,app(sndsplit(0,nil),sndsplit(0,false))) # answer(goal). [resolve(9176,b,82,a)]. given #1284 (T,wt=9): 481 ->_s0(leq(sndsplit(0,x),y),leq(x,y)). [ur(42,a,82,a)]. given #1285 (T,wt=7): 12533 ->*_s0(leq(sndsplit(0,0),x),true). [ur(87,a,481,a,b,572,a)]. given #1286 (T,wt=8): 12525 ->*_s0(leq(sndsplit(0,length(nil)),x),true). [ur(87,a,481,a,b,4651,a)]. given #1287 (T,wt=8): 12534 ->*_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): 12514 -->_s0(empty(nil),leq(sndsplit(0,s(x)),0)) # answer(goal). [resolve(481,a,7454,b)]. given #1290 (F,wt=9): 12515 -->_s0(true,leq(sndsplit(0,s(x)),length(nil))) # answer(goal). [resolve(481,a,4637,b)]. given #1291 (F,wt=10): 9179 -->_s0(true,length(nil)) | -->_s0(0,sndsplit(length(nil),false)) # answer(goal). [resolve(2634,c,4430,a)]. given #1292 (F,wt=10): 9204 -->_s0(true,length(nil)) | -->_s0(0,empty(cons(x,y))) # answer(goal). [resolve(2634,c,580,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): 12620 ->*_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): 12648 ->*_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): 9205 -->_s0(true,length(nil)) | -->_s0(0,head(cons(false,x))) # answer(goal). [resolve(2634,c,575,a)]. given #1299 (F,wt=10): 9206 -->_s0(true,length(nil)) | -->_s0(0,leq(s(x),0)) # answer(goal). [resolve(2634,c,571,a)]. given #1300 (F,wt=10): 9208 -->_s0(true,length(nil)) | -->_s0(0,tail(cons(x,false))) # answer(goal). [resolve(2634,c,564,a)]. given #1301 (F,wt=10): 9262 -->_s0(true,sndsplit(0,x)) | -->_s0(x,app(nil,false)) # answer(goal). [resolve(2701,b,53,b)]. given #1302 (T,wt=8): 12644 ->*_s0(fstsplit(sndsplit(0,length(nil)),x),nil). [ur(87,a,485,a,b,4760,a)]. given #1303 (T,wt=8): 12649 ->*_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): 12697 -->_s0(true,sndsplit(0,app(sndsplit(0,nil),false))) # answer(goal). [resolve(488,a,9262,b)]. given #1308 (F,wt=9): 12699 -->_s0(true,app(sndsplit(0,app(nil,nil)),false)) # answer(goal). [resolve(488,a,5200,b)]. given #1309 (F,wt=9): 12700 -->_s0(true,app(sndsplit(0,nil),app(nil,false))) # answer(goal). [resolve(488,a,2748,b)]. given #1310 (F,wt=9): 12762 -->_s0(nil,app(sndsplit(0,cons(x,y)),z)) # answer(goal). [ur(8581,b,2778,a,c,488,a)]. given #1311 (T,wt=7): 12755 ->*_s0(app(sndsplit(0,nil),x),x). [ur(87,a,488,a,b,581,a)]. given #1312 (T,wt=8): 12753 ->*_s0(app(sndsplit(0,nil),empty(nil)),true). [ur(87,a,488,a,b,630,a)]. given #1313 (T,wt=8): 12754 ->*_s0(app(sndsplit(0,nil),length(nil)),0). [ur(87,a,488,a,b,625,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): 12763 -->_s0(nil,app(sndsplit(0,nil),cons(x,y))) # answer(goal). [ur(8581,b,1532,a,c,488,a)]. given #1317 (F,wt=9): 12776 -->_s0(true,app(sndsplit(0,mapf(x,nil)),false)) # answer(goal). [ur(2105,b,488,a,c,11966,a)]. given #1318 (F,wt=9): 12777 -->_s0(true,app(sndsplit(0,fstsplit(0,x)),false)) # answer(goal). [ur(2105,b,488,a,c,9717,a)]. given #1319 (F,wt=9): 12795 -->_s0(true,app(nil,app(sndsplit(0,nil),false))) # answer(goal). [resolve(12755,a,2496,b)]. given #1320 (T,wt=9): 1056 ->*_s0(tail(cons(x,tail(cons(y,z)))),z). [ur(87,a,85,a,b,564,a)]. given #1321 (T,wt=9): 1058 ->*_s0(head(cons(tail(cons(x,y)),z)),y). [ur(87,a,67,a,b,564,a)]. given #1322 (T,wt=9): 1060 ->*_s0(tail(cons(x,sndsplit(s(y),nil))),nil). [ur(87,a,85,a,b,565,a)]. given #1323 (T,wt=9): 1061 ->*_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): 12811 -->_s0(true,app(sndsplit(0,sndsplit(0,nil)),false)) # answer(goal). [ur(2105,b,488,a,c,12755,a)]. given #1326 (F,wt=9): 12812 -->_s0(true,app(app(nil,sndsplit(0,nil)),false)) # answer(goal). [ur(2105,b,138,a,c,12755,a)]. given #1327 (F,wt=10): 9263 -->_s0(true,sndsplit(x,app(nil,false))) | -->_s0(x,0) # answer(goal). [resolve(2701,b,52,b)]. given #1328 (F,wt=10): 9287 -->_s0(true,app(nil,head(sndsplit(0,cons(false,x))))) # answer(goal). [resolve(2290,a,2496,b)]. given #1329 (T,wt=8): 13053 ->*_s0(sndsplit(head(cons(0,x)),y),y). [ur(87,a,271,a,b,567,a)]. given #1330 (T,wt=9): 1063 ->*_s0(head(cons(sndsplit(s(x),nil),y)),nil). [ur(87,a,67,a,b,565,a)]. given #1331 (T,wt=9): 1068 ->*_s0(tail(cons(x,leq(s(y),0))),false). [ur(87,a,85,a,b,571,a)]. given #1332 (T,wt=9): 1071 ->*_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): 9289 -->_s0(true,sndsplit(0,head(sndsplit(0,cons(false,x))))) # answer(goal). [resolve(2290,a,2479,b)]. given #1335 (F,wt=10): 9291 -->_s0(true,head(app(nil,sndsplit(0,cons(false,x))))) # answer(goal). [resolve(2290,a,2453,b)]. given #1336 (F,wt=10): 9292 -->_s0(true,head(sndsplit(0,sndsplit(0,cons(false,x))))) # answer(goal). [resolve(2290,a,2425,b)]. given #1337 (F,wt=10): 9336 -->_s0(true,app(nil,x)) | -->_s0(x,app(nil,false)) # answer(goal). [resolve(2748,b,36,b)]. given #1338 (T,wt=9): 1111 ->*_s0(tail(cons(x,head(cons(y,z)))),y). [ur(87,a,85,a,b,575,a)]. given #1339 (T,wt=9): 1113 ->*_s0(head(cons(head(cons(x,y)),z)),x). [ur(87,a,67,a,b,575,a)]. given #1340 (T,wt=9): 1115 ->*_s0(tail(cons(x,fstsplit(s(y),nil))),nil). [ur(87,a,85,a,b,576,a)]. given #1341 (T,wt=9): 1117 ->*_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): 9337 -->_s0(true,app(x,app(nil,false))) | -->_s0(x,nil) # answer(goal). [resolve(2748,b,35,b)]. given #1344 (F,wt=10): 9396 -->_s0(true,sndsplit(app(nil,0),x)) | -->_s0(x,false) # answer(goal). [resolve(3430,b,53,b)]. given #1345 (F,wt=10): 9397 -->_s0(true,sndsplit(x,false)) | -->_s0(x,app(nil,0)) # answer(goal). [resolve(3430,b,52,b)]. given #1346 (F,wt=9): 13245 -->_s0(true,sndsplit(app(sndsplit(0,nil),0),false)) # answer(goal). [resolve(9397,b,488,a)]. given #1347 (T,wt=9): 1124 ->*_s0(tail(cons(x,empty(cons(y,z)))),false). [ur(87,a,85,a,b,580,a)]. given #1348 (T,wt=9): 1126 ->*_s0(head(cons(empty(cons(x,y)),z)),false). [ur(87,a,67,a,b,580,a)]. given #1349 (T,wt=9): 1128 ->*_s0(tail(cons(x,sndsplit(0,length(nil)))),0). [ur(87,a,85,a,b,623,a)]. given #1350 (T,wt=9): 1129 ->*_s0(sndsplit(s(0),cons(x,length(nil))),0). [ur(87,a,83,a,b,623,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=9): 13246 -->_s0(true,sndsplit(app(mapf(x,nil),0),false)) # answer(goal). [resolve(9397,b,463,a)]. given #1353 (F,wt=9): 13248 -->_s0(true,sndsplit(app(fstsplit(0,x),0),false)) # answer(goal). [resolve(9397,b,213,a)]. given #1354 (F,wt=9): 13249 -->_s0(true,sndsplit(app(app(nil,nil),0),false)) # answer(goal). [resolve(9397,b,138,a)]. given #1355 (F,wt=10): 9411 -->_s0(true,app(nil,empty(sndsplit(0,cons(x,y))))) # answer(goal). [resolve(2350,a,2496,b)]. given #1356 (T,wt=9): 1131 ->*_s0(head(cons(sndsplit(0,length(nil)),x)),0). [ur(87,a,67,a,b,623,a)]. given #1357 (T,wt=9): 1160 ->*_s0(tail(cons(x,app(nil,length(nil)))),0). [ur(87,a,85,a,b,625,a)]. given #1358 (T,wt=9): 1162 ->*_s0(head(cons(app(nil,length(nil)),x)),0). [ur(87,a,67,a,b,625,a)]. given #1359 (T,wt=9): 1165 ->*_s0(tail(cons(x,sndsplit(0,empty(nil)))),true). [ur(87,a,85,a,b,628,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): 9413 -->_s0(true,sndsplit(0,empty(sndsplit(0,cons(x,y))))) # answer(goal). [resolve(2350,a,2479,b)]. given #1362 (F,wt=10): 9415 -->_s0(true,empty(app(nil,sndsplit(0,cons(x,y))))) # answer(goal). [resolve(2350,a,2452,b)]. given #1363 (F,wt=10): 9416 -->_s0(true,empty(sndsplit(0,sndsplit(0,cons(x,y))))) # answer(goal). [resolve(2350,a,2424,b)]. given #1364 (F,wt=10): 9431 -->_s0(nil,tail(cons(x,sndsplit(0,cons(y,z))))) # answer(goal). [ur(2423,b,561,a,c,2350,a)]. given #1365 (T,wt=9): 1166 ->*_s0(sndsplit(s(0),cons(x,empty(nil))),true). [ur(87,a,83,a,b,628,a)]. given #1366 (T,wt=9): 1168 ->*_s0(head(cons(sndsplit(0,empty(nil)),x)),true). [ur(87,a,67,a,b,628,a)]. given #1367 (T,wt=9): 1171 ->*_s0(tail(cons(x,app(nil,empty(nil)))),true). [ur(87,a,85,a,b,630,a)]. given #1368 (T,wt=9): 1173 ->*_s0(head(cons(app(nil,empty(nil)),x)),true). [ur(87,a,67,a,b,630,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): 9432 -->_s0(nil,head(cons(sndsplit(0,cons(x,y)),z))) # answer(goal). [ur(2423,b,286,a,c,2350,a)]. given #1371 (F,wt=10): 9499 -->_s0(true,app(nil,head(app(cons(false,x),y)))) # answer(goal). [resolve(2606,a,2496,b)]. given #1372 (F,wt=10): 9501 -->_s0(true,sndsplit(0,head(app(cons(false,x),y)))) # answer(goal). [resolve(2606,a,2479,b)]. given #1373 (F,wt=10): 9503 -->_s0(true,head(app(nil,app(cons(false,x),y)))) # answer(goal). [resolve(2606,a,2453,b)]. given #1374 (T,wt=9): 1175 ->*_s0(tail(cons(x,s(empty(nil)))),s(true)). [ur(87,a,85,a,b,692,a)]. given #1375 (T,wt=9): 1177 ->*_s0(head(cons(s(empty(nil)),x)),s(true)). [ur(87,a,67,a,b,692,a)]. given #1376 (T,wt=9): 1207 ->*_s0(tail(cons(x,tail(empty(nil)))),tail(true)). [ur(87,a,85,a,b,751,a)]. given #1377 (T,wt=9): 1209 ->*_s0(head(cons(tail(empty(nil)),x)),tail(true)). [ur(87,a,67,a,b,751,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): 9504 -->_s0(true,head(sndsplit(0,app(cons(false,x),y)))) # answer(goal). [resolve(2606,a,2425,b)]. given #1380 (F,wt=10): 9532 -->_s0(true,app(nil,empty(app(cons(x,y),z)))) # answer(goal). [resolve(2778,a,2496,b)]. given #1381 (F,wt=10): 9534 -->_s0(true,sndsplit(0,empty(app(cons(x,y),z)))) # answer(goal). [resolve(2778,a,2479,b)]. given #1382 (F,wt=10): 9536 -->_s0(true,empty(app(nil,app(cons(x,y),z)))) # answer(goal). [resolve(2778,a,2452,b)]. given #1383 (T,wt=9): 1211 ->*_s0(tail(cons(x,length(empty(nil)))),length(true)). [ur(87,a,85,a,b,777,a)]. given #1384 (T,wt=9): 1213 ->*_s0(head(cons(length(empty(nil)),x)),length(true)). [ur(87,a,67,a,b,777,a)]. given #1385 (T,wt=9): 1215 ->*_s0(tail(cons(x,head(empty(nil)))),head(true)). [ur(87,a,85,a,b,803,a)]. given #1386 (T,wt=9): 1217 ->*_s0(head(cons(head(empty(nil)),x)),head(true)). [ur(87,a,67,a,b,803,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): 9537 -->_s0(true,empty(sndsplit(0,app(cons(x,y),z)))) # answer(goal). [resolve(2778,a,2424,b)]. given #1389 (F,wt=10): 9552 -->_s0(nil,tail(cons(x,app(cons(y,z),u)))) # answer(goal). [ur(2423,b,561,a,c,2778,a)]. given #1390 (F,wt=10): 9553 -->_s0(nil,head(cons(app(cons(x,y),z),u))) # answer(goal). [ur(2423,b,286,a,c,2778,a)]. given #1391 (F,wt=10): 9638 -->_s0(true,leq(s(x),y)) | -->_s0(y,length(nil)) # answer(goal). [resolve(4637,b,43,b)]. given #1392 (T,wt=8): 13414 ->*_s0(mapf(x,head(cons(nil,y))),nil). [ur(87,a,278,a,b,568,a)]. given #1393 (T,wt=9): 1219 ->*_s0(tail(cons(x,empty(empty(nil)))),empty(true)). [ur(87,a,85,a,b,829,a)]. given #1394 (T,wt=9): 1221 ->*_s0(head(cons(empty(empty(nil)),x)),empty(true)). [ur(87,a,67,a,b,829,a)]. given #1395 (T,wt=9): 1249 ->*_s0(tail(cons(x,s(length(nil)))),s(0)). [ur(87,a,85,a,b,888,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=9): 13418 -->_s0(true,leq(s(x),length(sndsplit(0,nil)))) # answer(goal). [resolve(9638,b,482,a)]. given #1398 (F,wt=9): 13419 -->_s0(true,leq(s(x),length(mapf(y,nil)))) # answer(goal). [resolve(9638,b,457,a)]. given #1399 (F,wt=9): 13422 -->_s0(true,leq(s(x),length(fstsplit(0,y)))) # answer(goal). [resolve(9638,b,207,a)]. given #1400 (F,wt=9): 13423 -->_s0(true,leq(s(x),length(app(nil,nil)))) # answer(goal). [resolve(9638,b,132,a)]. given #1401 (T,wt=9): 1252 ->*_s0(head(cons(s(length(nil)),x)),s(0)). [ur(87,a,67,a,b,888,a)]. given #1402 (T,wt=9): 1254 ->*_s0(tail(cons(x,tail(length(nil)))),tail(0)). [ur(87,a,85,a,b,914,a)]. given #1403 (T,wt=9): 1256 ->*_s0(head(cons(tail(length(nil)),x)),tail(0)). [ur(87,a,67,a,b,914,a)]. given #1404 (T,wt=9): 1258 ->*_s0(tail(cons(x,length(length(nil)))),length(0)). [ur(87,a,85,a,b,940,a)]. given #1405 (A,wt=10): 280 ->_s0(leq(x,head(cons(y,z))),leq(x,y)). [ur(43,a,67,a)]. given #1406 (F,wt=10): 9639 -->_s0(true,leq(x,length(nil))) | -->_s0(x,s(y)) # answer(goal). [resolve(4637,b,42,b)]. given #1407 (F,wt=9): 13500 -->_s0(true,leq(length(cons(x,y)),length(nil))) # answer(goal). [resolve(9639,b,68,a)]. given #1408 (F,wt=10): 9640 -->_s0(true,app(app(nil,nil),x)) | -->_s0(x,false) # answer(goal). [resolve(5200,b,36,b)]. given #1409 (F,wt=10): 9641 -->_s0(true,app(x,false)) | -->_s0(x,app(nil,nil)) # answer(goal). [resolve(5200,b,35,b)]. given #1410 (T,wt=9): 1260 ->*_s0(head(cons(length(length(nil)),x)),length(0)). [ur(87,a,67,a,b,940,a)]. given #1411 (T,wt=9): 1262 ->*_s0(tail(cons(x,head(length(nil)))),head(0)). [ur(87,a,85,a,b,966,a)]. given #1412 (T,wt=9): 1264 ->*_s0(head(cons(head(length(nil)),x)),head(0)). [ur(87,a,67,a,b,966,a)]. given #1413 (T,wt=9): 1293 ->*_s0(tail(cons(x,empty(length(nil)))),empty(0)). [ur(87,a,85,a,b,1026,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): 13502 -->_s0(true,app(app(sndsplit(0,nil),nil),false)) # answer(goal). [resolve(9641,b,488,a)]. given #1416 (F,wt=9): 13503 -->_s0(true,app(app(mapf(x,nil),nil),false)) # answer(goal). [resolve(9641,b,463,a)]. given #1417 (F,wt=9): 13505 -->_s0(true,app(app(fstsplit(0,x),nil),false)) # answer(goal). [resolve(9641,b,213,a)]. given #1418 (F,wt=9): 13506 -->_s0(true,app(app(app(nil,nil),nil),false)) # answer(goal). [resolve(9641,b,138,a)]. given #1419 (T,wt=8): 13549 ->*_s0(leq(head(cons(0,x)),y),true). [ur(87,a,281,a,b,572,a)]. given #1420 (T,wt=9): 1295 ->*_s0(head(cons(empty(length(nil)),x)),empty(0)). [ur(87,a,67,a,b,1026,a)]. given #1421 (T,wt=9): 1300 ->_s0(s(s(app(nil,x))),s(s(x))). [ur(59,a,114,a)]. given #1422 (T,wt=9): 1305 ->_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): 9742 -->_s0(empty(nil),app(fstsplit(0,x),app(nil,false))) # answer(goal). [ur(2220,b,213,a,c,691,a)]. given #1425 (F,wt=10): 9743 -->_s0(empty(nil),app(fstsplit(0,x),sndsplit(0,false))) # answer(goal). [ur(2220,b,213,a,c,637,a)]. given #1426 (F,wt=10): 9744 -->_s0(true,app(fstsplit(0,x),empty(cons(y,z)))) # answer(goal). [ur(2105,b,213,a,c,1127,a)]. given #1427 (F,wt=10): 9745 -->_s0(true,app(fstsplit(0,x),head(cons(false,y)))) # answer(goal). [ur(2105,b,213,a,c,1114,a)]. given #1428 (T,wt=9): 1318 ->_s0(length(s(app(nil,x))),length(s(x))). [ur(41,a,114,a)]. given #1429 (T,wt=9): 1319 ->_s0(head(s(app(nil,x))),head(s(x))). [ur(40,a,114,a)]. given #1430 (T,wt=9): 1322 ->_s0(empty(s(app(nil,x))),empty(s(x))). [ur(37,a,114,a)]. given #1431 (T,wt=9): 1329 ->_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=10): 9746 -->_s0(true,app(fstsplit(0,x),leq(s(y),0))) # answer(goal). [ur(2105,b,213,a,c,1072,a)]. given #1434 (F,wt=10): 9747 -->_s0(true,app(fstsplit(0,x),tail(cons(y,false)))) # answer(goal). [ur(2105,b,213,a,c,1059,a)]. given #1435 (F,wt=10): 9748 -->_s0(empty(nil),app(nil,app(fstsplit(0,x),false))) # answer(goal). [resolve(9717,a,7411,b)]. given #1436 (F,wt=10): 9749 -->_s0(empty(nil),sndsplit(0,app(fstsplit(0,x),false))) # answer(goal). [resolve(9717,a,7395,b)]. given #1437 (T,wt=8): 13680 ->*_s0(fstsplit(head(cons(0,x)),y),nil). [ur(87,a,285,a,b,578,a)]. given #1438 (T,wt=9): 1334 ->_s0(tail(tail(app(nil,x))),tail(tail(x))). [ur(54,a,119,a)]. given #1439 (T,wt=9): 1347 ->_s0(length(tail(app(nil,x))),length(tail(x))). [ur(41,a,119,a)]. given #1440 (T,wt=9): 1348 ->_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): 9752 -->_s0(true,head(cons(app(fstsplit(0,x),false),y))) # answer(goal). [resolve(9717,a,2492,b)]. given #1443 (F,wt=10): 9754 -->_s0(true,tail(cons(x,app(fstsplit(0,y),false)))) # answer(goal). [resolve(9717,a,2476,b)]. given #1444 (F,wt=10): 9757 -->_s0(true,x) | -->_s0(x,app(fstsplit(0,y),false)) # answer(goal). [resolve(9717,a,2105,c)]. given #1445 (F,wt=10): 9767 -->_s0(empty(nil),app(app(nil,fstsplit(0,x)),false)) # answer(goal). [ur(2220,b,138,a,c,9717,a)]. given #1446 (T,wt=9): 1351 ->_s0(empty(tail(app(nil,x))),empty(tail(x))). [ur(37,a,119,a)]. given #1447 (T,wt=9): 1358 ->_s0(s(length(app(nil,x))),s(length(x))). [ur(59,a,132,a)]. given #1448 (T,wt=8): 13778 ->*_s0(s(length(app(nil,nil))),s(0)). [ur(87,a,1358,a,b,888,a)]. given #1449 (T,wt=9): 1363 ->_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): 10155 -->_s0(true,app(nil,sndsplit(length(nil),app(nil,false)))) # answer(goal). [resolve(4423,a,2496,b)]. given #1452 (F,wt=10): 10157 -->_s0(true,sndsplit(0,sndsplit(length(nil),app(nil,false)))) # answer(goal). [resolve(4423,a,2479,b)]. given #1453 (F,wt=10): 10177 -->_s0(true,sndsplit(app(nil,length(nil)),app(nil,false))) # answer(goal). [ur(2105,b,121,a,c,4423,a)]. given #1454 (F,wt=10): 10178 -->_s0(true,sndsplit(length(nil),app(nil,app(nil,false)))) # answer(goal). [ur(2105,b,120,a,c,4423,a)]. given #1455 (T,wt=8): 13800 ->*_s0(tail(length(app(nil,nil))),tail(0)). [ur(87,a,1363,a,b,914,a)]. given #1456 (T,wt=8): 13870 ->*_s0(app(head(cons(nil,x)),y),y). [ur(87,a,288,a,b,581,a)]. given #1457 (T,wt=9): 1376 ->_s0(length(length(app(nil,x))),length(length(x))). [ur(41,a,132,a)]. given #1458 (T,wt=8): 13933 ->*_s0(length(length(app(nil,nil))),length(0)). [ur(87,a,1376,a,b,940,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): 10214 -->_s0(true,app(nil,sndsplit(length(nil),sndsplit(0,false)))) # answer(goal). [resolve(4427,a,2496,b)]. given #1461 (F,wt=10): 10216 -->_s0(true,sndsplit(0,sndsplit(length(nil),sndsplit(0,false)))) # answer(goal). [resolve(4427,a,2479,b)]. given #1462 (F,wt=10): 10235 -->_s0(true,sndsplit(app(nil,length(nil)),sndsplit(0,false))) # answer(goal). [ur(2105,b,121,a,c,4427,a)]. given #1463 (F,wt=10): 10236 -->_s0(true,sndsplit(length(nil),app(nil,sndsplit(0,false)))) # answer(goal). [ur(2105,b,120,a,c,4427,a)]. given #1464 (T,wt=9): 1377 ->_s0(head(length(app(nil,x))),head(length(x))). [ur(40,a,132,a)]. given #1465 (T,wt=8): 13959 ->*_s0(head(length(app(nil,nil))),head(0)). [ur(87,a,1377,a,b,966,a)]. given #1466 (T,wt=9): 1380 ->_s0(empty(length(app(nil,x))),empty(length(x))). [ur(37,a,132,a)]. given #1467 (T,wt=8): 13980 ->*_s0(empty(length(app(nil,nil))),empty(0)). [ur(87,a,1380,a,b,1026,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): 10259 -->_s0(true,app(nil,sndsplit(app(nil,length(nil)),false))) # answer(goal). [resolve(4495,a,2496,b)]. given #1470 (F,wt=10): 10261 -->_s0(true,sndsplit(0,sndsplit(app(nil,length(nil)),false))) # answer(goal). [resolve(4495,a,2479,b)]. given #1471 (F,wt=10): 10283 -->_s0(true,sndsplit(app(nil,app(nil,length(nil))),false)) # answer(goal). [ur(2105,b,121,a,c,4495,a)]. given #1472 (F,wt=10): 10289 -->_s0(true,app(nil,sndsplit(0,sndsplit(length(nil),false)))) # answer(goal). [resolve(4499,a,2496,b)]. given #1473 (T,wt=9): 1495 ->*_s0(tail(cons(x,length(app(nil,nil)))),0). [ur(87,a,85,a,b,1356,a)]. given #1474 (T,wt=9): 1497 ->*_s0(head(cons(length(app(nil,nil)),x)),0). [ur(87,a,67,a,b,1356,a)]. given #1475 (T,wt=9): 1504 ->_s0(s(head(app(nil,x))),s(head(x))). [ur(59,a,133,a)]. given #1476 (T,wt=9): 1509 ->_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): 10291 -->_s0(true,sndsplit(0,sndsplit(0,sndsplit(length(nil),false)))) # answer(goal). [resolve(4499,a,2479,b)]. given #1479 (F,wt=10): 10306 -->_s0(empty(nil),sndsplit(length(nil),sndsplit(length(nil),false))) # answer(goal). [ur(2220,b,321,a,c,4499,a)]. given #1480 (F,wt=10): 10312 -->_s0(true,sndsplit(app(nil,0),sndsplit(length(nil),false))) # answer(goal). [ur(2105,b,121,a,c,4499,a)]. given #1481 (F,wt=10): 10313 -->_s0(true,sndsplit(0,app(nil,sndsplit(length(nil),false)))) # answer(goal). [ur(2105,b,120,a,c,4499,a)]. given #1482 (T,wt=9): 1522 ->_s0(length(head(app(nil,x))),length(head(x))). [ur(41,a,133,a)]. given #1483 (T,wt=9): 1523 ->_s0(head(head(app(nil,x))),head(head(x))). [ur(40,a,133,a)]. given #1484 (T,wt=9): 1526 ->_s0(empty(head(app(nil,x))),empty(head(x))). [ur(37,a,133,a)]. given #1485 (T,wt=9): 1535 ->_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): 10318 -->_s0(true,app(nil,app(nil,sndsplit(length(nil),false)))) # answer(goal). [resolve(4501,a,2496,b)]. given #1488 (F,wt=10): 10335 -->_s0(true,app(fstsplit(0,x),sndsplit(length(nil),false))) # answer(goal). [ur(2105,b,213,a,c,4501,a)]. given #1489 (F,wt=10): 10336 -->_s0(true,app(app(nil,nil),sndsplit(length(nil),false))) # answer(goal). [ur(2105,b,138,a,c,4501,a)]. given #1490 (F,wt=10): 10341 -->_s0(empty(nil),sndsplit(length(nil),x)) | -->_s0(x,false) # answer(goal). [resolve(7440,b,53,b)]. given #1491 (T,wt=8): 14077 ->*_s0(s(empty(app(nil,nil))),s(true)). [ur(87,a,1535,a,b,692,a)]. given #1492 (T,wt=9): 1540 ->_s0(tail(empty(app(nil,x))),tail(empty(x))). [ur(54,a,136,a)]. given #1493 (T,wt=8): 14101 ->*_s0(tail(empty(app(nil,nil))),tail(true)). [ur(87,a,1540,a,b,751,a)]. given #1494 (T,wt=9): 1553 ->_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): 10342 -->_s0(empty(nil),sndsplit(x,false)) | -->_s0(x,length(nil)) # answer(goal). [resolve(7440,b,52,b)]. given #1497 (F,wt=9): 14134 -->_s0(empty(nil),sndsplit(length(sndsplit(0,nil)),false)) # answer(goal). [resolve(10342,b,482,a)]. given #1498 (F,wt=9): 14135 -->_s0(empty(nil),sndsplit(length(mapf(x,nil)),false)) # answer(goal). [resolve(10342,b,457,a)]. given #1499 (F,wt=9): 14138 -->_s0(empty(nil),sndsplit(length(fstsplit(0,x)),false)) # answer(goal). [resolve(10342,b,207,a)]. given #1500 (T,wt=8): 14123 ->*_s0(length(empty(app(nil,nil))),length(true)). [ur(87,a,1553,a,b,777,a)]. given #1501 (T,wt=9): 1554 ->_s0(head(empty(app(nil,x))),head(empty(x))). [ur(40,a,136,a)]. given #1502 (T,wt=8): 14157 ->*_s0(head(empty(app(nil,nil))),head(true)). [ur(87,a,1554,a,b,803,a)]. given #1503 (T,wt=9): 1557 ->_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=9): 14139 -->_s0(empty(nil),sndsplit(length(app(nil,nil)),false)) # answer(goal). [resolve(10342,b,132,a)]. given #1506 (F,wt=10): 10358 -->_s0(true,app(nil,leq(s(x),app(nil,0)))) # answer(goal). [resolve(4549,a,2496,b)]. given #1507 (F,wt=10): 10360 -->_s0(true,sndsplit(0,leq(s(x),app(nil,0)))) # answer(goal). [resolve(4549,a,2479,b)]. given #1508 (F,wt=10): 10377 -->_s0(true,leq(app(nil,s(x)),app(nil,0))) # answer(goal). [ur(2105,b,131,a,c,4549,a)]. given #1509 (T,wt=8): 14179 ->*_s0(empty(empty(app(nil,nil))),empty(true)). [ur(87,a,1557,a,b,829,a)]. given #1510 (T,wt=9): 1562 ->*_s0(tail(cons(x,empty(app(nil,nil)))),true). [ur(87,a,85,a,b,1533,a)]. given #1511 (T,wt=9): 1564 ->*_s0(head(cons(empty(app(nil,nil)),x)),true). [ur(87,a,67,a,b,1533,a)]. given #1512 (T,wt=9): 1597 ->_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): 10378 -->_s0(true,leq(s(x),app(nil,app(nil,0)))) # answer(goal). [ur(2105,b,130,a,c,4549,a)]. given #1515 (F,wt=10): 10379 -->_s0(true,leq(s(s(x)),s(app(nil,0)))) # answer(goal). [ur(2105,b,72,a,c,4549,a)]. given #1516 (F,wt=10): 10402 -->_s0(empty(nil),empty(x)) | -->_s0(x,cons(y,z)) # answer(goal). [resolve(7452,b,37,b)]. given #1517 (F,wt=10): 10403 -->_s0(empty(nil),head(x)) | -->_s0(x,cons(false,y)) # answer(goal). [resolve(7453,b,40,b)]. given #1518 (T,wt=9): 1602 ->_s0(tail(s(fstsplit(0,x))),tail(s(nil))). [ur(54,a,189,a)]. given #1519 (T,wt=9): 1615 ->_s0(length(s(fstsplit(0,x))),length(s(nil))). [ur(41,a,189,a)]. given #1520 (T,wt=9): 1616 ->_s0(head(s(fstsplit(0,x))),head(s(nil))). [ur(40,a,189,a)]. given #1521 (T,wt=9): 1619 ->_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): 10404 -->_s0(empty(nil),leq(s(x),y)) | -->_s0(y,0) # answer(goal). [resolve(7454,b,43,b)]. given #1524 (F,wt=10): 10405 -->_s0(empty(nil),leq(x,0)) | -->_s0(x,s(y)) # answer(goal). [resolve(7454,b,42,b)]. given #1525 (F,wt=9): 14269 -->_s0(empty(nil),leq(length(cons(x,y)),0)) # answer(goal). [resolve(10405,b,68,a)]. given #1526 (F,wt=10): 10406 -->_s0(empty(nil),tail(x)) | -->_s0(x,cons(y,false)) # answer(goal). [resolve(7456,b,54,b)]. given #1527 (T,wt=8): 14266 ->*_s0(sndsplit(length(cons(x,y)),nil),nil). [ur(87,a,296,a,b,565,a)]. given #1528 (T,wt=9): 1624 ->_s0(s(tail(fstsplit(0,x))),s(tail(nil))). [ur(59,a,194,a)]. given #1529 (T,wt=9): 1629 ->_s0(tail(tail(fstsplit(0,x))),tail(tail(nil))). [ur(54,a,194,a)]. given #1530 (T,wt=9): 1642 ->_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): 10422 -->_s0(true,app(nil,leq(app(nil,s(x)),0))) # answer(goal). [resolve(4684,a,2496,b)]. given #1533 (F,wt=10): 10424 -->_s0(true,sndsplit(0,leq(app(nil,s(x)),0))) # answer(goal). [resolve(4684,a,2479,b)]. given #1534 (F,wt=10): 10439 -->_s0(true,leq(app(nil,app(nil,s(x))),0)) # answer(goal). [ur(2105,b,131,a,c,4684,a)]. given #1535 (F,wt=10): 10440 -->_s0(true,leq(s(app(nil,s(x))),s(0))) # answer(goal). [ur(2105,b,72,a,c,4684,a)]. given #1536 (T,wt=9): 1643 ->_s0(head(tail(fstsplit(0,x))),head(tail(nil))). [ur(40,a,194,a)]. given #1537 (T,wt=9): 1646 ->_s0(empty(tail(fstsplit(0,x))),empty(tail(nil))). [ur(37,a,194,a)]. given #1538 (T,wt=9): 1652 ->_s0(s(length(fstsplit(0,x))),s(length(nil))). [ur(59,a,207,a)]. given #1539 (T,wt=8): 14332 ->*_s0(s(length(fstsplit(0,x))),s(0)). [ur(87,a,1652,a,b,888,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): 10707 -->_s0(true,app(nil,tail(app(cons(x,nil),false)))) # answer(goal). [resolve(5776,a,2496,b)]. given #1542 (F,wt=10): 10709 -->_s0(true,sndsplit(0,tail(app(cons(x,nil),false)))) # answer(goal). [resolve(5776,a,2479,b)]. given #1543 (F,wt=10): 10711 -->_s0(true,tail(app(nil,app(cons(x,nil),false)))) # answer(goal). [resolve(5776,a,2455,b)]. given #1544 (F,wt=10): 10712 -->_s0(true,tail(sndsplit(0,app(cons(x,nil),false)))) # answer(goal). [resolve(5776,a,2427,b)]. given #1545 (T,wt=9): 1657 ->_s0(tail(length(fstsplit(0,x))),tail(length(nil))). [ur(54,a,207,a)]. given #1546 (T,wt=8): 14355 ->*_s0(tail(length(fstsplit(0,x))),tail(0)). [ur(87,a,1657,a,b,914,a)]. given #1547 (T,wt=9): 1670 ->_s0(length(length(fstsplit(0,x))),length(length(nil))). [ur(41,a,207,a)]. given #1548 (T,wt=8): 14374 ->*_s0(length(length(fstsplit(0,x))),length(0)). [ur(87,a,1670,a,b,940,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): 10757 -->_s0(empty(nil),head(fstsplit(s(x),cons(false,y)))) # answer(goal). [resolve(233,a,7453,b)]. given #1551 (F,wt=10): 10874 -->_s0(empty(nil),empty(fstsplit(s(x),cons(y,z)))) # answer(goal). [resolve(236,a,7452,b)]. given #1552 (F,wt=10): 11277 -->_s0(nil,x) | -->_s0(x,app(cons(y,z),u)) # answer(goal). [resolve(8581,b,2778,a)]. given #1553 (F,wt=10): 11278 -->_s0(nil,x) | -->_s0(x,sndsplit(0,cons(y,z))) # answer(goal). [resolve(8581,b,2350,a)]. given #1554 (T,wt=9): 1671 ->_s0(head(length(fstsplit(0,x))),head(length(nil))). [ur(40,a,207,a)]. given #1555 (T,wt=8): 14399 ->*_s0(head(length(fstsplit(0,x))),head(0)). [ur(87,a,1671,a,b,966,a)]. given #1556 (T,wt=9): 1674 ->_s0(empty(length(fstsplit(0,x))),empty(length(nil))). [ur(37,a,207,a)]. given #1557 (T,wt=8): 14418 ->*_s0(empty(length(fstsplit(0,x))),empty(0)). [ur(87,a,1674,a,b,1026,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): 11279 -->_s0(nil,x) | -->_s0(x,app(nil,cons(y,z))) # answer(goal). [resolve(8581,b,1532,a)]. given #1560 (F,wt=10): 11391 -->_s0(nil,app(fstsplit(s(x),cons(y,z)),u)) # answer(goal). [resolve(8581,c,238,a),unit_del(b,2778)]. given #1561 (F,wt=10): 11559 -->_s0(nil,sndsplit(0,fstsplit(s(x),cons(y,z)))) # answer(goal). [ur(8581,b,2350,a,c,220,a)]. given #1562 (F,wt=10): 11561 -->_s0(nil,sndsplit(s(0),cons(x,cons(y,z)))) # answer(goal). [ur(8581,b,2350,a,c,83,a)]. given #1563 (T,wt=9): 1678 ->*_s0(tail(cons(x,length(fstsplit(0,y)))),0). [ur(87,a,85,a,b,1650,a)]. given #1564 (T,wt=9): 1680 ->*_s0(head(cons(length(fstsplit(0,x)),y)),0). [ur(87,a,67,a,b,1650,a)]. given #1565 (T,wt=9): 1722 ->_s0(s(head(fstsplit(0,x))),s(head(nil))). [ur(59,a,208,a)]. given #1566 (T,wt=9): 1727 ->_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): 11562 -->_s0(nil,app(nil,fstsplit(s(x),cons(y,z)))) # answer(goal). [ur(8581,b,1532,a,c,237,a)]. given #1569 (F,wt=10): 11979 -->_s0(empty(nil),app(mapf(x,nil),app(nil,false))) # answer(goal). [ur(2220,b,463,a,c,691,a)]. given #1570 (F,wt=10): 11980 -->_s0(empty(nil),app(mapf(x,nil),sndsplit(0,false))) # answer(goal). [ur(2220,b,463,a,c,637,a)]. given #1571 (F,wt=10): 11981 -->_s0(true,app(mapf(x,nil),sndsplit(length(nil),false))) # answer(goal). [ur(2105,b,463,a,c,4501,a)]. given #1572 (T,wt=9): 1740 ->_s0(length(head(fstsplit(0,x))),length(head(nil))). [ur(41,a,208,a)]. given #1573 (T,wt=9): 1741 ->_s0(head(head(fstsplit(0,x))),head(head(nil))). [ur(40,a,208,a)]. given #1574 (T,wt=9): 1744 ->_s0(empty(head(fstsplit(0,x))),empty(head(nil))). [ur(37,a,208,a)]. given #1575 (T,wt=9): 1750 ->_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): 11982 -->_s0(true,app(mapf(x,nil),empty(cons(y,z)))) # answer(goal). [ur(2105,b,463,a,c,1127,a)]. given #1578 (F,wt=10): 11983 -->_s0(true,app(mapf(x,nil),head(cons(false,y)))) # answer(goal). [ur(2105,b,463,a,c,1114,a)]. given #1579 (F,wt=10): 11984 -->_s0(true,app(mapf(x,nil),leq(s(y),0))) # answer(goal). [ur(2105,b,463,a,c,1072,a)]. given #1580 (F,wt=10): 11985 -->_s0(true,app(mapf(x,nil),tail(cons(y,false)))) # answer(goal). [ur(2105,b,463,a,c,1059,a)]. given #1581 (T,wt=8): 14497 ->*_s0(s(empty(fstsplit(0,x))),s(true)). [ur(87,a,1750,a,b,692,a)]. given #1582 (T,wt=9): 1755 ->_s0(tail(empty(fstsplit(0,x))),tail(empty(nil))). [ur(54,a,211,a)]. given #1583 (T,wt=8): 14519 ->*_s0(tail(empty(fstsplit(0,x))),tail(true)). [ur(87,a,1755,a,b,751,a)]. given #1584 (T,wt=9): 1768 ->_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): 11986 -->_s0(empty(nil),app(nil,app(mapf(x,nil),false))) # answer(goal). [resolve(11966,a,7411,b)]. given #1587 (F,wt=10): 11988 -->_s0(empty(nil),sndsplit(0,app(mapf(x,nil),false))) # answer(goal). [resolve(11966,a,7395,b)]. given #1588 (F,wt=10): 11992 -->_s0(true,head(cons(app(mapf(x,nil),false),y))) # answer(goal). [resolve(11966,a,2492,b)]. given #1589 (F,wt=10): 11994 -->_s0(true,tail(cons(x,app(mapf(y,nil),false)))) # answer(goal). [resolve(11966,a,2476,b)]. given #1590 (T,wt=8): 14538 ->*_s0(length(empty(fstsplit(0,x))),length(true)). [ur(87,a,1768,a,b,777,a)]. given #1591 (T,wt=9): 1769 ->_s0(head(empty(fstsplit(0,x))),head(empty(nil))). [ur(40,a,211,a)]. given #1592 (T,wt=8): 14560 ->*_s0(head(empty(fstsplit(0,x))),head(true)). [ur(87,a,1769,a,b,803,a)]. given #1593 (T,wt=9): 1772 ->_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): 11997 -->_s0(true,x) | -->_s0(x,app(mapf(y,nil),false)) # answer(goal). [resolve(11966,a,2105,c)]. given #1596 (F,wt=10): 12006 -->_s0(empty(nil),app(app(nil,mapf(x,nil)),false)) # answer(goal). [ur(2220,b,138,a,c,11966,a)]. given #1597 (F,wt=10): 12120 -->_s0(true,sndsplit(length(nil),sndsplit(0,sndsplit(0,false)))) # answer(goal). [ur(2105,b,470,a,c,4427,a)]. given #1598 (F,wt=10): 12121 -->_s0(true,sndsplit(length(nil),sndsplit(0,app(nil,false)))) # answer(goal). [ur(2105,b,470,a,c,4423,a)]. given #1599 (T,wt=8): 14579 ->*_s0(empty(empty(fstsplit(0,x))),empty(true)). [ur(87,a,1772,a,b,829,a)]. given #1600 (T,wt=9): 1777 ->*_s0(tail(cons(x,empty(fstsplit(0,y)))),true). [ur(87,a,85,a,b,1748,a)]. given #1601 (T,wt=9): 1779 ->*_s0(head(cons(empty(fstsplit(0,x)),y)),true). [ur(87,a,67,a,b,1748,a)]. given #1602 (T,wt=9): 1783 ->_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): 12122 -->_s0(true,sndsplit(s(0),sndsplit(0,cons(x,false)))) # answer(goal). [ur(2105,b,470,a,c,634,a)]. given #1605 (F,wt=10): 12136 -->_s0(true,sndsplit(0,sndsplit(0,x))) | -->_s0(x,false) # answer(goal). [resolve(9118,b,53,b)]. given #1606 (F,wt=10): 12137 -->_s0(true,sndsplit(0,sndsplit(x,false))) | -->_s0(x,0) # answer(goal). [resolve(9118,b,52,b)]. given #1607 (F,wt=10): 12138 -->_s0(true,sndsplit(tail(cons(x,0)),sndsplit(0,false))) # answer(goal). [resolve(9119,b,85,a)]. given #1608 (T,wt=9): 1788 ->_s0(tail(s(leq(0,x))),tail(s(true))). [ur(54,a,339,a)]. given #1609 (T,wt=9): 1801 ->_s0(length(s(leq(0,x))),length(s(true))). [ur(41,a,339,a)]. given #1610 (T,wt=9): 1802 ->_s0(head(s(leq(0,x))),head(s(true))). [ur(40,a,339,a)]. given #1611 (T,wt=9): 1805 ->_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): 12140 -->_s0(true,sndsplit(head(cons(0,x)),sndsplit(0,false))) # answer(goal). [resolve(9119,b,67,a)]. given #1614 (F,wt=10): 12141 -->_s0(true,app(nil,sndsplit(0,x))) | -->_s0(x,false) # answer(goal). [resolve(9175,b,53,b)]. given #1615 (F,wt=10): 12142 -->_s0(true,app(nil,sndsplit(x,false))) | -->_s0(x,0) # answer(goal). [resolve(9175,b,52,b)]. given #1616 (F,wt=10): 12224 -->_s0(empty(nil),sndsplit(sndsplit(0,app(nil,0)),false)) # answer(goal). [ur(2220,b,471,a,c,3398,a)]. given #1617 (T,wt=8): 14669 ->*_s0(leq(length(cons(x,y)),0),false). [ur(87,a,306,a,b,571,a)]. given #1618 (T,wt=9): 1858 ->_s0(s(tail(leq(0,x))),s(tail(true))). [ur(59,a,344,a)]. given #1619 (T,wt=9): 1863 ->_s0(tail(tail(leq(0,x))),tail(tail(true))). [ur(54,a,344,a)]. given #1620 (T,wt=9): 1876 ->_s0(length(tail(leq(0,x))),length(tail(true))). [ur(41,a,344,a)]. given #1621 (A,wt=10): 307 ->_s0(length(length(cons(x,y))),length(s(length(y)))). [ur(41,a,68,a)]. given #1622 (F,wt=10): 12229 -->_s0(empty(nil),sndsplit(sndsplit(0,0),app(nil,false))) # answer(goal). [ur(2220,b,471,a,c,689,a)]. given #1623 (F,wt=10): 12230 -->_s0(empty(nil),sndsplit(sndsplit(0,0),sndsplit(0,false))) # answer(goal). [ur(2220,b,471,a,c,635,a)]. given #1624 (F,wt=10): 12232 -->_s0(true,sndsplit(sndsplit(0,0),sndsplit(length(nil),false))) # answer(goal). [ur(2105,b,471,a,c,4499,a)]. given #1625 (F,wt=10): 12233 -->_s0(true,sndsplit(sndsplit(0,app(nil,length(nil))),false)) # answer(goal). [ur(2105,b,471,a,c,4495,a)]. given #1626 (T,wt=9): 1877 ->_s0(head(tail(leq(0,x))),head(tail(true))). [ur(40,a,344,a)]. given #1627 (T,wt=9): 1880 ->_s0(empty(tail(leq(0,x))),empty(tail(true))). [ur(37,a,344,a)]. given #1628 (T,wt=9): 1885 ->_s0(s(length(leq(0,x))),s(length(true))). [ur(59,a,357,a)]. given #1629 (T,wt=9): 1890 ->_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): 12234 -->_s0(true,sndsplit(sndsplit(0,length(nil)),sndsplit(0,false))) # answer(goal). [ur(2105,b,471,a,c,4427,a)]. given #1632 (F,wt=10): 12235 -->_s0(true,sndsplit(sndsplit(0,length(nil)),app(nil,false))) # answer(goal). [ur(2105,b,471,a,c,4423,a)]. given #1633 (F,wt=10): 12236 -->_s0(true,sndsplit(sndsplit(0,0),empty(cons(x,y)))) # answer(goal). [ur(2105,b,471,a,c,1125,a)]. given #1634 (F,wt=10): 12237 -->_s0(true,sndsplit(sndsplit(0,0),head(cons(false,x)))) # answer(goal). [ur(2105,b,471,a,c,1112,a)]. given #1635 (T,wt=9): 1903 ->_s0(length(length(leq(0,x))),length(length(true))). [ur(41,a,357,a)]. given #1636 (T,wt=9): 1904 ->_s0(head(length(leq(0,x))),head(length(true))). [ur(40,a,357,a)]. given #1637 (T,wt=9): 1907 ->_s0(empty(length(leq(0,x))),empty(length(true))). [ur(37,a,357,a)]. given #1638 (T,wt=9): 1912 ->_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): 12238 -->_s0(true,sndsplit(sndsplit(0,0),leq(s(x),0))) # answer(goal). [ur(2105,b,471,a,c,1069,a)]. given #1641 (F,wt=10): 12239 -->_s0(true,sndsplit(sndsplit(0,0),tail(cons(x,false)))) # answer(goal). [ur(2105,b,471,a,c,1057,a)]. given #1642 (F,wt=10): 12240 -->_s0(true,sndsplit(sndsplit(0,s(0)),cons(x,false))) # answer(goal). [ur(2105,b,471,a,c,634,a)]. given #1643 (F,wt=10): 12241 -->_s0(empty(nil),app(nil,sndsplit(sndsplit(0,0),false))) # answer(goal). [resolve(12211,a,7411,b)]. given #1644 (T,wt=9): 1917 ->_s0(tail(head(leq(0,x))),tail(head(true))). [ur(54,a,358,a)]. given #1645 (T,wt=9): 1930 ->_s0(length(head(leq(0,x))),length(head(true))). [ur(41,a,358,a)]. given #1646 (T,wt=9): 1931 ->_s0(head(head(leq(0,x))),head(head(true))). [ur(40,a,358,a)]. given #1647 (T,wt=9): 1934 ->_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): 12243 -->_s0(empty(nil),sndsplit(0,sndsplit(sndsplit(0,0),false))) # answer(goal). [resolve(12211,a,7395,b)]. given #1650 (F,wt=10): 12246 -->_s0(true,head(cons(sndsplit(sndsplit(0,0),false),x))) # answer(goal). [resolve(12211,a,2492,b)]. given #1651 (F,wt=10): 12247 -->_s0(true,tail(cons(x,sndsplit(sndsplit(0,0),false)))) # answer(goal). [resolve(12211,a,2476,b)]. given #1652 (F,wt=10): 12250 -->_s0(true,x) | -->_s0(x,sndsplit(sndsplit(0,0),false)) # answer(goal). [resolve(12211,a,2105,c)]. given #1653 (T,wt=8): 14864 ->*_s0(fstsplit(length(cons(x,y)),nil),nil). [ur(87,a,310,a,b,576,a)]. given #1654 (T,wt=9): 1939 ->_s0(s(empty(leq(0,x))),s(empty(true))). [ur(59,a,361,a)]. given #1655 (T,wt=9): 1944 ->_s0(tail(empty(leq(0,x))),tail(empty(true))). [ur(54,a,361,a)]. given #1656 (T,wt=9): 1957 ->_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): 12260 -->_s0(empty(nil),sndsplit(sndsplit(0,sndsplit(0,0)),false)) # answer(goal). [ur(2220,b,471,a,c,12211,a)]. given #1659 (F,wt=10): 12261 -->_s0(empty(nil),sndsplit(app(nil,sndsplit(0,0)),false)) # answer(goal). [ur(2220,b,121,a,c,12211,a)]. given #1660 (F,wt=10): 12265 -->_s0(true,sndsplit(s(sndsplit(0,0)),cons(x,false))) # answer(goal). [ur(2105,b,83,a,c,12211,a)]. given #1661 (F,wt=10): 12271 -->_s0(true,app(nil,sndsplit(sndsplit(0,length(nil)),false))) # answer(goal). [resolve(12159,a,2496,b)]. given #1662 (T,wt=9): 1958 ->_s0(head(empty(leq(0,x))),head(empty(true))). [ur(40,a,361,a)]. given #1663 (T,wt=9): 1961 ->_s0(empty(empty(leq(0,x))),empty(empty(true))). [ur(37,a,361,a)]. given #1664 (T,wt=9): 1993 ->_s0(s(s(mapf(x,nil))),s(s(nil))). [ur(59,a,439,a)]. given #1665 (T,wt=9): 1998 ->_s0(tail(s(mapf(x,nil))),tail(s(nil))). [ur(54,a,439,a)]. given #1666 (A,wt=12): 312 ->_s0(app(x,length(cons(y,z))),app(x,s(length(z)))). [ur(36,a,68,a)]. given #1667 (F,wt=10): 12273 -->_s0(true,sndsplit(0,sndsplit(sndsplit(0,length(nil)),false))) # answer(goal). [resolve(12159,a,2479,b)]. given #1668 (F,wt=10): 12293 -->_s0(true,sndsplit(sndsplit(0,sndsplit(0,length(nil))),false)) # answer(goal). [ur(2105,b,471,a,c,12159,a)]. given #1669 (F,wt=10): 12295 -->_s0(true,sndsplit(app(nil,sndsplit(0,length(nil))),false)) # answer(goal). [ur(2105,b,121,a,c,12159,a)]. given #1670 (F,wt=10): 12351 -->_s0(true,app(fstsplit(s(x),nil),app(nil,false))) # answer(goal). [resolve(263,a,2748,b)]. given #1671 (T,wt=9): 2011 ->_s0(length(s(mapf(x,nil))),length(s(nil))). [ur(41,a,439,a)]. given #1672 (T,wt=9): 2012 ->_s0(head(s(mapf(x,nil))),head(s(nil))). [ur(40,a,439,a)]. given #1673 (T,wt=9): 2015 ->_s0(empty(s(mapf(x,nil))),empty(s(nil))). [ur(37,a,439,a)]. given #1674 (T,wt=9): 2020 ->_s0(s(tail(mapf(x,nil))),s(tail(nil))). [ur(59,a,444,a)]. given #1675 (A,wt=12): 313 ->_s0(app(length(cons(x,y)),z),app(s(length(y)),z)). [ur(35,a,68,a)]. given #1676 (F,wt=10): 12352 -->_s0(true,app(fstsplit(s(x),nil),sndsplit(0,false))) # answer(goal). [resolve(263,a,2591,b)]. given #1677 (F,wt=10): 12397 -->_s0(nil,app(fstsplit(s(x),nil),cons(y,z))) # answer(goal). [ur(8581,b,1532,a,c,263,a)]. given #1678 (F,wt=10): 12415 -->_s0(true,app(nil,app(fstsplit(s(x),nil),false))) # answer(goal). [resolve(12395,a,2496,b)]. given #1679 (F,wt=10): 12417 -->_s0(true,sndsplit(0,app(fstsplit(s(x),nil),false))) # answer(goal). [resolve(12395,a,2479,b)]. given #1680 (T,wt=9): 2025 ->_s0(tail(tail(mapf(x,nil))),tail(tail(nil))). [ur(54,a,444,a)]. given #1681 (T,wt=9): 2038 ->_s0(length(tail(mapf(x,nil))),length(tail(nil))). [ur(41,a,444,a)]. given #1682 (T,wt=9): 2039 ->_s0(head(tail(mapf(x,nil))),head(tail(nil))). [ur(40,a,444,a)]. given #1683 (T,wt=9): 2042 ->_s0(empty(tail(mapf(x,nil))),empty(tail(nil))). [ur(37,a,444,a)]. given #1684 (A,wt=16): 322 ->_s0(ring(x,y,z,u,w,length(nil)),ring(x,y,z,u,w,0)). [ur(51,a,69,a)]. given #1685 (F,wt=10): 12431 -->_s0(true,app(app(nil,fstsplit(s(x),nil)),false)) # answer(goal). [ur(2105,b,138,a,c,12395,a)]. given #1686 (F,wt=10): 12468 -->_s0(empty(nil),leq(s(x),sndsplit(0,length(nil)))) # answer(goal). [ur(2220,b,480,a,c,4606,a)]. given #1687 (F,wt=10): 12471 -->_s0(true,leq(app(nil,s(x)),sndsplit(0,0))) # answer(goal). [ur(2105,b,480,a,c,4684,a)]. given #1688 (F,wt=10): 12472 -->_s0(true,leq(s(x),sndsplit(0,app(nil,0)))) # answer(goal). [ur(2105,b,480,a,c,4549,a)]. given #1689 (T,wt=9): 2048 ->_s0(s(length(mapf(x,nil))),s(length(nil))). [ur(59,a,457,a)]. given #1690 (T,wt=8): 15028 ->*_s0(s(length(mapf(x,nil))),s(0)). [ur(87,a,2048,a,b,888,a)]. given #1691 (T,wt=9): 2053 ->_s0(tail(length(mapf(x,nil))),tail(length(nil))). [ur(54,a,457,a)]. given #1692 (T,wt=8): 15048 ->*_s0(tail(length(mapf(x,nil))),tail(0)). [ur(87,a,2053,a,b,914,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): 12473 -->_s0(true,leq(s(s(x)),sndsplit(0,s(0)))) # answer(goal). [ur(2105,b,480,a,c,1070,a)]. given #1695 (F,wt=10): 12479 -->_s0(true,app(nil,leq(s(x),sndsplit(0,0)))) # answer(goal). [resolve(12460,a,2496,b)]. given #1696 (F,wt=10): 12481 -->_s0(true,sndsplit(0,leq(s(x),sndsplit(0,0)))) # answer(goal). [resolve(12460,a,2479,b)]. given #1697 (F,wt=10): 12498 -->_s0(true,leq(s(x),sndsplit(0,sndsplit(0,0)))) # answer(goal). [ur(2105,b,480,a,c,12460,a)]. given #1698 (T,wt=9): 2066 ->_s0(length(length(mapf(x,nil))),length(length(nil))). [ur(41,a,457,a)]. given #1699 (T,wt=8): 15070 ->*_s0(length(length(mapf(x,nil))),length(0)). [ur(87,a,2066,a,b,940,a)]. given #1700 (T,wt=9): 2067 ->_s0(head(length(mapf(x,nil))),head(length(nil))). [ur(40,a,457,a)]. given #1701 (T,wt=8): 15089 ->*_s0(head(length(mapf(x,nil))),head(0)). [ur(87,a,2067,a,b,966,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): 12499 -->_s0(true,leq(s(x),app(nil,sndsplit(0,0)))) # answer(goal). [ur(2105,b,130,a,c,12460,a)]. given #1704 (F,wt=10): 12500 -->_s0(true,leq(s(s(x)),s(sndsplit(0,0)))) # answer(goal). [ur(2105,b,72,a,c,12460,a)]. given #1705 (F,wt=10): 12509 -->_s0(true,app(tail(cons(x,nil)),sndsplit(0,false))) # answer(goal). [resolve(9176,b,85,a)]. given #1706 (F,wt=10): 12510 -->_s0(true,app(sndsplit(s(x),nil),sndsplit(0,false))) # answer(goal). [resolve(9176,b,84,a)]. given #1707 (T,wt=9): 2070 ->_s0(empty(length(mapf(x,nil))),empty(length(nil))). [ur(37,a,457,a)]. Low Water (keep): wt=11.000, iters=6666 given #1708 (T,wt=8): 15111 ->*_s0(empty(length(mapf(x,nil))),empty(0)). [ur(87,a,2070,a,b,1026,a)]. given #1709 (T,wt=9): 2074 ->*_s0(tail(cons(x,length(mapf(y,nil)))),0). [ur(87,a,85,a,b,2046,a)]. given #1710 (T,wt=9): 2076 ->*_s0(head(cons(length(mapf(x,nil)),y)),0). [ur(87,a,67,a,b,2046,a)]. given #1711 (A,wt=16): 325 ->_s0(ring(x,y,length(nil),z,u,w),ring(x,y,0,z,u,w)). [ur(48,a,69,a)]. given #1712 (F,wt=10): 12512 -->_s0(true,app(head(cons(nil,x)),sndsplit(0,false))) # answer(goal). [resolve(9176,b,67,a)]. given #1713 (F,wt=10): 12543 -->_s0(empty(nil),leq(sndsplit(0,s(x)),length(nil))) # answer(goal). [ur(2220,b,481,a,c,4606,a)]. given #1714 (F,wt=10): 12546 -->_s0(true,leq(sndsplit(0,s(x)),sndsplit(0,0))) # answer(goal). [ur(2105,b,481,a,c,12460,a)]. given #1715 (F,wt=10): 12547 -->_s0(true,leq(sndsplit(0,app(nil,s(x))),0)) # answer(goal). [ur(2105,b,481,a,c,4684,a)]. given #1716 (T,wt=9): 2107 ->_s0(s(head(mapf(x,nil))),s(head(nil))). [ur(59,a,458,a)]. given #1717 (T,wt=9): 2112 ->_s0(tail(head(mapf(x,nil))),tail(head(nil))). [ur(54,a,458,a)]. given #1718 (T,wt=9): 2125 ->_s0(length(head(mapf(x,nil))),length(head(nil))). [ur(41,a,458,a)]. given #1719 (T,wt=9): 2126 ->_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): 12548 -->_s0(true,leq(sndsplit(0,s(x)),app(nil,0))) # answer(goal). [ur(2105,b,481,a,c,4549,a)]. given #1722 (F,wt=10): 12549 -->_s0(true,leq(sndsplit(0,s(s(x))),s(0))) # answer(goal). [ur(2105,b,481,a,c,1070,a)]. given #1723 (F,wt=10): 12579 -->_s0(true,app(nil,leq(sndsplit(0,s(x)),0))) # answer(goal). [resolve(12534,a,2496,b)]. given #1724 (F,wt=10): 12581 -->_s0(true,sndsplit(0,leq(sndsplit(0,s(x)),0))) # answer(goal). [resolve(12534,a,2479,b)]. given #1725 (T,wt=9): 2129 ->_s0(empty(head(mapf(x,nil))),empty(head(nil))). [ur(37,a,458,a)]. given #1726 (T,wt=9): 2134 ->_s0(s(empty(mapf(x,nil))),s(empty(nil))). [ur(59,a,461,a)]. given #1727 (T,wt=8): 15147 ->*_s0(s(empty(mapf(x,nil))),s(true)). [ur(87,a,2134,a,b,692,a)]. given #1728 (T,wt=9): 2139 ->_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): 12598 -->_s0(true,leq(sndsplit(0,sndsplit(0,s(x))),0)) # answer(goal). [ur(2105,b,481,a,c,12534,a)]. given #1731 (F,wt=10): 12599 -->_s0(true,leq(app(nil,sndsplit(0,s(x))),0)) # answer(goal). [ur(2105,b,131,a,c,12534,a)]. given #1732 (F,wt=10): 12600 -->_s0(true,leq(s(sndsplit(0,s(x))),s(0))) # answer(goal). [ur(2105,b,72,a,c,12534,a)]. given #1733 (F,wt=10): 12669 -->_s0(true,sndsplit(0,app(nil,x))) | -->_s0(x,false) # answer(goal). [resolve(9262,b,36,b)]. given #1734 (T,wt=8): 15157 ->*_s0(tail(empty(mapf(x,nil))),tail(true)). [ur(87,a,2139,a,b,751,a)]. given #1735 (T,wt=9): 2152 ->_s0(length(empty(mapf(x,nil))),length(empty(nil))). [ur(41,a,461,a)]. given #1736 (T,wt=8): 15170 ->*_s0(length(empty(mapf(x,nil))),length(true)). [ur(87,a,2152,a,b,777,a)]. given #1737 (T,wt=9): 2153 ->_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=10): 12670 -->_s0(true,sndsplit(0,app(x,false))) | -->_s0(x,nil) # answer(goal). [resolve(9262,b,35,b)]. given #1740 (F,wt=10): 12765 -->_s0(empty(nil),app(sndsplit(0,mapf(x,nil)),false)) # answer(goal). [ur(2220,b,488,a,c,11966,a)]. given #1741 (F,wt=10): 12766 -->_s0(empty(nil),app(sndsplit(0,fstsplit(0,x)),false)) # answer(goal). [ur(2220,b,488,a,c,9717,a)]. given #1742 (F,wt=10): 12767 -->_s0(empty(nil),app(sndsplit(0,app(nil,nil)),false)) # answer(goal). [ur(2220,b,488,a,c,5160,a)]. given #1743 (T,wt=8): 15180 ->*_s0(head(empty(mapf(x,nil))),head(true)). [ur(87,a,2153,a,b,803,a)]. given #1744 (T,wt=9): 2156 ->_s0(empty(empty(mapf(x,nil))),empty(empty(nil))). [ur(37,a,461,a)]. given #1745 (T,wt=8): 15195 ->*_s0(empty(empty(mapf(x,nil))),empty(true)). [ur(87,a,2156,a,b,829,a)]. given #1746 (T,wt=9): 2161 ->*_s0(tail(cons(x,empty(mapf(y,nil)))),true). [ur(87,a,85,a,b,2132,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): 12773 -->_s0(empty(nil),app(sndsplit(0,nil),app(nil,false))) # answer(goal). [ur(2220,b,488,a,c,691,a)]. given #1749 (F,wt=10): 12774 -->_s0(empty(nil),app(sndsplit(0,nil),sndsplit(0,false))) # answer(goal). [ur(2220,b,488,a,c,637,a)]. given #1750 (F,wt=10): 12775 -->_s0(true,app(sndsplit(0,fstsplit(s(x),nil)),false)) # answer(goal). [ur(2105,b,488,a,c,12395,a)]. given #1751 (F,wt=10): 12778 -->_s0(true,app(sndsplit(0,nil),sndsplit(length(nil),false))) # answer(goal). [ur(2105,b,488,a,c,4501,a)]. given #1752 (T,wt=9): 2163 ->*_s0(head(cons(empty(mapf(x,nil)),y)),true). [ur(87,a,67,a,b,2132,a)]. given #1753 (T,wt=9): 2168 ->_s0(s(s(sndsplit(0,x))),s(s(x))). [ur(59,a,464,a)]. given #1754 (T,wt=9): 2173 ->_s0(tail(s(sndsplit(0,x))),tail(s(x))). [ur(54,a,464,a)]. given #1755 (T,wt=9): 2186 ->_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=10): 12779 -->_s0(true,app(sndsplit(0,nil),empty(cons(x,y)))) # answer(goal). [ur(2105,b,488,a,c,1127,a)]. given #1758 (F,wt=10): 12780 -->_s0(true,app(sndsplit(0,nil),head(cons(false,x)))) # answer(goal). [ur(2105,b,488,a,c,1114,a)]. given #1759 (F,wt=10): 12781 -->_s0(true,app(sndsplit(0,nil),leq(s(x),0))) # answer(goal). [ur(2105,b,488,a,c,1072,a)]. given #1760 (F,wt=10): 12782 -->_s0(true,app(sndsplit(0,nil),tail(cons(x,false)))) # answer(goal). [ur(2105,b,488,a,c,1059,a)]. given #1761 (T,wt=9): 2187 ->_s0(head(s(sndsplit(0,x))),head(s(x))). [ur(40,a,464,a)]. given #1762 (T,wt=9): 2190 ->_s0(empty(s(sndsplit(0,x))),empty(s(x))). [ur(37,a,464,a)]. given #1763 (T,wt=9): 2225 ->_s0(s(tail(sndsplit(0,x))),s(tail(x))). [ur(59,a,469,a)]. given #1764 (T,wt=9): 2230 ->_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=10): 12790 -->_s0(empty(nil),app(nil,app(sndsplit(0,nil),false))) # answer(goal). [resolve(12755,a,7411,b)]. given #1767 (F,wt=10): 12792 -->_s0(empty(nil),sndsplit(0,app(sndsplit(0,nil),false))) # answer(goal). [resolve(12755,a,7395,b)]. given #1768 (F,wt=10): 12796 -->_s0(true,head(cons(app(sndsplit(0,nil),false),x))) # answer(goal). [resolve(12755,a,2492,b)]. given #1769 (F,wt=10): 12797 -->_s0(true,tail(cons(x,app(sndsplit(0,nil),false)))) # answer(goal). [resolve(12755,a,2476,b)]. given #1770 (T,wt=9): 2243 ->_s0(length(tail(sndsplit(0,x))),length(tail(x))). [ur(41,a,469,a)]. given #1771 (T,wt=9): 2244 ->_s0(head(tail(sndsplit(0,x))),head(tail(x))). [ur(40,a,469,a)]. given #1772 (T,wt=9): 2247 ->_s0(empty(tail(sndsplit(0,x))),empty(tail(x))). [ur(37,a,469,a)]. given #1773 (T,wt=9): 2257 ->_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): 12800 -->_s0(true,x) | -->_s0(x,app(sndsplit(0,nil),false)) # answer(goal). [resolve(12755,a,2105,c)]. given #1776 (F,wt=10): 12809 -->_s0(empty(nil),app(sndsplit(0,sndsplit(0,nil)),false)) # answer(goal). [ur(2220,b,488,a,c,12755,a)]. given #1777 (F,wt=10): 12810 -->_s0(empty(nil),app(app(nil,sndsplit(0,nil)),false)) # answer(goal). [ur(2220,b,138,a,c,12755,a)]. given #1778 (F,wt=10): 12893 -->_s0(nil,sndsplit(0,head(cons(cons(x,y),z)))) # answer(goal). [ur(8581,b,2350,a,c,270,a)]. given #1779 (T,wt=8): 15288 ->*_s0(s(length(sndsplit(0,nil))),s(0)). [ur(87,a,2257,a,b,888,a)]. given #1780 (T,wt=9): 2262 ->_s0(tail(length(sndsplit(0,x))),tail(length(x))). [ur(54,a,482,a)]. given #1781 (T,wt=8): 15310 ->*_s0(tail(length(sndsplit(0,nil))),tail(0)). [ur(87,a,2262,a,b,914,a)]. given #1782 (T,wt=9): 2275 ->_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): 12980 -->_s0(true,app(nil,sndsplit(head(cons(0,x)),false))) # answer(goal). [resolve(271,a,9175,b)]. given #1785 (F,wt=10): 12981 -->_s0(true,sndsplit(0,sndsplit(head(cons(0,x)),false))) # answer(goal). [resolve(271,a,9118,b)]. given #1786 (F,wt=10): 12983 -->_s0(empty(nil),sndsplit(head(cons(length(nil),x)),false)) # answer(goal). [resolve(271,a,7440,b)]. given #1787 (F,wt=10): 12984 -->_s0(true,sndsplit(head(cons(app(nil,0),x)),false)) # answer(goal). [resolve(271,a,3430,b)]. given #1788 (T,wt=8): 15326 ->*_s0(length(length(sndsplit(0,nil))),length(0)). [ur(87,a,2275,a,b,940,a)]. given #1789 (T,wt=9): 2276 ->_s0(head(length(sndsplit(0,x))),head(length(x))). [ur(40,a,482,a)]. given #1790 (T,wt=8): 15345 ->*_s0(head(length(sndsplit(0,nil))),head(0)). [ur(87,a,2276,a,b,966,a)]. given #1791 (T,wt=9): 2279 ->_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): 12985 -->_s0(true,sndsplit(head(cons(0,x)),app(nil,false))) # answer(goal). [resolve(271,a,2701,b)]. given #1794 (F,wt=10): 13056 -->_s0(nil,sndsplit(head(cons(0,x)),cons(y,z))) # answer(goal). [ur(8581,b,2350,a,c,271,a)]. given #1795 (F,wt=10): 13071 -->_s0(true,sndsplit(head(cons(sndsplit(0,0),x)),false)) # answer(goal). [ur(2105,b,271,a,c,12211,a)]. given #1796 (F,wt=10): 13082 -->_s0(true,sndsplit(tail(cons(x,0)),app(nil,false))) # answer(goal). [resolve(9263,b,85,a)]. given #1797 (T,wt=8): 15361 ->*_s0(empty(length(sndsplit(0,nil))),empty(0)). [ur(87,a,2279,a,b,1026,a)]. given #1798 (T,wt=9): 2284 ->*_s0(tail(cons(x,length(sndsplit(0,nil)))),0). [ur(87,a,85,a,b,2255,a)]. given #1799 (T,wt=9): 2286 ->*_s0(head(cons(length(sndsplit(0,nil)),x)),0). [ur(87,a,67,a,b,2255,a)]. given #1800 (T,wt=9): 2292 ->_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): 13107 -->_s0(true,sndsplit(sndsplit(0,head(cons(0,x))),false)) # answer(goal). [ur(2105,b,471,a,c,13053,a)]. given #1803 (F,wt=10): 13109 -->_s0(true,sndsplit(app(nil,head(cons(0,x))),false)) # answer(goal). [ur(2105,b,121,a,c,13053,a)]. given #1804 (F,wt=10): 13172 -->_s0(true,app(nil,app(nil,x))) | -->_s0(x,false) # answer(goal). [resolve(9336,b,36,b)]. given #1805 (F,wt=10): 13173 -->_s0(true,app(nil,app(x,false))) | -->_s0(x,nil) # answer(goal). [resolve(9336,b,35,b)]. given #1806 (T,wt=9): 2297 ->_s0(tail(head(sndsplit(0,x))),tail(head(x))). [ur(54,a,483,a)]. given #1807 (T,wt=9): 2310 ->_s0(length(head(sndsplit(0,x))),length(head(x))). [ur(41,a,483,a)]. given #1808 (T,wt=9): 2311 ->_s0(head(head(sndsplit(0,x))),head(head(x))). [ur(40,a,483,a)]. given #1809 (T,wt=9): 2314 ->_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): 13242 -->_s0(true,app(tail(cons(x,nil)),app(nil,false))) # answer(goal). [resolve(9337,b,85,a)]. given #1812 (F,wt=10): 13243 -->_s0(true,app(sndsplit(s(x),nil),app(nil,false))) # answer(goal). [resolve(9337,b,84,a)]. given #1813 (F,wt=10): 13244 -->_s0(true,app(head(cons(nil,x)),app(nil,false))) # answer(goal). [resolve(9337,b,67,a)]. given #1814 (F,wt=10): 13247 -->_s0(true,sndsplit(app(fstsplit(s(x),nil),0),false)) # answer(goal). [resolve(9397,b,263,a)]. given #1815 (T,wt=9): 2353 ->_s0(s(empty(sndsplit(0,x))),s(empty(x))). [ur(59,a,486,a)]. given #1816 (T,wt=8): 15428 ->*_s0(s(empty(sndsplit(0,nil))),s(true)). [ur(87,a,2353,a,b,692,a)]. given #1817 (T,wt=9): 2358 ->_s0(tail(empty(sndsplit(0,x))),tail(empty(x))). [ur(54,a,486,a)]. given #1818 (T,wt=8): 15445 ->*_s0(tail(empty(sndsplit(0,nil))),tail(true)). [ur(87,a,2358,a,b,751,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): 13250 -->_s0(true,sndsplit(tail(cons(x,app(nil,0))),false)) # answer(goal). [resolve(9397,b,85,a)]. given #1821 (F,wt=10): 13251 -->_s0(true,sndsplit(app(nil,x),false)) | -->_s0(x,0) # answer(goal). [resolve(9397,b,36,b)]. given #1822 (F,wt=10): 13252 -->_s0(true,sndsplit(app(x,0),false)) | -->_s0(x,nil) # answer(goal). [resolve(9397,b,35,b)]. given #1823 (F,wt=10): 13416 -->_s0(true,leq(s(x),length(tail(cons(y,nil))))) # answer(goal). [resolve(9638,b,557,a)]. given #1824 (T,wt=9): 2371 ->_s0(length(empty(sndsplit(0,x))),length(empty(x))). [ur(41,a,486,a)]. given #1825 (T,wt=8): 15468 ->*_s0(length(empty(sndsplit(0,nil))),length(true)). [ur(87,a,2371,a,b,777,a)]. given #1826 (T,wt=9): 2372 ->_s0(head(empty(sndsplit(0,x))),head(empty(x))). [ur(40,a,486,a)]. given #1827 (T,wt=8): 15485 ->*_s0(head(empty(sndsplit(0,nil))),head(true)). [ur(87,a,2372,a,b,803,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): 13417 -->_s0(true,leq(s(x),length(sndsplit(s(y),nil)))) # answer(goal). [resolve(9638,b,532,a)]. given #1830 (F,wt=10): 13420 -->_s0(true,leq(s(x),length(head(cons(nil,y))))) # answer(goal). [resolve(9638,b,282,a)]. given #1831 (F,wt=10): 13421 -->_s0(true,leq(s(x),length(fstsplit(s(y),nil)))) # answer(goal). [resolve(9638,b,257,a)]. given #1832 (F,wt=10): 13424 -->_s0(true,leq(s(x),tail(cons(y,length(nil))))) # answer(goal). [resolve(9638,b,85,a)]. given #1833 (T,wt=9): 2375 ->_s0(empty(empty(sndsplit(0,x))),empty(empty(x))). [ur(37,a,486,a)]. given #1834 (T,wt=8): 15510 ->*_s0(empty(empty(sndsplit(0,nil))),empty(true)). [ur(87,a,2375,a,b,829,a)]. given #1835 (T,wt=9): 2381 ->*_s0(tail(cons(x,empty(sndsplit(0,nil)))),true). [ur(87,a,85,a,b,2351,a)]. given #1836 (T,wt=9): 2383 ->*_s0(head(cons(empty(sndsplit(0,nil)),x)),true). [ur(87,a,67,a,b,2351,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): 13425 -->_s0(true,leq(s(x),head(cons(length(nil),y)))) # answer(goal). [resolve(9638,b,67,a)]. given #1839 (F,wt=10): 13426 -->_s0(true,leq(s(x),length(y))) | -->_s0(y,nil) # answer(goal). [resolve(9638,b,41,b)]. given #1840 (F,wt=10): 13471 -->_s0(empty(nil),leq(s(x),head(cons(0,y)))) # answer(goal). [resolve(280,a,7454,b)]. given #1841 (F,wt=10): 13499 -->_s0(true,leq(tail(cons(x,s(y))),length(nil))) # answer(goal). [resolve(9639,b,85,a)]. given #1842 (T,wt=9): 2385 ->*_s0(tail(sndsplit(0,cons(x,length(nil)))),0). [ur(87,a,469,a,b,622,a)]. given #1843 (T,wt=9): 2386 ->*_s0(tail(app(nil,cons(x,length(nil)))),0). [ur(87,a,119,a,b,622,a)]. given #1844 (T,wt=9): 2388 ->*_s0(sndsplit(0,tail(cons(x,length(nil)))),0). [ur(87,a,82,a,b,622,a)]. given #1845 (T,wt=9): 2390 ->*_s0(app(nil,tail(cons(x,length(nil)))),0). [ur(87,a,61,a,b,622,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): 13501 -->_s0(true,leq(head(cons(s(x),y)),length(nil))) # answer(goal). [resolve(9639,b,67,a)]. given #1848 (F,wt=10): 13504 -->_s0(true,app(app(fstsplit(s(x),nil),nil),false)) # answer(goal). [resolve(9641,b,263,a)]. given #1849 (F,wt=10): 13507 -->_s0(true,app(tail(cons(x,app(nil,nil))),false)) # answer(goal). [resolve(9641,b,85,a)]. given #1850 (F,wt=10): 13508 -->_s0(true,app(head(cons(app(nil,nil),x)),false)) # answer(goal). [resolve(9641,b,67,a)]. given #1851 (T,wt=9): 2391 ->*_s0(head(sndsplit(0,cons(length(nil),x))),0). [ur(87,a,483,a,b,624,a)]. given #1852 (T,wt=9): 2392 ->*_s0(head(app(nil,cons(length(nil),x))),0). [ur(87,a,133,a,b,624,a)]. given #1853 (T,wt=9): 2394 ->*_s0(sndsplit(0,head(cons(length(nil),x))),0). [ur(87,a,82,a,b,624,a)]. given #1854 (T,wt=9): 2396 ->*_s0(app(nil,head(cons(length(nil),x))),0). [ur(87,a,61,a,b,624,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): 13509 -->_s0(true,app(app(nil,x),false)) | -->_s0(x,nil) # answer(goal). [resolve(9641,b,36,b)]. given #1857 (F,wt=10): 13510 -->_s0(true,app(app(x,nil),false)) | -->_s0(x,nil) # answer(goal). [resolve(9641,b,35,b)]. given #1858 (F,wt=10): 13528 -->_s0(empty(nil),leq(head(cons(s(x),y)),0)) # answer(goal). [resolve(281,a,7454,b)]. given #1859 (F,wt=10): 13727 -->_s0(true,app(app(nil,head(cons(nil,x))),false)) # answer(goal). [resolve(287,a,9641,b)]. given #1860 (T,wt=9): 2564 ->*_s0(tail(sndsplit(0,cons(x,empty(nil)))),true). [ur(87,a,469,a,b,627,a)]. given #1861 (T,wt=9): 2565 ->*_s0(tail(app(nil,cons(x,empty(nil)))),true). [ur(87,a,119,a,b,627,a)]. given #1862 (T,wt=9): 2567 ->*_s0(sndsplit(0,tail(cons(x,empty(nil)))),true). [ur(87,a,82,a,b,627,a)]. given #1863 (T,wt=9): 2569 ->*_s0(app(nil,tail(cons(x,empty(nil)))),true). [ur(87,a,61,a,b,627,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): 13755 -->_s0(nil,app(nil,head(cons(cons(x,y),z)))) # answer(goal). [ur(8581,b,1532,a,c,287,a)]. given #1866 (F,wt=10): 13758 -->_s0(true,app(fstsplit(0,x),y)) | -->_s0(y,false) # answer(goal). [resolve(9757,b,36,b)]. given #1867 (F,wt=10): 13759 -->_s0(true,app(x,false)) | -->_s0(x,fstsplit(0,y)) # answer(goal). [resolve(9757,b,35,b)]. given #1868 (F,wt=8): 15544 -->_s0(true,app(fstsplit(length(nil),x),false)) # answer(goal). [resolve(13759,b,335,a)]. given #1869 (T,wt=9): 2571 ->*_s0(head(sndsplit(0,cons(empty(nil),x))),true). [ur(87,a,483,a,b,629,a)]. given #1870 (T,wt=9): 2572 ->*_s0(head(app(nil,cons(empty(nil),x))),true). [ur(87,a,133,a,b,629,a)]. given #1871 (T,wt=9): 2574 ->*_s0(sndsplit(0,head(cons(empty(nil),x))),true). [ur(87,a,82,a,b,629,a)]. given #1872 (T,wt=9): 2576 ->*_s0(app(nil,head(cons(empty(nil),x))),true). [ur(87,a,61,a,b,629,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=9): 15543 -->_s0(true,app(fstsplit(sndsplit(0,0),x),false)) # answer(goal). [resolve(13759,b,485,a)]. given #1875 (F,wt=9): 15546 -->_s0(true,app(fstsplit(app(nil,0),x),false)) # answer(goal). [resolve(13759,b,135,a)]. given #1876 (F,wt=10): 13807 -->_s0(true,app(head(cons(fstsplit(0,x),y)),false)) # answer(goal). [resolve(288,a,9757,b)]. given #1877 (F,wt=10): 13808 -->_s0(true,app(app(head(cons(nil,x)),nil),false)) # answer(goal). [resolve(288,a,9641,b)]. given #1878 (T,wt=9): 2583 ->*_s0(sndsplit(0,sndsplit(0,sndsplit(0,x))),x). [ur(87,a,82,a,b,635,a)]. given #1879 (T,wt=9): 2585 ->*_s0(app(nil,sndsplit(0,sndsplit(0,x))),x). [ur(87,a,61,a,b,635,a)]. given #1880 (T,wt=9): 2596 ->*_s0(sndsplit(0,app(nil,sndsplit(0,x))),x). [ur(87,a,82,a,b,637,a)]. given #1881 (T,wt=9): 2598 ->*_s0(app(nil,app(nil,sndsplit(0,x))),x). [ur(87,a,61,a,b,637,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=10): 13809 -->_s0(true,sndsplit(app(head(cons(nil,x)),0),false)) # answer(goal). [resolve(288,a,9397,b)]. given #1884 (F,wt=10): 13810 -->_s0(true,app(nil,app(head(cons(nil,x)),false))) # answer(goal). [resolve(288,a,9336,b)]. given #1885 (F,wt=10): 13811 -->_s0(true,sndsplit(0,app(head(cons(nil,x)),false))) # answer(goal). [resolve(288,a,9262,b)]. given #1886 (F,wt=10): 13872 -->_s0(nil,app(head(cons(cons(x,y),z)),u)) # answer(goal). [ur(8581,b,2778,a,c,288,a)]. given #1887 (T,wt=9): 2604 ->*_s0(head(app(cons(empty(nil),x),y)),true). [ur(87,a,108,a,b,629,a)]. given #1888 (T,wt=9): 2605 ->*_s0(head(app(cons(length(nil),x),y)),0). [ur(87,a,108,a,b,624,a)]. given #1889 (T,wt=9): 2637 ->*_s0(sndsplit(0,sndsplit(0,mapf(x,nil))),nil). [ur(87,a,82,a,b,639,a)]. given #1890 (T,wt=9): 2639 ->*_s0(app(nil,sndsplit(0,mapf(x,nil))),nil). [ur(87,a,61,a,b,639,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=10): 13873 -->_s0(nil,app(head(cons(nil,x)),cons(y,z))) # answer(goal). [ur(8581,b,1532,a,c,288,a)]. given #1893 (F,wt=10): 13886 -->_s0(true,app(head(cons(sndsplit(0,nil),x)),false)) # answer(goal). [ur(2105,b,288,a,c,12755,a)]. given #1894 (F,wt=10): 13888 -->_s0(true,app(head(cons(mapf(x,nil),y)),false)) # answer(goal). [ur(2105,b,288,a,c,11966,a)]. given #1895 (F,wt=10): 13926 -->_s0(true,app(sndsplit(0,head(cons(nil,x))),false)) # answer(goal). [ur(2105,b,488,a,c,13870,a)]. given #1896 (T,wt=9): 2641 ->*_s0(sndsplit(0,app(nil,mapf(x,nil))),nil). [ur(87,a,82,a,b,641,a)]. given #1897 (T,wt=9): 2643 ->*_s0(app(nil,app(nil,mapf(x,nil))),nil). [ur(87,a,61,a,b,641,a)]. given #1898 (T,wt=9): 2647 ->*_s0(sndsplit(0,sndsplit(0,leq(0,x))),true). [ur(87,a,82,a,b,678,a)]. given #1899 (T,wt=9): 2649 ->*_s0(app(nil,sndsplit(0,leq(0,x))),true). [ur(87,a,61,a,b,678,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=10): 14132 -->_s0(empty(nil),sndsplit(length(tail(cons(x,nil))),false)) # answer(goal). [resolve(10342,b,557,a)]. given #1902 (F,wt=10): 14133 -->_s0(empty(nil),sndsplit(length(sndsplit(s(x),nil)),false)) # answer(goal). [resolve(10342,b,532,a)]. given #1903 (F,wt=10): 14136 -->_s0(empty(nil),sndsplit(length(head(cons(nil,x))),false)) # answer(goal). [resolve(10342,b,282,a)]. given #1904 (F,wt=10): 14137 -->_s0(empty(nil),sndsplit(length(fstsplit(s(x),nil)),false)) # answer(goal). [resolve(10342,b,257,a)]. given #1905 (T,wt=9): 2652 ->*_s0(sndsplit(0,leq(s(0),s(x))),true). [ur(87,a,82,a,b,679,a)]. given #1906 (T,wt=9): 2653 ->*_s0(leq(s(s(0)),s(s(x))),true). [ur(87,a,72,a,b,679,a)]. given #1907 (T,wt=9): 2655 ->*_s0(app(nil,leq(s(0),s(x))),true). [ur(87,a,61,a,b,679,a)]. given #1908 (T,wt=9): 2688 ->*_s0(sndsplit(0,app(nil,leq(0,x))),true). [ur(87,a,82,a,b,681,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=10): 14140 -->_s0(empty(nil),sndsplit(tail(cons(x,length(nil))),false)) # answer(goal). [resolve(10342,b,85,a)]. given #1911 (F,wt=10): 14141 -->_s0(empty(nil),sndsplit(length(x),false)) | -->_s0(x,nil) # answer(goal). [resolve(10342,b,41,b)]. given #1912 (F,wt=10): 14222 -->_s0(empty(nil),head(cons(x,y))) | -->_s0(x,false) # answer(goal). [resolve(10403,b,55,b)]. given #1913 (F,wt=10): 14267 -->_s0(empty(nil),leq(s(x),tail(cons(y,0)))) # answer(goal). [resolve(10404,b,85,a)]. given #1914 (T,wt=9): 2690 ->*_s0(app(nil,app(nil,leq(0,x))),true). [ur(87,a,61,a,b,681,a)]. given #1915 (T,wt=9): 2693 ->*_s0(sndsplit(0,sndsplit(0,fstsplit(0,x))),nil). [ur(87,a,82,a,b,683,a)]. given #1916 (T,wt=9): 2695 ->*_s0(app(nil,sndsplit(0,fstsplit(0,x))),nil). [ur(87,a,61,a,b,683,a)]. given #1917 (T,wt=9): 2697 ->*_s0(sndsplit(0,app(nil,fstsplit(0,x))),nil). [ur(87,a,82,a,b,685,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=10): 14268 -->_s0(empty(nil),leq(tail(cons(x,s(y))),0)) # answer(goal). [resolve(10405,b,85,a)]. given #1920 (F,wt=10): 14270 -->_s0(empty(nil),tail(cons(x,y))) | -->_s0(y,false) # answer(goal). [resolve(10406,b,56,b)]. given #1921 (F,wt=10): 14393 -->_s0(nil,app(x,y)) | -->_s0(x,cons(z,u)) # answer(goal). [resolve(11277,b,35,b)]. given #1922 (F,wt=10): 14394 -->_s0(nil,sndsplit(0,x)) | -->_s0(x,cons(y,z)) # answer(goal). [resolve(11278,b,53,b)]. given #1923 (T,wt=9): 2699 ->*_s0(app(nil,app(nil,fstsplit(0,x))),nil). [ur(87,a,61,a,b,685,a)]. given #1924 (T,wt=9): 2707 ->*_s0(sndsplit(0,sndsplit(0,app(nil,x))),x). [ur(87,a,82,a,b,689,a)]. given #1925 (T,wt=9): 2709 ->*_s0(app(nil,sndsplit(0,app(nil,x))),x). [ur(87,a,61,a,b,689,a)]. given #1926 (T,wt=9): 2754 ->*_s0(sndsplit(0,app(nil,app(nil,x))),x). [ur(87,a,82,a,b,691,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=10): 14395 -->_s0(nil,sndsplit(x,cons(y,z))) | -->_s0(x,0) # answer(goal). [resolve(11278,b,52,b)]. given #1929 (F,wt=10): 14437 -->_s0(nil,app(nil,x)) | -->_s0(x,cons(y,z)) # answer(goal). [resolve(11279,b,36,b)]. given #1930 (F,wt=10): 14438 -->_s0(nil,app(x,cons(y,z))) | -->_s0(x,nil) # answer(goal). [resolve(11279,b,35,b)]. given #1931 (F,wt=10): 14589 -->_s0(true,app(mapf(x,nil),y)) | -->_s0(y,false) # answer(goal). [resolve(11997,b,36,b)]. given #1932 (T,wt=9): 2756 ->*_s0(app(nil,app(nil,app(nil,x))),x). [ur(87,a,61,a,b,691,a)]. given #1933 (T,wt=9): 2759 ->*_s0(length(sndsplit(0,cons(x,nil))),s(0)). [ur(87,a,482,a,b,1251,a)]. given #1934 (T,wt=9): 2760 ->*_s0(length(app(nil,cons(x,nil))),s(0)). [ur(87,a,132,a,b,1251,a)]. given #1935 (T,wt=9): 2762 ->*_s0(sndsplit(0,length(cons(x,nil))),s(0)). [ur(87,a,82,a,b,1251,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=10): 14590 -->_s0(true,app(x,false)) | -->_s0(x,mapf(y,nil)) # answer(goal). [resolve(11997,b,35,b)]. given #1938 (F,wt=9): 15808 -->_s0(true,app(mapf(x,sndsplit(0,nil)),false)) # answer(goal). [resolve(14590,b,478,a)]. given #1939 (F,wt=9): 15809 -->_s0(true,app(mapf(x,mapf(y,nil)),false)) # answer(goal). [resolve(14590,b,453,a)]. given #1940 (F,wt=9): 15812 -->_s0(true,app(mapf(x,fstsplit(0,y)),false)) # answer(goal). [resolve(14590,b,203,a)]. given #1941 (T,wt=9): 2764 ->*_s0(app(nil,length(cons(x,nil))),s(0)). [ur(87,a,61,a,b,1251,a)]. given #1942 (T,wt=9): 2765 ->*_s0(s(sndsplit(0,app(nil,x))),s(x)). [ur(87,a,464,a,b,1299,a)]. given #1943 (T,wt=9): 2766 ->*_s0(s(app(nil,app(nil,x))),s(x)). [ur(87,a,114,a,b,1299,a)]. given #1944 (T,wt=9): 2768 ->*_s0(sndsplit(0,s(app(nil,x))),s(x)). [ur(87,a,82,a,b,1299,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=9): 15813 -->_s0(true,app(mapf(x,app(nil,nil)),false)) # answer(goal). [resolve(14590,b,128,a)]. given #1947 (F,wt=10): 14624 -->_s0(true,sndsplit(0,sndsplit(tail(cons(x,0)),false))) # answer(goal). [resolve(12137,b,85,a)]. given #1948 (F,wt=10): 14671 -->_s0(empty(nil),leq(length(cons(x,y)),length(nil))) # answer(goal). [ur(2220,b,306,a,c,4606,a)]. given #1949 (F,wt=10): 14673 -->_s0(true,leq(length(cons(x,y)),sndsplit(0,0))) # answer(goal). [ur(2105,b,306,a,c,12460,a)]. given #1950 (T,wt=9): 2770 ->*_s0(app(nil,s(app(nil,x))),s(x)). [ur(87,a,61,a,b,1299,a)]. given #1951 (T,wt=9): 2771 ->*_s0(tail(sndsplit(0,app(nil,x))),tail(x)). [ur(87,a,469,a,b,1328,a)]. given #1952 (T,wt=9): 2772 ->*_s0(tail(app(nil,app(nil,x))),tail(x)). [ur(87,a,119,a,b,1328,a)]. given #1953 (T,wt=9): 2774 ->*_s0(sndsplit(0,tail(app(nil,x))),tail(x)). [ur(87,a,82,a,b,1328,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=10): 14674 -->_s0(true,leq(length(cons(x,y)),app(nil,0))) # answer(goal). [ur(2105,b,306,a,c,4549,a)]. given #1956 (F,wt=10): 14675 -->_s0(true,app(nil,sndsplit(tail(cons(x,0)),false))) # answer(goal). [resolve(12142,b,85,a)]. given #1957 (F,wt=10): 14681 -->_s0(true,app(nil,leq(length(cons(x,y)),0))) # answer(goal). [resolve(14669,a,2496,b)]. given #1958 (F,wt=10): 14683 -->_s0(true,sndsplit(0,leq(length(cons(x,y)),0))) # answer(goal). [resolve(14669,a,2479,b)]. given #1959 (T,wt=9): 2776 ->*_s0(app(nil,tail(app(nil,x))),tail(x)). [ur(87,a,61,a,b,1328,a)]. given #1960 (T,wt=9): 2805 ->*_s0(length(sndsplit(0,app(nil,x))),length(x)). [ur(87,a,482,a,b,1357,a)]. given #1961 (T,wt=9): 2806 ->*_s0(length(app(nil,app(nil,x))),length(x)). [ur(87,a,132,a,b,1357,a)]. given #1962 (T,wt=9): 2808 ->*_s0(sndsplit(0,length(app(nil,x))),length(x)). [ur(87,a,82,a,b,1357,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=10): 14704 -->_s0(true,leq(sndsplit(0,length(cons(x,y))),0)) # answer(goal). [ur(2105,b,481,a,c,14669,a)]. given #1965 (F,wt=10): 14707 -->_s0(true,leq(app(nil,length(cons(x,y))),0)) # answer(goal). [ur(2105,b,131,a,c,14669,a)]. given #1966 (F,wt=10): 14708 -->_s0(true,leq(s(length(cons(x,y))),s(0))) # answer(goal). [ur(2105,b,72,a,c,14669,a)]. given #1967 (F,wt=10): 14865 -->_s0(true,sndsplit(sndsplit(0,0),x)) | -->_s0(x,false) # answer(goal). [resolve(12250,b,53,b)]. given #1968 (T,wt=9): 2810 ->*_s0(app(nil,length(app(nil,x))),length(x)). [ur(87,a,61,a,b,1357,a)]. given #1969 (T,wt=9): 2811 ->*_s0(head(sndsplit(0,app(nil,x))),head(x)). [ur(87,a,483,a,b,1503,a)]. given #1970 (T,wt=9): 2812 ->*_s0(head(app(nil,app(nil,x))),head(x)). [ur(87,a,133,a,b,1503,a)]. given #1971 (T,wt=9): 2814 ->*_s0(sndsplit(0,head(app(nil,x))),head(x)). [ur(87,a,82,a,b,1503,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=10): 14866 -->_s0(true,sndsplit(x,false)) | -->_s0(x,sndsplit(0,0)) # answer(goal). [resolve(12250,b,52,b)]. given #1974 (F,wt=8): 15838 -->_s0(true,sndsplit(sndsplit(length(nil),0),false)) # answer(goal). [resolve(14866,b,321,a)]. given #1975 (F,wt=9): 15837 -->_s0(true,sndsplit(sndsplit(sndsplit(0,0),0),false)) # answer(goal). [resolve(14866,b,471,a)]. given #1976 (F,wt=9): 15840 -->_s0(true,sndsplit(sndsplit(app(nil,0),0),false)) # answer(goal). [resolve(14866,b,121,a)]. given #1977 (T,wt=9): 2816 ->*_s0(app(nil,head(app(nil,x))),head(x)). [ur(87,a,61,a,b,1503,a)]. given #1978 (T,wt=9): 2817 ->*_s0(empty(sndsplit(0,app(nil,x))),empty(x)). [ur(87,a,486,a,b,1534,a)]. given #1979 (T,wt=9): 2818 ->*_s0(empty(app(nil,app(nil,x))),empty(x)). [ur(87,a,136,a,b,1534,a)]. given #1980 (T,wt=9): 2820 ->*_s0(sndsplit(0,empty(app(nil,x))),empty(x)). [ur(87,a,82,a,b,1534,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=10): 15185 -->_s0(true,sndsplit(0,app(tail(cons(x,nil)),false))) # answer(goal). [resolve(12670,b,85,a)]. given #1983 (F,wt=10): 15186 -->_s0(true,sndsplit(0,app(sndsplit(s(x),nil),false))) # answer(goal). [resolve(12670,b,84,a)]. given #1984 (F,wt=10): 15293 -->_s0(true,app(sndsplit(0,nil),x)) | -->_s0(x,false) # answer(goal). [resolve(12800,b,36,b)]. given #1985 (F,wt=10): 15294 -->_s0(true,app(x,false)) | -->_s0(x,sndsplit(0,nil)) # answer(goal). [resolve(12800,b,35,b)]. given #1986 (T,wt=9): 2822 ->*_s0(app(nil,empty(app(nil,x))),empty(x)). [ur(87,a,61,a,b,1534,a)]. given #1987 (T,wt=9): 2823 ->*_s0(s(sndsplit(0,fstsplit(0,x))),s(nil)). [ur(87,a,464,a,b,1596,a)]. given #1988 (T,wt=9): 2824 ->*_s0(s(app(nil,fstsplit(0,x))),s(nil)). [ur(87,a,114,a,b,1596,a)]. given #1989 (T,wt=9): 2826 ->*_s0(sndsplit(0,s(fstsplit(0,x))),s(nil)). [ur(87,a,82,a,b,1596,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=8): 15850 -->_s0(true,app(sndsplit(length(nil),nil),false)) # answer(goal). [resolve(15294,b,321,a)]. given #1992 (F,wt=9): 15849 -->_s0(true,app(sndsplit(sndsplit(0,0),nil),false)) # answer(goal). [resolve(15294,b,471,a)]. given #1993 (F,wt=9): 15852 -->_s0(true,app(sndsplit(app(nil,0),nil),false)) # answer(goal). [resolve(15294,b,121,a)]. given #1994 (F,wt=10): 15384 -->_s0(true,app(nil,app(tail(cons(x,nil)),false))) # answer(goal). [resolve(13173,b,85,a)]. given #1995 (T,wt=9): 2828 ->*_s0(app(nil,s(fstsplit(0,x))),s(nil)). [ur(87,a,61,a,b,1596,a)]. given #1996 (T,wt=9): 2857 ->*_s0(tail(sndsplit(0,fstsplit(0,x))),tail(nil)). [ur(87,a,469,a,b,1623,a)]. given #1997 (T,wt=9): 2858 ->*_s0(tail(app(nil,fstsplit(0,x))),tail(nil)). [ur(87,a,119,a,b,1623,a)]. given #1998 (T,wt=9): 2860 ->*_s0(sndsplit(0,tail(fstsplit(0,x))),tail(nil)). [ur(87,a,82,a,b,1623,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=10): 15385 -->_s0(true,app(nil,app(sndsplit(s(x),nil),false))) # answer(goal). [resolve(13173,b,84,a)]. given #2001 (F,wt=10): 15456 -->_s0(true,sndsplit(app(nil,tail(cons(x,0))),false)) # answer(goal). [resolve(13251,b,85,a)]. given #2002 (F,wt=10): 15457 -->_s0(true,sndsplit(app(tail(cons(x,nil)),0),false)) # answer(goal). [resolve(13252,b,85,a)]. given #2003 (F,wt=10): 15458 -->_s0(true,sndsplit(app(sndsplit(s(x),nil),0),false)) # answer(goal). [resolve(13252,b,84,a)]. given #2004 (T,wt=9): 2862 ->*_s0(app(nil,tail(fstsplit(0,x))),tail(nil)). [ur(87,a,61,a,b,1623,a)]. given #2005 (T,wt=9): 2863 ->*_s0(length(sndsplit(0,fstsplit(0,x))),length(nil)). [ur(87,a,482,a,b,1651,a)]. given #2006 (T,wt=9): 2864 ->*_s0(length(app(nil,fstsplit(0,x))),length(nil)). [ur(87,a,132,a,b,1651,a)]. given #2007 (T,wt=9): 2866 ->*_s0(sndsplit(0,length(fstsplit(0,x))),length(nil)). [ur(87,a,82,a,b,1651,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=10): 15531 -->_s0(true,app(app(nil,tail(cons(x,nil))),false)) # answer(goal). [resolve(13509,b,85,a)]. given #2010 (F,wt=10): 15532 -->_s0(true,app(app(nil,sndsplit(s(x),nil)),false)) # answer(goal). [resolve(13509,b,84,a)]. given #2011 (F,wt=10): 15533 -->_s0(true,app(app(tail(cons(x,nil)),nil),false)) # answer(goal). [resolve(13510,b,85,a)]. given #2012 (F,wt=10): 15534 -->_s0(true,app(app(sndsplit(s(x),nil),nil),false)) # answer(goal). [resolve(13510,b,84,a)]. given #2013 (T,wt=9): 2868 ->*_s0(app(nil,length(fstsplit(0,x))),length(nil)). [ur(87,a,61,a,b,1651,a)]. given #2014 (T,wt=9): 2869 ->*_s0(head(sndsplit(0,fstsplit(0,x))),head(nil)). [ur(87,a,483,a,b,1721,a)]. given #2015 (T,wt=9): 2870 ->*_s0(head(app(nil,fstsplit(0,x))),head(nil)). [ur(87,a,133,a,b,1721,a)]. given #2016 (T,wt=9): 2872 ->*_s0(sndsplit(0,head(fstsplit(0,x))),head(nil)). [ur(87,a,82,a,b,1721,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=10): 15545 -->_s0(true,app(fstsplit(head(cons(0,x)),y),false)) # answer(goal). [resolve(13759,b,285,a)]. given #2019 (F,wt=10): 15547 -->_s0(true,app(tail(cons(x,fstsplit(0,y))),false)) # answer(goal). [resolve(13759,b,85,a)]. given #2020 (F,wt=10): 15548 -->_s0(true,app(fstsplit(x,y),false)) | -->_s0(x,0) # answer(goal). [resolve(13759,b,38,b)]. given #2021 (F,wt=10): 15687 -->_s0(nil,app(tail(cons(x,cons(y,z))),u)) # answer(goal). [resolve(14393,b,85,a)]. given #2022 (T,wt=9): 2874 ->*_s0(app(nil,head(fstsplit(0,x))),head(nil)). [ur(87,a,61,a,b,1721,a)]. given #2023 (T,wt=9): 2875 ->*_s0(empty(sndsplit(0,fstsplit(0,x))),empty(nil)). [ur(87,a,486,a,b,1749,a)]. given #2024 (T,wt=9): 2876 ->*_s0(empty(app(nil,fstsplit(0,x))),empty(nil)). [ur(87,a,136,a,b,1749,a)]. given #2025 (T,wt=9): 2878 ->*_s0(sndsplit(0,empty(fstsplit(0,x))),empty(nil)). [ur(87,a,82,a,b,1749,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=10): 15688 -->_s0(nil,sndsplit(0,tail(cons(x,cons(y,z))))) # answer(goal). [resolve(14394,b,85,a)]. given #2028 (F,wt=10): 15772 -->_s0(nil,sndsplit(tail(cons(x,0)),cons(y,z))) # answer(goal). [resolve(14395,b,85,a)]. given #2029 (F,wt=10): 15773 -->_s0(nil,app(nil,tail(cons(x,cons(y,z))))) # answer(goal). [resolve(14437,b,85,a)]. given #2030 (F,wt=10): 15774 -->_s0(nil,app(tail(cons(x,nil)),cons(y,z))) # answer(goal). [resolve(14438,b,85,a)]. given #2031 (T,wt=9): 2880 ->*_s0(app(nil,empty(fstsplit(0,x))),empty(nil)). [ur(87,a,61,a,b,1749,a)]. given #2032 (T,wt=9): 2908 ->*_s0(s(sndsplit(0,leq(0,x))),s(true)). [ur(87,a,464,a,b,1782,a)]. given #2033 (T,wt=9): 2909 ->*_s0(s(app(nil,leq(0,x))),s(true)). [ur(87,a,114,a,b,1782,a)]. given #2034 (T,wt=9): 2911 ->*_s0(sndsplit(0,s(leq(0,x))),s(true)). [ur(87,a,82,a,b,1782,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=10): 15775 -->_s0(nil,app(sndsplit(s(x),nil),cons(y,z))) # answer(goal). [resolve(14438,b,84,a)]. given #2037 (F,wt=10): 15810 -->_s0(true,app(mapf(x,head(cons(nil,y))),false)) # answer(goal). [resolve(14590,b,278,a)]. given #2038 (F,wt=10): 15811 -->_s0(true,app(mapf(x,fstsplit(s(y),nil)),false)) # answer(goal). [resolve(14590,b,253,a)]. given #2039 (F,wt=10): 15814 -->_s0(true,app(tail(cons(x,mapf(y,nil))),false)) # answer(goal). [resolve(14590,b,85,a)]. given #2040 (T,wt=9): 2913 ->*_s0(app(nil,s(leq(0,x))),s(true)). [ur(87,a,61,a,b,1782,a)]. given #2041 (T,wt=9): 2914 ->*_s0(tail(sndsplit(0,leq(0,x))),tail(true)). [ur(87,a,469,a,b,1857,a)]. given #2042 (T,wt=9): 2915 ->*_s0(tail(app(nil,leq(0,x))),tail(true)). [ur(87,a,119,a,b,1857,a)]. given #2043 (T,wt=9): 2917 ->*_s0(sndsplit(0,tail(leq(0,x))),tail(true)). [ur(87,a,82,a,b,1857,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=10): 15815 -->_s0(true,app(mapf(x,y),false)) | -->_s0(y,nil) # answer(goal). [resolve(14590,b,45,b)]. given #2046 (F,wt=10): 15839 -->_s0(true,sndsplit(sndsplit(head(cons(0,x)),0),false)) # answer(goal). [resolve(14866,b,271,a)]. given #2047 (F,wt=10): 15841 -->_s0(true,sndsplit(tail(cons(x,sndsplit(0,0))),false)) # answer(goal). [resolve(14866,b,85,a)]. given #2048 (F,wt=10): 15842 -->_s0(true,sndsplit(sndsplit(s(0),cons(x,0)),false)) # answer(goal). [resolve(14866,b,83,a)]. given #2049 (T,wt=9): 2919 ->*_s0(app(nil,tail(leq(0,x))),tail(true)). [ur(87,a,61,a,b,1857,a)]. given #2050 (T,wt=9): 2920 ->*_s0(length(sndsplit(0,leq(0,x))),length(true)). [ur(87,a,482,a,b,1884,a)]. given #2051 (T,wt=9): 2921 ->*_s0(length(app(nil,leq(0,x))),length(true)). [ur(87,a,132,a,b,1884,a)]. given #2052 (T,wt=9): 2923 ->*_s0(sndsplit(0,length(leq(0,x))),length(true)). [ur(87,a,82,a,b,1884,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=10): 15843 -->_s0(true,sndsplit(sndsplit(0,x),false)) | -->_s0(x,0) # answer(goal). [resolve(14866,b,53,b)]. given #2055 (F,wt=10): 15844 -->_s0(true,sndsplit(sndsplit(x,0),false)) | -->_s0(x,0) # answer(goal). [resolve(14866,b,52,b)]. given #2056 (F,wt=10): 15851 -->_s0(true,app(sndsplit(head(cons(0,x)),nil),false)) # answer(goal). [resolve(15294,b,271,a)]. given #2057 (F,wt=10): 15853 -->_s0(true,app(tail(cons(x,sndsplit(0,nil))),false)) # answer(goal). [resolve(15294,b,85,a)]. given #2058 (T,wt=9): 2925 ->*_s0(app(nil,length(leq(0,x))),length(true)). [ur(87,a,61,a,b,1884,a)]. given #2059 (T,wt=9): 2926 ->*_s0(head(sndsplit(0,leq(0,x))),head(true)). [ur(87,a,483,a,b,1911,a)]. given #2060 (T,wt=9): 2927 ->*_s0(head(app(nil,leq(0,x))),head(true)). [ur(87,a,133,a,b,1911,a)]. given #2061 (T,wt=9): 2929 ->*_s0(sndsplit(0,head(leq(0,x))),head(true)). [ur(87,a,82,a,b,1911,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=10): 15854 -->_s0(true,app(sndsplit(s(0),cons(x,nil)),false)) # answer(goal). [resolve(15294,b,83,a)]. given #2064 (F,wt=10): 15855 -->_s0(true,app(sndsplit(0,x),false)) | -->_s0(x,nil) # answer(goal). [resolve(15294,b,53,b)]. given #2065 (F,wt=10): 15856 -->_s0(true,app(sndsplit(x,nil),false)) | -->_s0(x,0) # answer(goal). [resolve(15294,b,52,b)]. given #2066 (F,wt=10): 15873 -->_s0(true,app(fstsplit(tail(cons(x,0)),y),false)) # answer(goal). [resolve(15548,b,85,a)]. given #2067 (T,wt=9): 2931 ->*_s0(app(nil,head(leq(0,x))),head(true)). [ur(87,a,61,a,b,1911,a)]. given #2068 (T,wt=9): 2933 ->*_s0(f(x,app(nil,y)),f(x,y)). [ur(87,a,115,a,b,86,a)]. given #2069 (T,wt=9): 2959 ->*_s0(empty(sndsplit(0,leq(0,x))),empty(true)). [ur(87,a,486,a,b,1938,a)]. given #2070 (T,wt=9): 2960 ->*_s0(empty(app(nil,leq(0,x))),empty(true)). [ur(87,a,136,a,b,1938,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=10): 15886 -->_s0(true,app(mapf(x,tail(cons(y,nil))),false)) # answer(goal). [resolve(15815,b,85,a)]. given #2073 (F,wt=10): 15887 -->_s0(true,app(mapf(x,sndsplit(s(y),nil)),false)) # answer(goal). [resolve(15815,b,84,a)]. given #2074 (F,wt=10): 15892 -->_s0(true,sndsplit(sndsplit(0,tail(cons(x,0))),false)) # answer(goal). [resolve(15843,b,85,a)]. given #2075 (F,wt=10): 15893 -->_s0(true,sndsplit(sndsplit(tail(cons(x,0)),0),false)) # answer(goal). [resolve(15844,b,85,a)]. given #2076 (T,wt=9): 2962 ->*_s0(sndsplit(0,empty(leq(0,x))),empty(true)). [ur(87,a,82,a,b,1938,a)]. given #2077 (T,wt=9): 2964 ->*_s0(app(nil,empty(leq(0,x))),empty(true)). [ur(87,a,61,a,b,1938,a)]. given #2078 (T,wt=9): 2965 ->*_s0(s(sndsplit(0,mapf(x,nil))),s(nil)). [ur(87,a,464,a,b,1992,a)]. given #2079 (T,wt=9): 2966 ->*_s0(s(app(nil,mapf(x,nil))),s(nil)). [ur(87,a,114,a,b,1992,a)]. given #2080 (A,wt=21): 401 ->_s0(ring(x,leq(s(y),s(z)),u,w,v5,v6),ring(x,leq(y,z),u,w,v5,v6)). [ur(47,a,72,a)]. given #2081 (F,wt=10): 15898 -->_s0(true,app(sndsplit(0,tail(cons(x,nil))),false)) # answer(goal). [resolve(15855,b,85,a)]. given #2082 (F,wt=10): 15899 -->_s0(true,app(sndsplit(0,sndsplit(s(x),nil)),false)) # answer(goal). [resolve(15855,b,84,a)]. given #2083 (F,wt=10): 15900 -->_s0(true,app(sndsplit(tail(cons(x,0)),nil),false)) # answer(goal). [resolve(15856,b,85,a)]. given #2084 (F,wt=11): 2491 -->_s0(true,length(cons(x,y))) | -->*_s0(s(length(y)),false) # answer(goal). [resolve(2105,b,68,a)]. given #2085 (T,wt=9): 2968 ->*_s0(sndsplit(0,s(mapf(x,nil))),s(nil)). [ur(87,a,82,a,b,1992,a)]. given #2086 (T,wt=9): 2970 ->*_s0(app(nil,s(mapf(x,nil))),s(nil)). [ur(87,a,61,a,b,1992,a)]. given #2087 (T,wt=9): 2971 ->*_s0(tail(sndsplit(0,mapf(x,nil))),tail(nil)). [ur(87,a,469,a,b,2019,a)]. given #2088 (T,wt=9): 2972 ->*_s0(tail(app(nil,mapf(x,nil))),tail(nil)). [ur(87,a,119,a,b,2019,a)]. given #2089 (A,wt=21): 402 ->_s0(ring(leq(s(x),s(y)),z,u,w,v5,v6),ring(leq(x,y),z,u,w,v5,v6)). [ur(46,a,72,a)]. given #2090 (F,wt=11): 2498 -->_s0(true,s(x)) | -->*_s0(s(y),false) | -->_s0(x,y) # answer(goal). [resolve(2105,b,59,b)]. given #2091 (F,wt=11): 2503 -->_s0(true,tail(x)) | -->*_s0(tail(y),false) | -->_s0(x,y) # answer(goal). [resolve(2105,b,54,b)]. given #2092 (F,wt=9): 17003 -->_s0(true,tail(sndsplit(length(nil),cons(x,false)))) # answer(goal). [ur(2503,b,2223,a,c,321,a)]. given #2093 (F,wt=10): 16994 -->_s0(true,tail(app(sndsplit(0,cons(x,nil)),false))) # answer(goal). [ur(2503,b,5776,a,c,488,a)]. given #2094 (T,wt=9): 2974 ->*_s0(sndsplit(0,tail(mapf(x,nil))),tail(nil)). [ur(87,a,82,a,b,2019,a)]. given #2095 (T,wt=9): 2976 ->*_s0(app(nil,tail(mapf(x,nil))),tail(nil)). [ur(87,a,61,a,b,2019,a)]. given #2096 (T,wt=9): 2977 ->*_s0(length(sndsplit(0,mapf(x,nil))),length(nil)). [ur(87,a,482,a,b,2047,a)]. given #2097 (T,wt=9): 2978 ->*_s0(length(app(nil,mapf(x,nil))),length(nil)). [ur(87,a,132,a,b,2047,a)]. given #2098 (A,wt=13): 403 ->_s0(mapf(x,leq(s(y),s(z))),mapf(x,leq(y,z))). [ur(45,a,72,a)]. given #2099 (F,wt=10): 16995 -->_s0(true,tail(app(cons(x,nil),sndsplit(0,false)))) # answer(goal). [ur(2503,b,5776,a,c,487,a)]. given #2100 (F,wt=10): 17000 -->_s0(true,tail(app(app(nil,cons(x,nil)),false))) # answer(goal). [ur(2503,b,5776,a,c,138,a)]. given #2101 (F,wt=10): 17001 -->_s0(true,tail(app(cons(x,nil),app(nil,false)))) # answer(goal). [ur(2503,b,5776,a,c,137,a)]. given #2102 (F,wt=10): 17002 -->_s0(true,tail(sndsplit(sndsplit(0,0),cons(x,false)))) # answer(goal). [ur(2503,b,2223,a,c,471,a)]. given #2103 (T,wt=9): 2980 ->*_s0(sndsplit(0,length(mapf(x,nil))),length(nil)). [ur(87,a,82,a,b,2047,a)]. given #2104 (T,wt=9): 2982 ->*_s0(app(nil,length(mapf(x,nil))),length(nil)). [ur(87,a,61,a,b,2047,a)]. given #2105 (T,wt=9): 2984 ->*_s0(f(app(nil,x),y),f(x,y)). [ur(87,a,116,a,b,86,a)]. given #2106 (T,wt=9): 3010 ->*_s0(head(sndsplit(0,mapf(x,nil))),head(nil)). [ur(87,a,483,a,b,2106,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=10): 17006 -->_s0(true,tail(sndsplit(app(nil,0),cons(x,false)))) # answer(goal). [ur(2503,b,2223,a,c,121,a)]. given #2109 (F,wt=10): 17008 -->_s0(true,tail(app(sndsplit(0,nil),cons(x,false)))) # answer(goal). [ur(2503,b,1327,a,c,488,a)]. given #2110 (F,wt=10): 17009 -->_s0(true,tail(app(mapf(x,nil),cons(y,false)))) # answer(goal). [ur(2503,b,1327,a,c,463,a)]. given #2111 (F,wt=10): 17013 -->_s0(true,tail(app(fstsplit(0,x),cons(y,false)))) # answer(goal). [ur(2503,b,1327,a,c,213,a)]. given #2112 (T,wt=9): 3011 ->*_s0(head(app(nil,mapf(x,nil))),head(nil)). [ur(87,a,133,a,b,2106,a)]. given #2113 (T,wt=9): 3013 ->*_s0(sndsplit(0,head(mapf(x,nil))),head(nil)). [ur(87,a,82,a,b,2106,a)]. given #2114 (T,wt=9): 3015 ->*_s0(app(nil,head(mapf(x,nil))),head(nil)). [ur(87,a,61,a,b,2106,a)]. given #2115 (T,wt=9): 3016 ->*_s0(empty(sndsplit(0,mapf(x,nil))),empty(nil)). [ur(87,a,486,a,b,2133,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=10): 17014 -->_s0(true,tail(app(app(nil,nil),cons(x,false)))) # answer(goal). [ur(2503,b,1327,a,c,138,a)]. given #2118 (F,wt=11): 2516 -->_s0(true,length(x)) | -->*_s0(length(y),false) | -->_s0(x,y) # answer(goal). [resolve(2105,b,41,b)]. given #2119 (F,wt=11): 2517 -->_s0(true,head(x)) | -->*_s0(head(y),false) | -->_s0(x,y) # answer(goal). [resolve(2105,b,40,b)]. given #2120 (F,wt=9): 18128 -->_s0(true,head(sndsplit(length(nil),cons(false,x)))) # answer(goal). [ur(2517,b,2290,a,c,321,a)]. given #2121 (T,wt=9): 3017 ->*_s0(empty(app(nil,mapf(x,nil))),empty(nil)). [ur(87,a,136,a,b,2133,a)]. given #2122 (T,wt=9): 3019 ->*_s0(sndsplit(0,empty(mapf(x,nil))),empty(nil)). [ur(87,a,82,a,b,2133,a)]. given #2123 (T,wt=9): 3021 ->*_s0(app(nil,empty(mapf(x,nil))),empty(nil)). [ur(87,a,61,a,b,2133,a)]. given #2124 (T,wt=9): 3022 ->*_s0(s(sndsplit(0,sndsplit(0,x))),s(x)). [ur(87,a,464,a,b,2167,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=10): 18122 -->_s0(true,head(app(sndsplit(0,cons(false,x)),y))) # answer(goal). [ur(2517,b,2606,a,c,488,a)]. given #2127 (F,wt=10): 18125 -->_s0(true,head(app(app(nil,cons(false,x)),y))) # answer(goal). [ur(2517,b,2606,a,c,138,a)]. given #2128 (F,wt=10): 18126 -->_s0(true,head(app(app(cons(false,x),y),z))) # answer(goal). [ur(2517,b,2606,a,c,113,a)]. given #2129 (F,wt=10): 18127 -->_s0(true,head(sndsplit(sndsplit(0,0),cons(false,x)))) # answer(goal). [ur(2517,b,2290,a,c,471,a)]. given #2130 (T,wt=9): 3023 ->*_s0(s(app(nil,sndsplit(0,x))),s(x)). [ur(87,a,114,a,b,2167,a)]. given #2131 (T,wt=9): 3025 ->*_s0(sndsplit(0,s(sndsplit(0,x))),s(x)). [ur(87,a,82,a,b,2167,a)]. given #2132 (T,wt=9): 3027 ->*_s0(app(nil,s(sndsplit(0,x))),s(x)). [ur(87,a,61,a,b,2167,a)]. given #2133 (T,wt=9): 3028 ->*_s0(tail(sndsplit(0,sndsplit(0,x))),tail(x)). [ur(87,a,469,a,b,2224,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): 18132 -->_s0(true,head(sndsplit(app(nil,0),cons(false,x)))) # answer(goal). [ur(2517,b,2290,a,c,121,a)]. given #2136 (F,wt=10): 18134 -->_s0(true,head(app(sndsplit(0,nil),cons(false,x)))) # answer(goal). [ur(2517,b,1502,a,c,488,a)]. given #2137 (F,wt=10): 18135 -->_s0(true,head(app(mapf(x,nil),cons(false,y)))) # answer(goal). [ur(2517,b,1502,a,c,463,a)]. given #2138 (F,wt=10): 18140 -->_s0(true,head(app(fstsplit(0,x),cons(false,y)))) # answer(goal). [ur(2517,b,1502,a,c,213,a)]. given #2139 (T,wt=9): 3029 ->*_s0(tail(app(nil,sndsplit(0,x))),tail(x)). [ur(87,a,119,a,b,2224,a)]. given #2140 (T,wt=9): 3031 ->*_s0(sndsplit(0,tail(sndsplit(0,x))),tail(x)). [ur(87,a,82,a,b,2224,a)]. given #2141 (T,wt=9): 3033 ->*_s0(app(nil,tail(sndsplit(0,x))),tail(x)). [ur(87,a,61,a,b,2224,a)]. given #2142 (T,wt=9): 3035 ->*_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): 18141 -->_s0(true,head(app(app(nil,nil),cons(false,x)))) # answer(goal). [ur(2517,b,1502,a,c,138,a)]. given #2145 (F,wt=11): 2520 -->_s0(true,empty(x)) | -->*_s0(empty(y),false) | -->_s0(x,y) # answer(goal). [resolve(2105,b,37,b)]. given #2146 (F,wt=9): 18688 -->_s0(true,empty(sndsplit(length(nil),cons(x,y)))) # answer(goal). [ur(2520,b,2350,a,c,321,a)]. given #2147 (F,wt=10): 18629 -->_s0(true,empty(app(app(cons(x,y),z),u))) # answer(goal). [resolve(2520,c,113,a),unit_del(b,2778)]. given #2148 (T,wt=9): 3061 ->*_s0(length(sndsplit(0,sndsplit(0,x))),length(x)). [ur(87,a,482,a,b,2256,a)]. given #2149 (T,wt=9): 3062 ->*_s0(length(app(nil,sndsplit(0,x))),length(x)). [ur(87,a,132,a,b,2256,a)]. given #2150 (T,wt=9): 3064 ->*_s0(sndsplit(0,length(sndsplit(0,x))),length(x)). [ur(87,a,82,a,b,2256,a)]. given #2151 (T,wt=9): 3066 ->*_s0(app(nil,length(sndsplit(0,x))),length(x)). [ur(87,a,61,a,b,2256,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=10): 18684 -->_s0(true,empty(app(sndsplit(0,cons(x,y)),z))) # answer(goal). [ur(2520,b,2778,a,c,488,a)]. given #2154 (F,wt=10): 18686 -->_s0(true,empty(app(app(nil,cons(x,y)),z))) # answer(goal). [ur(2520,b,2778,a,c,138,a)]. given #2155 (F,wt=10): 18687 -->_s0(true,empty(sndsplit(sndsplit(0,0),cons(x,y)))) # answer(goal). [ur(2520,b,2350,a,c,471,a)]. given #2156 (F,wt=10): 18692 -->_s0(true,empty(sndsplit(app(nil,0),cons(x,y)))) # answer(goal). [ur(2520,b,2350,a,c,121,a)]. given #2157 (T,wt=9): 3067 ->*_s0(head(sndsplit(0,sndsplit(0,x))),head(x)). [ur(87,a,483,a,b,2291,a)]. given #2158 (T,wt=9): 3068 ->*_s0(head(app(nil,sndsplit(0,x))),head(x)). [ur(87,a,133,a,b,2291,a)]. given #2159 (T,wt=9): 3070 ->*_s0(sndsplit(0,head(sndsplit(0,x))),head(x)). [ur(87,a,82,a,b,2291,a)]. given #2160 (T,wt=9): 3072 ->*_s0(app(nil,head(sndsplit(0,x))),head(x)). [ur(87,a,61,a,b,2291,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): 18694 -->_s0(true,empty(app(sndsplit(0,nil),cons(x,y)))) # answer(goal). [ur(2520,b,1532,a,c,488,a)]. given #2163 (F,wt=10): 18695 -->_s0(true,empty(app(mapf(x,nil),cons(y,z)))) # answer(goal). [ur(2520,b,1532,a,c,463,a)]. given #2164 (F,wt=10): 18700 -->_s0(true,empty(app(fstsplit(0,x),cons(y,z)))) # answer(goal). [ur(2520,b,1532,a,c,213,a)]. given #2165 (F,wt=10): 18701 -->_s0(true,empty(app(app(nil,nil),cons(x,y)))) # answer(goal). [ur(2520,b,1532,a,c,138,a)]. given #2166 (T,wt=9): 3073 ->*_s0(empty(sndsplit(0,sndsplit(0,x))),empty(x)). [ur(87,a,486,a,b,2352,a)]. given #2167 (T,wt=9): 3074 ->*_s0(empty(app(nil,sndsplit(0,x))),empty(x)). [ur(87,a,136,a,b,2352,a)]. given #2168 (T,wt=9): 3076 ->*_s0(sndsplit(0,empty(sndsplit(0,x))),empty(x)). [ur(87,a,82,a,b,2352,a)]. given #2169 (T,wt=9): 3078 ->*_s0(app(nil,empty(sndsplit(0,x))),empty(x)). [ur(87,a,61,a,b,2352,a)]. given #2170 (A,wt=11): 411 ->_s0(empty(leq(s(x),s(y))),empty(leq(x,y))). [ur(37,a,72,a)]. given #2171 (F,wt=11): 2683 -->_s0(true,sndsplit(0,x)) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal). [resolve(2479,b,87,c)]. given #2172 (F,wt=9): 19285 -->_s0(true,sndsplit(0,length(nil))) | -->*_s0(0,false) # answer(goal). [resolve(2683,b,69,a)]. given #2173 (F,wt=10): 19274 -->_s0(true,sndsplit(0,sndsplit(0,x))) | -->*_s0(x,false) # answer(goal). [resolve(2683,b,82,a)]. given #2174 (F,wt=10): 19282 -->_s0(true,sndsplit(0,mapf(x,nil))) | -->*_s0(nil,false) # answer(goal). [resolve(2683,b,74,a)]. given #2175 (T,wt=9): 3107 ->*_s0(cons(app(nil,x),y),cons(x,y)). [ur(87,a,118,a,b,86,a)]. given #2176 (T,wt=9): 3251 ->*_s0(sndsplit(x,app(nil,y)),sndsplit(x,y)). [ur(87,a,120,a,b,86,a)]. given #2177 (T,wt=9): 3391 ->*_s0(sndsplit(app(nil,0),app(nil,x)),x). [ur(87,a,121,a,b,689,a)]. given #2178 (T,wt=9): 3392 ->*_s0(sndsplit(app(nil,0),fstsplit(0,x)),nil). [ur(87,a,121,a,b,683,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=10): 19290 -->_s0(true,sndsplit(0,fstsplit(0,x))) | -->*_s0(nil,false) # answer(goal). [resolve(2683,b,64,a)]. given #2181 (F,wt=10): 19291 -->_s0(true,sndsplit(0,app(nil,x))) | -->*_s0(x,false) # answer(goal). [resolve(2683,b,61,a)]. given #2182 (F,wt=11): 2684 -->_s0(true,mapf(x,nil)) | -->_s0(nil,y) | -->*_s0(y,false) # answer(goal). [resolve(2487,b,87,c)]. given #2183 (F,wt=8): 20094 -->_s0(true,mapf(x,nil)) | -->_s0(nil,false) # answer(goal). [resolve(2684,c,86,a)]. given #2184 (T,wt=9): 3393 ->*_s0(sndsplit(app(nil,0),leq(0,x)),true). [ur(87,a,121,a,b,678,a)]. given #2185 (T,wt=9): 3394 ->*_s0(sndsplit(app(nil,0),mapf(x,nil)),nil). [ur(87,a,121,a,b,639,a)]. given #2186 (T,wt=9): 3395 ->*_s0(sndsplit(app(nil,0),sndsplit(0,x)),x). [ur(87,a,121,a,b,635,a)]. given #2187 (T,wt=9): 3400 ->*_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): 20087 -->_s0(true,mapf(x,nil)) | -->_s0(nil,app(nil,false)) # answer(goal). [resolve(2684,c,581,a)]. given #2190 (F,wt=10): 20091 -->_s0(true,mapf(x,nil)) | -->_s0(nil,sndsplit(0,false)) # answer(goal). [resolve(2684,c,567,a)]. given #2191 (F,wt=11): 2685 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,y) | -->*_s0(y,false) # answer(goal). [resolve(2495,b,87,c)]. given #2192 (F,wt=8): 20210 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,false) # answer(goal). [resolve(2685,c,86,a)]. given #2193 (T,wt=9): 3434 ->*_s0(sndsplit(app(nil,app(nil,0)),x),x). [ur(87,a,121,a,b,3398,a)]. given #2194 (T,wt=9): 3438 ->*_s0(sndsplit(0,sndsplit(app(nil,0),x)),x). [ur(87,a,82,a,b,3398,a)]. given #2195 (T,wt=9): 3440 ->*_s0(app(nil,sndsplit(app(nil,0),x)),x). [ur(87,a,61,a,b,3398,a)]. given #2196 (T,wt=9): 3884 ->*_s0(length(sndsplit(0,fstsplit(s(x),nil))),0). [ur(87,a,482,a,b,3857,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): 20203 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,app(nil,false)) # answer(goal). [resolve(2685,c,581,a)]. given #2199 (F,wt=10): 20207 -->_s0(true,fstsplit(0,x)) | -->_s0(nil,sndsplit(0,false)) # answer(goal). [resolve(2685,c,567,a)]. given #2200 (F,wt=10): 20284 -->_s0(true,sndsplit(length(nil),sndsplit(app(nil,0),false))) # answer(goal). [ur(2105,b,321,a,c,3438,a)]. given #2201 (F,wt=11): 2741 -->_s0(true,app(nil,x)) | -->_s0(x,y) | -->*_s0(y,false) # answer(goal). [resolve(2496,b,87,c)]. given #2202 (T,wt=9): 3885 ->*_s0(length(app(nil,fstsplit(s(x),nil))),0). [ur(87,a,132,a,b,3857,a)]. given #2203 (T,wt=9): 3887 ->*_s0(sndsplit(0,length(fstsplit(s(x),nil))),0). [ur(87,a,82,a,b,3857,a)]. given #2204 (T,wt=9): 3889 ->*_s0(app(nil,length(fstsplit(s(x),nil))),0). [ur(87,a,61,a,b,3857,a)]. given #2205 (T,wt=9): 3976 ->*_s0(empty(sndsplit(0,fstsplit(s(x),nil))),true). [ur(87,a,486,a,b,3948,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=9): 20732 -->_s0(true,app(nil,length(nil))) | -->*_s0(0,false) # answer(goal). [resolve(2741,b,69,a)]. given #2208 (F,wt=10): 20729 -->_s0(true,app(nil,sndsplit(0,x))) | -->*_s0(x,false) # answer(goal). [resolve(2741,b,82,a)]. given #2209 (F,wt=10): 20730 -->_s0(true,app(nil,mapf(x,nil))) | -->*_s0(nil,false) # answer(goal). [resolve(2741,b,74,a)]. given #2210 (F,wt=10): 20736 -->_s0(true,app(nil,fstsplit(0,x))) | -->*_s0(nil,false) # answer(goal). [resolve(2741,b,64,a)]. given #2211 (T,wt=9): 3977 ->*_s0(empty(app(nil,fstsplit(s(x),nil))),true). [ur(87,a,136,a,b,3948,a)]. given #2212 (T,wt=9): 3979 ->*_s0(sndsplit(0,empty(fstsplit(s(x),nil))),true). [ur(87,a,82,a,b,3948,a)]. given #2213 (T,wt=9): 3981 ->*_s0(app(nil,empty(fstsplit(s(x),nil))),true). [ur(87,a,61,a,b,3948,a)]. given #2214 (T,wt=9): 3988 ->*_s0(s(head(cons(length(nil),x))),s(0)). [ur(87,a,264,a,b,888,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=10): 20737 -->_s0(true,app(nil,app(nil,x))) | -->*_s0(x,false) # answer(goal). [resolve(2741,b,61,a)]. given #2217 (F,wt=11): 3079 -->_s0(true,s(empty(cons(x,y)))) | -->*_s0(s(false),false) # answer(goal). [resolve(139,a,2105,b)]. given #2218 (F,wt=11): 3141 -->_s0(true,tail(empty(cons(x,y)))) | -->*_s0(tail(false),false) # answer(goal). [resolve(144,a,2105,b)]. given #2219 (F,wt=11): 3168 -->_s0(true,length(empty(cons(x,y)))) | -->*_s0(length(false),false) # answer(goal). [resolve(157,a,2105,b)]. given #2220 (T,wt=9): 3989 ->*_s0(s(head(cons(empty(nil),x))),s(true)). [ur(87,a,264,a,b,692,a)]. given #2221 (T,wt=9): 4022 ->*_s0(tail(head(cons(length(nil),x))),tail(0)). [ur(87,a,269,a,b,914,a)]. given #2222 (T,wt=9): 4023 ->*_s0(tail(head(cons(empty(nil),x))),tail(true)). [ur(87,a,269,a,b,751,a)]. given #2223 (T,wt=9): 4026 ->*_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): 3195 -->_s0(true,head(empty(cons(x,y)))) | -->*_s0(head(false),false) # answer(goal). [resolve(158,a,2105,b)]. given #2226 (F,wt=11): 3222 -->_s0(true,empty(empty(cons(x,y)))) | -->*_s0(empty(false),false) # answer(goal). [resolve(161,a,2105,b)]. given #2227 (F,wt=11): 3282 -->_s0(true,f(x,empty(nil))) | -->*_s0(f(x,true),false) # answer(goal). [resolve(165,a,2105,b)]. given #2228 (F,wt=11): 3309 -->_s0(true,f(empty(nil),x)) | -->*_s0(f(true,x),false) # answer(goal). [resolve(166,a,2105,b)]. given #2229 (T,wt=9): 4088 ->*_s0(length(head(cons(sndsplit(0,nil),x))),0). [ur(87,a,282,a,b,2255,a)]. given #2230 (T,wt=9): 4090 ->*_s0(length(head(cons(mapf(x,nil),y))),0). [ur(87,a,282,a,b,2046,a)]. given #2231 (T,wt=9): 4093 ->*_s0(length(head(cons(fstsplit(0,x),y))),0). [ur(87,a,282,a,b,1650,a)]. given #2232 (T,wt=9): 4095 ->*_s0(length(head(cons(app(nil,nil),x))),0). [ur(87,a,282,a,b,1356,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): 3336 -->_s0(true,cons(x,empty(nil))) | -->*_s0(cons(x,true),false) # answer(goal). [resolve(167,a,2105,b)]. given #2235 (F,wt=11): 3363 -->_s0(true,cons(empty(nil),x)) | -->*_s0(cons(true,x),false) # answer(goal). [resolve(168,a,2105,b)]. given #2236 (F,wt=11): 3445 -->_s0(true,sndsplit(x,empty(nil))) | -->*_s0(sndsplit(x,true),false) # answer(goal). [resolve(170,a,2105,b)]. given #2237 (F,wt=11): 3472 -->_s0(true,sndsplit(empty(nil),x)) | -->*_s0(sndsplit(true,x),false) # answer(goal). [resolve(171,a,2105,b)]. given #2238 (T,wt=9): 4097 ->*_s0(length(head(cons(length(nil),x))),length(0)). [ur(87,a,282,a,b,940,a)]. given #2239 (T,wt=9): 4098 ->*_s0(length(head(cons(empty(nil),x))),length(true)). [ur(87,a,282,a,b,777,a)]. given #2240 (T,wt=9): 4126 ->*_s0(length(sndsplit(0,head(cons(nil,x)))),0). [ur(87,a,482,a,b,4099,a)]. given #2241 (T,wt=9): 4128 ->*_s0(length(app(nil,head(cons(nil,x)))),0). [ur(87,a,132,a,b,4099,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): 3499 -->_s0(true,mapf(x,empty(nil))) | -->*_s0(mapf(x,true),false) # answer(goal). [resolve(178,a,2105,b)]. given #2244 (F,wt=11): 3553 -->_s0(true,mapf(empty(nil),x)) | -->*_s0(mapf(true,x),false) # answer(goal). [resolve(179,a,2105,b)]. given #2245 (F,wt=11): 3580 -->_s0(true,leq(x,empty(nil))) | -->*_s0(leq(x,true),false) # answer(goal). [resolve(180,a,2105,b)]. given #2246 (F,wt=11): 3607 -->_s0(true,leq(empty(nil),x)) | -->*_s0(leq(true,x),false) # answer(goal). [resolve(181,a,2105,b)]. given #2247 (T,wt=9): 4130 ->*_s0(sndsplit(0,length(head(cons(nil,x)))),0). [ur(87,a,82,a,b,4099,a)]. given #2248 (T,wt=9): 4132 ->*_s0(app(nil,length(head(cons(nil,x)))),0). [ur(87,a,61,a,b,4099,a)]. given #2249 (T,wt=9): 4139 ->*_s0(head(head(cons(length(nil),x))),head(0)). [ur(87,a,283,a,b,966,a)]. given #2250 (T,wt=9): 4140 ->*_s0(head(head(cons(empty(nil),x))),head(true)). [ur(87,a,283,a,b,803,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): 3635 -->_s0(true,fstsplit(x,empty(nil))) | -->*_s0(fstsplit(x,true),false) # answer(goal). [resolve(184,a,2105,b)]. given #2253 (F,wt=11): 3690 -->_s0(true,fstsplit(empty(nil),x)) | -->*_s0(fstsplit(true,x),false) # answer(goal). [resolve(185,a,2105,b)]. given #2254 (F,wt=11): 3717 -->_s0(true,app(x,empty(nil))) | -->*_s0(app(x,true),false) # answer(goal). [resolve(187,a,2105,b)]. given #2255 (F,wt=11): 3744 -->_s0(true,app(empty(nil),x)) | -->*_s0(app(true,x),false) # answer(goal). [resolve(188,a,2105,b)]. given #2256 (T,wt=9): 4143 ->*_s0(head(head(cons(cons(x,y),z))),x). [ur(87,a,283,a,b,575,a)]. given #2257 (T,wt=9): 4174 ->*_s0(empty(head(cons(sndsplit(0,nil),x))),true). [ur(87,a,286,a,b,2351,a)]. given #2258 (T,wt=9): 4176 ->*_s0(empty(head(cons(mapf(x,nil),y))),true). [ur(87,a,286,a,b,2132,a)]. given #2259 (T,wt=9): 4179 ->*_s0(empty(head(cons(fstsplit(0,x),y))),true). [ur(87,a,286,a,b,1748,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): 3771 -->_s0(true,s(fstsplit(s(x),nil))) | -->*_s0(s(nil),false) # answer(goal). [resolve(239,a,2105,b)]. given #2262 (F,wt=11): 3829 -->_s0(true,tail(fstsplit(s(x),nil))) | -->*_s0(tail(nil),false) # answer(goal). [resolve(244,a,2105,b)]. given #2263 (F,wt=11): 3856 -->_s0(true,length(fstsplit(s(x),nil))) | -->*_s0(length(nil),false) # answer(goal). [resolve(257,a,2105,b)]. given #2264 (F,wt=11): 3890 -->_s0(true,head(fstsplit(s(x),nil))) | -->*_s0(head(nil),false) # answer(goal). [resolve(258,a,2105,b)]. given #2265 (T,wt=9): 4181 ->*_s0(empty(head(cons(app(nil,nil),x))),true). [ur(87,a,286,a,b,1533,a)]. given #2266 (T,wt=9): 4182 ->*_s0(empty(head(cons(length(nil),x))),empty(0)). [ur(87,a,286,a,b,1026,a)]. given #2267 (T,wt=9): 4183 ->*_s0(empty(head(cons(empty(nil),x))),empty(true)). [ur(87,a,286,a,b,829,a)]. given #2268 (T,wt=9): 4184 ->*_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=10): 21566 -->_s0(nil,head(sndsplit(0,cons(cons(x,y),z)))) # answer(goal). [ur(8581,b,4184,a,c,483,a)]. given #2271 (F,wt=10): 21569 -->_s0(nil,head(app(nil,cons(cons(x,y),z)))) # answer(goal). [ur(8581,b,4184,a,c,133,a)]. given #2272 (F,wt=10): 21570 -->_s0(nil,head(app(cons(cons(x,y),z),u))) # answer(goal). [ur(8581,b,4184,a,c,108,a)]. given #2273 (F,wt=11): 3982 -->_s0(true,s(head(cons(x,y)))) | -->*_s0(s(x),false) # answer(goal). [resolve(264,a,2105,b)]. given #2274 (T,wt=9): 4246 ->*_s0(empty(sndsplit(0,head(cons(nil,x)))),true). [ur(87,a,486,a,b,4185,a)]. given #2275 (T,wt=9): 4248 ->*_s0(empty(app(nil,head(cons(nil,x)))),true). [ur(87,a,136,a,b,4185,a)]. given #2276 (T,wt=9): 4250 ->*_s0(sndsplit(0,empty(head(cons(nil,x)))),true). [ur(87,a,82,a,b,4185,a)]. given #2277 (T,wt=9): 4252 ->*_s0(app(nil,empty(head(cons(nil,x)))),true). [ur(87,a,61,a,b,4185,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): 4016 -->_s0(true,tail(head(cons(x,y)))) | -->*_s0(tail(x),false) # answer(goal). [resolve(269,a,2105,b)]. given #2280 (F,wt=11): 4085 -->_s0(true,length(head(cons(x,y)))) | -->*_s0(length(x),false) # answer(goal). [resolve(282,a,2105,b)]. given #2281 (F,wt=11): 4133 -->_s0(true,head(head(cons(x,y)))) | -->*_s0(head(x),false) # answer(goal). [resolve(283,a,2105,b)]. given #2282 (F,wt=11): 4171 -->_s0(true,empty(head(cons(x,y)))) | -->*_s0(empty(x),false) # answer(goal). [resolve(286,a,2105,b)]. given #2283 (T,wt=9): 4336 ->*_s0(mapf(x,app(nil,y)),mapf(x,y)). [ur(87,a,128,a,b,86,a)]. given #2284 (T,wt=9): 4363 ->*_s0(mapf(x,app(nil,app(nil,nil))),nil). [ur(87,a,128,a,b,4335,a)]. given #2285 (T,wt=9): 4365 ->*_s0(sndsplit(0,mapf(x,app(nil,nil))),nil). [ur(87,a,82,a,b,4335,a)]. given #2286 (T,wt=9): 4367 ->*_s0(app(nil,mapf(x,app(nil,nil))),nil). [ur(87,a,61,a,b,4335,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): 4253 -->_s0(true,f(x,length(nil))) | -->*_s0(f(x,0),false) # answer(goal). [resolve(315,a,2105,b)]. given #2289 (F,wt=11): 4280 -->_s0(true,f(length(nil),x)) | -->*_s0(f(0,x),false) # answer(goal). [resolve(316,a,2105,b)]. given #2290 (F,wt=11): 4307 -->_s0(true,cons(x,length(nil))) | -->*_s0(cons(x,0),false) # answer(goal). [resolve(317,a,2105,b)]. given #2291 (F,wt=11): 4368 -->_s0(true,cons(length(nil),x)) | -->*_s0(cons(0,x),false) # answer(goal). [resolve(318,a,2105,b)]. given #2292 (T,wt=9): 4460 ->*_s0(mapf(app(nil,x),y),mapf(x,y)). [ur(87,a,129,a,b,86,a)]. given #2293 (T,wt=9): 4497 ->*_s0(tail(cons(x,sndsplit(length(nil),y))),y). [ur(87,a,85,a,b,4430,a)]. given #2294 (T,wt=9): 4498 ->*_s0(sndsplit(s(length(nil)),cons(x,y)),y). [ur(87,a,83,a,b,4430,a)]. given #2295 (T,wt=9): 4500 ->*_s0(head(cons(sndsplit(length(nil),x),y)),x). [ur(87,a,67,a,b,4430,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): 21658 -->_s0(true,sndsplit(length(cons(x,nil)),cons(y,false))) # answer(goal). [ur(2105,b,296,a,c,4498,a)]. given #2298 (F,wt=11): 4395 -->_s0(true,sndsplit(x,length(nil))) | -->*_s0(sndsplit(x,0),false) # answer(goal). [resolve(320,a,2105,b)]. given #2299 (F,wt=11): 4422 -->_s0(true,sndsplit(length(nil),x)) | -->*_s0(sndsplit(0,x),false) # answer(goal). [resolve(321,a,2105,b)]. given #2300 (F,wt=11): 4519 -->_s0(true,mapf(x,length(nil))) | -->*_s0(mapf(x,0),false) # answer(goal). [resolve(328,a,2105,b)]. given #2301 (T,wt=9): 4505 ->*_s0(sndsplit(app(nil,length(nil)),empty(nil)),true). [ur(87,a,121,a,b,4428,a)]. given #2302 (T,wt=9): 4506 ->*_s0(sndsplit(length(nil),app(nil,empty(nil))),true). [ur(87,a,120,a,b,4428,a)]. given #2303 (T,wt=9): 4509 ->*_s0(sndsplit(0,sndsplit(length(nil),empty(nil))),true). [ur(87,a,82,a,b,4428,a)]. given #2304 (T,wt=9): 4511 ->*_s0(app(nil,sndsplit(length(nil),empty(nil))),true). [ur(87,a,61,a,b,4428,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): 4576 -->_s0(true,mapf(length(nil),x)) | -->*_s0(mapf(0,x),false) # answer(goal). [resolve(329,a,2105,b)]. given #2307 (F,wt=11): 4604 -->_s0(true,leq(x,length(nil))) | -->*_s0(leq(x,0),false) # answer(goal). [resolve(330,a,2105,b)]. given #2308 (F,wt=11): 4649 -->_s0(true,leq(length(nil),x)) | -->*_s0(leq(0,x),false) # answer(goal). [resolve(331,a,2105,b)]. given #2309 (F,wt=11): 4732 -->_s0(true,fstsplit(x,length(nil))) | -->*_s0(fstsplit(x,0),false) # answer(goal). [resolve(334,a,2105,b)]. given #2310 (T,wt=9): 4512 ->*_s0(sndsplit(app(nil,length(nil)),length(nil)),0). [ur(87,a,121,a,b,4429,a)]. given #2311 (T,wt=9): 4513 ->*_s0(sndsplit(length(nil),app(nil,length(nil))),0). [ur(87,a,120,a,b,4429,a)]. given #2312 (T,wt=9): 4516 ->*_s0(sndsplit(0,sndsplit(length(nil),length(nil))),0). [ur(87,a,82,a,b,4429,a)]. given #2313 (T,wt=9): 4518 ->*_s0(app(nil,sndsplit(length(nil),length(nil))),0). [ur(87,a,61,a,b,4429,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): 4759 -->_s0(true,fstsplit(length(nil),x)) | -->*_s0(fstsplit(0,x),false) # answer(goal). [resolve(335,a,2105,b)]. given #2316 (F,wt=11): 4819 -->_s0(true,app(x,length(nil))) | -->*_s0(app(x,0),false) # answer(goal). [resolve(337,a,2105,b)]. given #2317 (F,wt=11): 4846 -->_s0(true,app(length(nil),x)) | -->*_s0(app(0,x),false) # answer(goal). [resolve(338,a,2105,b)]. given #2318 (F,wt=11): 4873 -->_s0(true,s(leq(s(x),0))) | -->*_s0(s(false),false) # answer(goal). [resolve(364,a,2105,b)]. given #2319 (T,wt=9): 4548 ->*_s0(leq(s(0),app(nil,s(x))),true). [ur(87,a,130,a,b,679,a)]. given #2320 (T,wt=9): 4550 ->*_s0(leq(x,app(nil,y)),leq(x,y)). [ur(87,a,130,a,b,86,a)]. given #2321 (T,wt=9): 4641 ->*_s0(leq(s(x),app(nil,length(nil))),false). [ur(87,a,130,a,b,4606,a)]. given #2322 (T,wt=9): 4643 ->*_s0(sndsplit(0,leq(s(x),length(nil))),false). [ur(87,a,82,a,b,4606,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): 21742 -->_s0(true,sndsplit(length(nil),leq(s(x),length(nil)))) # answer(goal). [resolve(4643,a,4422,b)]. given #2325 (F,wt=11): 4935 -->_s0(true,tail(leq(s(x),0))) | -->*_s0(tail(false),false) # answer(goal). [resolve(369,a,2105,b)]. given #2326 (F,wt=11): 4962 -->_s0(true,length(leq(s(x),0))) | -->*_s0(length(false),false) # answer(goal). [resolve(382,a,2105,b)]. given #2327 (F,wt=11): 4989 -->_s0(true,head(leq(s(x),0))) | -->*_s0(head(false),false) # answer(goal). [resolve(383,a,2105,b)]. given #2328 (T,wt=9): 4644 ->*_s0(leq(s(s(x)),s(length(nil))),false). [ur(87,a,72,a,b,4606,a)]. given #2329 (T,wt=9): 4646 ->*_s0(app(nil,leq(s(x),length(nil))),false). [ur(87,a,61,a,b,4606,a)]. given #2330 (T,wt=9): 4681 ->*_s0(leq(app(nil,s(x)),length(nil)),false). [ur(87,a,131,a,b,4606,a)]. given #2331 (T,wt=9): 4682 ->*_s0(leq(app(nil,s(0)),s(x)),true). [ur(87,a,131,a,b,679,a)]. given #2332 (A,wt=17): 429 ->_s0(mapf(mapf(x,cons(y,z)),u),mapf(app(f(x,y),mapf(x,z)),u)). [ur(44,a,73,a)]. given #2333 (F,wt=10): 21806 -->_s0(true,leq(s(s(x)),length(cons(y,nil)))) # answer(goal). [ur(2105,b,305,a,c,4644,a)]. given #2334 (F,wt=11): 5043 -->_s0(true,empty(leq(s(x),0))) | -->*_s0(empty(false),false) # answer(goal). [resolve(386,a,2105,b)]. given #2335 (F,wt=11): 5070 -->_s0(true,s(sndsplit(s(x),nil))) | -->*_s0(s(nil),false) # answer(goal). [resolve(514,a,2105,b)]. given #2336 (F,wt=11): 5097 -->_s0(true,tail(sndsplit(s(x),nil))) | -->*_s0(tail(nil),false) # answer(goal). [resolve(519,a,2105,b)]. given #2337 (T,wt=9): 4685 ->*_s0(leq(app(nil,x),y),leq(x,y)). [ur(87,a,131,a,b,86,a)]. given #2338 (T,wt=9): 4716 ->*_s0(tail(cons(x,leq(length(nil),y))),true). [ur(87,a,85,a,b,4651,a)]. given #2339 (T,wt=9): 4719 ->*_s0(head(cons(leq(length(nil),x),y)),true). [ur(87,a,67,a,b,4651,a)]. given #2340 (T,wt=9): 4726 ->*_s0(leq(app(nil,app(nil,0)),x),true). [ur(87,a,131,a,b,4683,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): 5124 -->_s0(true,length(sndsplit(s(x),nil))) | -->*_s0(length(nil),false) # answer(goal). [resolve(532,a,2105,b)]. given #2343 (F,wt=11): 5212 -->_s0(true,head(sndsplit(s(x),nil))) | -->*_s0(head(nil),false) # answer(goal). [resolve(533,a,2105,b)]. given #2344 (F,wt=11): 5301 -->_s0(true,s(tail(cons(x,y)))) | -->*_s0(s(y),false) # answer(goal). [resolve(539,a,2105,b)]. given #2345 (F,wt=11): 5336 -->_s0(true,tail(tail(cons(x,y)))) | -->*_s0(tail(y),false) # answer(goal). [resolve(544,a,2105,b)]. given #2346 (T,wt=9): 4728 ->*_s0(sndsplit(0,leq(app(nil,0),x)),true). [ur(87,a,82,a,b,4683,a)]. given #2347 (T,wt=9): 4729 ->*_s0(leq(s(app(nil,0)),s(x)),true). [ur(87,a,72,a,b,4683,a)]. given #2348 (T,wt=9): 4731 ->*_s0(app(nil,leq(app(nil,0),x)),true). [ur(87,a,61,a,b,4683,a)]. given #2349 (T,wt=9): 4789 ->*_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): 5373 -->_s0(true,length(tail(cons(x,y)))) | -->*_s0(length(y),false) # answer(goal). [resolve(557,a,2105,b)]. given #2352 (F,wt=11): 5459 -->_s0(true,head(tail(cons(x,y)))) | -->*_s0(head(y),false) # answer(goal). [resolve(558,a,2105,b)]. given #2353 (F,wt=11): 5496 -->_s0(true,empty(tail(cons(x,y)))) | -->*_s0(empty(y),false) # answer(goal). [resolve(561,a,2105,b)]. given #2354 (F,wt=11): 5590 -->_s0(true,head(cons(tail(cons(x,sndsplit(0,false))),y))) # answer(goal). [resolve(633,a,2492,b)]. given #2355 (T,wt=9): 4815 ->*_s0(tail(cons(x,fstsplit(length(nil),y))),nil). [ur(87,a,85,a,b,4760,a)]. given #2356 (T,wt=9): 4817 ->*_s0(head(cons(fstsplit(length(nil),x),y)),nil). [ur(87,a,67,a,b,4760,a)]. given #2357 (T,wt=9): 4904 ->*_s0(fstsplit(app(nil,x),y),fstsplit(x,y)). [ur(87,a,135,a,b,86,a)]. given #2358 (T,wt=9): 4930 ->*_s0(fstsplit(app(nil,app(nil,0)),x),nil). [ur(87,a,135,a,b,4902,a)]. given #2359 (A,wt=15): 432 ->_s0(length(mapf(x,cons(y,z))),length(app(f(x,y),mapf(x,z)))). [ur(41,a,73,a)]. given #2360 (F,wt=11): 5592 -->_s0(true,tail(cons(x,tail(cons(y,sndsplit(0,false)))))) # answer(goal). [resolve(633,a,2476,b)]. given #2361 (F,wt=11): 5593 -->_s0(true,x) | -->_s0(x,tail(cons(y,sndsplit(0,false)))) # answer(goal). [resolve(633,a,2105,c)]. given #2362 (F,wt=11): 5605 -->_s0(true,tail(tail(cons(x,cons(y,sndsplit(0,false)))))) # answer(goal). [ur(2105,b,544,a,c,633,a)]. given #2363 (F,wt=11): 5607 -->_s0(true,tail(head(cons(cons(x,sndsplit(0,false)),y)))) # answer(goal). [ur(2105,b,269,a,c,633,a)]. given #2364 (T,wt=9): 4932 ->*_s0(sndsplit(0,fstsplit(app(nil,0),x)),nil). [ur(87,a,82,a,b,4902,a)]. given #2365 (T,wt=9): 4934 ->*_s0(app(nil,fstsplit(app(nil,0),x)),nil). [ur(87,a,61,a,b,4902,a)]. given #2366 (T,wt=9): 5017 ->*_s0(app(x,app(nil,y)),app(x,y)). [ur(87,a,137,a,b,86,a)]. given #2367 (T,wt=9): 5153 ->*_s0(app(app(nil,nil),app(nil,x)),x). [ur(87,a,138,a,b,691,a)]. given #2368 (A,wt=15): 433 ->_s0(head(mapf(x,cons(y,z))),head(app(f(x,y),mapf(x,z)))). [ur(40,a,73,a)]. given #2369 (F,wt=11): 5610 -->_s0(true,head(cons(sndsplit(s(0),cons(x,false)),y))) # answer(goal). [resolve(634,a,2492,b)]. given #2370 (F,wt=11): 5612 -->_s0(true,tail(cons(x,sndsplit(s(0),cons(y,false))))) # answer(goal). [resolve(634,a,2476,b)]. given #2371 (F,wt=11): 5613 -->_s0(true,x) | -->_s0(x,sndsplit(s(0),cons(y,false))) # answer(goal). [resolve(634,a,2105,c)]. given #2372 (F,wt=11): 5627 -->_s0(true,sndsplit(s(s(0)),cons(x,cons(y,false)))) # answer(goal). [ur(2105,b,83,a,c,634,a)]. given #2373 (T,wt=9): 5154 ->*_s0(app(app(nil,nil),fstsplit(0,x)),nil). [ur(87,a,138,a,b,685,a)]. given #2374 (T,wt=9): 5155 ->*_s0(app(app(nil,nil),leq(0,x)),true). [ur(87,a,138,a,b,681,a)]. given #2375 (T,wt=9): 5156 ->*_s0(app(app(nil,nil),mapf(x,nil)),nil). [ur(87,a,138,a,b,641,a)]. given #2376 (T,wt=9): 5157 ->*_s0(app(app(nil,nil),sndsplit(0,x)),x). [ur(87,a,138,a,b,637,a)]. given #2377 (A,wt=17): 434 ->_s0(fstsplit(x,mapf(y,cons(z,u))),fstsplit(x,app(f(y,z),mapf(y,u)))). [ur(39,a,73,a)]. given #2378 (F,wt=11): 5629 -->_s0(true,head(cons(head(cons(sndsplit(0,false),x)),y))) # answer(goal). [resolve(636,a,2492,b)]. given #2379 (F,wt=11): 5631 -->_s0(true,tail(cons(x,head(cons(sndsplit(0,false),y))))) # answer(goal). [resolve(636,a,2476,b)]. given #2380 (F,wt=11): 5632 -->_s0(true,x) | -->_s0(x,head(cons(sndsplit(0,false),y))) # answer(goal). [resolve(636,a,2105,c)]. given #2381 (F,wt=11): 5645 -->_s0(true,head(tail(cons(x,cons(sndsplit(0,false),y))))) # answer(goal). [ur(2105,b,558,a,c,636,a)]. given #2382 (T,wt=9): 5161 ->*_s0(app(app(nil,x),y),app(x,y)). [ur(87,a,138,a,b,86,a)]. given #2383 (T,wt=9): 5189 ->*_s0(length(sndsplit(0,sndsplit(s(x),nil))),0). [ur(87,a,482,a,b,5125,a)]. given #2384 (T,wt=9): 5191 ->*_s0(length(app(nil,sndsplit(s(x),nil))),0). [ur(87,a,132,a,b,5125,a)]. given #2385 (T,wt=9): 5193 ->*_s0(sndsplit(0,length(sndsplit(s(x),nil))),0). [ur(87,a,82,a,b,5125,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): 5647 -->_s0(true,head(head(cons(cons(sndsplit(0,false),x),y)))) # answer(goal). [ur(2105,b,283,a,c,636,a)]. given #2388 (F,wt=11): 5764 -->_s0(true,head(cons(tail(cons(x,app(nil,false))),y))) # answer(goal). [resolve(688,a,2492,b)]. given #2389 (F,wt=11): 5766 -->_s0(true,tail(cons(x,tail(cons(y,app(nil,false)))))) # answer(goal). [resolve(688,a,2476,b)]. given #2390 (F,wt=11): 5767 -->_s0(true,x) | -->_s0(x,tail(cons(y,app(nil,false)))) # answer(goal). [resolve(688,a,2105,c)]. given #2391 (T,wt=9): 5195 ->*_s0(app(nil,length(sndsplit(s(x),nil))),0). [ur(87,a,61,a,b,5125,a)]. given #2392 (T,wt=9): 5205 ->*_s0(app(app(nil,app(nil,nil)),x),x). [ur(87,a,138,a,b,5160,a)]. given #2393 (T,wt=9): 5208 ->*_s0(sndsplit(0,app(app(nil,nil),x)),x). [ur(87,a,82,a,b,5160,a)]. given #2394 (T,wt=9): 5210 ->*_s0(app(nil,app(app(nil,nil),x)),x). [ur(87,a,61,a,b,5160,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): 21988 -->_s0(true,sndsplit(length(nil),app(app(nil,nil),false))) # answer(goal). [resolve(5208,a,4422,b)]. given #2397 (F,wt=11): 5781 -->_s0(true,tail(tail(cons(x,cons(y,app(nil,false)))))) # answer(goal). [ur(2105,b,544,a,c,688,a)]. given #2398 (F,wt=11): 5783 -->_s0(true,tail(head(cons(cons(x,app(nil,false)),y)))) # answer(goal). [ur(2105,b,269,a,c,688,a)]. given #2399 (F,wt=11): 5787 -->_s0(true,head(cons(head(cons(app(nil,false),x)),y))) # answer(goal). [resolve(690,a,2492,b)]. given #2400 (T,wt=9): 5294 ->*_s0(empty(sndsplit(0,sndsplit(s(x),nil))),true). [ur(87,a,486,a,b,5239,a)]. given #2401 (T,wt=9): 5296 ->*_s0(empty(app(nil,sndsplit(s(x),nil))),true). [ur(87,a,136,a,b,5239,a)]. given #2402 (T,wt=9): 5298 ->*_s0(sndsplit(0,empty(sndsplit(s(x),nil))),true). [ur(87,a,82,a,b,5239,a)]. given #2403 (T,wt=9): 5300 ->*_s0(app(nil,empty(sndsplit(s(x),nil))),true). [ur(87,a,61,a,b,5239,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): 5789 -->_s0(true,tail(cons(x,head(cons(app(nil,false),y))))) # answer(goal). [resolve(690,a,2476,b)]. given #2406 (F,wt=11): 5790 -->_s0(true,x) | -->_s0(x,head(cons(app(nil,false),y))) # answer(goal). [resolve(690,a,2105,c)]. given #2407 (F,wt=11): 5804 -->_s0(true,head(tail(cons(x,cons(app(nil,false),y))))) # answer(goal). [ur(2105,b,558,a,c,690,a)]. given #2408 (F,wt=11): 5806 -->_s0(true,head(head(cons(cons(app(nil,false),x),y)))) # answer(goal). [ur(2105,b,283,a,c,690,a)]. given #2409 (T,wt=9): 5307 ->*_s0(s(tail(cons(x,length(nil)))),s(0)). [ur(87,a,539,a,b,888,a)]. given #2410 (T,wt=9): 5308 ->*_s0(s(tail(cons(x,empty(nil)))),s(true)). [ur(87,a,539,a,b,692,a)]. given #2411 (T,wt=9): 5342 ->*_s0(tail(tail(cons(x,length(nil)))),tail(0)). [ur(87,a,544,a,b,914,a)]. given #2412 (T,wt=9): 5343 ->*_s0(tail(tail(cons(x,empty(nil)))),tail(true)). [ur(87,a,544,a,b,751,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): 5836 -->_s0(true,s(s(empty(nil)))) | -->*_s0(s(s(true)),false) # answer(goal). [resolve(693,a,2105,b)]. given #2415 (F,wt=11): 5863 -->_s0(true,tail(s(empty(nil)))) | -->*_s0(tail(s(true)),false) # answer(goal). [resolve(698,a,2105,b)]. given #2416 (F,wt=11): 5890 -->_s0(true,length(s(empty(nil)))) | -->*_s0(length(s(true)),false) # answer(goal). [resolve(711,a,2105,b)]. given #2417 (F,wt=11): 5917 -->_s0(true,head(s(empty(nil)))) | -->*_s0(head(s(true)),false) # answer(goal). [resolve(712,a,2105,b)]. given #2418 (T,wt=9): 5346 ->*_s0(tail(tail(cons(x,cons(y,z)))),z). [ur(87,a,544,a,b,564,a)]. given #2419 (T,wt=9): 5378 ->*_s0(length(tail(cons(x,sndsplit(0,nil)))),0). [ur(87,a,557,a,b,2255,a)]. given #2420 (T,wt=9): 5380 ->*_s0(length(tail(cons(x,mapf(y,nil)))),0). [ur(87,a,557,a,b,2046,a)]. given #2421 (T,wt=9): 5383 ->*_s0(length(tail(cons(x,fstsplit(0,y)))),0). [ur(87,a,557,a,b,1650,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): 5971 -->_s0(true,empty(s(empty(nil)))) | -->*_s0(empty(s(true)),false) # answer(goal). [resolve(715,a,2105,b)]. given #2424 (F,wt=11): 5998 -->_s0(true,s(tail(empty(nil)))) | -->*_s0(s(tail(true)),false) # answer(goal). [resolve(752,a,2105,b)]. given #2425 (F,wt=11): 6025 -->_s0(true,tail(tail(empty(nil)))) | -->*_s0(tail(tail(true)),false) # answer(goal). [resolve(757,a,2105,b)]. given #2426 (F,wt=11): 6052 -->_s0(true,length(tail(empty(nil)))) | -->*_s0(length(tail(true)),false) # answer(goal). [resolve(770,a,2105,b)]. given #2427 (T,wt=9): 5385 ->*_s0(length(tail(cons(x,app(nil,nil)))),0). [ur(87,a,557,a,b,1356,a)]. given #2428 (T,wt=9): 5387 ->*_s0(length(tail(cons(x,length(nil)))),length(0)). [ur(87,a,557,a,b,940,a)]. given #2429 (T,wt=9): 5388 ->*_s0(length(tail(cons(x,empty(nil)))),length(true)). [ur(87,a,557,a,b,777,a)]. given #2430 (T,wt=9): 5452 ->*_s0(length(sndsplit(0,tail(cons(x,nil)))),0). [ur(87,a,482,a,b,5389,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): 6106 -->_s0(true,head(tail(empty(nil)))) | -->*_s0(head(tail(true)),false) # answer(goal). [resolve(771,a,2105,b)]. given #2433 (F,wt=11): 6133 -->_s0(true,empty(tail(empty(nil)))) | -->*_s0(empty(tail(true)),false) # answer(goal). [resolve(774,a,2105,b)]. given #2434 (F,wt=11): 6160 -->_s0(true,s(length(empty(nil)))) | -->*_s0(s(length(true)),false) # answer(goal). [resolve(778,a,2105,b)]. given #2435 (F,wt=11): 6187 -->_s0(true,tail(length(empty(nil)))) | -->*_s0(tail(length(true)),false) # answer(goal). [resolve(783,a,2105,b)]. given #2436 (T,wt=9): 5454 ->*_s0(length(app(nil,tail(cons(x,nil)))),0). [ur(87,a,132,a,b,5389,a)]. given #2437 (T,wt=9): 5456 ->*_s0(sndsplit(0,length(tail(cons(x,nil)))),0). [ur(87,a,82,a,b,5389,a)]. given #2438 (T,wt=9): 5458 ->*_s0(app(nil,length(tail(cons(x,nil)))),0). [ur(87,a,61,a,b,5389,a)]. given #2439 (T,wt=9): 5465 ->*_s0(head(tail(cons(x,length(nil)))),head(0)). [ur(87,a,558,a,b,966,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): 6241 -->_s0(true,length(length(empty(nil)))) | -->*_s0(length(length(true)),false) # answer(goal). [resolve(796,a,2105,b)]. given #2442 (F,wt=11): 6268 -->_s0(true,head(length(empty(nil)))) | -->*_s0(head(length(true)),false) # answer(goal). [resolve(797,a,2105,b)]. given #2443 (F,wt=11): 6295 -->_s0(true,empty(length(empty(nil)))) | -->*_s0(empty(length(true)),false) # answer(goal). [resolve(800,a,2105,b)]. given #2444 (F,wt=11): 6322 -->_s0(true,s(head(empty(nil)))) | -->*_s0(s(head(true)),false) # answer(goal). [resolve(804,a,2105,b)]. given #2445 (T,wt=9): 5466 ->*_s0(head(tail(cons(x,empty(nil)))),head(true)). [ur(87,a,558,a,b,803,a)]. given #2446 (T,wt=9): 5469 ->*_s0(head(tail(cons(x,cons(y,z)))),y). [ur(87,a,558,a,b,575,a)]. given #2447 (T,wt=9): 5501 ->*_s0(empty(tail(cons(x,sndsplit(0,nil)))),true). [ur(87,a,561,a,b,2351,a)]. given #2448 (T,wt=9): 5503 ->*_s0(empty(tail(cons(x,mapf(y,nil)))),true). [ur(87,a,561,a,b,2132,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): 6376 -->_s0(true,tail(head(empty(nil)))) | -->*_s0(tail(head(true)),false) # answer(goal). [resolve(809,a,2105,b)]. given #2451 (F,wt=11): 6403 -->_s0(true,length(head(empty(nil)))) | -->*_s0(length(head(true)),false) # answer(goal). [resolve(822,a,2105,b)]. given #2452 (F,wt=11): 6430 -->_s0(true,head(head(empty(nil)))) | -->*_s0(head(head(true)),false) # answer(goal). [resolve(823,a,2105,b)]. given #2453 (F,wt=11): 6457 -->_s0(true,empty(head(empty(nil)))) | -->*_s0(empty(head(true)),false) # answer(goal). [resolve(826,a,2105,b)]. given #2454 (T,wt=9): 5506 ->*_s0(empty(tail(cons(x,fstsplit(0,y)))),true). [ur(87,a,561,a,b,1748,a)]. given #2455 (T,wt=9): 5508 ->*_s0(empty(tail(cons(x,app(nil,nil)))),true). [ur(87,a,561,a,b,1533,a)]. given #2456 (T,wt=9): 5509 ->*_s0(empty(tail(cons(x,length(nil)))),empty(0)). [ur(87,a,561,a,b,1026,a)]. given #2457 (T,wt=9): 5510 ->*_s0(empty(tail(cons(x,empty(nil)))),empty(true)). [ur(87,a,561,a,b,829,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): 6526 -->_s0(true,s(empty(empty(nil)))) | -->*_s0(s(empty(true)),false) # answer(goal). [resolve(830,a,2105,b)]. given #2460 (F,wt=11): 6553 -->_s0(true,tail(empty(empty(nil)))) | -->*_s0(tail(empty(true)),false) # answer(goal). [resolve(835,a,2105,b)]. given #2461 (F,wt=11): 6580 -->_s0(true,length(empty(empty(nil)))) | -->*_s0(length(empty(true)),false) # answer(goal). [resolve(848,a,2105,b)]. given #2462 (F,wt=11): 6607 -->_s0(true,head(empty(empty(nil)))) | -->*_s0(head(empty(true)),false) # answer(goal). [resolve(849,a,2105,b)]. given #2463 (T,wt=9): 5511 ->*_s0(empty(tail(cons(x,cons(y,z)))),false). [ur(87,a,561,a,b,580,a)]. given #2464 (T,wt=9): 5541 ->*_s0(empty(sndsplit(0,tail(cons(x,nil)))),true). [ur(87,a,486,a,b,5512,a)]. given #2465 (T,wt=9): 5543 ->*_s0(empty(app(nil,tail(cons(x,nil)))),true). [ur(87,a,136,a,b,5512,a)]. given #2466 (T,wt=9): 5545 ->*_s0(sndsplit(0,empty(tail(cons(x,nil)))),true). [ur(87,a,82,a,b,5512,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=10): 22173 -->_s0(nil,tail(sndsplit(0,cons(x,cons(y,z))))) # answer(goal). [ur(8581,b,5511,a,c,469,a)]. given #2469 (F,wt=10): 22175 -->_s0(nil,tail(app(nil,cons(x,cons(y,z))))) # answer(goal). [ur(8581,b,5511,a,c,119,a)]. given #2470 (F,wt=11): 6661 -->_s0(true,empty(empty(empty(nil)))) | -->*_s0(empty(empty(true)),false) # answer(goal). [resolve(852,a,2105,b)]. given #2471 (F,wt=11): 6688 -->_s0(true,s(s(length(nil)))) | -->*_s0(s(s(0)),false) # answer(goal). [resolve(889,a,2105,b)]. given #2472 (T,wt=9): 5547 ->*_s0(app(nil,empty(tail(cons(x,nil)))),true). [ur(87,a,61,a,b,5512,a)]. given #2473 (T,wt=9): 5717 ->*_s0(sndsplit(length(nil),empty(cons(x,y))),false). [ur(87,a,145,a,b,4430,a)]. given #2474 (T,wt=9): 7933 ->*_s0(sndsplit(length(nil),tail(cons(x,y))),y). [ur(87,a,321,a,b,1057,a)]. given #2475 (T,wt=9): 7996 ->*_s0(sndsplit(length(nil),sndsplit(s(x),nil)),nil). [ur(87,a,321,a,b,1062,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): 6715 -->_s0(true,tail(s(length(nil)))) | -->*_s0(tail(s(0)),false) # answer(goal). [resolve(894,a,2105,b)]. given #2478 (F,wt=11): 6742 -->_s0(true,length(s(length(nil)))) | -->*_s0(length(s(0)),false) # answer(goal). [resolve(907,a,2105,b)]. given #2479 (F,wt=11): 6796 -->_s0(true,head(s(length(nil)))) | -->*_s0(head(s(0)),false) # answer(goal). [resolve(908,a,2105,b)]. given #2480 (F,wt=11): 6823 -->_s0(true,empty(s(length(nil)))) | -->*_s0(empty(s(0)),false) # answer(goal). [resolve(911,a,2105,b)]. given #2481 (T,wt=9): 8018 ->*_s0(sndsplit(length(nil),leq(s(x),0)),false). [ur(87,a,321,a,b,1069,a)]. given #2482 (T,wt=9): 8108 ->*_s0(sndsplit(length(nil),head(cons(x,y))),x). [ur(87,a,321,a,b,1112,a)]. given #2483 (T,wt=9): 8142 ->*_s0(sndsplit(length(nil),fstsplit(s(x),nil)),nil). [ur(87,a,321,a,b,1116,a)]. given #2484 (T,wt=9): 8212 ->*_s0(sndsplit(length(nil),sndsplit(0,length(nil))),0). [ur(87,a,321,a,b,1130,a)]. given #2485 (A,wt=17): 473 ->_s0(ring(x,y,z,u,sndsplit(0,w),v5),ring(x,y,z,u,w,v5)). [ur(50,a,82,a)]. given #2486 (F,wt=11): 6850 -->_s0(true,s(tail(length(nil)))) | -->*_s0(s(tail(0)),false) # answer(goal). [resolve(915,a,2105,b)]. given #2487 (F,wt=11): 6877 -->_s0(true,tail(tail(length(nil)))) | -->*_s0(tail(tail(0)),false) # answer(goal). [resolve(920,a,2105,b)]. given #2488 (F,wt=11): 6931 -->_s0(true,length(tail(length(nil)))) | -->*_s0(length(tail(0)),false) # answer(goal). [resolve(933,a,2105,b)]. given #2489 (F,wt=11): 6958 -->_s0(true,head(tail(length(nil)))) | -->*_s0(head(tail(0)),false) # answer(goal). [resolve(934,a,2105,b)]. given #2490 (T,wt=9): 8258 ->*_s0(sndsplit(length(nil),sndsplit(0,empty(nil))),true). [ur(87,a,321,a,b,1167,a)]. given #2491 (T,wt=9): 8306 ->*_s0(sndsplit(length(nil),s(empty(nil))),s(true)). [ur(87,a,321,a,b,1176,a)]. given #2492 (T,wt=9): 8340 ->*_s0(sndsplit(length(nil),tail(empty(nil))),tail(true)). [ur(87,a,321,a,b,1208,a)]. given #2493 (T,wt=9): 8352 ->*_s0(sndsplit(length(nil),length(empty(nil))),length(true)). [ur(87,a,321,a,b,1212,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): 6985 -->_s0(true,empty(tail(length(nil)))) | -->*_s0(empty(tail(0)),false) # answer(goal). [resolve(937,a,2105,b)]. given #2496 (F,wt=11): 7012 -->_s0(true,s(length(length(nil)))) | -->*_s0(s(length(0)),false) # answer(goal). [resolve(941,a,2105,b)]. given #2497 (F,wt=11): 7066 -->_s0(true,tail(length(length(nil)))) | -->*_s0(tail(length(0)),false) # answer(goal). [resolve(946,a,2105,b)]. given #2498 (F,wt=11): 7093 -->_s0(true,length(length(length(nil)))) | -->*_s0(length(length(0)),false) # answer(goal). [resolve(959,a,2105,b)]. given #2499 (T,wt=9): 8386 ->*_s0(sndsplit(length(nil),head(empty(nil))),head(true)). [ur(87,a,321,a,b,1216,a)]. given #2500 (T,wt=9): 8398 ->*_s0(sndsplit(length(nil),empty(empty(nil))),empty(true)). [ur(87,a,321,a,b,1220,a)]. given #2501 (T,wt=9): 8425 ->*_s0(sndsplit(length(nil),s(length(nil))),s(0)). [ur(87,a,321,a,b,1250,a)]. given #2502 (T,wt=9): 8437 ->*_s0(sndsplit(length(nil),tail(length(nil))),tail(0)). [ur(87,a,321,a,b,1255,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): 7120 -->_s0(true,head(length(length(nil)))) | -->*_s0(head(length(0)),false) # answer(goal). [resolve(960,a,2105,b)]. given #2505 (F,wt=11): 7147 -->_s0(true,empty(length(length(nil)))) | -->*_s0(empty(length(0)),false) # answer(goal). [resolve(963,a,2105,b)]. given #2506 (F,wt=11): 7251 -->_s0(empty(nil),empty(sndsplit(0,x))) | -->*_s0(empty(x),false) # answer(goal). [resolve(2220,b,486,a)]. given #2507 (F,wt=11): 7252 -->_s0(empty(nil),head(sndsplit(0,x))) | -->*_s0(head(x),false) # answer(goal). [resolve(2220,b,483,a)]. given #2508 (T,wt=9): 8447 ->*_s0(f(x,fstsplit(0,y)),f(x,nil)). [ur(87,a,190,a,b,86,a)]. given #2509 (T,wt=9): 8474 ->*_s0(sndsplit(length(nil),length(length(nil))),length(0)). [ur(87,a,321,a,b,1259,a)]. given #2510 (T,wt=9): 8486 ->*_s0(sndsplit(length(nil),head(length(nil))),head(0)). [ur(87,a,321,a,b,1263,a)]. given #2511 (T,wt=9): 8496 ->*_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): 7253 -->_s0(empty(nil),length(sndsplit(0,x))) | -->*_s0(length(x),false) # answer(goal). [resolve(2220,b,482,a)]. given #2514 (F,wt=11): 7254 -->_s0(empty(nil),tail(sndsplit(0,x))) | -->*_s0(tail(x),false) # answer(goal). [resolve(2220,b,469,a)]. given #2515 (F,wt=11): 7255 -->_s0(empty(nil),s(sndsplit(0,x))) | -->*_s0(s(x),false) # answer(goal). [resolve(2220,b,464,a)]. given #2516 (F,wt=11): 7256 -->_s0(empty(nil),head(mapf(x,nil))) | -->*_s0(head(nil),false) # answer(goal). [resolve(2220,b,458,a)]. given #2517 (T,wt=9): 8520 ->*_s0(sndsplit(length(nil),empty(length(nil))),empty(0)). [ur(87,a,321,a,b,1294,a)]. given #2518 (T,wt=9): 8542 ->*_s0(cons(x,fstsplit(0,y)),cons(x,nil)). [ur(87,a,192,a,b,86,a)]. given #2519 (T,wt=9): 8667 ->*_s0(cons(fstsplit(0,x),y),cons(nil,y)). [ur(87,a,193,a,b,86,a)]. given #2520 (T,wt=9): 8713 ->*_s0(sndsplit(length(nil),length(app(nil,nil))),0). [ur(87,a,321,a,b,1496,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): 7257 -->_s0(empty(nil),length(mapf(x,nil))) | -->*_s0(length(nil),false) # answer(goal). [resolve(2220,b,457,a)]. given #2523 (F,wt=11): 7258 -->_s0(empty(nil),tail(mapf(x,nil))) | -->*_s0(tail(nil),false) # answer(goal). [resolve(2220,b,444,a)]. given #2524 (F,wt=11): 7259 -->_s0(empty(nil),s(mapf(x,nil))) | -->*_s0(s(nil),false) # answer(goal). [resolve(2220,b,439,a)]. given #2525 (F,wt=11): 7265 -->_s0(empty(nil),empty(leq(0,x))) | -->*_s0(empty(true),false) # answer(goal). [resolve(2220,b,361,a)]. given #2526 (T,wt=9): 8724 ->*_s0(sndsplit(x,fstsplit(0,y)),sndsplit(x,nil)). [ur(87,a,195,a,b,86,a)]. given #2527 (T,wt=9): 8800 ->*_s0(sndsplit(fstsplit(0,x),y),sndsplit(nil,y)). [ur(87,a,196,a,b,86,a)]. given #2528 (T,wt=9): 8894 ->*_s0(sndsplit(length(nil),empty(app(nil,nil))),true). [ur(87,a,321,a,b,1563,a)]. given #2529 (T,wt=9): 8915 ->*_s0(sndsplit(length(nil),length(fstsplit(0,x))),0). [ur(87,a,321,a,b,1679,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): 7266 -->_s0(empty(nil),head(leq(0,x))) | -->*_s0(head(true),false) # answer(goal). [resolve(2220,b,358,a)]. given #2532 (F,wt=11): 7267 -->_s0(empty(nil),length(leq(0,x))) | -->*_s0(length(true),false) # answer(goal). [resolve(2220,b,357,a)]. given #2533 (F,wt=11): 7268 -->_s0(empty(nil),tail(leq(0,x))) | -->*_s0(tail(true),false) # answer(goal). [resolve(2220,b,344,a)]. given #2534 (F,wt=11): 7269 -->_s0(empty(nil),s(leq(0,x))) | -->*_s0(s(true),false) # answer(goal). [resolve(2220,b,339,a)]. given #2535 (T,wt=9): 8949 ->*_s0(sndsplit(length(nil),empty(fstsplit(0,x))),true). [ur(87,a,321,a,b,1778,a)]. given #2536 (T,wt=9): 8982 ->*_s0(sndsplit(length(nil),length(mapf(x,nil))),0). [ur(87,a,321,a,b,2075,a)]. given #2537 (T,wt=9): 9016 ->*_s0(sndsplit(length(nil),empty(mapf(x,nil))),true). [ur(87,a,321,a,b,2162,a)]. given #2538 (T,wt=9): 9155 ->*_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): 7298 -->_s0(empty(nil),head(fstsplit(0,x))) | -->*_s0(head(nil),false) # answer(goal). [resolve(2220,b,208,a)]. given #2541 (F,wt=11): 7299 -->_s0(empty(nil),length(fstsplit(0,x))) | -->*_s0(length(nil),false) # answer(goal). [resolve(2220,b,207,a)]. given #2542 (F,wt=11): 7300 -->_s0(empty(nil),tail(fstsplit(0,x))) | -->*_s0(tail(nil),false) # answer(goal). [resolve(2220,b,194,a)]. given #2543 (F,wt=11): 7301 -->_s0(empty(nil),s(fstsplit(0,x))) | -->*_s0(s(nil),false) # answer(goal). [resolve(2220,b,189,a)]. given #2544 (T,wt=9): 9211 ->*_s0(mapf(x,app(nil,fstsplit(0,y))),nil). [ur(87,a,128,a,b,9154,a)]. given #2545 (T,wt=9): 9213 ->*_s0(sndsplit(0,mapf(x,fstsplit(0,y))),nil). [ur(87,a,82,a,b,9154,a)]. given #2546 (T,wt=9): 9215 ->*_s0(app(nil,mapf(x,fstsplit(0,y))),nil). [ur(87,a,61,a,b,9154,a)]. given #2547 (T,wt=9): 9232 ->*_s0(sndsplit(length(nil),length(sndsplit(0,nil))),0). [ur(87,a,321,a,b,2285,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): 7344 -->_s0(empty(nil),empty(app(nil,x))) | -->*_s0(empty(x),false) # answer(goal). [resolve(2220,b,136,a)]. given #2550 (F,wt=11): 7347 -->_s0(empty(nil),head(app(nil,x))) | -->*_s0(head(x),false) # answer(goal). [resolve(2220,b,133,a)]. given #2551 (F,wt=11): 7348 -->_s0(empty(nil),length(app(nil,x))) | -->*_s0(length(x),false) # answer(goal). [resolve(2220,b,132,a)]. given #2552 (F,wt=11): 7361 -->_s0(empty(nil),tail(app(nil,x))) | -->*_s0(tail(x),false) # answer(goal). [resolve(2220,b,119,a)]. given #2553 (T,wt=9): 9242 ->*_s0(mapf(fstsplit(0,x),y),mapf(nil,y)). [ur(87,a,204,a,b,86,a)]. given #2554 (T,wt=9): 9316 ->*_s0(leq(x,fstsplit(0,y)),leq(x,nil)). [ur(87,a,205,a,b,86,a)]. given #2555 (T,wt=9): 9376 ->*_s0(leq(fstsplit(0,x),y),leq(nil,y)). [ur(87,a,206,a,b,86,a)]. given #2556 (T,wt=9): 9462 ->*_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): 7366 -->_s0(empty(nil),s(app(nil,x))) | -->*_s0(s(x),false) # answer(goal). [resolve(2220,b,114,a)]. given #2559 (F,wt=11): 7438 -->_s0(empty(nil),x) | -->_s0(x,app(app(nil,nil),false)) # answer(goal). [resolve(2220,c,5160,a)]. given #2560 (F,wt=11): 7439 -->_s0(empty(nil),x) | -->_s0(x,leq(s(y),length(nil))) # answer(goal). [resolve(2220,c,4606,a)]. given #2561 (F,wt=11): 7441 -->_s0(empty(nil),x) | -->_s0(x,sndsplit(app(nil,0),false)) # answer(goal). [resolve(2220,c,3398,a)]. given #2562 (T,wt=9): 9483 ->*_s0(sndsplit(length(nil),empty(sndsplit(0,nil))),true). [ur(87,a,321,a,b,2382,a)]. given #2563 (T,wt=9): 9564 ->*_s0(fstsplit(fstsplit(0,x),y),fstsplit(nil,y)). [ur(87,a,210,a,b,86,a)]. given #2564 (T,wt=9): 9618 ->*_s0(app(x,fstsplit(0,y)),app(x,nil)). [ur(87,a,212,a,b,86,a)]. given #2565 (T,wt=9): 9657 ->*_s0(f(length(nil),empty(nil)),f(0,true)). [ur(87,a,316,a,b,3283,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): 7442 -->_s0(empty(nil),x) | -->_s0(x,app(nil,app(nil,false))) # answer(goal). [resolve(2220,c,691,a)]. given #2568 (F,wt=11): 7444 -->_s0(empty(nil),x) | -->_s0(x,sndsplit(0,app(nil,false))) # answer(goal). [resolve(2220,c,689,a)]. given #2569 (F,wt=11): 7446 -->_s0(empty(nil),x) | -->_s0(x,app(nil,sndsplit(0,false))) # answer(goal). [resolve(2220,c,637,a)]. given #2570 (F,wt=11): 7448 -->_s0(empty(nil),x) | -->_s0(x,sndsplit(0,sndsplit(0,false))) # answer(goal). [resolve(2220,c,635,a)]. given #2571 (T,wt=9): 9659 ->*_s0(f(empty(nil),empty(nil)),f(true,true)). [ur(87,a,166,a,b,3283,a)]. given #2572 (T,wt=9): 9668 ->*_s0(f(empty(nil),length(nil)),f(true,0)). [ur(87,a,315,a,b,3310,a)]. given #2573 (T,wt=9): 9710 ->*_s0(app(fstsplit(0,x),app(nil,y)),y). [ur(87,a,213,a,b,691,a)]. given #2574 (T,wt=9): 9711 ->*_s0(app(fstsplit(0,x),fstsplit(0,y)),nil). [ur(87,a,213,a,b,685,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): 7467 -->_s0(empty(nil),head(sndsplit(0,cons(app(nil,false),x)))) # answer(goal). [ur(2220,b,483,a,c,690,a)]. given #2577 (F,wt=11): 7468 -->_s0(empty(nil),head(sndsplit(0,cons(sndsplit(0,false),x)))) # answer(goal). [ur(2220,b,483,a,c,636,a)]. given #2578 (F,wt=11): 7470 -->_s0(empty(nil),tail(sndsplit(0,cons(x,app(nil,false))))) # answer(goal). [ur(2220,b,469,a,c,688,a)]. given #2579 (F,wt=11): 7471 -->_s0(empty(nil),tail(sndsplit(0,cons(x,sndsplit(0,false))))) # answer(goal). [ur(2220,b,469,a,c,633,a)]. given #2580 (T,wt=9): 9712 ->*_s0(app(fstsplit(0,x),leq(0,y)),true). [ur(87,a,213,a,b,681,a)]. given #2581 (T,wt=9): 9713 ->*_s0(app(fstsplit(0,x),mapf(y,nil)),nil). [ur(87,a,213,a,b,641,a)]. given #2582 (T,wt=9): 9714 ->*_s0(app(fstsplit(0,x),sndsplit(0,y)),y). [ur(87,a,213,a,b,637,a)]. given #2583 (T,wt=9): 9718 ->*_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): 7483 -->_s0(empty(nil),sndsplit(app(nil,0),empty(cons(x,y)))) # answer(goal). [ur(2220,b,145,a,c,3398,a)]. given #2586 (F,wt=11): 7491 -->_s0(empty(nil),head(app(nil,cons(app(nil,false),x)))) # answer(goal). [ur(2220,b,133,a,c,690,a)]. given #2587 (F,wt=11): 7492 -->_s0(empty(nil),head(app(nil,cons(sndsplit(0,false),x)))) # answer(goal). [ur(2220,b,133,a,c,636,a)]. given #2588 (F,wt=11): 7502 -->_s0(empty(nil),sndsplit(app(nil,s(0)),cons(x,false))) # answer(goal). [ur(2220,b,121,a,c,634,a)]. given #2589 (T,wt=9): 9761 ->*_s0(app(app(nil,fstsplit(0,x)),y),y). [ur(87,a,138,a,b,9717,a)]. given #2590 (T,wt=9): 9764 ->*_s0(sndsplit(0,app(fstsplit(0,x),y)),y). [ur(87,a,82,a,b,9717,a)]. given #2591 (T,wt=9): 9766 ->*_s0(app(nil,app(fstsplit(0,x),y)),y). [ur(87,a,61,a,b,9717,a)]. given #2592 (T,wt=9): 9771 ->*_s0(cons(length(nil),empty(nil)),cons(0,true)). [ur(87,a,318,a,b,3337,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): 22496 -->_s0(true,sndsplit(length(nil),app(fstsplit(0,x),false))) # answer(goal). [resolve(9764,a,4422,b)]. given #2595 (F,wt=11): 7505 -->_s0(empty(nil),sndsplit(s(0),app(nil,cons(x,false)))) # answer(goal). [ur(2220,b,120,a,c,634,a)]. given #2596 (F,wt=11): 7506 -->_s0(empty(nil),tail(app(nil,cons(x,app(nil,false))))) # answer(goal). [ur(2220,b,119,a,c,688,a)]. given #2597 (F,wt=11): 7507 -->_s0(empty(nil),tail(app(nil,cons(x,sndsplit(0,false))))) # answer(goal). [ur(2220,b,119,a,c,633,a)]. given #2598 (T,wt=9): 9773 ->*_s0(cons(empty(nil),empty(nil)),cons(true,true)). [ur(87,a,168,a,b,3337,a)]. given #2599 (T,wt=9): 9782 ->*_s0(cons(empty(nil),length(nil)),cons(true,0)). [ur(87,a,317,a,b,3364,a)]. given #2600 (T,wt=9): 9836 ->*_s0(sndsplit(length(nil),empty(nil)),sndsplit(0,true)). [ur(87,a,321,a,b,3446,a)]. given #2601 (T,wt=9): 9838 ->*_s0(sndsplit(empty(nil),empty(nil)),sndsplit(true,true)). [ur(87,a,171,a,b,3446,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): 7509 -->_s0(empty(nil),head(app(cons(app(nil,false),x),y))) # answer(goal). [ur(2220,b,108,a,c,690,a)]. given #2604 (F,wt=11): 7510 -->_s0(empty(nil),head(app(cons(sndsplit(0,false),x),y))) # answer(goal). [ur(2220,b,108,a,c,636,a)]. given #2605 (F,wt=11): 7513 -->_s0(empty(nil),tail(cons(x,app(app(nil,nil),false)))) # answer(goal). [ur(2220,b,85,a,c,5160,a)]. given #2606 (F,wt=11): 7514 -->_s0(empty(nil),tail(cons(x,leq(s(y),length(nil))))) # answer(goal). [ur(2220,b,85,a,c,4606,a)]. given #2607 (T,wt=9): 9848 ->*_s0(sndsplit(empty(nil),length(nil)),sndsplit(true,0)). [ur(87,a,320,a,b,3473,a)]. given #2608 (T,wt=9): 9868 ->*_s0(mapf(length(nil),empty(nil)),mapf(0,true)). [ur(87,a,329,a,b,3500,a)]. given #2609 (T,wt=9): 9870 ->*_s0(mapf(empty(nil),empty(nil)),mapf(true,true)). [ur(87,a,179,a,b,3500,a)]. given #2610 (T,wt=9): 9879 ->*_s0(mapf(empty(nil),length(nil)),mapf(true,0)). [ur(87,a,328,a,b,3554,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): 7516 -->_s0(empty(nil),tail(cons(x,sndsplit(app(nil,0),false)))) # answer(goal). [ur(2220,b,85,a,c,3398,a)]. given #2613 (F,wt=11): 7517 -->_s0(empty(nil),tail(cons(x,app(nil,app(nil,false))))) # answer(goal). [ur(2220,b,85,a,c,691,a)]. given #2614 (F,wt=11): 7519 -->_s0(empty(nil),tail(cons(x,sndsplit(0,app(nil,false))))) # answer(goal). [ur(2220,b,85,a,c,689,a)]. given #2615 (F,wt=11): 7521 -->_s0(empty(nil),tail(cons(x,app(nil,sndsplit(0,false))))) # answer(goal). [ur(2220,b,85,a,c,637,a)]. given #2616 (T,wt=9): 9889 ->*_s0(leq(length(nil),empty(nil)),leq(0,true)). [ur(87,a,331,a,b,3581,a)]. given #2617 (T,wt=9): 9891 ->*_s0(leq(empty(nil),empty(nil)),leq(true,true)). [ur(87,a,181,a,b,3581,a)]. given #2618 (T,wt=9): 9901 ->*_s0(leq(empty(nil),length(nil)),leq(true,0)). [ur(87,a,330,a,b,3609,a)]. given #2619 (T,wt=9): 9921 ->*_s0(fstsplit(length(nil),empty(nil)),fstsplit(0,true)). [ur(87,a,335,a,b,3636,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): 7523 -->_s0(empty(nil),tail(cons(x,sndsplit(0,sndsplit(0,false))))) # answer(goal). [ur(2220,b,85,a,c,635,a)]. given #2622 (F,wt=11): 7531 -->_s0(empty(nil),sndsplit(s(app(nil,0)),cons(x,false))) # answer(goal). [ur(2220,b,83,a,c,3398,a)]. given #2623 (F,wt=11): 7532 -->_s0(empty(nil),sndsplit(s(0),cons(x,app(nil,false)))) # answer(goal). [ur(2220,b,83,a,c,689,a)]. given #2624 (F,wt=11): 7533 -->_s0(empty(nil),sndsplit(s(0),cons(x,sndsplit(0,false)))) # answer(goal). [ur(2220,b,83,a,c,635,a)]. given #2625 (T,wt=9): 9923 ->*_s0(fstsplit(empty(nil),empty(nil)),fstsplit(true,true)). [ur(87,a,185,a,b,3636,a)]. given #2626 (T,wt=9): 9932 ->*_s0(fstsplit(empty(nil),length(nil)),fstsplit(true,0)). [ur(87,a,334,a,b,3691,a)]. given #2627 (T,wt=9): 9942 ->*_s0(app(length(nil),empty(nil)),app(0,true)). [ur(87,a,338,a,b,3718,a)]. given #2628 (T,wt=9): 9944 ->*_s0(app(empty(nil),empty(nil)),app(true,true)). [ur(87,a,188,a,b,3718,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): 7539 -->_s0(empty(nil),sndsplit(0,head(cons(app(nil,false),x)))) # answer(goal). [ur(2220,b,82,a,c,690,a)]. given #2631 (F,wt=11): 7541 -->_s0(empty(nil),sndsplit(0,tail(cons(x,app(nil,false))))) # answer(goal). [ur(2220,b,82,a,c,688,a)]. given #2632 (F,wt=11): 7542 -->_s0(empty(nil),sndsplit(0,head(cons(sndsplit(0,false),x)))) # answer(goal). [ur(2220,b,82,a,c,636,a)]. given #2633 (F,wt=11): 7544 -->_s0(empty(nil),sndsplit(0,sndsplit(s(0),cons(x,false)))) # answer(goal). [ur(2220,b,82,a,c,634,a)]. given #2634 (T,wt=9): 9953 ->*_s0(app(empty(nil),length(nil)),app(true,0)). [ur(87,a,337,a,b,3745,a)]. given #2635 (T,wt=9): 10047 ->*_s0(tail(fstsplit(s(0),cons(x,y))),nil). [ur(87,a,219,a,b,682,a)]. given #2636 (T,wt=9): 10085 ->*_s0(f(length(nil),length(nil)),f(0,0)). [ur(87,a,316,a,b,4254,a)]. given #2637 (T,wt=9): 10118 ->*_s0(cons(length(nil),length(nil)),cons(0,0)). [ur(87,a,318,a,b,4308,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): 7545 -->_s0(empty(nil),sndsplit(0,tail(cons(x,sndsplit(0,false))))) # answer(goal). [ur(2220,b,82,a,c,633,a)]. given #2640 (F,wt=11): 7551 -->_s0(empty(nil),head(cons(app(app(nil,nil),false),x))) # answer(goal). [ur(2220,b,67,a,c,5160,a)]. given #2641 (F,wt=11): 7552 -->_s0(empty(nil),head(cons(leq(s(x),length(nil)),y))) # answer(goal). [ur(2220,b,67,a,c,4606,a)]. given #2642 (F,wt=11): 7554 -->_s0(empty(nil),head(cons(sndsplit(app(nil,0),false),x))) # answer(goal). [ur(2220,b,67,a,c,3398,a)]. given #2643 (T,wt=9): 10141 ->*_s0(sndsplit(length(nil),length(nil)),sndsplit(0,0)). [ur(87,a,321,a,b,4396,a)]. given #2644 (T,wt=9): 10298 ->*_s0(sndsplit(length(nil),sndsplit(length(nil),x)),x). [ur(87,a,321,a,b,4499,a)]. given #2645 (T,wt=9): 10343 ->*_s0(mapf(length(nil),length(nil)),mapf(0,0)). [ur(87,a,329,a,b,4520,a)]. given #2646 (T,wt=9): 10389 ->*_s0(leq(length(nil),length(nil)),leq(0,0)). [ur(87,a,331,a,b,4607,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): 7555 -->_s0(empty(nil),head(cons(app(nil,app(nil,false)),x))) # answer(goal). [ur(2220,b,67,a,c,691,a)]. given #2649 (F,wt=11): 7557 -->_s0(empty(nil),head(cons(sndsplit(0,app(nil,false)),x))) # answer(goal). [ur(2220,b,67,a,c,689,a)]. given #2650 (F,wt=11): 7559 -->_s0(empty(nil),head(cons(app(nil,sndsplit(0,false)),x))) # answer(goal). [ur(2220,b,67,a,c,637,a)]. given #2651 (F,wt=11): 7561 -->_s0(empty(nil),head(cons(sndsplit(0,sndsplit(0,false)),x))) # answer(goal). [ur(2220,b,67,a,c,635,a)]. given #2652 (T,wt=9): 10453 ->*_s0(sndsplit(length(nil),leq(length(nil),x)),true). [ur(87,a,321,a,b,4717,a)]. given #2653 (T,wt=9): 10477 ->*_s0(fstsplit(length(nil),length(nil)),fstsplit(0,0)). [ur(87,a,335,a,b,4733,a)]. given #2654 (T,wt=9): 10504 ->*_s0(sndsplit(length(nil),fstsplit(length(nil),x)),nil). [ur(87,a,321,a,b,4816,a)]. given #2655 (T,wt=9): 10517 ->*_s0(app(length(nil),length(nil)),app(0,0)). [ur(87,a,338,a,b,4820,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): 7572 -->_s0(empty(nil),app(nil,head(cons(app(nil,false),x)))) # answer(goal). [ur(2220,b,61,a,c,690,a)]. given #2658 (F,wt=11): 7574 -->_s0(empty(nil),app(nil,tail(cons(x,app(nil,false))))) # answer(goal). [ur(2220,b,61,a,c,688,a)]. given #2659 (F,wt=11): 7575 -->_s0(empty(nil),app(nil,head(cons(sndsplit(0,false),x)))) # answer(goal). [ur(2220,b,61,a,c,636,a)]. given #2660 (F,wt=11): 7577 -->_s0(empty(nil),app(nil,sndsplit(s(0),cons(x,false)))) # answer(goal). [ur(2220,b,61,a,c,634,a)]. given #2661 (T,wt=9): 10767 ->*_s0(head(fstsplit(s(x),cons(y,z))),y). [ur(87,a,233,a,b,575,a)]. given #2662 (T,wt=9): 10837 ->*_s0(length(cons(x,empty(nil))),s(length(true))). [ur(87,a,68,a,b,6161,a)]. given #2663 (T,wt=9): 10877 ->*_s0(empty(fstsplit(s(x),cons(y,z))),false). [ur(87,a,236,a,b,580,a)]. ============================== PROOF ================================= % Proof 1 at 0.43 (+ 0.02) seconds: goal. % Length of proof is 24. % Level of proof is 5. % Maximum clause weight is 21.000. % Given clauses 2663. 3 ->_s0(x1,y) -> ->_s0(empty(x1),empty(y)) # label(congruence) # label(non_clause). [assumption]. 9 ->_s0(x2,y) -> ->_s0(leq(x1,x2),leq(x1,y)) # label(congruence) # label(non_clause). [assumption]. 33 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 34 (exists x13 exists x14 exists x15 (->*_s0(empty(fstsplit(x13,x14)),false) & ->*_s0(leq(x13,length(x15)),true) & ->*_s0(empty(fstsplit(x13,x15)),false))) # label(goal) # label(non_clause) # label(goal). [goal]. 37 -->_s0(x,y) | ->_s0(empty(x),empty(y)) # label(congruence). [clausify(3)]. 43 -->_s0(x,y) | ->_s0(leq(z,x),leq(z,y)) # label(congruence). [clausify(9)]. 62 ->_s0(empty(cons(x,y)),false) # label(replacement). [assumption]. 65 ->_s0(fstsplit(s(x),cons(y,z)),cons(y,fstsplit(x,z))) # label(replacement). [assumption]. 68 ->_s0(length(cons(x,y)),s(length(y))) # label(replacement). [assumption]. 70 ->_s0(leq(0,x),true) # label(replacement). [assumption]. 72 ->_s0(leq(s(x),s(y)),leq(x,y)) # label(replacement). [assumption]. 86 ->*_s0(x,x) # label(reflexivity). [assumption]. 87 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(33)]. 88 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->*_s0(empty(fstsplit(x,z)),false) # label(goal) # answer(goal). [deny(34)]. 236 ->_s0(empty(fstsplit(s(x),cons(y,z))),empty(cons(y,fstsplit(x,z)))). [ur(37,a,65,a)]. 305 ->_s0(leq(x,length(cons(y,z))),leq(x,s(length(z)))). [ur(43,a,68,a)]. 572 ->*_s0(leq(0,x),true). [ur(87,a,70,a,b,86,a)]. 580 ->*_s0(empty(cons(x,y)),false). [ur(87,a,62,a,b,86,a)]. 584 -->*_s0(empty(fstsplit(x,y)),false) | -->*_s0(leq(x,length(z)),true) | -->_s0(empty(fstsplit(x,z)),u) | -->*_s0(u,false) # answer(goal). [resolve(88,c,87,c)]. 679 ->*_s0(leq(s(0),s(x)),true). [ur(87,a,72,a,b,572,a)]. 10877 ->*_s0(empty(fstsplit(s(x),cons(y,z))),false). [ur(87,a,236,a,b,580,a)]. 14623 ->*_s0(leq(s(0),length(cons(x,y))),true). [ur(87,a,305,a,b,679,a)]. 22714 -->*_s0(leq(s(x),length(cons(y,z))),true) # answer(goal). [ur(584,a,10877,a,c,236,a,d,580,a)]. 22715 $F # answer(goal). [resolve(22714,a,14623,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=2663. Generated=47569. Kept=22680. proofs=1. Usable=2628. Sos=19851. Demods=0. Limbo=50, Disabled=204. Hints=0. Kept_by_rule=0, Deleted_by_rule=0. Forward_subsumed=9954. Back_subsumed=150. Sos_limit_deleted=14935. 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=50605. Nonunit_bsub_feature_tests=2428. Megabytes=44.15. User_CPU=0.43, System_CPU=0.02, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 1 proof. Process 3157870 exit (max_proofs) Tue Jul 30 08:24:40 2024 The problem is feasible.