/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


NO

We split firstr-order part and higher-order part, and do modular checking by a general modularity.

******** FO SN check ********
Check non-SN using NTI (Non-Termination Inference by Payet)

******** Computation rules ********
 (1)  f(g(X,Y),X,U) => f(U,U,U)
 (2)  g(V,W) => V
 (3)  g(P,X1) => X1

forward+backward process killed -- 4 rule(s) generated

NO

let R be the TRS under consideration

f(g(_1,_2),_1,_3) -> f(_3,_3,_3) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 1 is a position in r0
we have r0|p0 = _3
g(_4,_5) -> _4 is in R
let l'0 be the left-hand side of this rule
theta0 = {_3/g(_4,_5)} is a mgu of r0|p0 and l'0

==> f(g(_1,_2),_1,g(_3,_4)) -> f(g(_3,_4),_3,g(_3,_4)) is in EU_R^1
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {_1/_3, _2/_4}
let theta' = {}
we have r|p = f(g(_3,_4),_3,g(_3,_4)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(g(_3,_4),_3,g(_3,_4)) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=1, depth k=2
4 rule(s) generated
>>NO


******** Signature ********
 cons : (d,e) -> e
 f : (b,b,b) -> a
 false : c
 filter : ((d -> c),e) -> e
 filter2 : (c,(d -> c),d,e) -> e
 g : (b,b) -> b
 map : ((d -> d),e) -> e
 nil : e
 true : c
******** Computation Rules ********
 (1)  f(g(X,Y),X,U) => f(U,U,U)
 (2)  g(V,W) => V
 (3)  g(P,X1) => X1
 (4)  map(Z1,nil) => nil
 (5)  map(G1,cons(V1,W1)) => cons(G1[V1],map(G1,W1))
 (6)  filter(J1,nil) => nil
 (7)  filter(F2,cons(Y2,U2)) => filter2(F2[Y2],F2,Y2,U2)
 (8)  filter2(true,H2,W2,P2) => cons(W2,filter(H2,P2))
 (9)  filter2(false,F3,Y3,U3) => filter(F3,U3)

NO