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


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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(0,1,X) => f(X,X,X)
 (2)  f(Y,U,V) => 2
 (3)  0 => 2
 (4)  1 => 2
 (5)  g(W,W,P) => P
 (6)  g(X1,Y1,Y1) => X1

forward process killed -- 344 rule(s) generated
forward+backward process killed -- 416 rule(s) generated

NO

let R be the TRS under consideration

f(0,1,_1) -> f(_1,_1,_1) is in elim_R(R)
let l0 be the left-hand side of this rule
p0 = 0 is a position in l0
we have l0|p0 = 0
g(_2,_2,_3) -> _3 is in R
let r'0 be the right-hand side of this rule
theta0 = {_3/0} is a mgu of l0|p0 and r'0

==> f(g(_1,_1,0),1,_2) -> f(_2,_2,_2) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 0.0 is a position in l1
we have l1|p1 = _1
1 -> 2 is in R
let r'1 be the right-hand side of this rule
theta1 = {_1/2} is a mgu of l1|p1 and r'1

==> f(g(1,2,0),1,_1) -> f(_1,_1,_1) is in EU_R^2
let l2 be the left-hand side of this rule
p2 = 0.1 is a position in l2
we have l2|p2 = 2
0 -> 2 is in R
let r'2 be the right-hand side of this rule
theta2 = {} is a mgu of l2|p2 and r'2

==> f(g(1,0,0),1,_1) -> f(_1,_1,_1) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 1 is a position in l3
we have l3|p3 = 1
g(_2,_3,_3) -> _2 is in R
let r'3 be the right-hand side of this rule
theta3 = {_2/1} is a mgu of l3|p3 and r'3

==> f(g(1,0,0),g(1,_1,_1),_2) -> f(_2,_2,_2) is in EU_R^4
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {_1/0, _2/g(1,0,0)}
let theta' = {}
we have r|p = f(_2,_2,_2) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(g(1,0,0),g(1,0,0),g(1,0,0)) is non-terminating w.r.t. R

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


******** Signature ********
 0 : a
 1 : a
 2 : a
 cons : (d,e) -> e
 f : (a,a,a) -> a
 false : c
 filter : ((d -> c),e) -> e
 filter2 : (c,(d -> c),d,e) -> e
 g : (b,b,b) -> b
 map : ((d -> d),e) -> e
 nil : e
 true : c
******** Computation Rules ********
 (1)  f(0,1,X) => f(X,X,X)
 (2)  f(Y,U,V) => 2
 (3)  0 => 2
 (4)  1 => 2
 (5)  g(W,W,P) => P
 (6)  g(X1,Y1,Y1) => X1
 (7)  map(G1,nil) => nil
 (8)  map(H1,cons(W1,P1)) => cons(H1[W1],map(H1,P1))
 (9)  filter(F2,nil) => nil
 (10)  filter(Z2,cons(U2,V2)) => filter2(Z2[U2],Z2,U2,V2)
 (11)  filter2(true,I2,P2,X3) => cons(P2,filter(I2,X3))
 (12)  filter2(false,Z3,U3,V3) => filter(Z3,V3)

NO