/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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)  X + 0 => X
 (2)  Y + s(U) => s(Y + U)
 (3)  f(0,s(0),V) => f(V,V + V,V)
 (4)  g(W,P) => W
 (5)  g(X1,Y1) => Y1

backward process killed -- 1411 rule(s) generated
forward+backward process killed -- 1105 rule(s) generated

NO

let R be the TRS under consideration

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

==> f(0,s(0),g(_1,_2)) -> f(_1,plus(g(_1,_2),g(_1,_2)),g(_1,_2)) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 1.0 is a position in r1
we have r1|p1 = g(_1,_2)
g(_3,_4) -> _4 is in R
let l'1 be the left-hand side of this rule
theta1 = {_1/_3, _2/_4} is a mgu of r1|p1 and l'1

==> f(0,s(0),g(_1,_2)) -> f(_1,plus(_2,g(_1,_2)),g(_1,_2)) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 1.1 is a position in r2
we have r2|p2 = g(_1,_2)
g(_3,_4) -> _3 is in R
let l'2 be the left-hand side of this rule
theta2 = {_1/_3, _2/_4} is a mgu of r2|p2 and l'2

==> f(0,s(0),g(_1,_2)) -> f(_1,plus(_2,_1),g(_1,_2)) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 1 is a position in r3
we have r3|p3 = plus(_2,_1)
plus(_3,0) -> _3 is in R
let l'3 be the left-hand side of this rule
theta3 = {_1/0, _2/_3} is a mgu of r3|p3 and l'3

==> f(0,s(0),g(0,_1)) -> f(0,_1,g(0,_1)) 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/s(0)}
let theta' = {}
we have r|p = f(0,_1,g(0,_1)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(0,s(0),g(0,s(0))) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=4, depth k=3
874 rule(s) generated
>>NO


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

NO