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


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


NO

Problem 1: 

(VAR X Y)
(RULES
0 -> n__0
activate(n__0) -> 0
activate(n__s(X)) -> s(X)
activate(X) -> X
diff(X,Y) -> if(leq(X,Y),n__0,n__s(diff(p(X),Y)))
if(false,X,Y) -> activate(Y)
if(true,X,Y) -> activate(X)
leq(0,Y) -> true
leq(s(X),0) -> false
leq(s(X),s(Y)) -> leq(X,Y)
p(0) -> 0
p(s(X)) -> X
s(X) -> n__s(X)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__0) -> 0#
 ACTIVATE(n__s(X)) -> S(X)
 DIFF(X,Y) -> DIFF(p(X),Y)
 DIFF(X,Y) -> IF(leq(X,Y),n__0,n__s(diff(p(X),Y)))
 DIFF(X,Y) -> LEQ(X,Y)
 DIFF(X,Y) -> P(X)
 IF(false,X,Y) -> ACTIVATE(Y)
 IF(true,X,Y) -> ACTIVATE(X)
 LEQ(s(X),s(Y)) -> LEQ(X,Y)
-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__s(X)) -> s(X)
 activate(X) -> X
 diff(X,Y) -> if(leq(X,Y),n__0,n__s(diff(p(X),Y)))
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 leq(0,Y) -> true
 leq(s(X),0) -> false
 leq(s(X),s(Y)) -> leq(X,Y)
 p(0) -> 0
 p(s(X)) -> X
 s(X) -> n__s(X)

Problem 1: 

Infinite Processor:
-> Pairs:
 ACTIVATE(n__0) -> 0#
 ACTIVATE(n__s(X)) -> S(X)
 DIFF(X,Y) -> DIFF(p(X),Y)
 DIFF(X,Y) -> IF(leq(X,Y),n__0,n__s(diff(p(X),Y)))
 DIFF(X,Y) -> LEQ(X,Y)
 DIFF(X,Y) -> P(X)
 IF(false,X,Y) -> ACTIVATE(Y)
 IF(true,X,Y) -> ACTIVATE(X)
 LEQ(s(X),s(Y)) -> LEQ(X,Y)
-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__s(X)) -> s(X)
 activate(X) -> X
 diff(X,Y) -> if(leq(X,Y),n__0,n__s(diff(p(X),Y)))
 if(false,X,Y) -> activate(Y)
 if(true,X,Y) -> activate(X)
 leq(0,Y) -> true
 leq(s(X),0) -> false
 leq(s(X),s(Y)) -> leq(X,Y)
 p(0) -> 0
 p(s(X)) -> X
 s(X) -> n__s(X)
-> Pairs in cycle:
 DIFF(X,Y) -> DIFF(p(X),Y)

The problem is infinite.