/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

Problem 1: 

(VAR X Y)
(RULES
add(0,X) -> X
add(s(X),Y) -> s(add(X,Y))
fact(X) -> if(zero(X),s(0),prod(X,fact(p(X))))
if(false,X,Y) -> Y
if(true,X,Y) -> X
p(s(X)) -> X
prod(0,X) -> 0
prod(s(X),Y) -> add(Y,prod(X,Y))
zero(0) -> true
zero(s(X)) -> false
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ADD(s(X),Y) -> ADD(X,Y)
 FACT(X) -> FACT(p(X))
 FACT(X) -> IF(zero(X),s(0),prod(X,fact(p(X))))
 FACT(X) -> P(X)
 FACT(X) -> PROD(X,fact(p(X)))
 FACT(X) -> ZERO(X)
 PROD(s(X),Y) -> ADD(Y,prod(X,Y))
 PROD(s(X),Y) -> PROD(X,Y)
-> Rules:
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fact(X) -> if(zero(X),s(0),prod(X,fact(p(X))))
 if(false,X,Y) -> Y
 if(true,X,Y) -> X
 p(s(X)) -> X
 prod(0,X) -> 0
 prod(s(X),Y) -> add(Y,prod(X,Y))
 zero(0) -> true
 zero(s(X)) -> false

Problem 1: 

Infinite Processor:
-> Pairs:
 ADD(s(X),Y) -> ADD(X,Y)
 FACT(X) -> FACT(p(X))
 FACT(X) -> IF(zero(X),s(0),prod(X,fact(p(X))))
 FACT(X) -> P(X)
 FACT(X) -> PROD(X,fact(p(X)))
 FACT(X) -> ZERO(X)
 PROD(s(X),Y) -> ADD(Y,prod(X,Y))
 PROD(s(X),Y) -> PROD(X,Y)
-> Rules:
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fact(X) -> if(zero(X),s(0),prod(X,fact(p(X))))
 if(false,X,Y) -> Y
 if(true,X,Y) -> X
 p(s(X)) -> X
 prod(0,X) -> 0
 prod(s(X),Y) -> add(Y,prod(X,Y))
 zero(0) -> true
 zero(s(X)) -> false
-> Pairs in cycle:
 FACT(X) -> FACT(p(X))

The problem is infinite.