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


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


NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S)
(RULES
add(0,X:S) -> X:S
add(s(X:S),Y:S) -> s(add(X:S,Y:S))
fact(X:S) -> if(zero(X:S),s(0),prod(X:S,fact(p(X:S))))
if(ffalse,X:S,Y:S) -> Y:S
if(ttrue,X:S,Y:S) -> X:S
p(s(X:S)) -> X:S
prod(0,X:S) -> 0
prod(s(X:S),Y:S) -> add(Y:S,prod(X:S,Y:S))
zero(0) -> ttrue
zero(s(X:S)) -> ffalse
)

Problem 1: 

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

Problem 1: 

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

The problem is infinite.