/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 v_NonEmpty:S X:S Y:S)
(RULES
diff(X:S,Y:S) -> if(leq(X:S,Y:S),0,s(diff(p(X:S),Y:S)))
if(ffalse,X:S,Y:S) -> Y:S
if(ttrue,X:S,Y:S) -> X:S
leq(0,Y:S) -> ttrue
leq(s(X:S),0) -> ffalse
leq(s(X:S),s(Y:S)) -> leq(X:S,Y:S)
p(0) -> 0
p(s(X:S)) -> X:S
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 DIFF(X:S,Y:S) -> DIFF(p(X:S),Y:S)
 DIFF(X:S,Y:S) -> IF(leq(X:S,Y:S),0,s(diff(p(X:S),Y:S)))
 DIFF(X:S,Y:S) -> LEQ(X:S,Y:S)
 DIFF(X:S,Y:S) -> P(X:S)
 LEQ(s(X:S),s(Y:S)) -> LEQ(X:S,Y:S)
-> Rules:
 diff(X:S,Y:S) -> if(leq(X:S,Y:S),0,s(diff(p(X:S),Y:S)))
 if(ffalse,X:S,Y:S) -> Y:S
 if(ttrue,X:S,Y:S) -> X:S
 leq(0,Y:S) -> ttrue
 leq(s(X:S),0) -> ffalse
 leq(s(X:S),s(Y:S)) -> leq(X:S,Y:S)
 p(0) -> 0
 p(s(X:S)) -> X:S

Problem 1: 

Infinite Processor:
-> Pairs:
 DIFF(X:S,Y:S) -> DIFF(p(X:S),Y:S)
 DIFF(X:S,Y:S) -> IF(leq(X:S,Y:S),0,s(diff(p(X:S),Y:S)))
 DIFF(X:S,Y:S) -> LEQ(X:S,Y:S)
 DIFF(X:S,Y:S) -> P(X:S)
 LEQ(s(X:S),s(Y:S)) -> LEQ(X:S,Y:S)
-> Rules:
 diff(X:S,Y:S) -> if(leq(X:S,Y:S),0,s(diff(p(X:S),Y:S)))
 if(ffalse,X:S,Y:S) -> Y:S
 if(ttrue,X:S,Y:S) -> X:S
 leq(0,Y:S) -> ttrue
 leq(s(X:S),0) -> ffalse
 leq(s(X:S),s(Y:S)) -> leq(X:S,Y:S)
 p(0) -> 0
 p(s(X:S)) -> X:S
-> Pairs in cycle:
 DIFF(X:S,Y:S) -> DIFF(p(X:S),Y:S)

The problem is infinite.