/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR X XS)
(STRATEGY CONTEXTSENSITIVE
(head 1)
(incr 1)
(nats)
(odds)
(pairs)
(tail 1)
(0)
(cons 1)
(s 1)
)
(RULES
head(cons(X,XS)) -> X
incr(cons(X,XS)) -> cons(s(X),incr(XS))
nats -> cons(0,incr(nats))
odds -> incr(pairs)
pairs -> cons(0,incr(odds))
tail(cons(X,XS)) -> XS
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 head(cons(X,XS)) -> X
 incr(cons(X,XS)) -> cons(s(X),incr(XS))
 nats -> cons(0,incr(nats))
 odds -> incr(pairs)
 pairs -> cons(0,incr(odds))
 tail(cons(X,XS)) -> XS
-> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ODDS -> INCR(pairs)
 ODDS -> PAIRS
 TAIL(cons(X,XS)) -> XS
-> Rules:
 head(cons(X,XS)) -> X
 incr(cons(X,XS)) -> cons(s(X),incr(XS))
 nats -> cons(0,incr(nats))
 odds -> incr(pairs)
 pairs -> cons(0,incr(odds))
 tail(cons(X,XS)) -> XS
-> Unhiding Rules:
 incr(nats) -> INCR(nats)
 incr(nats) -> NATS
 incr(odds) -> INCR(odds)
 incr(odds) -> ODDS
 incr(XS) -> INCR(XS)
 incr(x2) -> x2

Problem 1: 

SCC Processor:
-> Pairs:
 ODDS -> INCR(pairs)
 ODDS -> PAIRS
 TAIL(cons(X,XS)) -> XS
-> Rules:
 head(cons(X,XS)) -> X
 incr(cons(X,XS)) -> cons(s(X),incr(XS))
 nats -> cons(0,incr(nats))
 odds -> incr(pairs)
 pairs -> cons(0,incr(odds))
 tail(cons(X,XS)) -> XS
-> Unhiding rules:
 incr(nats) -> INCR(nats)
 incr(nats) -> NATS
 incr(odds) -> INCR(odds)
 incr(odds) -> ODDS
 incr(XS) -> INCR(XS)
 incr(x2) -> x2
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.