/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 Y)
(STRATEGY CONTEXTSENSITIVE
(adx 1)
(hd 1)
(incr 1)
(nats)
(tl 1)
(zeros)
(0)
(cons)
(s)
)
(RULES
adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
hd(cons(X,Y)) -> X
incr(cons(X,Y)) -> cons(s(X),incr(Y))
nats -> adx(zeros)
tl(cons(X,Y)) -> Y
zeros -> cons(0,zeros)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
 hd(cons(X,Y)) -> X
 incr(cons(X,Y)) -> cons(s(X),incr(Y))
 nats -> adx(zeros)
 tl(cons(X,Y)) -> Y
 zeros -> cons(0,zeros)
-> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ADX(cons(X,Y)) -> INCR(cons(X,adx(Y)))
 HD(cons(X,Y)) -> X
 NATS -> ADX(zeros)
 NATS -> ZEROS
 TL(cons(X,Y)) -> Y
-> Rules:
 adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
 hd(cons(X,Y)) -> X
 incr(cons(X,Y)) -> cons(s(X),incr(Y))
 nats -> adx(zeros)
 tl(cons(X,Y)) -> Y
 zeros -> cons(0,zeros)
-> Unhiding Rules:
 adx(Y) -> ADX(Y)
 adx(x2) -> x2
 incr(Y) -> INCR(Y)
 incr(x2) -> x2
 zeros -> ZEROS

Problem 1: 

SCC Processor:
-> Pairs:
 ADX(cons(X,Y)) -> INCR(cons(X,adx(Y)))
 HD(cons(X,Y)) -> X
 NATS -> ADX(zeros)
 NATS -> ZEROS
 TL(cons(X,Y)) -> Y
-> Rules:
 adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
 hd(cons(X,Y)) -> X
 incr(cons(X,Y)) -> cons(s(X),incr(Y))
 nats -> adx(zeros)
 tl(cons(X,Y)) -> Y
 zeros -> cons(0,zeros)
-> Unhiding rules:
 adx(Y) -> ADX(Y)
 adx(x2) -> x2
 incr(Y) -> INCR(Y)
 incr(x2) -> x2
 zeros -> ZEROS
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.