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


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YES

Problem 1: 

(VAR v_NonEmpty:S a:S k:S ls:S x:S)
(RULES
r1(cons(x:S,k:S),a:S) -> r1(k:S,cons(x:S,a:S))
r1(empty,a:S) -> a:S
rev(ls:S) -> r1(ls:S,empty)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 r1(cons(x:S,k:S),a:S) -> r1(k:S,cons(x:S,a:S))
 r1(empty,a:S) -> a:S
 rev(ls:S) -> r1(ls:S,empty)
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 R1(cons(x:S,k:S),a:S) -> R1(k:S,cons(x:S,a:S))
 REV(ls:S) -> R1(ls:S,empty)
-> Rules:
 r1(cons(x:S,k:S),a:S) -> r1(k:S,cons(x:S,a:S))
 r1(empty,a:S) -> a:S
 rev(ls:S) -> r1(ls:S,empty)

Problem 1: 

SCC Processor:
-> Pairs:
 R1(cons(x:S,k:S),a:S) -> R1(k:S,cons(x:S,a:S))
 REV(ls:S) -> R1(ls:S,empty)
-> Rules:
 r1(cons(x:S,k:S),a:S) -> r1(k:S,cons(x:S,a:S))
 r1(empty,a:S) -> a:S
 rev(ls:S) -> r1(ls:S,empty)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 R1(cons(x:S,k:S),a:S) -> R1(k:S,cons(x:S,a:S))
->->-> Rules:
 r1(cons(x:S,k:S),a:S) -> r1(k:S,cons(x:S,a:S))
 r1(empty,a:S) -> a:S
 rev(ls:S) -> r1(ls:S,empty)

Problem 1: 

Subterm Processor:
-> Pairs:
 R1(cons(x:S,k:S),a:S) -> R1(k:S,cons(x:S,a:S))
-> Rules:
 r1(cons(x:S,k:S),a:S) -> r1(k:S,cons(x:S,a:S))
 r1(empty,a:S) -> a:S
 rev(ls:S) -> r1(ls:S,empty)
->Projection:
 pi(R1) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 r1(cons(x:S,k:S),a:S) -> r1(k:S,cons(x:S,a:S))
 r1(empty,a:S) -> a:S
 rev(ls:S) -> r1(ls:S,empty)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.