/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 x)
(RULES
evenodd(0,s(0)) -> false
evenodd(s(x),s(0)) -> evenodd(x,0)
evenodd(x,0) -> not(evenodd(x,s(0)))
not(false) -> true
not(true) -> false
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 evenodd(0,s(0)) -> false
 evenodd(s(x),s(0)) -> evenodd(x,0)
 evenodd(x,0) -> not(evenodd(x,s(0)))
 not(false) -> true
 not(true) -> false
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 EVENODD(s(x),s(0)) -> EVENODD(x,0)
 EVENODD(x,0) -> EVENODD(x,s(0))
 EVENODD(x,0) -> NOT(evenodd(x,s(0)))
-> Rules:
 evenodd(0,s(0)) -> false
 evenodd(s(x),s(0)) -> evenodd(x,0)
 evenodd(x,0) -> not(evenodd(x,s(0)))
 not(false) -> true
 not(true) -> false

Problem 1: 

SCC Processor:
-> Pairs:
 EVENODD(s(x),s(0)) -> EVENODD(x,0)
 EVENODD(x,0) -> EVENODD(x,s(0))
 EVENODD(x,0) -> NOT(evenodd(x,s(0)))
-> Rules:
 evenodd(0,s(0)) -> false
 evenodd(s(x),s(0)) -> evenodd(x,0)
 evenodd(x,0) -> not(evenodd(x,s(0)))
 not(false) -> true
 not(true) -> false
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 EVENODD(s(x),s(0)) -> EVENODD(x,0)
 EVENODD(x,0) -> EVENODD(x,s(0))
->->-> Rules:
 evenodd(0,s(0)) -> false
 evenodd(s(x),s(0)) -> evenodd(x,0)
 evenodd(x,0) -> not(evenodd(x,s(0)))
 not(false) -> true
 not(true) -> false

Problem 1: 

Subterm Processor:
-> Pairs:
 EVENODD(s(x),s(0)) -> EVENODD(x,0)
 EVENODD(x,0) -> EVENODD(x,s(0))
-> Rules:
 evenodd(0,s(0)) -> false
 evenodd(s(x),s(0)) -> evenodd(x,0)
 evenodd(x,0) -> not(evenodd(x,s(0)))
 not(false) -> true
 not(true) -> false
->Projection:
 pi(EVENODD) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 EVENODD(x,0) -> EVENODD(x,s(0))
-> Rules:
 evenodd(0,s(0)) -> false
 evenodd(s(x),s(0)) -> evenodd(x,0)
 evenodd(x,0) -> not(evenodd(x,s(0)))
 not(false) -> true
 not(true) -> false
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.