/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 v_NonEmpty:S x:S)
(RULES
fib(0) -> 0
fib(s(0)) -> s(0)
fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 FIB(s(s(x:S))) -> FIB(s(x:S))
 FIB(s(s(x:S))) -> FIB(x:S)
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))

Problem 1: 

SCC Processor:
-> Pairs:
 FIB(s(s(x:S))) -> FIB(s(x:S))
 FIB(s(s(x:S))) -> FIB(x:S)
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 FIB(s(s(x:S))) -> FIB(s(x:S))
 FIB(s(s(x:S))) -> FIB(x:S)
->->-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 FIB(s(s(x:S))) -> FIB(s(x:S))
 FIB(s(s(x:S))) -> FIB(x:S)
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
->Projection:
 pi(FIB) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.