/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 x1)
(RULES
a(b(x1)) -> b(c(x1))
a(x1) -> b(x1)
a(x1) -> x1
c(c(x1)) -> a(c(a(x1)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(b(x1)) -> C(x1)
 C(c(x1)) -> A(c(a(x1)))
 C(c(x1)) -> A(x1)
 C(c(x1)) -> C(a(x1))
-> Rules:
 a(b(x1)) -> b(c(x1))
 a(x1) -> b(x1)
 a(x1) -> x1
 c(c(x1)) -> a(c(a(x1)))

Problem 1: 

SCC Processor:
-> Pairs:
 A(b(x1)) -> C(x1)
 C(c(x1)) -> A(c(a(x1)))
 C(c(x1)) -> A(x1)
 C(c(x1)) -> C(a(x1))
-> Rules:
 a(b(x1)) -> b(c(x1))
 a(x1) -> b(x1)
 a(x1) -> x1
 c(c(x1)) -> a(c(a(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(b(x1)) -> C(x1)
 C(c(x1)) -> A(c(a(x1)))
 C(c(x1)) -> A(x1)
 C(c(x1)) -> C(a(x1))
->->-> Rules:
 a(b(x1)) -> b(c(x1))
 a(x1) -> b(x1)
 a(x1) -> x1
 c(c(x1)) -> a(c(a(x1)))

Problem 1: 

Narrowing Processor:
-> Pairs:
 A(b(x1)) -> C(x1)
 C(c(x1)) -> A(c(a(x1)))
 C(c(x1)) -> A(x1)
 C(c(x1)) -> C(a(x1))
-> Rules:
 a(b(x1)) -> b(c(x1))
 a(x1) -> b(x1)
 a(x1) -> x1
 c(c(x1)) -> a(c(a(x1)))
->Narrowed Pairs:
->->Original Pair:
 C(c(x1)) -> A(c(a(x1)))
->-> Narrowed pairs:
 C(c(b(x1))) -> A(c(b(c(x1))))
 C(c(x1)) -> A(c(b(x1)))
 C(c(x1)) -> A(c(x1))
->->Original Pair:
 C(c(x1)) -> C(a(x1))
->-> Narrowed pairs:
 C(c(b(x1))) -> C(b(c(x1)))
 C(c(x1)) -> C(b(x1))
 C(c(x1)) -> C(x1)

Problem 1: 

SCC Processor:
-> Pairs:
 A(b(x1)) -> C(x1)
 C(c(b(x1))) -> A(c(b(c(x1))))
 C(c(b(x1))) -> C(b(c(x1)))
 C(c(x1)) -> A(c(b(x1)))
 C(c(x1)) -> A(c(x1))
 C(c(x1)) -> A(x1)
 C(c(x1)) -> C(b(x1))
 C(c(x1)) -> C(x1)
-> Rules:
 a(b(x1)) -> b(c(x1))
 a(x1) -> b(x1)
 a(x1) -> x1
 c(c(x1)) -> a(c(a(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(b(x1)) -> C(x1)
 C(c(x1)) -> A(c(x1))
 C(c(x1)) -> A(x1)
 C(c(x1)) -> C(x1)
->->-> Rules:
 a(b(x1)) -> b(c(x1))
 a(x1) -> b(x1)
 a(x1) -> x1
 c(c(x1)) -> a(c(a(x1)))

Problem 1: 

Subterm Processor:
-> Pairs:
 A(b(x1)) -> C(x1)
 C(c(x1)) -> A(c(x1))
 C(c(x1)) -> A(x1)
 C(c(x1)) -> C(x1)
-> Rules:
 a(b(x1)) -> b(c(x1))
 a(x1) -> b(x1)
 a(x1) -> x1
 c(c(x1)) -> a(c(a(x1)))
->Projection:
 pi(A) = 1
 pi(C) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 C(c(x1)) -> A(c(x1))
-> Rules:
 a(b(x1)) -> b(c(x1))
 a(x1) -> b(x1)
 a(x1) -> x1
 c(c(x1)) -> a(c(a(x1)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.