/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)
(RULES
a(c(x)) -> x
a(d(x)) -> d(c(b(a(x))))
b(c(x)) -> c(d(a(b(x))))
b(d(x)) -> x
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(d(x)) -> A(x)
 A(d(x)) -> B(a(x))
 B(c(x)) -> A(b(x))
 B(c(x)) -> B(x)
-> Rules:
 a(c(x)) -> x
 a(d(x)) -> d(c(b(a(x))))
 b(c(x)) -> c(d(a(b(x))))
 b(d(x)) -> x

Problem 1: 

SCC Processor:
-> Pairs:
 A(d(x)) -> A(x)
 A(d(x)) -> B(a(x))
 B(c(x)) -> A(b(x))
 B(c(x)) -> B(x)
-> Rules:
 a(c(x)) -> x
 a(d(x)) -> d(c(b(a(x))))
 b(c(x)) -> c(d(a(b(x))))
 b(d(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(d(x)) -> A(x)
 A(d(x)) -> B(a(x))
 B(c(x)) -> A(b(x))
 B(c(x)) -> B(x)
->->-> Rules:
 a(c(x)) -> x
 a(d(x)) -> d(c(b(a(x))))
 b(c(x)) -> c(d(a(b(x))))
 b(d(x)) -> x

Problem 1: 

Narrowing Processor:
-> Pairs:
 A(d(x)) -> A(x)
 A(d(x)) -> B(a(x))
 B(c(x)) -> A(b(x))
 B(c(x)) -> B(x)
-> Rules:
 a(c(x)) -> x
 a(d(x)) -> d(c(b(a(x))))
 b(c(x)) -> c(d(a(b(x))))
 b(d(x)) -> x
->Narrowed Pairs:
->->Original Pair:
 A(d(x)) -> B(a(x))
->-> Narrowed pairs:
 A(d(c(x))) -> B(x)
 A(d(d(x))) -> B(d(c(b(a(x)))))
->->Original Pair:
 B(c(x)) -> A(b(x))
->-> Narrowed pairs:
 B(c(c(x))) -> A(c(d(a(b(x)))))
 B(c(d(x))) -> A(x)

Problem 1: 

SCC Processor:
-> Pairs:
 A(d(c(x))) -> B(x)
 A(d(d(x))) -> B(d(c(b(a(x)))))
 A(d(x)) -> A(x)
 B(c(c(x))) -> A(c(d(a(b(x)))))
 B(c(d(x))) -> A(x)
 B(c(x)) -> B(x)
-> Rules:
 a(c(x)) -> x
 a(d(x)) -> d(c(b(a(x))))
 b(c(x)) -> c(d(a(b(x))))
 b(d(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(d(c(x))) -> B(x)
 A(d(x)) -> A(x)
 B(c(d(x))) -> A(x)
 B(c(x)) -> B(x)
->->-> Rules:
 a(c(x)) -> x
 a(d(x)) -> d(c(b(a(x))))
 b(c(x)) -> c(d(a(b(x))))
 b(d(x)) -> x

Problem 1: 

Subterm Processor:
-> Pairs:
 A(d(c(x))) -> B(x)
 A(d(x)) -> A(x)
 B(c(d(x))) -> A(x)
 B(c(x)) -> B(x)
-> Rules:
 a(c(x)) -> x
 a(d(x)) -> d(c(b(a(x))))
 b(c(x)) -> c(d(a(b(x))))
 b(d(x)) -> x
->Projection:
 pi(A) = 1
 pi(B) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a(c(x)) -> x
 a(d(x)) -> d(c(b(a(x))))
 b(c(x)) -> c(d(a(b(x))))
 b(d(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.