/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 x:S)
(RULES
b(w(x:S)) -> w(b(x:S))
b(r(x:S)) -> r(b(x:S))
w(r(x:S)) -> r(w(x:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 B(w(x:S)) -> B(x:S)
 B(w(x:S)) -> W(b(x:S))
 B(r(x:S)) -> B(x:S)
 W(r(x:S)) -> W(x:S)
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))

Problem 1: 

SCC Processor:
-> Pairs:
 B(w(x:S)) -> B(x:S)
 B(w(x:S)) -> W(b(x:S))
 B(r(x:S)) -> B(x:S)
 W(r(x:S)) -> W(x:S)
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 W(r(x:S)) -> W(x:S)
->->-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->->Cycle:
->->-> Pairs:
 B(w(x:S)) -> B(x:S)
 B(r(x:S)) -> B(x:S)
->->-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 W(r(x:S)) -> W(x:S)
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->Projection:
 pi(W) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 B(w(x:S)) -> B(x:S)
 B(r(x:S)) -> B(x:S)
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->Projection:
 pi(B) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.