/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 x1)
(RULES
A(a(x1)) -> x1
A(b(x1)) -> b(a(B(A(x1))))
B(a(x1)) -> a(b(A(B(x1))))
B(b(x1)) -> x1
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 A(a(x1)) -> x1
 A(b(x1)) -> b(a(B(A(x1))))
 B(a(x1)) -> a(b(A(B(x1))))
 B(b(x1)) -> x1
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A#(b(x1)) -> A#(x1)
 A#(b(x1)) -> B#(A(x1))
 B#(a(x1)) -> A#(B(x1))
 B#(a(x1)) -> B#(x1)
-> Rules:
 A(a(x1)) -> x1
 A(b(x1)) -> b(a(B(A(x1))))
 B(a(x1)) -> a(b(A(B(x1))))
 B(b(x1)) -> x1

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.