/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
a(c(d(x:S))) -> c(x:S)
u(b(d(d(x:S)))) -> b(x:S)
v(a(a(x:S))) -> u(v(x:S))
v(a(c(x:S))) -> u(b(d(x:S)))
v(c(x:S)) -> b(x:S)
w(a(a(x:S))) -> u(w(x:S))
w(a(c(x:S))) -> u(b(d(x:S)))
w(c(x:S)) -> b(x:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 V(a(a(x:S))) -> U(v(x:S))
 V(a(a(x:S))) -> V(x:S)
 V(a(c(x:S))) -> U(b(d(x:S)))
 W(a(a(x:S))) -> U(w(x:S))
 W(a(a(x:S))) -> W(x:S)
 W(a(c(x:S))) -> U(b(d(x:S)))
-> Rules:
 a(c(d(x:S))) -> c(x:S)
 u(b(d(d(x:S)))) -> b(x:S)
 v(a(a(x:S))) -> u(v(x:S))
 v(a(c(x:S))) -> u(b(d(x:S)))
 v(c(x:S)) -> b(x:S)
 w(a(a(x:S))) -> u(w(x:S))
 w(a(c(x:S))) -> u(b(d(x:S)))
 w(c(x:S)) -> b(x:S)

Problem 1: 

SCC Processor:
-> Pairs:
 V(a(a(x:S))) -> U(v(x:S))
 V(a(a(x:S))) -> V(x:S)
 V(a(c(x:S))) -> U(b(d(x:S)))
 W(a(a(x:S))) -> U(w(x:S))
 W(a(a(x:S))) -> W(x:S)
 W(a(c(x:S))) -> U(b(d(x:S)))
-> Rules:
 a(c(d(x:S))) -> c(x:S)
 u(b(d(d(x:S)))) -> b(x:S)
 v(a(a(x:S))) -> u(v(x:S))
 v(a(c(x:S))) -> u(b(d(x:S)))
 v(c(x:S)) -> b(x:S)
 w(a(a(x:S))) -> u(w(x:S))
 w(a(c(x:S))) -> u(b(d(x:S)))
 w(c(x:S)) -> b(x:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 W(a(a(x:S))) -> W(x:S)
->->-> Rules:
 a(c(d(x:S))) -> c(x:S)
 u(b(d(d(x:S)))) -> b(x:S)
 v(a(a(x:S))) -> u(v(x:S))
 v(a(c(x:S))) -> u(b(d(x:S)))
 v(c(x:S)) -> b(x:S)
 w(a(a(x:S))) -> u(w(x:S))
 w(a(c(x:S))) -> u(b(d(x:S)))
 w(c(x:S)) -> b(x:S)
->->Cycle:
->->-> Pairs:
 V(a(a(x:S))) -> V(x:S)
->->-> Rules:
 a(c(d(x:S))) -> c(x:S)
 u(b(d(d(x:S)))) -> b(x:S)
 v(a(a(x:S))) -> u(v(x:S))
 v(a(c(x:S))) -> u(b(d(x:S)))
 v(c(x:S)) -> b(x:S)
 w(a(a(x:S))) -> u(w(x:S))
 w(a(c(x:S))) -> u(b(d(x:S)))
 w(c(x:S)) -> b(x:S)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 W(a(a(x:S))) -> W(x:S)
-> Rules:
 a(c(d(x:S))) -> c(x:S)
 u(b(d(d(x:S)))) -> b(x:S)
 v(a(a(x:S))) -> u(v(x:S))
 v(a(c(x:S))) -> u(b(d(x:S)))
 v(c(x:S)) -> b(x:S)
 w(a(a(x:S))) -> u(w(x:S))
 w(a(c(x:S))) -> u(b(d(x:S)))
 w(c(x:S)) -> b(x:S)
->Projection:
 pi(W) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 V(a(a(x:S))) -> V(x:S)
-> Rules:
 a(c(d(x:S))) -> c(x:S)
 u(b(d(d(x:S)))) -> b(x:S)
 v(a(a(x:S))) -> u(v(x:S))
 v(a(c(x:S))) -> u(b(d(x:S)))
 v(c(x:S)) -> b(x:S)
 w(a(a(x:S))) -> u(w(x:S))
 w(a(c(x:S))) -> u(b(d(x:S)))
 w(c(x:S)) -> b(x:S)
->Projection:
 pi(V) = 1

Problem 1.2: 

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

The problem is finite.