/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
e(g(X:S)) -> e(X:S)
f(a) -> f(c(a))
f(a) -> f(d(a))
f(c(a)) -> f(d(b))
f(c(b)) -> f(d(a))
f(c(X:S)) -> X:S
f(d(X:S)) -> X:S
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 E(g(X:S)) -> E(X:S)
 F(a) -> F(c(a))
 F(a) -> F(d(a))
 F(c(a)) -> F(d(b))
 F(c(b)) -> F(d(a))
-> Rules:
 e(g(X:S)) -> e(X:S)
 f(a) -> f(c(a))
 f(a) -> f(d(a))
 f(c(a)) -> f(d(b))
 f(c(b)) -> f(d(a))
 f(c(X:S)) -> X:S
 f(d(X:S)) -> X:S

Problem 1: 

SCC Processor:
-> Pairs:
 E(g(X:S)) -> E(X:S)
 F(a) -> F(c(a))
 F(a) -> F(d(a))
 F(c(a)) -> F(d(b))
 F(c(b)) -> F(d(a))
-> Rules:
 e(g(X:S)) -> e(X:S)
 f(a) -> f(c(a))
 f(a) -> f(d(a))
 f(c(a)) -> f(d(b))
 f(c(b)) -> f(d(a))
 f(c(X:S)) -> X:S
 f(d(X:S)) -> X:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 E(g(X:S)) -> E(X:S)
->->-> Rules:
 e(g(X:S)) -> e(X:S)
 f(a) -> f(c(a))
 f(a) -> f(d(a))
 f(c(a)) -> f(d(b))
 f(c(b)) -> f(d(a))
 f(c(X:S)) -> X:S
 f(d(X:S)) -> X:S

Problem 1: 

Subterm Processor:
-> Pairs:
 E(g(X:S)) -> E(X:S)
-> Rules:
 e(g(X:S)) -> e(X:S)
 f(a) -> f(c(a))
 f(a) -> f(d(a))
 f(c(a)) -> f(d(b))
 f(c(b)) -> f(d(a))
 f(c(X:S)) -> X:S
 f(d(X:S)) -> X:S
->Projection:
 pi(E) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 e(g(X:S)) -> e(X:S)
 f(a) -> f(c(a))
 f(a) -> f(d(a))
 f(c(a)) -> f(d(b))
 f(c(b)) -> f(d(a))
 f(c(X:S)) -> X:S
 f(d(X:S)) -> X:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.