/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 x)
(RULES
ap(ap(ff,x),x) -> ap(ap(x,ap(ff,x)),ap(ap(cons,x),nil))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ap(ap(ff,x),x) -> ap(ap(x,ap(ff,x)),ap(ap(cons,x),nil))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AP(ap(ff,x),x) -> AP(ap(x,ap(ff,x)),ap(ap(cons,x),nil))
 AP(ap(ff,x),x) -> AP(x,ap(ff,x))
-> Rules:
 ap(ap(ff,x),x) -> ap(ap(x,ap(ff,x)),ap(ap(cons,x),nil))

Problem 1: 

SCC Processor:
-> Pairs:
 AP(ap(ff,x),x) -> AP(ap(x,ap(ff,x)),ap(ap(cons,x),nil))
 AP(ap(ff,x),x) -> AP(x,ap(ff,x))
-> Rules:
 ap(ap(ff,x),x) -> ap(ap(x,ap(ff,x)),ap(ap(cons,x),nil))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.