/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 u v x y z)
(RULES
admit(x,.(u,.(v,.(w,z)))) -> cond(=(sum(x,u,v),w),.(u,.(v,.(w,admit(carry(x,u,v),z)))))
admit(x,nil) -> nil
cond(true,y) -> y
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 admit(x,.(u,.(v,.(w,z)))) -> cond(=(sum(x,u,v),w),.(u,.(v,.(w,admit(carry(x,u,v),z)))))
 admit(x,nil) -> nil
 cond(true,y) -> y
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ADMIT(x,.(u,.(v,.(w,z)))) -> ADMIT(carry(x,u,v),z)
 ADMIT(x,.(u,.(v,.(w,z)))) -> COND(=(sum(x,u,v),w),.(u,.(v,.(w,admit(carry(x,u,v),z)))))
-> Rules:
 admit(x,.(u,.(v,.(w,z)))) -> cond(=(sum(x,u,v),w),.(u,.(v,.(w,admit(carry(x,u,v),z)))))
 admit(x,nil) -> nil
 cond(true,y) -> y

Problem 1: 

SCC Processor:
-> Pairs:
 ADMIT(x,.(u,.(v,.(w,z)))) -> ADMIT(carry(x,u,v),z)
 ADMIT(x,.(u,.(v,.(w,z)))) -> COND(=(sum(x,u,v),w),.(u,.(v,.(w,admit(carry(x,u,v),z)))))
-> Rules:
 admit(x,.(u,.(v,.(w,z)))) -> cond(=(sum(x,u,v),w),.(u,.(v,.(w,admit(carry(x,u,v),z)))))
 admit(x,nil) -> nil
 cond(true,y) -> y
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ADMIT(x,.(u,.(v,.(w,z)))) -> ADMIT(carry(x,u,v),z)
->->-> Rules:
 admit(x,.(u,.(v,.(w,z)))) -> cond(=(sum(x,u,v),w),.(u,.(v,.(w,admit(carry(x,u,v),z)))))
 admit(x,nil) -> nil
 cond(true,y) -> y

Problem 1: 

Subterm Processor:
-> Pairs:
 ADMIT(x,.(u,.(v,.(w,z)))) -> ADMIT(carry(x,u,v),z)
-> Rules:
 admit(x,.(u,.(v,.(w,z)))) -> cond(=(sum(x,u,v),w),.(u,.(v,.(w,admit(carry(x,u,v),z)))))
 admit(x,nil) -> nil
 cond(true,y) -> y
->Projection:
 pi(ADMIT) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 admit(x,.(u,.(v,.(w,z)))) -> cond(=(sum(x,u,v),w),.(u,.(v,.(w,admit(carry(x,u,v),z)))))
 admit(x,nil) -> nil
 cond(true,y) -> y
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.