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

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 admit(x:S,.(u:S,.(v:S,.(w,z:S)))) -> cond(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S)))))
 admit(x:S,nil) -> nil
 cond(ttrue,y:S) -> y:S
-> 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:S,.(u:S,.(v:S,.(w,z:S)))) -> ADMIT(carry(x:S,u:S,v:S),z:S)
 ADMIT(x:S,.(u:S,.(v:S,.(w,z:S)))) -> COND(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S)))))
-> Rules:
 admit(x:S,.(u:S,.(v:S,.(w,z:S)))) -> cond(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S)))))
 admit(x:S,nil) -> nil
 cond(ttrue,y:S) -> y:S

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.