/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR v_NonEmpty:S v:S w:S xs:S xs':S y:S ys':S z:S)
(RULES
ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
ssp(nil,0) -> nil
sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
sub(z:S,0) -> z:S
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S

Conditional Termination Problem 2:
-> Pairs:
 SSP(cons(y:S,ys':S),v:S) -> SSP(ys':S,v:S)
 SSP(cons(y:S,ys':S),v:S) -> SSP(ys':S,w:S) | sub(v:S,y:S) ->* w:S
 SSP(cons(y:S,ys':S),v:S) -> SUB(v:S,y:S)
 SUB(s(v:S),s(w:S)) -> SUB(v:S,w:S)
-> QPairs:
 Empty
-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 SSP(cons(y:S,ys':S),v:S) -> SSP(ys':S,v:S)
 SSP(cons(y:S,ys':S),v:S) -> SSP(ys':S,w:S) | sub(v:S,y:S) ->* w:S
 SSP(cons(y:S,ys':S),v:S) -> SUB(v:S,y:S)
 SUB(s(v:S),s(w:S)) -> SUB(v:S,w:S)
-> QPairs:
 Empty
-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 SUB(s(v:S),s(w:S)) -> SUB(v:S,w:S)
-> QPairs:
 Empty
->->-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S
->->Cycle:
->->-> Pairs:
 SSP(cons(y:S,ys':S),v:S) -> SSP(ys':S,v:S)
 SSP(cons(y:S,ys':S),v:S) -> SSP(ys':S,w:S) | sub(v:S,y:S) ->* w:S
-> QPairs:
 Empty
->->-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S


The problem is decomposed in 2 subproblems.

Problem 1.2.1: 

Conditional Subterm Processor:
-> Pairs:
 SUB(s(v:S),s(w:S)) -> SUB(v:S,w:S)
-> QPairs:
 Empty
-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S
->Projection:
 pi(SUB) = 1

Problem 1.2.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2.2: 

Conditional Subterm Processor:
-> Pairs:
 SSP(cons(y:S,ys':S),v:S) -> SSP(ys':S,v:S)
 SSP(cons(y:S,ys':S),v:S) -> SSP(ys':S,w:S) | sub(v:S,y:S) ->* w:S
-> QPairs:
 Empty
-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S
->Projection:
 pi(SSP) = 1

Problem 1.2.2: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 ssp(cons(y:S,ys':S),v:S) -> cons(y:S,xs':S) | sub(v:S,y:S) ->* w:S, ssp(ys':S,w:S) ->* xs':S
 ssp(cons(y:S,ys':S),v:S) -> xs:S | ssp(ys':S,v:S) ->* xs:S
 ssp(nil,0) -> nil
 sub(s(v:S),s(w:S)) -> z:S | sub(v:S,w:S) ->* z:S
 sub(z:S,0) -> z:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.