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


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


YES

Problem 1: 

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

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

Problem 1: 

Dependency Pairs Processor:

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

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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


The problem is decomposed in 2 subproblems.

Problem 1.2.1: 

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

Problem 1.2.1: 

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

The problem is finite.

Problem 1.2.2: 

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

Problem 1.2.2: 

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

The problem is finite.