/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 x:S z:S)
(RULES
c -> t(k)
c -> t(l)
f(x:S) -> z:S | s(x:S) ->* z:S
g(x:S,x:S) -> h(x:S,x:S)
s(a) -> c
s(b) -> c
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 c -> t(k)
 c -> t(l)
 f(x:S) -> z:S | s(x:S) ->* z:S
 g(x:S,x:S) -> h(x:S,x:S)
 s(a) -> c
 s(b) -> c
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 S(a) -> C
 S(b) -> C
-> QPairs:
 Empty
-> Rules:
 c -> t(k)
 c -> t(l)
 f(x:S) -> z:S | s(x:S) ->* z:S
 g(x:S,x:S) -> h(x:S,x:S)
 s(a) -> c
 s(b) -> c

Conditional Termination Problem 2:
-> Pairs:
 F(x:S) -> S(x:S)
-> QPairs:
 S(a) -> C
 S(b) -> C
-> Rules:
 c -> t(k)
 c -> t(l)
 f(x:S) -> z:S | s(x:S) ->* z:S
 g(x:S,x:S) -> h(x:S,x:S)
 s(a) -> c
 s(b) -> c


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 S(a) -> C
 S(b) -> C
-> QPairs:
 Empty
-> Rules:
 c -> t(k)
 c -> t(l)
 f(x:S) -> z:S | s(x:S) ->* z:S
 g(x:S,x:S) -> h(x:S,x:S)
 s(a) -> c
 s(b) -> c
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 F(x:S) -> S(x:S)
-> QPairs:
 S(a) -> C
 S(b) -> C
-> Rules:
 c -> t(k)
 c -> t(l)
 f(x:S) -> z:S | s(x:S) ->* z:S
 g(x:S,x:S) -> h(x:S,x:S)
 s(a) -> c
 s(b) -> c
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.