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

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

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 A -> C
 A -> D
 B -> C
 B -> D
 S(c) -> K
 S(c) -> L
-> QPairs:
 Empty
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 c -> e
 d -> e
 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S)
 g(x:S,x:S) -> h(x:S,x:S)
 k -> e
 l -> e
 s(c) -> t(k)
 s(c) -> t(l)
 s(e) -> t(e)

Conditional Termination Problem 2:
-> Pairs:
 F(x:S) -> S(x:S)
-> QPairs:
 S(c) -> K
 S(c) -> L
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 c -> e
 d -> e
 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S)
 g(x:S,x:S) -> h(x:S,x:S)
 k -> e
 l -> e
 s(c) -> t(k)
 s(c) -> t(l)
 s(e) -> t(e)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 A -> C
 A -> D
 B -> C
 B -> D
 S(c) -> K
 S(c) -> L
-> QPairs:
 Empty
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 c -> e
 d -> e
 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S)
 g(x:S,x:S) -> h(x:S,x:S)
 k -> e
 l -> e
 s(c) -> t(k)
 s(c) -> t(l)
 s(e) -> t(e)
->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(c) -> K
 S(c) -> L
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 c -> e
 d -> e
 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S)
 g(x:S,x:S) -> h(x:S,x:S)
 k -> e
 l -> e
 s(c) -> t(k)
 s(c) -> t(l)
 s(e) -> t(e)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.