/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 x y)
(RULES
a -> c
a -> d
b -> c
b -> d
c -> e
c -> l
d -> m
f(x) -> x | x -> e
g(d,x,y) -> A | y -> x
h(x,y) -> g(x,y,f(k)) | y -> x
k -> l
k -> m
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 c -> e
 c -> l
 d -> m
 f(x) -> x | x -> e
 g(d,x,y) -> A | y -> x
 h(x,y) -> g(x,y,f(k)) | y -> x
 k -> l
 k -> m
-> 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
 H(x,y) -> F(k) | y -> x
 H(x,y) -> G(x,y,f(k)) | y -> x
 H(x,y) -> K | y -> x
-> QPairs:
 Empty
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 c -> e
 c -> l
 d -> m
 f(x) -> x | x -> e
 g(d,x,y) -> A | y -> x
 h(x,y) -> g(x,y,f(k)) | y -> x
 k -> l
 k -> m

Conditional Termination Problem 2:
-> Pairs:
 Empty
-> QPairs:
 A -> C
 A -> D
 B -> C
 B -> D
 H(x,y) -> F(k) | y -> x
 H(x,y) -> G(x,y,f(k)) | y -> x
 H(x,y) -> K | y -> x
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 c -> e
 c -> l
 d -> m
 f(x) -> x | x -> e
 g(d,x,y) -> A | y -> x
 h(x,y) -> g(x,y,f(k)) | y -> x
 k -> l
 k -> m


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 A -> C
 A -> D
 B -> C
 B -> D
 H(x,y) -> F(k) | y -> x
 H(x,y) -> G(x,y,f(k)) | y -> x
 H(x,y) -> K | y -> x
-> QPairs:
 Empty
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 c -> e
 c -> l
 d -> m
 f(x) -> x | x -> e
 g(d,x,y) -> A | y -> x
 h(x,y) -> g(x,y,f(k)) | y -> x
 k -> l
 k -> m
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 A -> C
 A -> D
 B -> C
 B -> D
 H(x,y) -> F(k) | y -> x
 H(x,y) -> G(x,y,f(k)) | y -> x
 H(x,y) -> K | y -> x
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 c -> e
 c -> l
 d -> m
 f(x) -> x | x -> e
 g(d,x,y) -> A | y -> x
 h(x,y) -> g(x,y,f(k)) | y -> x
 k -> l
 k -> m
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.