/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)
(RULES
p(q(x)) -> p(r(x))
q(h(x)) -> r(x)
r(x) -> r(h(x)) | s(x) -> 0
s(x) -> 1
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 P(q(x)) -> P(r(x))
 P(q(x)) -> R(x)
 Q(h(x)) -> R(x)
 R(x) -> R(h(x)) | s(x) -> 0
-> QPairs:
 Empty
-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1

Conditional Termination Problem 2:
-> Pairs:
 R(x) -> S(x)
-> QPairs:
 P(q(x)) -> P(r(x))
 P(q(x)) -> R(x)
 Q(h(x)) -> R(x)
 R(x) -> R(h(x)) | s(x) -> 0
-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 P(q(x)) -> P(r(x))
 P(q(x)) -> R(x)
 Q(h(x)) -> R(x)
 R(x) -> R(h(x)) | s(x) -> 0
-> QPairs:
 Empty
-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 R(x) -> R(h(x)) | s(x) -> 0
->->-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1
->->Cycle:
->->-> Pairs:
 P(q(x)) -> P(r(x))
->->-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1


The problem is decomposed in 2 subproblems.

Problem 1.1.1: 

Reduction Triple Processor:
-> Pairs:
 R(x) -> R(h(x)) | s(x) -> 0
-> QPairs:
 Empty
-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1
-> Usable rules:
 s(x) -> 1
->Interpretation type:
 Linear
->Coefficients:
 Integer Numbers
->Dimension:
 1
->Convex Domain:
 D[(x_1)] = ((1+x_1 >= 0) /\ (1-x_1 >= 0))
->Interpretation:
 
[delta] = 1
[s](x_1) = 0
[0] = 1
[1] = 0
[h](x_1) = 1
[R](x_1) = 1

Problem 1.1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.1.2: 

Reduction Triple Processor:
-> Pairs:
 P(q(x)) -> P(r(x))
-> QPairs:
 Empty
-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1
-> Usable rules:
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1
->Interpretation type:
 Linear
->Coefficients:
 Integer Numbers
->Dimension:
 1
->Convex Domain:
 D[(x_1)] = ((1-x_1 >= 0) /\ (1+x_1 >= 0))
->Interpretation:
 
[delta] = 1
[q](x_1) = 1
[r](x_1) = 0
[s](x_1) = -1
[0] = 0
[1] = -1
[h](x_1) = x_1
[P](x_1) = x_1

Problem 1.1.2: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 R(x) -> S(x)
-> QPairs:
 P(q(x)) -> P(r(x))
 P(q(x)) -> R(x)
 Q(h(x)) -> R(x)
 R(x) -> R(h(x)) | s(x) -> 0
-> Rules:
 p(q(x)) -> p(r(x))
 q(h(x)) -> r(x)
 r(x) -> r(h(x)) | s(x) -> 0
 s(x) -> 1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.