TRS Standard pair #516964166

details

property	value
status	complete
benchmark	07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n029.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.086599111557 seconds
cpu usage	0.019150425
max memory	1642496.0

stage attributes

key	value
output-size	1976
starexec-result	YES

output

/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_NonEmpty:S x:S)
(RULES
b(w(x:S)) -> w(b(x:S))
b(r(x:S)) -> r(b(x:S))
w(r(x:S)) -> r(w(x:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 B(w(x:S)) -> B(x:S)
 B(w(x:S)) -> W(b(x:S))
 B(r(x:S)) -> B(x:S)
 W(r(x:S)) -> W(x:S)
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))

Problem 1: 

SCC Processor:
-> Pairs:
 B(w(x:S)) -> B(x:S)
 B(w(x:S)) -> W(b(x:S))
 B(r(x:S)) -> B(x:S)
 W(r(x:S)) -> W(x:S)
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 W(r(x:S)) -> W(x:S)
->->-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->->Cycle:
->->-> Pairs:
 B(w(x:S)) -> B(x:S)
 B(r(x:S)) -> B(x:S)
->->-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 W(r(x:S)) -> W(x:S)
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->Projection:
 pi(W) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 B(w(x:S)) -> B(x:S)
 B(r(x:S)) -> B(x:S)
-> Rules:
 b(w(x:S)) -> w(b(x:S))
 b(r(x:S)) -> r(b(x:S))
 w(r(x:S)) -> r(w(x:S))
->Projection:
 pi(B) = 1

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