SRS Standard pair #516968340

details

property	value
status	complete
benchmark	z077.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.114508152008 seconds
cpu usage	0.019853196
max memory	2281472.0

stage attributes

key	value
output-size	2500
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 x1:S)
(RULES
d(0(x1:S)) -> 0(x1:S)
d(s(x1:S)) -> s(s(d(x1:S)))
f(0(x1:S)) -> s(0(x1:S))
f(s(x1:S)) -> d(f(x1:S))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 d(0(x1:S)) -> 0(x1:S)
 d(s(x1:S)) -> s(s(d(x1:S)))
 f(0(x1:S)) -> s(0(x1:S))
 f(s(x1:S)) -> d(f(x1:S))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 D(s(x1:S)) -> D(x1:S)
 F(s(x1:S)) -> D(f(x1:S))
 F(s(x1:S)) -> F(x1:S)
-> Rules:
 d(0(x1:S)) -> 0(x1:S)
 d(s(x1:S)) -> s(s(d(x1:S)))
 f(0(x1:S)) -> s(0(x1:S))
 f(s(x1:S)) -> d(f(x1:S))

Problem 1: 

SCC Processor:
-> Pairs:
 D(s(x1:S)) -> D(x1:S)
 F(s(x1:S)) -> D(f(x1:S))
 F(s(x1:S)) -> F(x1:S)
-> Rules:
 d(0(x1:S)) -> 0(x1:S)
 d(s(x1:S)) -> s(s(d(x1:S)))
 f(0(x1:S)) -> s(0(x1:S))
 f(s(x1:S)) -> d(f(x1:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 D(s(x1:S)) -> D(x1:S)
->->-> Rules:
 d(0(x1:S)) -> 0(x1:S)
 d(s(x1:S)) -> s(s(d(x1:S)))
 f(0(x1:S)) -> s(0(x1:S))
 f(s(x1:S)) -> d(f(x1:S))
->->Cycle:
->->-> Pairs:
 F(s(x1:S)) -> F(x1:S)
->->-> Rules:
 d(0(x1:S)) -> 0(x1:S)
 d(s(x1:S)) -> s(s(d(x1:S)))
 f(0(x1:S)) -> s(0(x1:S))
 f(s(x1:S)) -> d(f(x1:S))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 D(s(x1:S)) -> D(x1:S)
-> Rules:
 d(0(x1:S)) -> 0(x1:S)
 d(s(x1:S)) -> s(s(d(x1:S)))
 f(0(x1:S)) -> s(0(x1:S))
 f(s(x1:S)) -> d(f(x1:S))
->Projection:
 pi(D) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 d(0(x1:S)) -> 0(x1:S)
 d(s(x1:S)) -> s(s(d(x1:S)))
 f(0(x1:S)) -> s(0(x1:S))
 f(s(x1:S)) -> d(f(x1:S))
->Strongly Connected Components:
 There is no strongly connected component

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