SRS Standard pair #487091370

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	n143.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0183691 seconds
cpu usage	0.018148
user time	0.006706
system time	0.011442
max virtual memory	0.0
max residence set size	4284.0

stage attributes

key	value
starexec-result	YES

output

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

The problem is finite.

Problem 1.2: 

Subterm Processor:

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