SRS Relative pair #487081942

details

property	value
status	complete
benchmark	zr02new.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Mixed_relative_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.63713 seconds
cpu usage	7.49118
user time	7.06656
system time	0.424622
max virtual memory	1.9010036E7
max residence set size	1116892.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given RelTRS could be proven:

(0) RelTRS
(1) RelTRS Reverse [EQUIVALENT, 0 ms]
(2) RelTRS
(3) RelTRSRRRProof [EQUIVALENT, 49 ms]
(4) RelTRS
(5) RelTRSRRRProof [EQUIVALENT, 7 ms]
(6) RelTRS
(7) RelTRSRRRProof [EQUIVALENT, 48 ms]
(8) RelTRS
(9) RelTRSRRRProof [EQUIVALENT, 44 ms]
(10) RelTRS
(11) RIsEmptyProof [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   p(s(x1)) -> s(x1)
   n(s(x1)) -> s(x1)
   o(s(x1)) -> s(x1)
   o(n(x1)) -> n(o(x1))
   o(m(x1)) -> n(o(x1))
   n(o(p(x1))) -> o(n(x1))

The relative TRS consists of the following S rules:

   t(x1) -> t(c(n(x1)))
   p(n(x1)) -> m(p(x1))
   p(m(x1)) -> m(p(x1))
   n(p(x1)) -> p(n(x1))
   c(p(x1)) -> p(c(x1))
   c(m(x1)) -> m(c(x1))
   c(n(x1)) -> n(c(x1))
   c(o(x1)) -> o(c(x1))
   c(o(x1)) -> o(x1)


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(1) RelTRS Reverse (EQUIVALENT)
We have reversed the following relative TRS [REVERSE]:
The set of rules R is 
   p(s(x1)) -> s(x1)
   n(s(x1)) -> s(x1)
   o(s(x1)) -> s(x1)
   o(n(x1)) -> n(o(x1))
   o(m(x1)) -> n(o(x1))
   n(o(p(x1))) -> o(n(x1))

The set of rules S is 
   t(x1) -> t(c(n(x1)))
   p(n(x1)) -> m(p(x1))
   p(m(x1)) -> m(p(x1))
   n(p(x1)) -> p(n(x1))
   c(p(x1)) -> p(c(x1))
   c(m(x1)) -> m(c(x1))
   c(n(x1)) -> n(c(x1))
   c(o(x1)) -> o(c(x1))
   c(o(x1)) -> o(x1)

We have obtained the following relative TRS:
The set of rules R is 
   s(p(x1)) -> s(x1)
   s(n(x1)) -> s(x1)
   s(o(x1)) -> s(x1)
   n(o(x1)) -> o(n(x1))
   m(o(x1)) -> o(n(x1))
   p(o(n(x1))) -> n(o(x1))

The set of rules S is 
   t(x1) -> n(c(t(x1)))
   n(p(x1)) -> p(m(x1))
   m(p(x1)) -> p(m(x1))
   p(n(x1)) -> n(p(x1))
   p(c(x1)) -> c(p(x1))
   m(c(x1)) -> c(m(x1))
   n(c(x1)) -> c(n(x1))
   o(c(x1)) -> c(o(x1))
   o(c(x1)) -> o(x1)


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(2)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

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