SRS Standard pair #487091488

details

property	value
status	complete
benchmark	z074.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.5241 seconds
cpu usage	14.3881
user time	13.7302
system time	0.65791
max virtual memory	6.2398192E7
max residence set size	1807176.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 35 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 9 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (28) YES
    (29) QDP
        (30) UsableRulesProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) QDPOrderProof [EQUIVALENT, 33 ms]
        (33) QDP
        (34) PisEmptyProof [EQUIVALENT, 0 ms]
        (35) YES


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   r(r(x1)) -> s(r(x1))
   r(s(x1)) -> s(r(x1))
   r(n(x1)) -> s(r(x1))
   r(b(x1)) -> u(s(b(x1)))
   r(u(x1)) -> u(r(x1))
   s(u(x1)) -> u(s(x1))
   n(u(x1)) -> u(n(x1))
   t(r(u(x1))) -> t(c(r(x1)))
   t(s(u(x1))) -> t(c(r(x1)))
   t(n(u(x1))) -> t(c(r(x1)))
   c(u(x1)) -> u(c(x1))
   c(s(x1)) -> s(c(x1))
   c(r(x1)) -> r(c(x1))
   c(n(x1)) -> n(c(x1))
   c(n(x1)) -> n(x1)

Q is empty.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   r(r(x1)) -> r(s(x1))
   s(r(x1)) -> r(s(x1))
   n(r(x1)) -> r(s(x1))
   b(r(x1)) -> b(s(u(x1)))
   u(r(x1)) -> r(u(x1))
   u(s(x1)) -> s(u(x1))
   u(n(x1)) -> n(u(x1))
   u(r(t(x1))) -> r(c(t(x1)))
   u(s(t(x1))) -> r(c(t(x1)))
   u(n(t(x1))) -> r(c(t(x1)))
   u(c(x1)) -> c(u(x1))
   s(c(x1)) -> c(s(x1))
   r(c(x1)) -> c(r(x1))
   n(c(x1)) -> c(n(x1))
   n(c(x1)) -> n(x1)

Q is empty.

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