SRS Stand 10685 pair #381720040

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	n038.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.52474403381 seconds
cpu usage	26.213933549
max memory	3.739099136E9

stage attributes

key	value
output-size	14024
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 43 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 21 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, 1 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, 0 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.

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

(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))

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