SRS Standard pair #487091692

details

property	value
status	complete
benchmark	z091.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	AProVE
configuration	standard
runtime (wallclock)	4.37195 seconds
cpu usage	13.835
user time	13.2859
system time	0.549094
max virtual memory	8.3761348E7
max residence set size	1386296.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 5 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) UsableRulesProof [EQUIVALENT, 0 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) QDP
        (31) QDPOrderProof [EQUIVALENT, 25 ms]
        (32) QDP
        (33) QDPOrderProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) PisEmptyProof [EQUIVALENT, 0 ms]
        (36) YES


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

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

   r0(0(x1)) -> 0(r0(x1))
   r0(1(x1)) -> 1(r0(x1))
   r0(m(x1)) -> m(r0(x1))
   r1(0(x1)) -> 0(r1(x1))
   r1(1(x1)) -> 1(r1(x1))
   r1(m(x1)) -> m(r1(x1))
   r0(b(x1)) -> qr(0(b(x1)))
   r1(b(x1)) -> qr(1(b(x1)))
   0(qr(x1)) -> qr(0(x1))
   1(qr(x1)) -> qr(1(x1))
   m(qr(x1)) -> ql(m(x1))
   0(ql(x1)) -> ql(0(x1))
   1(ql(x1)) -> ql(1(x1))
   b(ql(0(x1))) -> 0(b(r0(x1)))
   b(ql(1(x1))) -> 1(b(r1(x1)))

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   R0(0(x1)) -> 0^1(r0(x1))
   R0(0(x1)) -> R0(x1)
   R0(1(x1)) -> 1^1(r0(x1))
   R0(1(x1)) -> R0(x1)
   R0(m(x1)) -> M(r0(x1))
   R0(m(x1)) -> R0(x1)
   R1(0(x1)) -> 0^1(r1(x1))
   R1(0(x1)) -> R1(x1)
   R1(1(x1)) -> 1^1(r1(x1))
   R1(1(x1)) -> R1(x1)
   R1(m(x1)) -> M(r1(x1))
   R1(m(x1)) -> R1(x1)
   R0(b(x1)) -> 0^1(b(x1))
   R1(b(x1)) -> 1^1(b(x1))
   0^1(qr(x1)) -> 0^1(x1)
   1^1(qr(x1)) -> 1^1(x1)
   M(qr(x1)) -> M(x1)
   0^1(ql(x1)) -> 0^1(x1)

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