SRS Standard pair #516968812

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	n082.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	4.80417299271 seconds
cpu usage	15.685909554
max memory	1.274179584E9

stage attributes

key	value
output-size	15071
starexec-result	YES

output

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


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 23 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 2 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, 101 ms]
        (32) QDP
        (33) PisEmptyProof [EQUIVALENT, 0 ms]
        (34) 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))

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