SRS Standard pair #487083364

details

property	value
status	complete
benchmark	pi.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Waldmann_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.25011 seconds
cpu usage	29.0097
user time	27.7177
system time	1.29203
max virtual memory	3.7508652E7
max residence set size	3269684.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 14 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPOrderProof [EQUIVALENT, 94 ms]
        (9) QDP
        (10) DependencyGraphProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 264 ms]
        (13) QDP
        (14) DependencyGraphProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPOrderProof [EQUIVALENT, 289 ms]
        (17) QDP
        (18) DependencyGraphProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QDPOrderProof [EQUIVALENT, 13 ms]
        (21) QDP
        (22) DependencyGraphProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPOrderProof [EQUIVALENT, 4 ms]
        (25) QDP
        (26) PisEmptyProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 2 ms]
        (30) QDP
        (31) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (32) YES


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

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

   3(1(x1)) -> 4(1(x1))
   5(9(x1)) -> 2(6(5(x1)))
   3(5(x1)) -> 8(9(7(x1)))
   9(x1) -> 3(2(3(x1)))
   8(4(x1)) -> 6(x1)
   2(6(x1)) -> 4(3(x1))
   3(8(x1)) -> 3(2(7(x1)))
   9(x1) -> 5(0(2(x1)))
   8(8(4(x1))) -> 1(9(x1))
   7(1(x1)) -> 6(9(x1))
   3(9(x1)) -> 9(3(x1))
   7(5(x1)) -> 1(0(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:

   5^1(9(x1)) -> 2^1(6(5(x1)))
   5^1(9(x1)) -> 5^1(x1)
   3^1(5(x1)) -> 8^1(9(7(x1)))
   3^1(5(x1)) -> 9^1(7(x1))
   3^1(5(x1)) -> 7^1(x1)
   9^1(x1) -> 3^1(2(3(x1)))
   9^1(x1) -> 2^1(3(x1))
   9^1(x1) -> 3^1(x1)
   2^1(6(x1)) -> 3^1(x1)
   3^1(8(x1)) -> 3^1(2(7(x1)))
   3^1(8(x1)) -> 2^1(7(x1))
   3^1(8(x1)) -> 7^1(x1)
   9^1(x1) -> 5^1(0(2(x1)))
   9^1(x1) -> 2^1(x1)
   8^1(8(4(x1))) -> 9^1(x1)
   7^1(1(x1)) -> 9^1(x1)
   3^1(9(x1)) -> 9^1(3(x1))
   3^1(9(x1)) -> 3^1(x1)

The TRS R consists of the following rules:

   3(1(x1)) -> 4(1(x1))
   5(9(x1)) -> 2(6(5(x1)))
   3(5(x1)) -> 8(9(7(x1)))
   9(x1) -> 3(2(3(x1)))

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to SRS Standard