SRS Stand 10685 pair #381718363

details

property	value
status	complete
benchmark	e.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n014.star.cs.uiowa.edu
space	Waldmann_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	16.2677180767 seconds
cpu usage	61.58952587
max memory	4.299943936E9

stage attributes

key	value
output-size	29889
starexec-result	YES

output

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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 9 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) QDPOrderProof [EQUIVALENT, 53 ms]
        (12) QDP
        (13) QDPOrderProof [EQUIVALENT, 292 ms]
        (14) QDP
        (15) DependencyGraphProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 258 ms]
        (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 73 ms]
        (20) QDP
        (21) DependencyGraphProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 239 ms]
        (24) QDP
        (25) DependencyGraphProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 77 ms]
        (28) QDP
        (29) QDPOrderProof [EQUIVALENT, 9 ms]
        (30) QDP
        (31) DependencyGraphProof [EQUIVALENT, 0 ms]
        (32) TRUE


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

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

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

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

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