TRS Context Sensitive pair #516978887

details

property	value
status	complete
benchmark	csrdiv.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	Maude_06

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.86286091805 seconds
cpu usage	18.669932822
max memory	1.307451392E9

stage attributes

key	value
output-size	22339
starexec-result	YES

output

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


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


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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given CSR could be proven:

(0) CSR
(1) CSRInnermostProof [EQUIVALENT, 5 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSDPReductionPairProof [EQUIVALENT, 56 ms]
        (9) QCSDP
        (10) QCSDPInstantiationProcessor [EQUIVALENT, 0 ms]
        (11) QCSDP
        (12) QCSDPReductionPairProof [EQUIVALENT, 17 ms]
        (13) QCSDP
        (14) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (15) AND
            (16) QCSDP
                (17) QCSDPReductionPairProof [EQUIVALENT, 115 ms]
                (18) QCSDP
                (19) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
                (20) TRUE
            (21) QCSDP
                (22) QCSDPSubtermProof [EQUIVALENT, 0 ms]
                (23) QCSDP
                (24) PIsEmptyProof [EQUIVALENT, 0 ms]
                (25) YES
    (26) QCSDP
        (27) QCSDPReductionPairProof [EQUIVALENT, 6 ms]
        (28) QCSDP
        (29) PIsEmptyProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) QCSDP
        (32) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (33) QCSDP
        (34) PIsEmptyProof [EQUIVALENT, 0 ms]
        (35) YES


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

(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   gt(0, Y) -> false
   gt(s(X), 0) -> true
   gt(s(X), s(Y)) -> gt(X, Y)
   p(0) -> 0
   p(s(X)) -> X
   if(true, X, Y) -> X
   if(false, X, Y) -> Y
   minus(X, Y) -> if(gt(Y, 0), minus(p(X), p(Y)), X)
   div(0, s(Y)) -> 0
   div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))

The replacement map contains the following entries:

gt: {1, 2}
0: empty set
false: empty set
s: {1}
true: empty set
p: {1}
if: {1}
minus: {1, 2}
div: {1, 2}

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

(1) CSRInnermostProof (EQUIVALENT)
The CSR is orthogonal. By [CS_Inn] we can switch to innermost.
----------------------------------------

(2)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   gt(0, Y) -> false
   gt(s(X), 0) -> true
   gt(s(X), s(Y)) -> gt(X, Y)
   p(0) -> 0
   p(s(X)) -> X
   if(true, X, Y) -> X
   if(false, X, Y) -> Y
   minus(X, Y) -> if(gt(Y, 0), minus(p(X), p(Y)), X)

popout

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

job log

popout

actions all output return to TRS Context Sensitive