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TRS Stand 20472 pair #381710918
details
property
value
status
complete
benchmark
14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n083.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.852859020233 seconds
cpu usage
0.849123226
max memory
1.947648E7
stage attributes
key
value
output-size
30572
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. !minus : [o * o] --> o !plus : [o * o] --> o 0 : [] --> o 1 : [] --> o BS : [o] --> o I : [o] --> o L : [o] --> o Log : [o] --> o Log!450 : [o] --> o Max : [o] --> o Min : [o] --> o N : [o * o * o] --> o O : [o] --> o Size : [o] --> o Val : [o] --> o WB : [o] --> o and : [o * o] --> o false : [] --> o ge : [o * o] --> o if : [o * o * o] --> o l : [] --> o not : [o] --> o r : [] --> o true : [] --> o O(0) => 0 !plus(0, X) => X !plus(X, 0) => X !plus(O(X), O(Y)) => O(!plus(X, Y)) !plus(O(X), I(Y)) => I(!plus(X, Y)) !plus(I(X), O(Y)) => I(!plus(X, Y)) !plus(I(X), I(Y)) => O(!plus(!plus(X, Y), I(0))) !plus(X, !plus(Y, Z)) => !plus(!plus(X, Y), Z) !minus(X, 0) => X !minus(0, X) => 0 !minus(O(X), O(Y)) => O(!minus(X, Y)) !minus(O(X), I(Y)) => I(!minus(!minus(X, Y), I(1))) !minus(I(X), O(Y)) => I(!minus(X, Y)) !minus(I(X), I(Y)) => O(!minus(X, Y)) not(true) => false not(false) => true and(X, true) => X and(X, false) => false if(true, X, Y) => X if(false, X, Y) => Y ge(O(X), O(Y)) => ge(X, Y) ge(O(X), I(Y)) => not(ge(Y, X)) ge(I(X), O(Y)) => ge(X, Y) ge(I(X), I(Y)) => ge(X, Y) ge(X, 0) => true ge(0, O(X)) => ge(0, X) ge(0, I(X)) => false Log!450(0) => 0 Log!450(I(X)) => !plus(Log!450(X), I(0)) Log!450(O(X)) => if(ge(X, I(0)), !plus(Log!450(X), I(0)), 0) Log(X) => !minus(Log!450(X), I(0)) Val(L(X)) => X Val(N(X, l, r)) => X Min(L(X)) => X Min(N(X, l, r)) => Min(l) Max(L(X)) => X Max(N(X, l, r)) => Max(r) BS(L(X)) => true BS(N(X, l, r)) => and(and(ge(X, Max(l)), ge(Min(r), X)), and(BS(l), BS(r))) Size(L(X)) => I(0) Size(N(X, l, r)) => !plus(!plus(Size(l), Size(r)), I(1)) WB(L(X)) => true WB(N(X, l, r)) => and(if(ge(Size(l), Size(r)), ge(I(0), !minus(Size(l), Size(r))), ge(I(0), !minus(Size(r), Size(l)))), and(WB(l), WB(r))) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): O(0) >? 0 !plus(0, X) >? X !plus(X, 0) >? X !plus(O(X), O(Y)) >? O(!plus(X, Y)) !plus(O(X), I(Y)) >? I(!plus(X, Y)) !plus(I(X), O(Y)) >? I(!plus(X, Y)) !plus(I(X), I(Y)) >? O(!plus(!plus(X, Y), I(0))) !plus(X, !plus(Y, Z)) >? !plus(!plus(X, Y), Z) !minus(X, 0) >? X !minus(0, X) >? 0 !minus(O(X), O(Y)) >? O(!minus(X, Y)) !minus(O(X), I(Y)) >? I(!minus(!minus(X, Y), I(1))) !minus(I(X), O(Y)) >? I(!minus(X, Y)) !minus(I(X), I(Y)) >? O(!minus(X, Y)) not(true) >? false not(false) >? true
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